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Creativity break: Why is algebra important to learn?

https://www.youtube.com/watch?v=H4g0GZsgq0I

vtt

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WEBVTT Kind: captions Language: en 00:00:01.002 --> 00:00:04.002 (marker scratching) 00:00:05.292 --> 00:00:08.459 (gentle upbeat music) 00:00:09.870 --> 00:00:13.490 - Algebra is really the unifying thread 00:00:13.490 --> 00:00:16.100 of almost all of mathematics. 00:00:16.100 --> 00:00:18.250 You may think algebra is boring, 00:00:18.250 --> 00:00:22.490 but it is the one tool you can use to not only understand, 00:00:22.490 --> 00:00:24.580 but unlock the universe. 00:00:24.580 --> 00:00:27.830 Creative algebra is used in computer game design. 00:00:27.830 --> 00:00:31.810 It powers how artificial intelligence works. 00:00:31.810 --> 00:00:34.880 Mastering algebra will provide you with the ability 00:00:34.880 --> 00:00:38.287 to decode and understand many complex systems. 00:00:38.287 --> 00:00:41.130 In my opinion, if you can master algebra, 00:00:41.130 --> 00:00:42.330 you can master anything.

Creativity break: What do you do to get into your creative zone?

https://www.youtube.com/watch?v=7WjlO5u3Vqo

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https://www.youtube.com/api/timedtext?v=7WjlO5u3Vqo&ei=uVWUZcy4GfWQvdIPvaOrsAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=E1A7181765BACBB97A21231A1C1D365D1B3BB2E2.C1FB1F6C51050ABCE239D8BB6C07DE326AA6525F&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.323 --> 00:00:02.740 (soft music) 00:00:03.717 --> 00:00:06.210 (marker scratches) 00:00:06.210 --> 00:00:08.877 (keyboard taps) 00:00:10.300 --> 00:00:14.050 - Whenever I wanna come up with a solution to a problem 00:00:14.050 --> 00:00:15.330 and I don't have it, 00:00:15.330 --> 00:00:20.100 my immediate reaction is to go outside and go on a walk. 00:00:20.100 --> 00:00:22.173 I love walking in all kinds of weather. 00:00:25.348 --> 00:00:27.203 I feel like with the peace and calm, 00:00:27.203 --> 00:00:31.100 moving away from the problem and stepping away from it, 00:00:31.100 --> 00:00:35.200 sometimes I get way better ideas and it inspires me. 00:00:35.200 --> 00:00:36.570 But, I also think there's something to be said 00:00:36.570 --> 00:00:38.930 about not being inspired. 00:00:38.930 --> 00:00:41.110 Like, not always as amazing. 00:00:41.110 --> 00:00:44.770 I feel like sometimes I get struck with inspiration 00:00:44.770 --> 00:00:47.900 for how I want to explain a Khan Academy video 00:00:47.900 --> 00:00:49.720 or how I wanna approach a piece of art 00:00:49.720 --> 00:00:52.830 or how I want to approach a math problem, 00:00:52.830 --> 00:00:54.540 but sometimes it doesn't come. 00:00:54.540 --> 00:00:56.830 And so I feel like what the best solution is 00:00:56.830 --> 00:00:58.770 when you are trying to get into that creative zone 00:00:58.770 --> 00:01:00.660 and you can't, is just do it 00:01:00.660 --> 00:01:03.470 and try to do something anyway. 00:01:03.470 --> 00:01:06.960 Like write something or write your equations, 00:01:06.960 --> 00:01:08.380 try to figure it out. 00:01:08.380 --> 00:01:10.530 And if you make mistakes, that's okay, 00:01:10.530 --> 00:01:11.830 because it's something to jump off of 00:01:11.830 --> 00:01:16.020 and sometimes seeing what you already know down on paper 00:01:16.020 --> 00:01:18.040 can help you come up with better ideas 00:01:18.040 --> 00:01:19.700 and can help you be more creative. 00:01:19.700 --> 00:01:22.010 - Forcing yourself to just conjure a solution, 00:01:22.010 --> 00:01:23.360 simply does not work. 00:01:23.360 --> 00:01:25.130 Instead, take a break from the task. 00:01:25.130 --> 00:01:26.070 Pick something else up, 00:01:26.070 --> 00:01:29.000 like a physical sport or even video games. 00:01:29.000 --> 00:01:31.060 And then come back to the original problem. 00:01:31.060 --> 00:01:32.838 That can do wonders. 00:01:32.838 --> 00:01:35.255 (soft music)

Creativity break: How does creativity play a role in your everyday life?

https://www.youtube.com/watch?v=eU8IfaoD-v8

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WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:02.583 (upbeat music) 00:00:10.310 --> 00:00:11.830 - Creativity is really important for me 00:00:11.830 --> 00:00:14.610 as like a future job, as a part of my future job 00:00:14.610 --> 00:00:18.370 I would want to do something that changes 00:00:18.370 --> 00:00:21.430 and then I can use problem solving skills constantly. 00:00:21.430 --> 00:00:24.560 I feel like when I make animations or when I figure 00:00:24.560 --> 00:00:26.010 out how to explain something, 00:00:28.080 --> 00:00:31.160 I love that because there's so many different solutions, 00:00:31.160 --> 00:00:33.770 but knowing that you can try to find and experiment 00:00:33.770 --> 00:00:36.630 with different ones and maybe create something beautiful 00:00:36.630 --> 00:00:39.990 is really, I don't know, inspiring to me. 00:00:39.990 --> 00:00:42.750 - Mathematicals educational initiative 00:00:42.750 --> 00:00:45.360 that I co-founded with a fellow mathematician, 00:00:45.360 --> 00:00:46.710 Jess Williams. 00:00:46.710 --> 00:00:50.400 And what we're trying to do is make maths fun and accessible 00:00:50.400 --> 00:00:54.240 and encourage more girls to pursue careers in maths. 00:00:54.240 --> 00:00:56.570 So creativity is essential here 00:00:56.570 --> 00:00:57.770 because we're trying to think 00:00:57.770 --> 00:01:01.540 of ways that people will enjoy maths 00:01:01.540 --> 00:01:03.960 and it will be fun and accessible to them. 00:01:03.960 --> 00:01:05.950 So different creative techniques that we've been 00:01:05.950 --> 00:01:09.750 using are trying to present mathematical problems 00:01:09.750 --> 00:01:14.500 in fun, short videos, and that explain the problem 00:01:14.500 --> 00:01:16.850 in a way that everybody will understand 00:01:16.850 --> 00:01:18.900 and will make them want to learn more 00:01:18.900 --> 00:01:21.900 and discover more about the topics that we're talking about. 00:01:21.900 --> 00:01:23.500 - I'm really lucky 00:01:23.500 --> 00:01:27.470 that I get to be creative every day in my work 00:01:27.470 --> 00:01:30.840 and I have been since I got into this field of data science. 00:01:30.840 --> 00:01:33.680 So in general, across the last decade, 00:01:33.680 --> 00:01:36.670 my work has really been about designing 00:01:36.670 --> 00:01:40.840 and testing innovative ways to capture human behavior 00:01:40.840 --> 00:01:43.230 within game-based assessments. 00:01:43.230 --> 00:01:44.900 So my collaborators and I, 00:01:44.900 --> 00:01:47.930 from the time I was in graduate school to now, 00:01:47.930 --> 00:01:50.220 use a variety of different modeling techniques 00:01:50.220 --> 00:01:51.200 from various fields, 00:01:51.200 --> 00:01:55.550 we'll pull things from engineering, aerospace, 00:01:55.550 --> 00:01:59.480 more basic mathematical models to help us achieve this goal. 00:01:59.480 --> 00:02:01.100 We get to think outside the box. 00:02:01.100 --> 00:02:04.130 We get to think about how we can pull in different types 00:02:04.130 --> 00:02:06.980 of thinking from different fields to help us better 00:02:06.980 --> 00:02:11.980 understand human behavior, human cognition, learning. 00:02:12.020 --> 00:02:14.600 So it's really exciting and really novel. 00:02:14.600 --> 00:02:17.370 And it's something that because of the field that I'm in 00:02:17.370 --> 00:02:20.433 I've been able to do this now for multiple years.

Creativity break: How can people get creative in algebra

https://www.youtube.com/watch?v=DXPz0-HCK80

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WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:02.583 (upbeat music) 00:00:10.280 --> 00:00:12.130 - In order to get more creative, 00:00:12.130 --> 00:00:13.730 I would encourage young people 00:00:13.730 --> 00:00:16.730 to be not afraid of making mistakes. 00:00:16.730 --> 00:00:21.510 It's okay to fail while exploring a new trail of thought. 00:00:21.510 --> 00:00:23.980 Know that usually there is more than one solution 00:00:23.980 --> 00:00:25.370 to the problem. 00:00:25.370 --> 00:00:30.370 Math is as much about posing problems as problem solving. 00:00:30.890 --> 00:00:33.810 And at that point, creativity is noticing 00:00:33.810 --> 00:00:36.060 where there is something worthwhile investigating. 00:00:36.060 --> 00:00:37.440 - As a student in math, 00:00:37.440 --> 00:00:39.100 I think it's important to remember 00:00:39.100 --> 00:00:44.100 that math isn't just like random symbols on paper. 00:00:44.100 --> 00:00:46.260 Like math can mean something 00:00:46.260 --> 00:00:49.770 and it's pretty powerful that you as a student 00:00:49.770 --> 00:00:51.730 can build something that uses math. 00:00:51.730 --> 00:00:53.840 Creativity in math isn't just about 00:00:53.840 --> 00:00:55.430 being able to pluck numbers from the air 00:00:55.430 --> 00:00:57.410 and like, oh yes, I know the solution. 00:00:57.410 --> 00:01:01.310 It's about being able to use problems 00:01:01.310 --> 00:01:02.993 that help with your daily life.

Creativity break: When did you first realize that you liked algebra

https://www.youtube.com/watch?v=4l1t-_Eb2MI

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WEBVTT Kind: captions Language: en 00:00:00.366 --> 00:00:04.116 (whimsical electronic music) 00:00:06.294 --> 00:00:08.544 (clicking) 00:00:11.230 --> 00:00:14.020 - One day, my family was building this fence 00:00:14.020 --> 00:00:17.260 around my chicken coop. 00:00:17.260 --> 00:00:19.400 'Cause there were problems with raccoons. 00:00:19.400 --> 00:00:22.400 And we wanted to make sure that the perimeter of the fence 00:00:22.400 --> 00:00:26.950 was twice the the length of the width. 00:00:26.950 --> 00:00:27.787 And I remember thinking, 00:00:27.787 --> 00:00:30.457 "This is exactly like my algebra class. 00:00:30.457 --> 00:00:35.457 "I'm actually doing things that are useful." 00:00:35.490 --> 00:00:39.040 Algebra wasn't just something that you do on paper, 00:00:39.040 --> 00:00:42.110 it was actually protecting the lives of my chickens. 00:00:42.110 --> 00:00:44.150 So I felt like that was a moment for me 00:00:44.150 --> 00:00:47.070 where math is useful to the world, 00:00:47.070 --> 00:00:49.580 and we're solving real problems with it, 00:00:49.580 --> 00:00:51.370 and it's really powerful. 00:00:51.370 --> 00:00:54.230 - So I realized that I first liked algebra, 00:00:54.230 --> 00:00:57.090 and just math in general, my first year in college, 00:00:57.090 --> 00:00:58.770 I was a little bit of a late bloomer 00:00:58.770 --> 00:01:00.730 in realizing the importance of math. 00:01:00.730 --> 00:01:02.940 I was taking an early statistics course 00:01:02.940 --> 00:01:04.700 for my psychology degree. 00:01:04.700 --> 00:01:06.690 And I really began to understand 00:01:06.690 --> 00:01:08.910 how the concepts that I were learning 00:01:10.370 --> 00:01:12.900 could help me understand the world around me better 00:01:12.900 --> 00:01:16.630 in a more concrete, fluid, and rich way. 00:01:16.630 --> 00:01:18.450 And so being able to make that connection 00:01:18.450 --> 00:01:20.710 from these things that I'm learning in the classroom 00:01:20.710 --> 00:01:21.660 out into the real world, 00:01:21.660 --> 00:01:23.470 so that I can under understand different phenomenon, 00:01:23.470 --> 00:01:26.650 I can understand how various things in our culture 00:01:26.650 --> 00:01:29.980 work and progress, really helped me 00:01:29.980 --> 00:01:32.220 and made me feel like I had a deeper understanding 00:01:32.220 --> 00:01:35.560 for the importance of math and algebra. 00:01:35.560 --> 00:01:37.810 And from that point I've really been in love.

Creativity break: How do you apply creativity in algebra

https://www.youtube.com/watch?v=2vAMs-KM7UA

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WEBVTT Kind: captions Language: en 00:00:00.176 --> 00:00:02.759 (gentle music) 00:00:10.610 --> 00:00:13.240 - So if you're trying to communicate a complex topic, 00:00:13.240 --> 00:00:15.980 such as mathematics or a mathematical problem 00:00:15.980 --> 00:00:17.410 to the general public, 00:00:17.410 --> 00:00:20.070 who might not be familiar with the specifics 00:00:20.070 --> 00:00:21.194 behind that problem, 00:00:21.194 --> 00:00:22.950 there are many different ways 00:00:22.950 --> 00:00:25.418 to help you get that concept across. 00:00:25.418 --> 00:00:27.250 And one of the ways that we do this 00:00:27.250 --> 00:00:29.870 in mathematical is to use videos 00:00:29.870 --> 00:00:32.700 and things that are visually appealing to people. 00:00:32.700 --> 00:00:34.980 So by using lots of visual aids, 00:00:34.980 --> 00:00:37.670 so bright colors and cartoons, 00:00:37.670 --> 00:00:40.610 and word prompts on your screen, 00:00:40.610 --> 00:00:44.620 you can engage and capture the audience in different ways 00:00:44.620 --> 00:00:45.773 that you might not be able to do 00:00:45.773 --> 00:00:47.700 if you're just speaking 00:00:47.700 --> 00:00:49.830 in terms of equations and mathematics. 00:00:49.830 --> 00:00:51.160 - When we're more creative 00:00:51.160 --> 00:00:53.600 about how we present and how we talk about math 00:00:53.600 --> 00:00:54.810 it makes it more relatable 00:00:54.810 --> 00:00:57.280 to people from a variety of backgrounds 00:00:57.280 --> 00:00:59.243 and cultures and experiences. 00:01:00.240 --> 00:01:01.710 When we are creative 00:01:01.710 --> 00:01:06.110 in how we explain or how we relate mathematical concepts, 00:01:06.110 --> 00:01:08.490 we can use things from sports, entertainment, 00:01:08.490 --> 00:01:11.140 or real world to help really ground the principles 00:01:11.140 --> 00:01:12.320 that we're learning 00:01:12.320 --> 00:01:14.940 and the theories that we're learning to something relatable. 00:01:14.940 --> 00:01:17.760 So the more creative we can be in explaining how math 00:01:17.760 --> 00:01:19.330 is related to the world around us, 00:01:19.330 --> 00:01:22.180 how it's related to things that we are invested in, 00:01:22.180 --> 00:01:25.010 the more likely it is to resonate with the people around us. 00:01:25.010 --> 00:01:27.110 - As soon as a problem is posed 00:01:27.110 --> 00:01:30.660 our instinct is to find the solution. 00:01:30.660 --> 00:01:33.340 But remember, often there's more than one solution 00:01:33.340 --> 00:01:35.401 and usually there's more than one path to it. 00:01:35.401 --> 00:01:37.984 (gentle music)

Creativity break: Why is creativity important in STEM jobs?

https://www.youtube.com/watch?v=ynvn3jqxcX4

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WEBVTT Kind: captions Language: en 00:00:00.323 --> 00:00:03.323 (soft upbeat music) 00:00:10.480 --> 00:00:14.760 - I think my idea of how creativity works in STEM jobs 00:00:14.760 --> 00:00:18.270 has changed since I've gone to college. 00:00:18.270 --> 00:00:20.240 I used to think that all the mathematicians 00:00:20.240 --> 00:00:22.890 would be locked away in some office 00:00:22.890 --> 00:00:24.130 and typing on the computers 00:00:24.130 --> 00:00:26.410 or writing down equations by themselves 00:00:26.410 --> 00:00:28.890 and coming up with incredibly beautiful ideas 00:00:28.890 --> 00:00:30.160 just by themselves. 00:00:30.160 --> 00:00:32.100 But I'm realizing now that I'm in college 00:00:32.100 --> 00:00:35.210 that mathematics and creativity, 00:00:35.210 --> 00:00:36.880 it's a lot about communication, 00:00:36.880 --> 00:00:37.713 and it's a lot about 00:00:37.713 --> 00:00:40.540 trying to build off of each other's ideas 00:00:40.540 --> 00:00:42.852 and bounce ideas off of each other 00:00:42.852 --> 00:00:47.200 and build upon ideas that have already been made 00:00:47.200 --> 00:00:48.940 by people decades ago. 00:00:48.940 --> 00:00:52.490 And I think that the facts that we all come with it, 00:00:52.490 --> 00:00:53.590 with our own perspectives, 00:00:53.590 --> 00:00:58.359 and different ideas and different ways of being creative 00:00:58.359 --> 00:01:01.020 allows math to advance further, 00:01:01.020 --> 00:01:03.760 because we can all combine our creative ideas 00:01:03.760 --> 00:01:04.960 into something bigger. 00:01:04.960 --> 00:01:07.700 - We collect data on everything, right? 00:01:07.700 --> 00:01:09.860 And so the ability to use that data 00:01:09.860 --> 00:01:13.510 in a smart, safe, and efficient way 00:01:13.510 --> 00:01:17.170 depends on new applications of mathematical concepts 00:01:17.170 --> 00:01:19.833 to these new and innovative data sets. 00:01:20.850 --> 00:01:22.150 As we get to that point, 00:01:22.150 --> 00:01:24.438 we'll start to be thinking outside the box a lot more, 00:01:24.438 --> 00:01:28.560 and we'll be a much more innovative, digital society, 00:01:28.560 --> 00:01:31.260 but that can't happen unless we start trying to be creative, 00:01:31.260 --> 00:01:33.839 and not just rely on tried and true. 00:01:33.839 --> 00:01:36.823 (soft upbeat music)

Creativity break: Why is creativity important in algebra?

https://www.youtube.com/watch?v=SjZfW07DbMo

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WEBVTT Kind: captions Language: en 00:00:00.198 --> 00:00:02.781 (upbeat music) 00:00:11.080 --> 00:00:13.620 - It's all about solving problems. 00:00:13.620 --> 00:00:16.210 It's not about, like maybe in previous years 00:00:16.210 --> 00:00:19.760 you've done multiplication table memorization. 00:00:19.760 --> 00:00:22.350 It's not like memorizing how to solve problems. 00:00:22.350 --> 00:00:24.880 It's learning the tools of how to solve problems 00:00:24.880 --> 00:00:28.760 and then using them and building them up in creative ways. 00:00:28.760 --> 00:00:31.330 So it really does remind me of art 00:00:31.330 --> 00:00:34.340 because if you are doing a painting or something, 00:00:34.340 --> 00:00:37.280 you have specific tools about maybe paint brushes 00:00:37.280 --> 00:00:39.700 or different techniques you can use 00:00:39.700 --> 00:00:41.600 to create something bigger. 00:00:41.600 --> 00:00:46.100 So I feel like algebra is really all about combining things 00:00:46.100 --> 00:00:48.980 that you already know how to do into something bigger. 00:00:48.980 --> 00:00:53.980 - So the word algebra comes from the Arabic word algebra 00:00:54.120 --> 00:00:59.120 that literally translates to reunion of broken parts. 00:00:59.720 --> 00:01:03.470 This is breaking apart of mathematical representations 00:01:03.470 --> 00:01:05.200 and putting it back together 00:01:05.200 --> 00:01:07.630 in the form of balanced equations 00:01:07.630 --> 00:01:09.530 is the essence of algebra. 00:01:09.530 --> 00:01:12.650 And the beautiful thing is that this balancing 00:01:12.650 --> 00:01:16.360 and solving of equations can be done in many different ways 00:01:16.360 --> 00:01:18.423 which is where creativity comes in.

Creativity in algebra

https://www.youtube.com/watch?v=nOBZM5QYcBc

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https://www.youtube.com/api/timedtext?v=nOBZM5QYcBc&ei=uVWUZebsGbuJp-oPrp6j8AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0B81554C15D967B5D8AF6F96765D41977EE23A7E.F11295401CED4B0E013C431ADC2D39CCCE621101&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.976 --> 00:00:03.559 (upbeat music) 00:00:11.120 --> 00:00:13.270 - Hi folks, Sal Khan here. 00:00:13.270 --> 00:00:16.014 And all I have to say is that algebra is perhaps 00:00:16.014 --> 00:00:20.840 the most pure way of expressing human thought. 00:00:20.840 --> 00:00:22.650 And like everything dealing with human thought, 00:00:22.650 --> 00:00:24.443 it's incredibly creative. 00:00:25.790 --> 00:00:28.160 But you don't have to take my word for it. 00:00:28.160 --> 00:00:31.800 We have some of my good friends to better draw that link 00:00:31.800 --> 00:00:34.871 between algebra and creativity. 00:00:34.871 --> 00:00:37.454 (upbeat music) 00:00:39.930 --> 00:00:42.460 - It's all out solving problems. 00:00:42.460 --> 00:00:45.050 It's not about like, maybe in previous years, 00:00:45.050 --> 00:00:48.580 you've done multiplication table memorization. 00:00:48.580 --> 00:00:51.170 It's not like memorizing how to solve problems. 00:00:51.170 --> 00:00:53.720 It's learning the tools of how to solve problems 00:00:53.720 --> 00:00:57.600 and then using them, and building them up in creative ways. 00:00:57.600 --> 00:01:00.170 So it's kind of like, it really does remind me of art, 00:01:00.170 --> 00:01:03.160 because if you are doing like a painting or something, 00:01:03.160 --> 00:01:06.120 you have like a specific tools about maybe paint brushes 00:01:06.120 --> 00:01:07.985 or different techniques you can use 00:01:07.985 --> 00:01:10.440 to create something bigger. 00:01:10.440 --> 00:01:14.940 So I feel like algebra is really all about combining things 00:01:14.940 --> 00:01:17.800 that you already know how to do into something bigger. 00:01:17.800 --> 00:01:22.800 - So the word algebra comes from the Arabic word al-jabr, 00:01:22.930 --> 00:01:27.930 that literally translates to reunion of broken parts. 00:01:28.560 --> 00:01:32.320 This breaking apart of mathematic representations 00:01:32.320 --> 00:01:34.030 and putting it back together 00:01:34.030 --> 00:01:36.470 in the form of balanced equations, 00:01:36.470 --> 00:01:38.390 is the essence of algebra. 00:01:38.390 --> 00:01:39.790 And the beautiful thing is that 00:01:39.790 --> 00:01:42.890 this balancing and solving of equations 00:01:42.890 --> 00:01:45.210 can be done in many different ways, 00:01:45.210 --> 00:01:47.805 which is where creativity comes in. 00:01:47.805 --> 00:01:50.388 (upbeat music) 00:01:52.320 --> 00:01:54.970 - So if you're trying to communicate a complex topic, 00:01:54.970 --> 00:01:57.700 such as mathematics or a mathematical problem 00:01:57.700 --> 00:02:00.740 to the general public who might not be familiar 00:02:00.740 --> 00:02:03.340 with the specifics behind that problem, 00:02:03.340 --> 00:02:04.670 there are many different ways 00:02:04.670 --> 00:02:07.530 to help you get that concept across. 00:02:07.530 --> 00:02:10.070 And one of the ways that we do this in mathematicals 00:02:10.070 --> 00:02:12.120 is to use videos and things 00:02:12.120 --> 00:02:14.420 that are visually appealing to people. 00:02:14.420 --> 00:02:16.700 So by using lots of visual aids, 00:02:16.700 --> 00:02:19.400 so bright colors and cartoons, 00:02:19.400 --> 00:02:22.330 and word prompts on your screen, 00:02:22.330 --> 00:02:25.520 you can engage and capture the audience 00:02:25.520 --> 00:02:27.950 in different ways that you might not be able to do 00:02:27.950 --> 00:02:29.920 if you're just speaking in terms 00:02:29.920 --> 00:02:31.540 of equations and mathematics. 00:02:31.540 --> 00:02:34.030 - When we're more creative about how we present, 00:02:34.030 --> 00:02:35.300 and how we talk about math, 00:02:35.300 --> 00:02:37.040 it makes it more relatable to people 00:02:37.040 --> 00:02:41.220 from a variety of backgrounds and cultures and experiences. 00:02:41.220 --> 00:02:44.820 When we are creative in how we explain, 00:02:44.820 --> 00:02:47.840 or how we relate mathematical concepts, 00:02:47.840 --> 00:02:51.150 we can use things from sports, entertainment, or real world 00:02:51.150 --> 00:02:53.827 to help really ground the principles that we're learning, 00:02:53.827 --> 00:02:56.660 and the theories that we're learning to something relatable. 00:02:56.660 --> 00:02:59.480 So the more creative we can be in explaining how math 00:02:59.480 --> 00:03:01.050 is related to the world around us, 00:03:01.050 --> 00:03:03.910 how it's related to things that we are invested in, 00:03:03.910 --> 00:03:06.820 the more likely it is to resonate with the people around us. 00:03:06.820 --> 00:03:08.850 - As soon as a problem is posed, 00:03:08.850 --> 00:03:12.380 our instinct is to find the solution. 00:03:12.380 --> 00:03:15.050 But remember, often there's more than one solution. 00:03:15.050 --> 00:03:17.972 And usually there's more than one path to it. 00:03:17.972 --> 00:03:20.889 (keyboard tapping) 00:03:23.060 --> 00:03:25.860 - One day my family was building this fence 00:03:25.860 --> 00:03:29.070 around my chicken coop 00:03:29.070 --> 00:03:31.530 'cause there were problems with raccoons. 00:03:31.530 --> 00:03:32.660 And we wanted to make sure that, 00:03:32.660 --> 00:03:34.847 like the the perimeter of the fence was like, 00:03:34.847 --> 00:03:38.920 twice the the length of the width. 00:03:38.920 --> 00:03:39.753 And I remember thinking, 00:03:39.753 --> 00:03:41.940 this is exactly like my algebra class. 00:03:41.940 --> 00:03:46.270 Like, I'm actually doing things that are useful. 00:03:46.270 --> 00:03:49.180 And actually, like algebra wasn't just something 00:03:49.180 --> 00:03:50.013 that you do on paper, 00:03:50.013 --> 00:03:52.370 it's something that like, it was actually like protecting 00:03:52.370 --> 00:03:53.920 the lives of my chickens. 00:03:53.920 --> 00:03:55.990 So I felt like that was a moment for me 00:03:55.990 --> 00:03:58.920 where like math is useful to the worlds, 00:03:58.920 --> 00:04:01.410 and we're solving real problems with it, 00:04:01.410 --> 00:04:03.180 and it's really powerful. 00:04:03.180 --> 00:04:06.050 - So I realized that I first liked algebra 00:04:06.050 --> 00:04:07.790 and just math in general. 00:04:07.790 --> 00:04:08.930 My first year in college, 00:04:08.930 --> 00:04:10.610 I was a little bit of a late bloomer 00:04:10.610 --> 00:04:12.570 in realizing the importance of math. 00:04:12.570 --> 00:04:14.770 I was taking an early statistics course 00:04:14.770 --> 00:04:16.550 for my psychology degree, 00:04:16.550 --> 00:04:19.660 and I really began to understand how the concepts 00:04:19.660 --> 00:04:23.400 that I were learning could help me understand 00:04:23.400 --> 00:04:26.532 the world around me better in a more concrete, 00:04:26.532 --> 00:04:28.470 fluid and rich way. 00:04:28.470 --> 00:04:30.280 And so being able to make that connection 00:04:30.280 --> 00:04:32.550 from these things that I'm learning in the classroom, 00:04:32.550 --> 00:04:33.490 out into the real world, 00:04:33.490 --> 00:04:35.300 so I can understand different phenomenon, 00:04:35.300 --> 00:04:37.770 I can understand how various things 00:04:37.770 --> 00:04:40.347 in our culture work and progress, 00:04:40.347 --> 00:04:42.550 really helped me and made me feel 00:04:42.550 --> 00:04:43.704 like I had a deeper understanding 00:04:43.704 --> 00:04:47.390 for the importance of math and algebra. 00:04:47.390 --> 00:04:49.724 And from that point, I've really been in love. 00:04:49.724 --> 00:04:52.307 (upbeat music) 00:04:54.870 --> 00:04:56.720 - In order to get more creative, 00:04:56.720 --> 00:04:59.840 I would encourage young people to be not afraid 00:04:59.840 --> 00:05:01.320 of making mistakes. 00:05:01.320 --> 00:05:06.130 It's okay to fail while exploring a new trail of thought. 00:05:06.130 --> 00:05:08.580 Know that usually there is more than one solution 00:05:08.580 --> 00:05:09.970 to the problem. 00:05:09.970 --> 00:05:14.970 Math is as much about posing problems as problem solving. 00:05:15.470 --> 00:05:18.410 And at that point, creativity is noticing 00:05:18.410 --> 00:05:20.830 where there is something worthwhile investigating. 00:05:20.830 --> 00:05:23.700 - As a student in math, I think it's important to remember 00:05:23.700 --> 00:05:28.690 that math isn't just like random symbols on paper. 00:05:28.690 --> 00:05:33.110 Like, math can mean something, and it's pretty powerful 00:05:33.110 --> 00:05:36.320 that you as a student, can build something that uses math. 00:05:36.320 --> 00:05:38.820 Creativity in math isn't just about being able 00:05:38.820 --> 00:05:40.340 to pluck numbers from the air and like, 00:05:40.340 --> 00:05:42.020 oh yes, I know the solution. 00:05:42.020 --> 00:05:45.930 It's about being able to use problems 00:05:45.930 --> 00:05:47.603 that help with your daily life.

Creative algebra at work

https://www.youtube.com/watch?v=Ep7diUpHuhs

vtt

https://www.youtube.com/api/timedtext?v=Ep7diUpHuhs&ei=uVWUZfySHJ2nvdIPvr2v-Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6B9358FE28E17555D027A7442897CF12AFE369.A71AFC7A07447AC574301EF22A48459F2994060C&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.254 --> 00:00:02.754 (light music) 00:00:11.780 --> 00:00:13.760 - Hi, everyone, Sal Khan here. 00:00:13.760 --> 00:00:16.700 I've always been drawn to creative things. 00:00:16.700 --> 00:00:19.380 I like to see, change new things in the world, 00:00:19.380 --> 00:00:20.450 and because of that, 00:00:20.450 --> 00:00:22.340 I've been drawn to careers 00:00:22.340 --> 00:00:25.130 where I can most apply my creativity, 00:00:25.130 --> 00:00:27.900 especially in an abstract sense. 00:00:27.900 --> 00:00:31.760 And algebra is perhaps the purest expression of creativity, 00:00:31.760 --> 00:00:33.700 and that's why I've worked in everything 00:00:33.700 --> 00:00:37.730 from computer programming, to product design, 00:00:37.730 --> 00:00:40.490 to a hedge fund analyst, 00:00:40.490 --> 00:00:42.130 where you're investing in stocks. 00:00:42.130 --> 00:00:43.040 And in all of them, 00:00:43.040 --> 00:00:47.670 it was incredibly creative and used a lot of algebra. 00:00:47.670 --> 00:00:49.290 But don't take my word for it. 00:00:49.290 --> 00:00:50.880 You're going to meet some of my friends 00:00:50.880 --> 00:00:53.280 who can tell you a lot more about the connection 00:00:53.280 --> 00:00:57.202 between algebra and work and creativity. 00:00:57.202 --> 00:00:58.626 (typewriter typing) 00:00:58.626 --> 00:01:01.800 (light music continues) 00:01:01.800 --> 00:01:04.830 - I think my idea of how creativity works 00:01:04.830 --> 00:01:09.420 in STEM jobs has changed since I've gotten to college. 00:01:09.420 --> 00:01:11.560 I used to think that all the mathematicians 00:01:11.560 --> 00:01:14.170 would be just locked away in some office 00:01:14.170 --> 00:01:17.060 and typing on their computers or writing down equations 00:01:17.060 --> 00:01:20.210 by themselves and coming up with incredibly beautiful ideas 00:01:20.210 --> 00:01:21.480 just by themselves. 00:01:21.480 --> 00:01:23.420 But I'm realizing now that I'm in college 00:01:23.420 --> 00:01:26.530 that mathematics and creativity, 00:01:26.530 --> 00:01:28.190 it's a lot about communication 00:01:28.190 --> 00:01:30.890 and it's a lot about trying to build off 00:01:30.890 --> 00:01:34.330 of each other's ideas and bounce ideas off of each other 00:01:34.330 --> 00:01:38.510 and build upon ideas that have already been made 00:01:38.510 --> 00:01:40.260 by people decades ago. 00:01:40.260 --> 00:01:43.820 And I think that the facts that we all come with it, 00:01:43.820 --> 00:01:46.717 with our own perspectives and different ideas 00:01:46.717 --> 00:01:49.990 and different ways of being creative, 00:01:49.990 --> 00:01:52.330 allows math to advance further. 00:01:52.330 --> 00:01:55.080 Because we can all combine our creative ideas 00:01:55.080 --> 00:01:56.270 into something bigger. 00:01:56.270 --> 00:01:58.603 - We collect data on everything. 00:01:59.690 --> 00:02:03.810 The ability to use that data in a smart, safe, 00:02:03.810 --> 00:02:07.120 and efficient way depends on new applications 00:02:07.120 --> 00:02:08.490 of mathematical concepts 00:02:08.490 --> 00:02:11.143 to these new and innovative data sets. 00:02:12.180 --> 00:02:13.470 As we get to that point, 00:02:13.470 --> 00:02:16.400 we'll start to be thinking outside the box a lot more 00:02:16.400 --> 00:02:19.870 and we'll be a much more innovative digital society. 00:02:19.870 --> 00:02:22.610 But that can't happen unless we start trying to be creative 00:02:22.610 --> 00:02:25.204 and not just rely on tried and true. 00:02:25.204 --> 00:02:26.552 (typewriter typing) 00:02:26.552 --> 00:02:29.580 (light music continues) 00:02:29.580 --> 00:02:31.440 - Creativity's really important for me 00:02:31.440 --> 00:02:33.840 as a future job, as a part of my future job. 00:02:33.840 --> 00:02:37.610 I would want to do something that changes 00:02:37.610 --> 00:02:40.680 and then I can use problem-solving skills constantly. 00:02:40.680 --> 00:02:42.620 I feel like when I make animations 00:02:42.620 --> 00:02:45.510 or when I figure out how to explain something, 00:02:45.510 --> 00:02:48.040 I am really, I love that, 00:02:48.040 --> 00:02:50.420 because it's, there's so many different solutions, 00:02:50.420 --> 00:02:53.010 but knowing that you can try to find and experiment 00:02:53.010 --> 00:02:55.840 with different ones and maybe create something beautiful 00:02:55.840 --> 00:02:59.220 is really, I don't know, inspiring to me. 00:02:59.220 --> 00:03:01.980 - Mathematigals is an educational initiative 00:03:01.980 --> 00:03:03.110 that I co-founded 00:03:03.110 --> 00:03:05.960 with a fellow mathematician, Jess Williams, 00:03:05.960 --> 00:03:08.530 and what we're trying to do is make maths fun 00:03:08.530 --> 00:03:10.900 and accessible and encourage more girls 00:03:10.900 --> 00:03:13.870 to pursue careers in maths. 00:03:13.870 --> 00:03:15.810 Creativity is essential here 00:03:15.810 --> 00:03:17.670 because we're trying to think of ways 00:03:17.670 --> 00:03:20.620 that people will enjoy maths 00:03:20.620 --> 00:03:23.400 and it will be fun and accessible to them. 00:03:23.400 --> 00:03:25.780 Different creative techniques that we've been using 00:03:25.780 --> 00:03:28.980 are trying to present mathematical problems 00:03:28.980 --> 00:03:31.980 in fun, short videos 00:03:31.980 --> 00:03:34.280 and that explain the problem in a way 00:03:34.280 --> 00:03:36.100 that everybody will understand 00:03:36.100 --> 00:03:38.170 and will make them want to learn more 00:03:38.170 --> 00:03:41.140 and discover more about the topics that we're talking about. 00:03:41.140 --> 00:03:46.140 - I'm really lucky that I get to be creative every day 00:03:46.140 --> 00:03:49.300 in my work and I have been since I got into this field 00:03:49.300 --> 00:03:50.460 of data science. 00:03:50.460 --> 00:03:54.340 In general, across the last decade, my work has really been 00:03:54.340 --> 00:03:58.530 about designing and testing innovative ways 00:03:58.530 --> 00:04:01.833 to capture human behavior within game-based assessments. 00:04:02.860 --> 00:04:04.160 My collaborators and I, 00:04:04.160 --> 00:04:07.170 from the time I was in graduate school to now, 00:04:07.170 --> 00:04:09.460 use a variety of different modeling techniques 00:04:09.460 --> 00:04:10.440 from various fields. 00:04:10.440 --> 00:04:12.910 We'll pull things from engineering, 00:04:12.910 --> 00:04:16.880 aerospace, more basic mathematical models, 00:04:16.880 --> 00:04:18.710 to help us achieve this goal. 00:04:18.710 --> 00:04:20.330 We get to think outside the box. 00:04:20.330 --> 00:04:23.360 We get to think about how we can pull in different types 00:04:23.360 --> 00:04:24.940 of thinking from different fields 00:04:24.940 --> 00:04:28.370 to help us better understand human behavior, 00:04:28.370 --> 00:04:30.463 human cognition, learning. 00:04:31.800 --> 00:04:33.840 It's really exciting and really novel, 00:04:33.840 --> 00:04:35.090 and it's something that, 00:04:35.090 --> 00:04:36.610 because of the field that I'm in, 00:04:36.610 --> 00:04:39.556 I've been able to do this now for multiple years. 00:04:39.556 --> 00:04:41.632 (typewriter typing) 00:04:41.632 --> 00:04:44.460 (light music continues) 00:04:44.460 --> 00:04:45.883 - Whenever I wanna have, 00:04:46.770 --> 00:04:49.500 come up with a solution to a problem and I don't have it, 00:04:49.500 --> 00:04:54.270 my immediate reaction is to go outside and go on a walk. 00:04:54.270 --> 00:04:56.420 I love walking in all kinds of weather. 00:04:56.420 --> 00:04:59.430 It's kind of, it's just, 00:04:59.430 --> 00:05:01.510 I feel like with the peace and calm, 00:05:01.510 --> 00:05:05.260 moving away from the problem and stepping away from it, 00:05:05.260 --> 00:05:09.350 sometimes I get way better ideas and it inspires me. 00:05:09.350 --> 00:05:10.720 But I also think there's something to be said 00:05:10.720 --> 00:05:13.560 about not being inspired. 00:05:13.560 --> 00:05:15.260 Not always is amazing. (laughing) 00:05:15.260 --> 00:05:18.940 I feel like sometimes I get struck with inspiration 00:05:18.940 --> 00:05:22.060 for how I want to explain a Khan Academy video 00:05:22.060 --> 00:05:23.880 or how I wanna approach a piece of art 00:05:23.880 --> 00:05:27.000 or how I want to approach a math problem. 00:05:27.000 --> 00:05:28.820 But sometimes, it doesn't come. 00:05:28.820 --> 00:05:30.990 So I feel like what the best solution is 00:05:30.990 --> 00:05:32.920 when you are trying to get into that creative zone 00:05:32.920 --> 00:05:34.820 and you can't is to just do it 00:05:34.820 --> 00:05:38.089 and try to do something anyway. 00:05:38.089 --> 00:05:41.120 Write something or write your equations. 00:05:41.120 --> 00:05:42.540 Try to figure it out. 00:05:42.540 --> 00:05:44.770 And if you make mistakes, that's okay. 00:05:44.770 --> 00:05:45.980 Because it's something to jump off of, 00:05:45.980 --> 00:05:49.370 and maybe, sometimes seeing what you already know 00:05:49.370 --> 00:05:52.200 down on paper can help you come up with better ideas 00:05:52.200 --> 00:05:53.860 and could help you be more creative. 00:05:53.860 --> 00:05:56.170 - Forcing yourself to just conjure a solution 00:05:56.170 --> 00:05:57.520 simply does not work. 00:05:57.520 --> 00:05:59.310 Instead, take a break from a task. 00:05:59.310 --> 00:06:01.730 Pick something else up, like a physical sport 00:06:01.730 --> 00:06:03.150 or even video games. 00:06:03.150 --> 00:06:05.210 And then come back to the original problem. 00:06:05.210 --> 00:06:06.665 That can do wonders. 00:06:06.665 --> 00:06:08.490 (typewriter typing) 00:06:08.490 --> 00:06:11.823 (light music continues) 00:06:13.647 --> 00:06:17.100 - One of my biggest passions is documentary filmmaking. 00:06:17.100 --> 00:06:19.390 I've been making videos since I was in middle school. 00:06:19.390 --> 00:06:23.440 And I remember being, it was always a challenge, 00:06:23.440 --> 00:06:25.070 because sometimes I wanted to do things, 00:06:25.070 --> 00:06:27.220 but I didn't have the equipment to do it. 00:06:27.220 --> 00:06:30.680 I really wanted to record myself in a certain way, 00:06:30.680 --> 00:06:33.810 but there was no way for anyone to hold the microphone, 00:06:33.810 --> 00:06:37.190 or I didn't have a dolly or any expensive camera equipment. 00:06:37.190 --> 00:06:40.230 So, I remember, 00:06:40.230 --> 00:06:41.440 I think the most important thing to do 00:06:41.440 --> 00:06:43.200 is just use what you have. 00:06:43.200 --> 00:06:47.040 I would tape a cross-country ski pole to my ceiling 00:06:47.040 --> 00:06:49.210 and hold the microphone that way. 00:06:49.210 --> 00:06:52.160 Or I would put a pillow in a box 00:06:52.160 --> 00:06:54.270 and then speak into the microphone with that 00:06:54.270 --> 00:06:56.460 as my makeshift sound studio 00:06:56.460 --> 00:07:01.460 or make a tripod out of a pile of books. 00:07:01.460 --> 00:07:04.870 And I feel like it's kinda the same with math. 00:07:04.870 --> 00:07:08.150 You are, sometimes, you don't know how to solve 00:07:08.150 --> 00:07:10.100 a really big problem, 00:07:10.100 --> 00:07:12.730 and you only have all the tools you've been taught 00:07:12.730 --> 00:07:13.880 up to that point. 00:07:13.880 --> 00:07:16.999 And maybe there is a fancier way of getting 00:07:16.999 --> 00:07:19.180 to the solution, but a lotta the time, 00:07:19.180 --> 00:07:21.780 it's just about combining things that you already have 00:07:21.780 --> 00:07:24.090 in your, that you've already learned, 00:07:24.090 --> 00:07:25.550 and coming up with a solution that way. 00:07:25.550 --> 00:07:29.250 And sometimes, that comes up with some really creative 00:07:29.250 --> 00:07:32.332 and unexpected solutions to problems. 00:07:32.332 --> 00:07:33.610 (typewriter typing) 00:07:33.610 --> 00:07:36.210 (light music continues) 00:07:36.210 --> 00:07:39.830 - Algebra is really the unifying thread 00:07:39.830 --> 00:07:42.460 of almost all of mathematics. 00:07:42.460 --> 00:07:44.370 You may think algebra is boring, 00:07:44.370 --> 00:07:47.300 but it is the one tool you can use 00:07:47.300 --> 00:07:50.950 to not only understand but unlock the universe. 00:07:50.950 --> 00:07:54.190 Creative algebra is used in computer game design. 00:07:54.190 --> 00:07:58.170 It powers how artificial intelligence works. 00:07:58.170 --> 00:08:00.340 Mastering algebra will provide you 00:08:00.340 --> 00:08:02.710 with the ability to decode and understand 00:08:02.710 --> 00:08:04.680 many complex systems. 00:08:04.680 --> 00:08:07.490 In my opinion, if you can master algebra, 00:08:07.490 --> 00:08:08.838 you can master anything. 00:08:08.838 --> 00:08:12.142 (light music continues)

The future of creativity in algebra

https://www.youtube.com/watch?v=Q-apRGBr3Xg

vtt

https://www.youtube.com/api/timedtext?v=Q-apRGBr3Xg&ei=uVWUZaWKEd6XhcIP-JSKoAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C2E243A0A31BEDF67C30C40D08F44B3C0FAA5F56.A71771D9CA5BE0779C641B90505EAF67EA586679&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:02.903 (upbeat music) 00:00:11.990 --> 00:00:13.850 - Hi everyone, Sal Khan here. 00:00:13.850 --> 00:00:16.090 If you look at most of human history, 00:00:16.090 --> 00:00:20.400 the top artists, the top musicians were also mathematicians 00:00:20.400 --> 00:00:23.600 and also scientists and also engineers. 00:00:23.600 --> 00:00:28.160 And this convergence between creativity and mathematics 00:00:28.160 --> 00:00:31.820 and science and engineering is only accelerating. 00:00:31.820 --> 00:00:35.370 In the careers of the future, algebra and creativity 00:00:35.370 --> 00:00:37.720 are gonna be that much more empowering, 00:00:37.720 --> 00:00:39.070 but don't take my word for it. 00:00:39.070 --> 00:00:41.030 You're about to meet some of my close friends 00:00:41.030 --> 00:00:42.870 who can better draw that link 00:00:42.870 --> 00:00:47.123 between algebra and creativity and the work of the future. 00:00:47.123 --> 00:00:49.790 (upbeat music) 00:00:53.017 --> 00:00:55.240 - The math underpins everything in our universe, 00:00:55.240 --> 00:00:58.800 so it impacts every corner of our society. 00:00:58.800 --> 00:01:00.990 But over the past decade in particular, 00:01:00.990 --> 00:01:03.450 the advances in computer technology 00:01:03.450 --> 00:01:05.640 and introduction of machine learning 00:01:05.640 --> 00:01:08.930 and artificial intelligence has been massive 00:01:08.930 --> 00:01:10.730 and we're only learning more and more 00:01:10.730 --> 00:01:12.910 and building better and better systems, 00:01:12.910 --> 00:01:15.150 and math underpins all of that 00:01:15.150 --> 00:01:17.910 and it's fundamental to all of those systems. 00:01:17.910 --> 00:01:21.840 And in fact, computer science is inherently linear algebra, 00:01:21.840 --> 00:01:25.730 so it's really foundational to those scientific advances. 00:01:25.730 --> 00:01:29.000 - One relatively recent example that really inspired me 00:01:29.000 --> 00:01:31.330 was the first real photo that scientists 00:01:31.330 --> 00:01:34.100 were able to capture of a black hole, 00:01:34.100 --> 00:01:37.360 the mysterious remnants of giant stars 00:01:37.360 --> 00:01:40.140 that lurk all over the universe. 00:01:40.140 --> 00:01:42.410 And it's the way that scientists used creativity 00:01:42.410 --> 00:01:45.690 and math to solve the problem that was so fascinating. 00:01:45.690 --> 00:01:47.780 You see, these black holes are so distant 00:01:47.780 --> 00:01:49.870 that there is no single telescope 00:01:49.870 --> 00:01:52.680 that is large enough to be able to actually see them. 00:01:52.680 --> 00:01:55.560 And the scientists came up with this clever idea, 00:01:55.560 --> 00:01:58.290 creating a network of small telescopes 00:01:58.290 --> 00:02:01.000 distributed all across the globe that were synchronized 00:02:01.000 --> 00:02:05.280 to capture and focus the same object at the same time 00:02:05.280 --> 00:02:08.130 creating a giant virtual telescope. 00:02:08.130 --> 00:02:10.800 Now the aperture of this giant virtual telescope 00:02:10.800 --> 00:02:15.150 is nearly the same size as a diameter of the Earth. 00:02:15.150 --> 00:02:17.520 And with that in place, the scientists and engineers 00:02:17.520 --> 00:02:20.230 were able to capture all the bits and pieces of data 00:02:20.230 --> 00:02:22.690 and put it all together into the first image 00:02:22.690 --> 00:02:25.810 of a black hole that is 53 million light years, 00:02:25.810 --> 00:02:30.060 which is 318 quintillion miles away. 00:02:30.060 --> 00:02:33.384 Now that's an impressive use of creativity and math. 00:02:33.384 --> 00:02:36.051 (upbeat music) 00:02:38.880 --> 00:02:41.540 - In the future, in order to add innovation, 00:02:41.540 --> 00:02:42.730 students are gonna need skills 00:02:42.730 --> 00:02:44.900 such as creative problem solving, 00:02:44.900 --> 00:02:48.370 so not looking at things from the same perspective, 00:02:48.370 --> 00:02:51.060 being able to ideate, so come up with new ideas 00:02:51.060 --> 00:02:52.610 and divergent thinking, right, 00:02:52.610 --> 00:02:54.290 the ability to come up with ideas 00:02:54.290 --> 00:02:57.350 that are drastically different from each other. 00:02:57.350 --> 00:02:59.320 Beyond creative problem solving, students will also 00:02:59.320 --> 00:03:01.600 need to show adaptability. 00:03:01.600 --> 00:03:03.730 So the ability to pivot as the world 00:03:03.730 --> 00:03:06.430 and constraints around us kind of pivot. 00:03:06.430 --> 00:03:08.890 The STEM field is constantly evolving 00:03:08.890 --> 00:03:10.790 and it's growing as we gain more knowledge, 00:03:10.790 --> 00:03:13.100 so students' ability to be creative and adapt 00:03:13.100 --> 00:03:16.470 as the field adapts will be critical for success, 00:03:16.470 --> 00:03:18.780 and for the ability to innovate as we move forward. 00:03:18.780 --> 00:03:20.410 - Communication skills are always 00:03:20.410 --> 00:03:23.570 going to be essential for furthering innovation. 00:03:23.570 --> 00:03:25.490 And this is because if you want to make 00:03:25.490 --> 00:03:27.650 a scientific advancement, you have to have 00:03:27.650 --> 00:03:29.260 a lot of people on your side. 00:03:29.260 --> 00:03:31.370 So you have to have funding bodies, 00:03:31.370 --> 00:03:33.210 you have to have other scientists, 00:03:33.210 --> 00:03:36.190 you have to have people interested in what you're doing. 00:03:36.190 --> 00:03:39.110 So this means you have to have the communication tools 00:03:39.110 --> 00:03:43.730 to communicate with all of those different areas of people. 00:03:43.730 --> 00:03:45.870 So different ways that you can learn to communicate 00:03:45.870 --> 00:03:48.790 with them are through things like presentations, 00:03:48.790 --> 00:03:51.840 through visual aids, through videos. 00:03:51.840 --> 00:03:54.550 When you're preparing for communication tools of the future, 00:03:54.550 --> 00:03:57.600 it's quite difficult to know what those will be. 00:03:57.600 --> 00:04:00.210 So if we think back to 10 years ago, 00:04:00.210 --> 00:04:02.460 we didn't have things like TikTok, 00:04:02.460 --> 00:04:04.100 which is now a huge avenue 00:04:04.100 --> 00:04:06.960 for communicating things to young people. 00:04:06.960 --> 00:04:09.310 So that is something that we've had to adapt to 00:04:09.310 --> 00:04:12.300 and to learn and tailor our communication 00:04:12.300 --> 00:04:15.640 during this new area of media. 00:04:15.640 --> 00:04:18.900 So having versatility, if students are able 00:04:18.900 --> 00:04:21.780 to take the skills that they have and apply them 00:04:21.780 --> 00:04:24.890 to new areas of communication, they'll be prepared 00:04:24.890 --> 00:04:27.058 for the communication tools of the future. 00:04:27.058 --> 00:04:29.725 (upbeat music) 00:04:33.357 --> 00:04:35.210 - There are so many ways that you can expand 00:04:35.210 --> 00:04:37.280 your creative and math skills without even 00:04:37.280 --> 00:04:38.730 really realizing that you're doing it. 00:04:38.730 --> 00:04:42.510 Like for me, I'm a big board game fan, 00:04:42.510 --> 00:04:44.840 and I realized that there's so many games 00:04:44.840 --> 00:04:49.740 that involve math and learning how to solve problems. 00:04:49.740 --> 00:04:54.150 And sometimes just when you're cooking. 00:04:54.150 --> 00:04:56.940 I love to bake, and so I feel like I'm constantly 00:04:56.940 --> 00:05:01.040 using fractions and learning how to do proportions, 00:05:01.040 --> 00:05:02.650 just because I'm doing things that I love. 00:05:02.650 --> 00:05:05.060 So I feel like the best way to expand 00:05:05.060 --> 00:05:07.410 your mathematical and creative skills 00:05:07.410 --> 00:05:09.220 are just doing what you love to do, 00:05:09.220 --> 00:05:12.503 because probably it has some kind of math in it, 00:05:12.503 --> 00:05:14.680 and some kind of creativity. 00:05:14.680 --> 00:05:17.970 - Try to connect what you're learning to your real life. 00:05:17.970 --> 00:05:20.560 It's really easy to be in the classroom 00:05:20.560 --> 00:05:23.280 and think that it's siloed, and it's orthogonal 00:05:23.280 --> 00:05:25.300 from the world around you. 00:05:25.300 --> 00:05:27.870 The more we can connect what we're learning 00:05:27.870 --> 00:05:29.790 in the classroom to our real life, 00:05:29.790 --> 00:05:32.410 whether it be sports or entertainment, 00:05:32.410 --> 00:05:36.070 politics, news, whatever, the connection that you make 00:05:36.070 --> 00:05:38.220 between math and your real life will really help you 00:05:38.220 --> 00:05:40.590 appreciate the skills and the methods 00:05:40.590 --> 00:05:42.530 and find ways to transfer them 00:05:42.530 --> 00:05:45.229 outside of just the classroom alone. 00:05:45.229 --> 00:05:47.896 (upbeat music) 00:05:51.300 --> 00:05:54.240 - One of the newest ways of thinking about problem solving 00:05:54.240 --> 00:05:58.970 for me is something that my math professor would tell me. 00:05:58.970 --> 00:06:02.450 He would say, "Don't be afraid to be stuck." 00:06:02.450 --> 00:06:06.760 And I think that a lot of the time when we are doing math 00:06:06.760 --> 00:06:10.200 and we get stuck, sometimes it can be, 00:06:10.200 --> 00:06:12.980 you can feel like, "Wow, this is a reflection of me 00:06:12.980 --> 00:06:14.570 and my mathematical abilities. 00:06:14.570 --> 00:06:16.660 Wow, maybe I shouldn't be doing math." 00:06:16.660 --> 00:06:20.100 But really a lot of the time, it's just an indication 00:06:20.100 --> 00:06:23.010 that you need to spend more time doing the math 00:06:23.010 --> 00:06:25.150 or figuring out what the problem is exactly. 00:06:25.150 --> 00:06:26.600 If you haven't gotten stuck yet, 00:06:26.600 --> 00:06:30.310 then you probably will get stuck at some point. 00:06:30.310 --> 00:06:33.220 So being stuck is just a part of math 00:06:33.220 --> 00:06:36.970 and it's kind of learning what to do 00:06:36.970 --> 00:06:39.817 when you are stuck is a really big part 00:06:40.954 --> 00:06:42.320 of being creative in math, 00:06:42.320 --> 00:06:44.980 and being able to solve problems in the future. 00:06:44.980 --> 00:06:49.690 - One example that I often use is I often 00:06:49.690 --> 00:06:54.690 try to solve problems both in the traditional algebraic way 00:06:56.670 --> 00:07:01.670 but I also try to visualize problems in 2D and 3D space 00:07:02.870 --> 00:07:04.210 to solve them more visually. 00:07:04.210 --> 00:07:07.440 And so I think the more ways that you can 00:07:07.440 --> 00:07:09.840 figure out how to solve a problem, 00:07:09.840 --> 00:07:12.380 the more ways that you can eventually sort of 00:07:12.380 --> 00:07:15.100 save in your toolbox and use later on 00:07:15.100 --> 00:07:17.260 to solve other problems. 00:07:17.260 --> 00:07:19.950 - There's lots of different tools and resources 00:07:19.950 --> 00:07:23.410 like apps and puzzle games that are gonna help you 00:07:23.410 --> 00:07:25.350 think about problems in new ways 00:07:25.350 --> 00:07:27.850 and help develop that critical thinking 00:07:27.850 --> 00:07:30.470 that you need to be able to apply your skills 00:07:30.470 --> 00:07:32.780 to a lot of different areas. 00:07:32.780 --> 00:07:35.150 And sometimes even starting at the answer 00:07:35.150 --> 00:07:37.450 and working backwards through the problem 00:07:37.450 --> 00:07:40.980 can help you see a different way of getting to the answer. 00:07:40.980 --> 00:07:42.250 - Students can combine new ways 00:07:42.250 --> 00:07:43.670 of thinking about problem solving 00:07:43.670 --> 00:07:45.440 by trying to look at it from different angles. 00:07:45.440 --> 00:07:47.200 Anytime you approach a problem, 00:07:47.200 --> 00:07:49.720 If you're just looking at it from your perspective, 00:07:49.720 --> 00:07:52.940 you're not gonna get a holistic view of the solution space. 00:07:52.940 --> 00:07:56.390 So try to have perspectives and look at the problem 00:07:56.390 --> 00:07:58.760 from multiple angles to understand 00:07:58.760 --> 00:08:00.610 all the ways in which it could be viewed. 00:08:00.610 --> 00:08:02.810 The more holistically you view a problem, 00:08:02.810 --> 00:08:05.100 the more paths you look at, the more efficient 00:08:05.100 --> 00:08:07.300 and effective you're gonna be at solving it. 00:08:08.393 --> 00:08:11.060 (upbeat music) 00:08:13.600 --> 00:08:15.640 - One of these that is most interesting to me 00:08:15.640 --> 00:08:18.840 is the field of robotics and the different ways 00:08:18.840 --> 00:08:22.220 machine learning will impact our society. 00:08:22.220 --> 00:08:25.670 So robotics combines lots of math, lots of science, 00:08:25.670 --> 00:08:29.340 lots of technology, but also socioeconomic factors 00:08:29.340 --> 00:08:31.700 such as human and robot trust. 00:08:31.700 --> 00:08:35.700 So how humans feel about robots, how they trust them, 00:08:35.700 --> 00:08:37.960 and human/robot teams in the workplace, 00:08:37.960 --> 00:08:42.800 so how humans and robots work together to accomplish a task. 00:08:42.800 --> 00:08:45.550 And creativity will be hugely important here, 00:08:45.550 --> 00:08:47.990 so creativity is not only gonna be important 00:08:47.990 --> 00:08:49.450 in designing the robots, 00:08:49.450 --> 00:08:52.880 they're very intricate, very complex systems, 00:08:52.880 --> 00:08:55.010 and it'll require creativity to know 00:08:55.010 --> 00:08:58.040 exactly how to design them to do their jobs, 00:08:58.040 --> 00:09:01.060 but also how to integrate them into our everyday lives 00:09:01.060 --> 00:09:04.560 which is a total different facet of creativity. 00:09:04.560 --> 00:09:06.540 And it's actually a new way of thinking 00:09:06.540 --> 00:09:08.740 because it hasn't really been done yet. 00:09:08.740 --> 00:09:10.747 So even though there are robots around us 00:09:10.747 --> 00:09:13.070 and we've seen them, you've got the Roomba 00:09:13.070 --> 00:09:15.210 who hoovers your living room, 00:09:15.210 --> 00:09:18.420 really where we're heading is for robots to be everywhere 00:09:18.420 --> 00:09:20.980 and to be a really integral part of our society. 00:09:20.980 --> 00:09:24.340 So preparing for that change and using creativity 00:09:24.340 --> 00:09:25.990 to figure out the best way to do that 00:09:25.990 --> 00:09:29.078 will be a really important step in innovation in the future. 00:09:29.078 --> 00:09:31.745 (upbeat music)

Creativity in biology

https://www.youtube.com/watch?v=OX0zcM1Bwuw

vtt

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en

WEBVTT Kind: captions Language: en 00:00:00.717 --> 00:00:05.717 (gentle rock music) (marker scratches) 00:00:11.860 --> 00:00:14.130 - Hi, everyone, Sal Khan here. 00:00:14.130 --> 00:00:16.740 Biology is the study of living systems, 00:00:16.740 --> 00:00:17.950 and you can look all around you 00:00:17.950 --> 00:00:20.740 and even at yourself to recognize that living systems 00:00:20.740 --> 00:00:21.660 and biology 00:00:21.660 --> 00:00:24.500 and nature is fundamentally creative. 00:00:24.500 --> 00:00:26.720 And for us to understand it, 00:00:26.720 --> 00:00:29.360 we have to be even more creative. 00:00:29.360 --> 00:00:31.340 But don't take my word for it. 00:00:31.340 --> 00:00:32.610 I'm gonna introduce you to some 00:00:32.610 --> 00:00:33.570 of my close friends 00:00:33.570 --> 00:00:37.290 who can even better draw this link between biology 00:00:37.290 --> 00:00:38.283 and creativity. 00:00:39.305 --> 00:00:43.010 (keyboard keys clicking) (marker scratching) 00:00:43.010 --> 00:00:45.350 - Creativity is super important in biology 00:00:45.350 --> 00:00:46.563 because it's hugely important 00:00:46.563 --> 00:00:48.470 (keyboard keys clicking) in the process of evolution. 00:00:48.470 --> 00:00:50.900 Evolution often takes a winding path 00:00:50.900 --> 00:00:52.650 to get to what we see now, 00:00:52.650 --> 00:00:54.697 and if we wanna follow this path 00:00:54.697 --> 00:00:57.210 in an attempt to understand it, 00:00:57.210 --> 00:00:59.260 sometimes we've gotta be as resourceful 00:00:59.260 --> 00:01:01.340 and clever as evolution has been. 00:01:01.340 --> 00:01:04.560 That requires creativity in how we solve problems, 00:01:04.560 --> 00:01:07.740 and even creativity in the questions we ask. 00:01:07.740 --> 00:01:10.350 - Creativity is so important 00:01:10.350 --> 00:01:12.880 for anybody who is thinking (keyboard keys clicking) 00:01:12.880 --> 00:01:14.750 about, who is studying biology. 00:01:14.750 --> 00:01:17.520 Because the question we're trying to understand is not 00:01:17.520 --> 00:01:19.700 just, take in all the information 00:01:19.700 --> 00:01:21.960 that we know about biology. 00:01:21.960 --> 00:01:25.430 We want people to imagine what biology, 00:01:25.430 --> 00:01:26.932 what the natural world, 00:01:26.932 --> 00:01:29.226 what the physical world, you know, 00:01:29.226 --> 00:01:32.160 what our bodies can actually do, 00:01:32.160 --> 00:01:33.980 what our brains can do. 00:01:33.980 --> 00:01:35.190 And to be able to do that, 00:01:35.190 --> 00:01:38.420 you need to think out of the box, you need to think 00:01:38.420 --> 00:01:41.040 about things that haven't been thought about before, 00:01:41.040 --> 00:01:42.810 and that is why biology, 00:01:42.810 --> 00:01:46.490 that is why creativity is so critical 00:01:46.490 --> 00:01:48.690 for anybody studying biology. 00:01:48.690 --> 00:01:51.400 - Creativity isn't exclusive just to the arts, 00:01:51.400 --> 00:01:53.113 but it also spans into science 00:01:53.113 --> 00:01:53.946 (keyboard keys clicking) and technology 00:01:53.946 --> 00:01:54.779 and engineering 00:01:54.779 --> 00:01:55.670 and mathematics. 00:01:55.670 --> 00:01:56.503 Creativity 00:01:56.503 --> 00:01:58.440 and science comes down to, 00:01:58.440 --> 00:02:00.760 thinking about a problem or a situation, 00:02:00.760 --> 00:02:02.550 and how best to approach that problem 00:02:02.550 --> 00:02:04.700 or situation from multiple angles. 00:02:04.700 --> 00:02:07.440 So, when you approach a problem in the real world, 00:02:07.440 --> 00:02:11.060 it won't be multiple choice, like you may have in school. 00:02:11.060 --> 00:02:13.150 It actually would be something that requires you 00:02:13.150 --> 00:02:15.880 to think about that particular situation, 00:02:15.880 --> 00:02:17.240 and apply other things you've learned 00:02:17.240 --> 00:02:18.430 about it to be creative, 00:02:18.430 --> 00:02:20.570 and to come up with answers 00:02:20.570 --> 00:02:22.870 that may not have been familiar to you before. 00:02:23.814 --> 00:02:28.080 (keyboard keys clicking) (marker scratching) 00:02:28.080 --> 00:02:29.960 - One question that people ask me is, 00:02:29.960 --> 00:02:32.670 how do I apply creativity 00:02:32.670 --> 00:02:33.924 to the presentations 00:02:33.924 --> 00:02:35.650 (keyboard keys clicking) that I give? 00:02:35.650 --> 00:02:39.860 And my secret sauce is to come up 00:02:39.860 --> 00:02:43.260 with a visual image that anybody, 00:02:43.260 --> 00:02:44.490 I don't if you're the adult, 00:02:44.490 --> 00:02:46.410 whether you're a fifth grader or second grader, 00:02:46.410 --> 00:02:48.810 that you can grasp that concept. 00:02:48.810 --> 00:02:50.350 And here's my favorite one. 00:02:50.350 --> 00:02:52.980 So every single time you move your body, 00:02:52.980 --> 00:02:55.090 there's whole bunches of neurochemicals 00:02:55.090 --> 00:02:57.700 that are released in your brain. 00:02:57.700 --> 00:03:00.080 And you've heard of these neurochemicals: dopamine, 00:03:00.080 --> 00:03:02.650 noradrenaline, serotonin. 00:03:02.650 --> 00:03:04.170 And so, that's the fact, 00:03:04.170 --> 00:03:06.190 but the image that I give is 00:03:06.190 --> 00:03:08.550 that every single time you move your body, 00:03:08.550 --> 00:03:11.330 it's like giving your brain a wonderful bubble bath 00:03:11.330 --> 00:03:14.100 of neurochemicals that enrich your brain, 00:03:14.100 --> 00:03:17.700 that change that neurochemical milieu, 00:03:17.700 --> 00:03:18.870 and that is the image 00:03:18.870 --> 00:03:22.020 that everybody that comes to my talks leaves with, 00:03:22.020 --> 00:03:23.191 and inspires them a little bit 00:03:23.191 --> 00:03:24.970 (gentle electronic music) to move their body more. 00:03:24.970 --> 00:03:27.170 So can you come up with that image, 00:03:27.170 --> 00:03:29.770 that playful, fun, 00:03:29.770 --> 00:03:32.840 but factually accurate image 00:03:32.840 --> 00:03:34.610 that conveys your message. 00:03:34.610 --> 00:03:36.860 That will be your secret sauce too. 00:03:36.860 --> 00:03:41.120 - Have you heard that the bees aren't doing great? 00:03:41.120 --> 00:03:43.040 Well, I've been studying that, (keyboard keys clicking) 00:03:43.040 --> 00:03:44.270 and trying to understand 00:03:44.270 --> 00:03:46.930 how their complex health issues connect 00:03:46.930 --> 00:03:48.690 to a curious little parasite 00:03:48.690 --> 00:03:52.500 that's in nearly every honeybee colony worldwide. 00:03:52.500 --> 00:03:55.910 It's called Varroa Destructor, by the way. 00:03:55.910 --> 00:03:58.960 Now, before I started this study, 00:03:58.960 --> 00:04:00.490 we thought the that it was an open 00:04:00.490 --> 00:04:02.950 and shut case, that the parasite was sucking 00:04:02.950 --> 00:04:06.840 out the bee's blood, sort of like a tick on a puppy, 00:04:06.840 --> 00:04:10.620 but I thought something more strange might be going on. 00:04:10.620 --> 00:04:13.000 The damage that it caused just didn't seem 00:04:13.000 --> 00:04:16.010 like the damage that would be caused by blood removal. 00:04:16.010 --> 00:04:19.000 The feeding process is super difficult to see though, 00:04:19.000 --> 00:04:22.420 so, I had this idea. 00:04:22.420 --> 00:04:25.880 I fed different color glowing food to the bees 00:04:25.880 --> 00:04:26.713 in their pollen 00:04:26.713 --> 00:04:27.730 and their sugar water, 00:04:27.730 --> 00:04:30.750 to color their organs specific colors. 00:04:30.750 --> 00:04:34.250 Then, when the parasite fed on the bees, 00:04:34.250 --> 00:04:36.510 I could tell which organ it was eating, 00:04:36.510 --> 00:04:39.760 based on which color was in its digestive system, 00:04:39.760 --> 00:04:43.430 and it turns out that they were eating the bee's liver, 00:04:43.430 --> 00:04:46.641 by the way, which is pretty weird, 00:04:46.641 --> 00:04:49.890 but, this kind of work is actually pretty fun. 00:04:49.890 --> 00:04:51.520 And it was definitely a place 00:04:51.520 --> 00:04:54.248 where creativity was rewarded in biology. 00:04:54.248 --> 00:04:59.248 (keyboard keys clicking) (marker scratching) 00:05:01.160 --> 00:05:04.380 Some of the world's greatest discoveries have been reached 00:05:04.380 --> 00:05:06.005 by applying creative thinking 00:05:06.005 --> 00:05:08.940 (keyboard keys clicking) to scientific questions. 00:05:08.940 --> 00:05:10.330 Here's a good example. 00:05:10.330 --> 00:05:13.480 I have been super inspired by the creativity 00:05:13.480 --> 00:05:15.840 of the Geiger-Marsden gold foil experiments, 00:05:15.840 --> 00:05:17.280 since I was in high school. 00:05:17.280 --> 00:05:20.380 They have helped us understand the structure of an atom, 00:05:20.380 --> 00:05:23.190 and atoms make up pretty much everything 00:05:23.190 --> 00:05:25.720 we can interact with, biological or otherwise. 00:05:25.720 --> 00:05:28.660 Like, you can't see an atom, 00:05:28.660 --> 00:05:31.670 so, you've gotta get creative to figure out 00:05:31.670 --> 00:05:33.590 how its pieces are all laid out. 00:05:33.590 --> 00:05:34.700 We used to think 00:05:34.700 --> 00:05:38.770 that its positive charge was pretty evenly spread out, 00:05:38.770 --> 00:05:41.810 but this research team fired a beam 00:05:41.810 --> 00:05:44.440 of positively charged particles at gold atoms, 00:05:44.440 --> 00:05:46.850 and found that a bunch of them bounced off, 00:05:46.850 --> 00:05:50.300 while even more of them passed straight through. 00:05:50.300 --> 00:05:53.740 And this suggested that the positive charge 00:05:53.740 --> 00:05:56.200 in the atom was concentrated in a small part, 00:05:56.200 --> 00:05:58.860 because some of the positive particles were upheld, 00:05:58.860 --> 00:06:02.980 like the two positive poles of like, two separate magnets, 00:06:02.980 --> 00:06:06.240 but much of the rest of the atom must be empty space, 00:06:06.240 --> 00:06:08.720 because a bunch of the particles passed right through. 00:06:08.720 --> 00:06:11.010 Because of this absolutely genius way 00:06:11.010 --> 00:06:13.050 of visualizing what we can't see, 00:06:13.050 --> 00:06:15.480 we now know the structure of the stuff 00:06:15.480 --> 00:06:18.833 that makes up the observable universe. 00:06:18.833 --> 00:06:20.140 (upbeat synthpop music) And, because 00:06:20.140 --> 00:06:22.160 of this pioneering research, 00:06:22.160 --> 00:06:25.310 we've got everything from nuclear power 00:06:25.310 --> 00:06:28.601 to MRI machines, even the life saving technology 00:06:28.601 --> 00:06:31.543 that's inside of the smoke detectors in your home. 00:06:31.543 --> 00:06:35.840 (keyboard keys clicking) (marker scratching) 00:06:35.840 --> 00:06:39.719 So, the first step discoveries is always the same. 00:06:39.719 --> 00:06:41.640 (keyboard keys clicking) Figure out your question. 00:06:41.640 --> 00:06:44.650 Maybe you wanna know where fireflies go during the day, 00:06:44.650 --> 00:06:47.610 or how mosquitoes find people to bite. 00:06:47.610 --> 00:06:50.810 And then you should create a hypothesis. 00:06:50.810 --> 00:06:52.177 Maybe mosquitoes find people 00:06:52.177 --> 00:06:54.230 by following the smell of sweat 00:06:54.230 --> 00:06:57.339 and their breath, then consider what must be true 00:06:57.339 --> 00:07:00.090 for your hypothesis to be true. 00:07:00.090 --> 00:07:03.120 You might not be able to test a mosquito's 00:07:03.120 --> 00:07:07.290 smell receptors directly, but if your hypothesis is true, 00:07:07.290 --> 00:07:08.359 people who are exercising, 00:07:08.359 --> 00:07:10.090 and thus exhaling a lot, 00:07:10.090 --> 00:07:11.460 and producing more sweat, 00:07:11.460 --> 00:07:13.253 should attract more mosquitoes. 00:07:14.207 --> 00:07:17.410 Actually, I probably shouldn't encourage you 00:07:17.410 --> 00:07:19.333 to experiment on humans. 00:07:20.300 --> 00:07:24.630 Why don't you maybe try the firefly question instead? 00:07:24.630 --> 00:07:26.839 - Young people can get creative in science, 00:07:26.839 --> 00:07:28.650 (keyboard keys clicking) by using not just science 00:07:28.650 --> 00:07:30.000 but other things that they're learning 00:07:30.000 --> 00:07:30.833 from their life, 00:07:30.833 --> 00:07:31.960 and connecting it to science 00:07:31.960 --> 00:07:33.670 or connecting science to other things 00:07:33.670 --> 00:07:35.840 in their life such as art, 00:07:35.840 --> 00:07:37.448 and other things that are outside 00:07:37.448 --> 00:07:40.210 of the traditional STEM fields. 00:07:40.210 --> 00:07:42.680 For example, when you're looking at, 00:07:42.680 --> 00:07:44.540 or wondering about how something works, 00:07:44.540 --> 00:07:48.240 like an mRNA vaccine, or how the organ systems work, 00:07:48.240 --> 00:07:50.960 you can use other aspects of your life, 00:07:50.960 --> 00:07:53.370 and learn to make, or draw analogies 00:07:53.370 --> 00:07:54.960 between different systems. 00:07:54.960 --> 00:07:57.330 That's a really important aspect of being creative 00:07:57.330 --> 00:07:58.870 and using critical thinking, 00:07:58.870 --> 00:08:00.550 because a lot of systems are similar 00:08:00.550 --> 00:08:02.830 to other systems, even though they use different names 00:08:02.830 --> 00:08:04.270 or look very different, 00:08:04.270 --> 00:08:05.820 and you can expand on your knowledge 00:08:05.820 --> 00:08:08.290 on something by being creative, 00:08:08.290 --> 00:08:10.190 or using other things outside of science 00:08:10.190 --> 00:08:12.640 to draw connections between different fields 00:08:12.640 --> 00:08:13.733 and different things.

Creative biology at work

https://www.youtube.com/watch?v=XMXmY11vDDA

vtt

https://www.youtube.com/api/timedtext?v=XMXmY11vDDA&ei=uVWUZbuQKNvTxN8Pju-O-Ao&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A89FE119AAE8F4B534730E451D3068EC3BA382B4.144F480E45BE6946A0FF301DE9BC83699CED90E9&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.140 --> 00:00:02.723 (upbeat music) 00:00:11.990 --> 00:00:13.920 - Hi everyone, Sal Khan here. 00:00:13.920 --> 00:00:18.530 From finding novel cures for a seemingly incurable disease 00:00:18.530 --> 00:00:21.210 to diagnosing what's going on with someone 00:00:23.126 --> 00:00:23.959 if you're a physician or a nurse, 00:00:23.959 --> 00:00:26.859 you can imagine there is incredible creativity in biology. 00:00:27.710 --> 00:00:29.290 And don't take my word for it. 00:00:29.290 --> 00:00:31.090 You're now going to meet some of my friends 00:00:31.090 --> 00:00:33.110 who can tell you more about that connection 00:00:33.110 --> 00:00:36.083 between biology and creativity. 00:00:40.580 --> 00:00:44.150 - All science careers involve creativity, 00:00:44.150 --> 00:00:45.130 think about it. 00:00:45.130 --> 00:00:47.520 We're asking and answering questions, 00:00:47.520 --> 00:00:50.210 and we're solving the world's problems. 00:00:50.210 --> 00:00:54.600 So the more creatively we can solve the world's problems, 00:00:54.600 --> 00:00:58.160 the more new ideas and concepts and approaches 00:00:58.160 --> 00:01:00.950 we can use to address the world's problems, 00:01:00.950 --> 00:01:02.100 the better off we'll be. 00:01:02.100 --> 00:01:04.070 - Creativity is the guiding force 00:01:04.070 --> 00:01:05.620 on the path to good science. 00:01:05.620 --> 00:01:08.090 So there isn't a science job out there 00:01:08.090 --> 00:01:10.620 that doesn't benefit from creativity. 00:01:10.620 --> 00:01:13.300 Like you could be an engineer, 00:01:13.300 --> 00:01:15.100 building more efficient transistors 00:01:15.100 --> 00:01:17.170 for tinier and tinier phones. 00:01:17.170 --> 00:01:18.590 You could be a climate scientist 00:01:18.590 --> 00:01:21.470 figuring out how we can reduce our carbon footprint 00:01:21.470 --> 00:01:23.730 and save the world from climate catastrophe, 00:01:23.730 --> 00:01:25.700 or an agricultural researcher 00:01:25.700 --> 00:01:28.550 deducing efficient ways to feed the planet, 00:01:28.550 --> 00:01:31.169 or maybe, an entomologist like me, 00:01:31.169 --> 00:01:33.380 understanding how relationships 00:01:33.380 --> 00:01:36.010 between organisms keep us all healthy. 00:01:36.010 --> 00:01:38.980 Creativity is important in all of these careers. 00:01:38.980 --> 00:01:43.980 - One really cool job is working for a science museum. 00:01:44.290 --> 00:01:48.294 And so the people who are like the chief directors 00:01:48.294 --> 00:01:51.160 or bioscientists, or what have you for science museums 00:01:51.160 --> 00:01:55.670 usually have a biology or a science background of some kind, 00:01:55.670 --> 00:01:58.600 maybe have gone through even being a PhD 00:01:58.600 --> 00:02:01.070 or a post doctoral fellow. 00:02:01.070 --> 00:02:06.070 And their job is to design exhibits for visitors to museums 00:02:08.290 --> 00:02:13.077 and come up with engaging ways to share ideas in science. 00:02:13.077 --> 00:02:16.060 And so I just think that's a really cool job 00:02:17.760 --> 00:02:19.760 that you might not immediately think of. 00:02:21.200 --> 00:02:24.320 (upbeat music) 00:02:24.320 --> 00:02:25.410 - As we move forward, 00:02:25.410 --> 00:02:30.410 as scientists, as biologists, the old adage is true. 00:02:31.820 --> 00:02:36.070 A picture is worth a thousand words. 00:02:36.070 --> 00:02:40.100 So what is that image, that graph, 00:02:40.100 --> 00:02:43.500 that graphic, or even that imagery 00:02:45.380 --> 00:02:49.770 that really gets to the core of your idea? 00:02:49.770 --> 00:02:51.770 It almost gets to advertising. 00:02:51.770 --> 00:02:56.770 You want that image to stick in your listener's minds. 00:02:57.470 --> 00:03:01.320 That both lets them understand 00:03:01.320 --> 00:03:05.400 the undeniably complex concept that you're trying to convey, 00:03:05.400 --> 00:03:08.230 but also makes it memorable. 00:03:08.230 --> 00:03:12.470 And developing that skill to come up with that picture 00:03:12.470 --> 00:03:15.680 that is truly worth a thousand words 00:03:15.680 --> 00:03:19.960 is going to be the skill that we will all need 00:03:19.960 --> 00:03:21.080 going into the future. 00:03:21.080 --> 00:03:23.720 - Creativity plays a role in my life 00:03:23.720 --> 00:03:25.890 pretty much every single day, 00:03:25.890 --> 00:03:27.780 by reminding me not to stop 00:03:27.780 --> 00:03:29.380 just because I've reached a setback. 00:03:29.380 --> 00:03:32.760 Like hitting a wall as you're moving towards a goal 00:03:32.760 --> 00:03:35.310 doesn't have to be the end for that goal. 00:03:35.310 --> 00:03:37.980 To me, it just means that the path to success 00:03:37.980 --> 00:03:40.030 isn't gonna be quite as straightforward 00:03:40.030 --> 00:03:41.300 as I originally thought. 00:03:41.300 --> 00:03:43.920 Like, the way around that wall may require me 00:03:43.920 --> 00:03:46.590 to climb over it, or tunnel under it, 00:03:46.590 --> 00:03:49.220 or maybe even dig straight through it. 00:03:49.220 --> 00:03:51.150 But if I'm creative enough, 00:03:51.150 --> 00:03:54.420 I can probably find a way to get to the other side. 00:03:54.420 --> 00:03:56.490 And this plays out for me in the lab, 00:03:56.490 --> 00:03:58.740 literally every single day. 00:03:58.740 --> 00:04:01.520 It fuels tenacity that can see you 00:04:01.520 --> 00:04:02.930 through things like graduate school 00:04:02.930 --> 00:04:04.730 if you ever choose to go that route. 00:04:09.280 --> 00:04:11.220 - I allow my brain to do the work 00:04:11.220 --> 00:04:13.510 to get into my creative zone. 00:04:13.510 --> 00:04:15.810 When I have a problem to resolve, 00:04:15.810 --> 00:04:17.260 sometimes I just sleep on it 00:04:17.260 --> 00:04:20.880 and I let my subconscious mind work 00:04:20.880 --> 00:04:24.730 through resolving problems, and solving problems. 00:04:24.730 --> 00:04:29.027 Our brains are always at work like trying defragment 00:04:30.590 --> 00:04:33.620 and break apart the things that we encounter. 00:04:33.620 --> 00:04:36.680 So I spend a little time thinking 00:04:36.680 --> 00:04:40.050 about how I can approach things creatively. 00:04:40.050 --> 00:04:42.790 And then, I spend a little time not thinking 00:04:42.790 --> 00:04:45.350 about those things and allowing my brain, 00:04:45.350 --> 00:04:48.480 and my subconscious mind to have an opportunity 00:04:48.480 --> 00:04:50.010 to do the work for me. 00:04:50.010 --> 00:04:52.560 A lot of times when I come back afterwards, 00:04:52.560 --> 00:04:53.870 I've got a great idea. 00:04:53.870 --> 00:04:57.460 I've got the answers, and I have new ways to solve 00:04:57.460 --> 00:05:00.040 and resolve things that I've been thinking about. 00:05:00.040 --> 00:05:02.020 - To get into my creative zone, 00:05:02.020 --> 00:05:03.910 I do something that I'd like to call 00:05:03.910 --> 00:05:06.110 productive procrastination. 00:05:06.110 --> 00:05:09.340 I start what I'm working on way before it's due, 00:05:09.340 --> 00:05:11.230 and then in fits and starts, 00:05:11.230 --> 00:05:14.860 I work while giving my mind permission 00:05:14.860 --> 00:05:19.800 to wander to things that absolutely are not on the agenda. 00:05:19.800 --> 00:05:24.200 It's encouraged some of my most creative experiences, 00:05:24.200 --> 00:05:27.180 some of my best songwriting, educational videos, 00:05:27.180 --> 00:05:29.580 and even scientific breakthroughs while I was supposed 00:05:29.580 --> 00:05:32.300 to be working on something totally unrelated. 00:05:32.300 --> 00:05:34.280 And this won't work for everyone, 00:05:34.280 --> 00:05:35.960 but my mind is most creative 00:05:35.960 --> 00:05:38.603 when it's free to go on unplanned adventures. 00:05:39.490 --> 00:05:41.210 Good music also helps. 00:05:41.210 --> 00:05:44.980 A great playlist, to me, is worth its weight and gold. 00:05:44.980 --> 00:05:46.610 My playlists are special 00:05:46.610 --> 00:05:49.638 because they only include instrumental music 00:05:49.638 --> 00:05:53.300 and songs in languages that I don't actually speak. 00:05:53.300 --> 00:05:54.840 So my thoughts don't get too pulled 00:05:54.840 --> 00:05:56.293 into the lyrics themselves. 00:06:03.620 --> 00:06:06.760 - I've used creative communication to solve problems related 00:06:06.760 --> 00:06:10.150 to especially people learning different science. 00:06:10.150 --> 00:06:13.720 For example, in chemistry, people sometimes have a hard time 00:06:13.720 --> 00:06:18.480 understanding subatomic particles and molecules and atoms 00:06:18.480 --> 00:06:22.210 and making those connections between quantities and numbers. 00:06:22.210 --> 00:06:23.990 So instead of jumping right into that, 00:06:23.990 --> 00:06:25.710 which can be very difficult for people, 00:06:25.710 --> 00:06:28.010 I've learned to be creative and use analogies 00:06:28.010 --> 00:06:30.040 or relating that to something that is more accessible, 00:06:30.040 --> 00:06:34.240 such as cooking or money or building something. 00:06:34.240 --> 00:06:36.080 And then when people can make their relation 00:06:36.080 --> 00:06:38.540 between something large and familiar 00:06:38.540 --> 00:06:41.960 to something small or subatomic and unfamiliar, 00:06:41.960 --> 00:06:44.860 it makes it easier for them to make those connections 00:06:44.860 --> 00:06:46.520 and build upon that knowledge. 00:06:46.520 --> 00:06:49.070 - So, several years ago, I started making videos 00:06:49.070 --> 00:06:52.690 of myself explaining biology and entomology in language 00:06:52.690 --> 00:06:55.690 that was accessible and familiar to people my age 00:06:55.690 --> 00:06:58.490 and people who don't fit the stereotypical model 00:06:58.490 --> 00:06:59.850 of a scientist. 00:06:59.850 --> 00:07:02.560 It's a choice that I'm really glad that I made actually. 00:07:02.560 --> 00:07:06.040 I've received so much positive feedback about videos 00:07:06.040 --> 00:07:08.440 no more complicated than me holding a bug 00:07:08.440 --> 00:07:13.290 in front of a camera, and actually, just like this. 00:07:13.290 --> 00:07:17.930 Me literally holding a bug in front of a camera 00:07:17.930 --> 00:07:20.123 and explaining what makes it tick. 00:07:21.010 --> 00:07:23.840 Note to self, I should make a video 00:07:23.840 --> 00:07:26.420 about what makes ticks tick. 00:07:26.420 --> 00:07:27.253 That'd be pretty cool. 00:07:27.253 --> 00:07:28.960 Wait, sorry. That's neither here nor there. 00:07:28.960 --> 00:07:32.120 The point of what I'm saying is the choice 00:07:32.120 --> 00:07:34.190 not to excise my personality, 00:07:34.190 --> 00:07:36.530 the choice to bring all of my quirkiness 00:07:36.530 --> 00:07:40.070 into how I communicate is what seems to make the difference. 00:07:40.070 --> 00:07:41.640 A big part of being creative 00:07:41.640 --> 00:07:44.010 really can be just figuring out 00:07:44.010 --> 00:07:45.740 how to bring all of you 00:07:45.740 --> 00:07:47.740 to whatever it is that you choose to do. 00:07:52.130 --> 00:07:55.290 - I think biology is so critical 00:07:55.290 --> 00:07:58.010 for everybody to learn 00:07:58.010 --> 00:08:03.010 because it defines who we are as human beings, as animals. 00:08:04.750 --> 00:08:07.670 It defines the whole animal kingdom. 00:08:07.670 --> 00:08:10.820 And then it goes on to define the whole plant kingdom, 00:08:10.820 --> 00:08:12.770 the insect kingdom. 00:08:12.770 --> 00:08:17.770 Understanding those principles of how living things 00:08:19.300 --> 00:08:24.300 are organized is not only a beautiful thing to understand, 00:08:24.340 --> 00:08:28.810 but it gives deep insight and deep appreciation 00:08:28.810 --> 00:08:31.150 for our own lives. 00:08:31.150 --> 00:08:36.150 And I think that is the core of why I find it so important 00:08:36.970 --> 00:08:41.970 that everybody study this beautiful area of academia. 00:08:43.200 --> 00:08:46.930 - Biology is super important to learn for so many reasons. 00:08:46.930 --> 00:08:49.653 But the reason that stands out most to me is, well, 00:08:51.750 --> 00:08:54.580 the rarity of life outside of our little corner 00:08:54.580 --> 00:08:55.890 of the universe. 00:08:55.890 --> 00:08:59.900 You might not know what I mean, but stick with me for a sec. 00:08:59.900 --> 00:09:04.080 So we are positively surrounded by biology 00:09:04.080 --> 00:09:05.810 every day here on Earth, 00:09:05.810 --> 00:09:07.490 but we haven't encountered life, 00:09:07.490 --> 00:09:10.910 or even evidence of life outside of this little blue marvel, 00:09:10.910 --> 00:09:14.950 even though there is so much cosmic real estate out there. 00:09:14.950 --> 00:09:17.340 Life is really complicated. 00:09:17.340 --> 00:09:20.650 And that goes for starting and sustaining life. 00:09:20.650 --> 00:09:22.940 Somehow, ancient organisms made it work here, 00:09:22.940 --> 00:09:24.760 but that doesn't mean that it's easy. 00:09:24.760 --> 00:09:28.260 All of us carry on this legacy of life, finding a way. 00:09:28.260 --> 00:09:32.700 But one day, maybe life will have to find a way through us. 00:09:32.700 --> 00:09:35.590 Maybe Earth becomes inhospitable for some reason, 00:09:35.590 --> 00:09:38.840 and we have to figure out how to live somewhere else. 00:09:38.840 --> 00:09:42.340 On that day, success will depend on how well 00:09:42.340 --> 00:09:45.020 we understand the heaps of obstacles 00:09:45.020 --> 00:09:48.403 that the stubbornness of life has already overcome.

The future of creativity in biology

https://www.youtube.com/watch?v=rBHbaYkn-rQ

vtt

https://www.youtube.com/api/timedtext?v=rBHbaYkn-rQ&ei=uVWUZYeJGbitp-oP0MWWoAc&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0C6073CCDC938F3EB82F1CFD9AEBA360F7C8E164.03D6B7B3D6F347401A44E2795951FB3AA4AD2231&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.380 --> 00:00:03.047 (upbeat music) 00:00:11.900 --> 00:00:13.850 - Hi everyone, Sal Khan here. 00:00:13.850 --> 00:00:16.330 I think we're about to enter what will be considered 00:00:16.330 --> 00:00:18.170 the golden age of biology, 00:00:18.170 --> 00:00:21.110 where not only do we understand or are starting understand 00:00:21.110 --> 00:00:22.830 the genetic basis of things, 00:00:22.830 --> 00:00:25.310 but we also have the power to control it. 00:00:25.310 --> 00:00:26.640 And if you're controlling it 00:00:26.640 --> 00:00:29.480 then the creativity gets to a whole other level. 00:00:29.480 --> 00:00:33.360 So in the decades to come, creativity and biology, 00:00:33.360 --> 00:00:35.060 and also other areas of STEM, 00:00:35.060 --> 00:00:38.390 like mathematics and computing are all going to 00:00:38.390 --> 00:00:42.540 converge to really transform humanity as we know it. 00:00:42.540 --> 00:00:43.890 But don't take my word for it, 00:00:43.890 --> 00:00:46.670 I'm about to introduce you to some close friends 00:00:46.670 --> 00:00:48.630 who can even better draw this link 00:00:48.630 --> 00:00:52.207 between the future of biology and the future of creativity. 00:00:52.207 --> 00:00:54.874 (upbeat music) 00:00:58.610 --> 00:00:59.970 - I think it's really exciting 00:00:59.970 --> 00:01:03.560 how biology and creativity have combined, 00:01:03.560 --> 00:01:08.560 particularly in the area of health and outcomes 00:01:08.650 --> 00:01:12.070 and how do we help people with blindness? 00:01:12.070 --> 00:01:15.380 How do we help people who are paraplegic 00:01:15.380 --> 00:01:19.130 where we can start to read the electrical activity 00:01:19.130 --> 00:01:22.790 of their intended movement and have a robot do that. 00:01:22.790 --> 00:01:27.790 So they can gain, you know, that activity again 00:01:27.850 --> 00:01:31.210 and have that power in their lives again. 00:01:31.210 --> 00:01:35.300 I think that is a classic and beautiful example 00:01:35.300 --> 00:01:39.630 of the combination of biology and creativity 00:01:39.630 --> 00:01:42.710 making our lives better every single day 00:01:42.710 --> 00:01:45.790 - Butterflies use something called structural color 00:01:45.790 --> 00:01:48.390 which involves bending light to generate color 00:01:48.390 --> 00:01:50.530 instead of using a bunch of pigment. 00:01:50.530 --> 00:01:53.090 So it definitely saves the butterflies a bunch of energy 00:01:53.090 --> 00:01:54.450 in making that pigment. 00:01:54.450 --> 00:01:56.720 But now, because of some observant 00:01:56.720 --> 00:01:59.930 and innovative scientists, it's saving us energy too. 00:01:59.930 --> 00:02:02.770 It's being used in screens around the world 00:02:02.770 --> 00:02:05.210 to make them more efficient at projecting color, 00:02:05.210 --> 00:02:07.140 which reduces the carbon footprint 00:02:07.140 --> 00:02:09.720 as some of our most common electronics. 00:02:09.720 --> 00:02:12.770 And how about the creativity of using mRNA, 00:02:12.770 --> 00:02:16.150 which is pretty much just biological text messages 00:02:16.150 --> 00:02:18.500 to give our bodies a heads up 00:02:18.500 --> 00:02:20.940 that they need to recognize dangerous viruses. 00:02:20.940 --> 00:02:23.040 It's the technology being used 00:02:23.040 --> 00:02:26.851 in some of our most innovative vaccines right now. 00:02:26.851 --> 00:02:29.518 (upbeat music) 00:02:32.607 --> 00:02:35.430 - I think it's going to be even more important 00:02:35.430 --> 00:02:40.430 to have the widest range of skill sets that you could have. 00:02:40.890 --> 00:02:45.890 So less specialization, more a jack of all trades, 00:02:48.840 --> 00:02:53.840 including design, design thinking, design work, 00:02:54.690 --> 00:02:57.623 together with that programming experience. 00:02:59.330 --> 00:03:04.330 So that you can jump into the new technological advances 00:03:04.330 --> 00:03:06.270 that are being made every day. 00:03:06.270 --> 00:03:10.290 We're gonna be so much more in virtual reality, 00:03:10.290 --> 00:03:13.760 can you not just use it, but can you program it? 00:03:13.760 --> 00:03:17.470 - I think the most important ones will be curiosity 00:03:17.470 --> 00:03:20.230 and keen eyed to observational skills. 00:03:20.230 --> 00:03:23.300 See, curiosity fuels the question why 00:03:23.300 --> 00:03:26.150 which is an essential part of every innovation, 00:03:26.150 --> 00:03:28.860 and keen observational skills allow us 00:03:28.860 --> 00:03:31.660 not to waste our efforts reinventing the wheel. 00:03:31.660 --> 00:03:35.530 Life has already solved so many of the toughest problems 00:03:35.530 --> 00:03:37.620 that the world can possibly throw at it. 00:03:37.620 --> 00:03:40.990 So why not figure out how biology has overcome an obstacle 00:03:40.990 --> 00:03:42.543 and adapt or improve on that? 00:03:42.543 --> 00:03:45.210 (upbeat music) 00:03:48.800 --> 00:03:51.950 I'd encourage every single one of you to spend some time 00:03:51.950 --> 00:03:53.660 immersed in a different culture 00:03:53.660 --> 00:03:56.350 or maybe even spend some time working 00:03:56.350 --> 00:03:58.160 in a totally different part of the world 00:03:58.160 --> 00:03:59.360 from where you grew up. 00:03:59.360 --> 00:04:03.320 Now, it doesn't have to be quite that drastic. 00:04:03.320 --> 00:04:08.090 It could be as simple as investing in relationships 00:04:08.090 --> 00:04:10.040 with people from other parts of the world. 00:04:10.040 --> 00:04:11.290 And while you're at it, 00:04:11.290 --> 00:04:13.570 I'd encourage you to learn a different language. 00:04:13.570 --> 00:04:17.070 Both of those experiences, I think, 00:04:17.070 --> 00:04:18.770 will stretch your mind in ways 00:04:18.770 --> 00:04:22.180 that help you consider other possibilities. 00:04:22.180 --> 00:04:24.520 - Students can expand their creative 00:04:24.520 --> 00:04:26.300 and scientific skill sets 00:04:26.300 --> 00:04:29.300 by thinking beyond the classroom and beyond the textbook, 00:04:29.300 --> 00:04:32.250 using that information from classroom and from the textbook 00:04:32.250 --> 00:04:34.790 and from other formal information sources 00:04:34.790 --> 00:04:38.400 and expanding that to learn more about both today's world 00:04:38.400 --> 00:04:40.880 and the world that you imagine for the future. 00:04:40.880 --> 00:04:43.660 That involves using those skills such as communication 00:04:43.660 --> 00:04:46.040 and problem solving and critical thinking 00:04:46.040 --> 00:04:48.800 to wonder not just about what is already known, 00:04:48.800 --> 00:04:51.090 but to wonder about what is not yet known, 00:04:51.090 --> 00:04:56.090 which involves using creativity to think and to wonder. 00:04:56.800 --> 00:04:58.960 And that also means communicating with other people 00:04:58.960 --> 00:05:01.289 to see how they wanna shape the world as well. 00:05:01.289 --> 00:05:03.956 (upbeat music) 00:05:06.830 --> 00:05:09.290 - We have the opportunity to work together 00:05:09.290 --> 00:05:12.003 with a variety of different voices, 00:05:12.940 --> 00:05:14.910 colleagues from all over the world 00:05:14.910 --> 00:05:19.630 who have different strengths that they bring, 00:05:19.630 --> 00:05:22.240 different perspectives that they bring about life 00:05:22.240 --> 00:05:24.330 and about how the world operates. 00:05:24.330 --> 00:05:26.640 And only when we bring those voices together, 00:05:26.640 --> 00:05:29.080 will we have a more complete picture 00:05:29.080 --> 00:05:31.520 about how the living world works. 00:05:31.520 --> 00:05:36.520 So in order to really solve the problems of the future, 00:05:37.150 --> 00:05:40.120 we're going to need to work together as a global community 00:05:40.120 --> 00:05:42.260 - Problems are not solved in isolation, 00:05:42.260 --> 00:05:45.380 they're solved in collaborative groups with other people 00:05:45.380 --> 00:05:47.850 and they're solved to be realistic. 00:05:47.850 --> 00:05:50.300 So you have to consider not just your own discipline 00:05:50.300 --> 00:05:54.240 or your own science, but also some economics and ethics 00:05:54.240 --> 00:05:56.280 and other things that relate to the real world, 00:05:56.280 --> 00:05:59.410 to help you reach a real world, but sensible solution. 00:05:59.410 --> 00:06:00.740 So it requires combining 00:06:00.740 --> 00:06:02.660 all those different ways of thinking, 00:06:02.660 --> 00:06:05.110 being communicative and problem solving 00:06:05.110 --> 00:06:06.460 and working with other people 00:06:06.460 --> 00:06:08.140 so that you can reach solutions 00:06:08.140 --> 00:06:09.470 that actually benefit the world. 00:06:09.470 --> 00:06:12.560 Because some solutions are gonna be great on paper, 00:06:12.560 --> 00:06:15.380 but in practice, they aren't really practical. 00:06:15.380 --> 00:06:19.290 So that's why using new ways of thinking to solve problems 00:06:19.290 --> 00:06:20.580 is really important. 00:06:20.580 --> 00:06:23.733 - As an example, for me, in my PhD project, 00:06:25.320 --> 00:06:27.350 even though my background has been in biology, 00:06:27.350 --> 00:06:32.140 the problem that really captured my interests 00:06:32.140 --> 00:06:37.140 and that I wanted to pursue involves mechanics and physics. 00:06:37.580 --> 00:06:42.160 And so it required learning a lot of some deep theories 00:06:43.200 --> 00:06:46.200 and ideas in physics that I wouldn't have thought of before. 00:06:46.200 --> 00:06:48.090 And now I kind approach, 00:06:48.090 --> 00:06:49.870 it sort of changed the way that I approach 00:06:49.870 --> 00:06:51.470 biological problems. 00:06:51.470 --> 00:06:54.710 Now I have this physics lens that I didn't have before, 00:06:54.710 --> 00:06:59.700 and that expands the of experiments I can think of 00:06:59.700 --> 00:07:02.308 or hypotheses that I could have for how something works. 00:07:02.308 --> 00:07:04.975 (upbeat music) 00:07:08.990 --> 00:07:13.890 - What are those biological solutions 00:07:13.890 --> 00:07:16.710 that can be solved with creativity 00:07:16.710 --> 00:07:18.640 that would change the world? 00:07:18.640 --> 00:07:23.640 And I always go to those health, biological changes. 00:07:25.670 --> 00:07:30.670 The cure for cancer, the cure for blindness, 00:07:30.700 --> 00:07:35.700 the cure for name, Alzheimer's disease, for example. 00:07:36.130 --> 00:07:40.950 The modulation of our crops 00:07:40.950 --> 00:07:44.720 that would allow us to feed the world, everybody, 00:07:44.720 --> 00:07:46.500 so there's no starvation. 00:07:46.500 --> 00:07:51.410 That is the goal that all of our creativity, 00:07:51.410 --> 00:07:55.410 kind of taken together, is headed towards. 00:07:55.410 --> 00:07:59.460 I think that's inspiring, I think that is doable, 00:07:59.460 --> 00:08:02.730 and with all the tools that we've been talking about, 00:08:02.730 --> 00:08:06.853 technology, storytelling, and inspiration, 00:08:08.690 --> 00:08:11.450 all of that together is going to get us there. 00:08:11.450 --> 00:08:13.200 - A creative approach to biology 00:08:13.200 --> 00:08:16.440 can help solve the problems of the future. 00:08:16.440 --> 00:08:20.940 I mean, if you think about natural systems, 00:08:20.940 --> 00:08:24.750 they don't have any waste, they recycle everything. 00:08:24.750 --> 00:08:26.820 Everything that goes into a natural system 00:08:26.820 --> 00:08:28.740 is used completely. 00:08:28.740 --> 00:08:32.650 And there are a lot of areas in which we can learn from that 00:08:32.650 --> 00:08:36.500 as people and the systems that we create and design. 00:08:36.500 --> 00:08:40.710 So if we can design ways to more efficiently use water, 00:08:40.710 --> 00:08:44.180 recycle and reduce the amount of waste we produce, 00:08:44.180 --> 00:08:47.708 that's gonna be one of the most important innovations 00:08:47.708 --> 00:08:49.080 of the future, right? 00:08:49.080 --> 00:08:52.570 Providing fresh and clean water 00:08:52.570 --> 00:08:55.040 to a growing population for this world. 00:08:55.040 --> 00:08:57.990 - New innovations that I think will help us approach 00:08:57.990 --> 00:09:00.170 science creatively in the future, 00:09:00.170 --> 00:09:03.860 really involve data such as machine learning 00:09:03.860 --> 00:09:05.440 and artificial intelligence, 00:09:05.440 --> 00:09:09.530 and using data to help humans make decisions collaboratively 00:09:09.530 --> 00:09:10.590 with either other humans, 00:09:10.590 --> 00:09:13.080 but also with artificial intelligence. 00:09:13.080 --> 00:09:15.470 There's so much data that exists in the world, 00:09:15.470 --> 00:09:18.520 collected from scientific and engineering observations, 00:09:18.520 --> 00:09:21.146 that we can take this information 00:09:21.146 --> 00:09:23.910 to help us make better decisions in the future. 00:09:23.910 --> 00:09:26.190 Because it's gonna be a combination of people thinking 00:09:26.190 --> 00:09:28.010 but also machines thinking, 00:09:28.010 --> 00:09:30.923 and that can help us make more powerful conclusions.

Creativity break: why is learning biology important?

https://www.youtube.com/watch?v=EHVC2ktR7ng

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WEBVTT Kind: captions Language: en 00:00:00.293 --> 00:00:03.293 (pencil scribbling) 00:00:05.471 --> 00:00:08.638 (gentle upbeat music) 00:00:09.900 --> 00:00:14.900 - I think biology is so critical for everybody to learn 00:00:15.349 --> 00:00:20.349 because it defines who we are as human beings, as animals. 00:00:22.550 --> 00:00:25.450 It defines the whole animal kingdom, 00:00:25.450 --> 00:00:28.271 and then it goes on to define the whole plant kingdom, 00:00:28.271 --> 00:00:30.570 the insect kingdom. 00:00:30.570 --> 00:00:33.490 Understanding those principles 00:00:33.490 --> 00:00:38.490 of how living things are organized 00:00:38.590 --> 00:00:42.130 is not only a beautiful thing to understand, 00:00:42.130 --> 00:00:45.845 but it gives deep insight and deep appreciation 00:00:45.845 --> 00:00:48.950 for our own lives, 00:00:48.950 --> 00:00:53.950 and I think that is the core of why I find it so important 00:00:54.780 --> 00:00:59.780 that everybody study this beautiful area of academia. 00:01:01.000 --> 00:01:04.730 - Biology is super important to learn for so many reasons. 00:01:04.730 --> 00:01:07.463 But the reason that stands out most to me is, well, 00:01:08.805 --> 00:01:11.520 the rarity of life outside 00:01:11.520 --> 00:01:13.690 of our little corner of the universe. 00:01:13.690 --> 00:01:15.650 You might not know what I mean, 00:01:15.650 --> 00:01:17.315 but stick with me for a sec. 00:01:17.315 --> 00:01:20.690 So we are positively surrounded 00:01:20.690 --> 00:01:23.620 by biology every day here on Earth, 00:01:23.620 --> 00:01:26.300 but we haven't encountered life or even evidence 00:01:26.300 --> 00:01:28.700 of life outside of this little blue marvel, 00:01:28.700 --> 00:01:32.750 even though there is so much cosmic real estate out there. 00:01:32.750 --> 00:01:35.140 Life is really complicated, 00:01:35.140 --> 00:01:38.440 and that goes for starting and sustaining life. 00:01:38.440 --> 00:01:40.740 Somehow ancient organisms made it work here, 00:01:40.740 --> 00:01:42.560 but that doesn't mean that it's easy. 00:01:42.560 --> 00:01:46.070 All of us carry on this legacy of life finding a way, 00:01:46.070 --> 00:01:50.500 but one day maybe life will have to find a way through us. 00:01:50.500 --> 00:01:53.490 Maybe Earth becomes inhospitable for some reason 00:01:53.490 --> 00:01:56.630 and we have to figure out how to live somewhere else. 00:01:56.630 --> 00:01:59.130 On that day, success will depend 00:01:59.130 --> 00:02:01.810 on how well we understand the heaps 00:02:01.810 --> 00:02:03.670 of obstacles that the stubbornness 00:02:03.670 --> 00:02:06.163 of life has already overcome.

Creativity break: why is creativity important in biology?

https://www.youtube.com/watch?v=RFezo2PlY3c

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https://www.youtube.com/api/timedtext?v=RFezo2PlY3c&ei=uVWUZdyzA4iCp-oPgp6riAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=42ED32913677C4A4CC273FE6570DC34E7DD5E503.E75330E4CD6BD425A37794C4B3C87F882DC58367&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:02.583 (upbeat music) 00:00:06.187 --> 00:00:09.650 (keyboard clicking) 00:00:09.650 --> 00:00:11.990 - Creativity is super important in biology 00:00:11.990 --> 00:00:14.980 because it's hugely important in the process of evolution. 00:00:14.980 --> 00:00:17.550 Evolution often takes a winding path 00:00:17.550 --> 00:00:18.971 to get to what we see now, 00:00:18.971 --> 00:00:21.770 and we wanna follow this path 00:00:21.770 --> 00:00:23.850 in an attempt to understand it. 00:00:23.850 --> 00:00:26.590 Sometimes we've gotta be as resourceful and clever 00:00:26.590 --> 00:00:27.960 as evolution has been. 00:00:27.960 --> 00:00:30.816 That requires creativity in how we solve problems, 00:00:30.816 --> 00:00:34.400 and even creativity in the questions we ask. 00:00:34.400 --> 00:00:37.834 - Creativity is so important for anybody 00:00:37.834 --> 00:00:41.380 who is thinking about, who is studying biology, 00:00:41.380 --> 00:00:43.800 because the question we're trying to understand 00:00:43.800 --> 00:00:46.330 is not just take in all the information 00:00:46.330 --> 00:00:48.610 that we know about biology. 00:00:48.610 --> 00:00:52.070 We want people to imagine what biology, 00:00:52.070 --> 00:00:55.110 what the natural world, what the physical world, 00:00:55.110 --> 00:01:00.110 what our bodies can actually do, what our brains can do. 00:01:00.600 --> 00:01:03.987 And to be able to do that, you need to think out of the box. 00:01:03.987 --> 00:01:05.690 You need to think about things 00:01:05.690 --> 00:01:07.670 that haven't been thought about before. 00:01:07.670 --> 00:01:11.540 And that is why biology, that is why creativity 00:01:11.540 --> 00:01:15.013 is so critical for anybody studying biology.

Creativity break: how do you apply creativity to biology?

https://www.youtube.com/watch?v=VDRc0vkkLNU

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WEBVTT Kind: captions Language: en 00:00:00.137 --> 00:00:02.804 (upbeat music) 00:00:10.400 --> 00:00:12.160 - One question that people ask me 00:00:12.160 --> 00:00:14.794 is how do I apply creativity 00:00:14.794 --> 00:00:18.090 to the presentations that I give? 00:00:18.090 --> 00:00:23.090 And my secret sauce is to come up with a visual image 00:00:24.670 --> 00:00:26.930 that anybody, I don't care if you're the adult, 00:00:26.930 --> 00:00:28.840 whether you're a fifth grader or second grader, 00:00:28.840 --> 00:00:32.780 that you can grasp that concept, and here's my favorite one. 00:00:32.780 --> 00:00:35.420 So every single time you move your body, 00:00:35.420 --> 00:00:37.510 there's whole bunches of neurochemicals 00:00:37.510 --> 00:00:40.150 that are released in your brain. 00:00:40.150 --> 00:00:41.970 And you've heard of these neurochemicals, 00:00:41.970 --> 00:00:44.960 dopamine, noradrenaline, serotonin. 00:00:44.960 --> 00:00:48.460 And so that's the fact, but the image that I give 00:00:48.460 --> 00:00:50.980 is that every single time you move your body, 00:00:50.980 --> 00:00:53.770 it's like giving your brain a wonderful bubble bath 00:00:53.770 --> 00:00:56.540 of neurochemicals that enrich your brain 00:00:56.540 --> 00:01:00.140 that change that neurochemical milieu, 00:01:00.140 --> 00:01:01.960 and that is the image that everybody 00:01:01.960 --> 00:01:04.460 that comes to my talks leaves with 00:01:04.460 --> 00:01:07.410 and inspires them a little bit to move their body more. 00:01:07.410 --> 00:01:09.610 So can you come up with that image, 00:01:09.610 --> 00:01:14.610 that playful fun, but factually accurate image 00:01:15.280 --> 00:01:17.040 that conveys your message? 00:01:17.040 --> 00:01:19.290 That will be your secret sauce too. 00:01:19.290 --> 00:01:23.550 - Have you heard that the bees aren't doing great? 00:01:23.550 --> 00:01:26.710 Well, I've been studying that and trying to understand 00:01:26.710 --> 00:01:28.970 how their complex health issues 00:01:28.970 --> 00:01:31.140 connect to a curious little parasite 00:01:31.140 --> 00:01:34.940 that's in nearly every honeybee colony worldwide. 00:01:34.940 --> 00:01:38.350 it's called Varroa destructor, by the way. 00:01:38.350 --> 00:01:41.950 Now, before I started this study, we thought 00:01:41.950 --> 00:01:44.010 that it was an open and shut case 00:01:44.010 --> 00:01:46.570 that the parasite was sucking out the bee's blood, 00:01:46.570 --> 00:01:49.280 sort of like a tick on a puppy, 00:01:49.280 --> 00:01:53.050 but I thought something more strange might be going on. 00:01:53.050 --> 00:01:55.700 The damage that it caused just didn't seem like 00:01:55.700 --> 00:01:58.450 the damage that would be caused by blood removal. 00:01:58.450 --> 00:02:01.430 The feeding process is super difficult to see though, 00:02:01.430 --> 00:02:04.860 so I had this idea. 00:02:04.860 --> 00:02:07.700 I fed different color glowing food 00:02:07.700 --> 00:02:10.180 to the bees in their pollen and their sugar water 00:02:10.180 --> 00:02:13.200 to color their organs specific colors. 00:02:13.200 --> 00:02:16.830 Then when the parasite fed on the bees, 00:02:16.830 --> 00:02:18.960 I could tell which organ it was eating 00:02:18.960 --> 00:02:22.200 based on which color was in its digestive system. 00:02:22.200 --> 00:02:25.890 And it turns out they were eating the bees' liver, 00:02:25.890 --> 00:02:29.460 by the way, which is pretty weird. 00:02:29.460 --> 00:02:32.330 But this kind of work is actually pretty fun, 00:02:32.330 --> 00:02:34.830 and it was definitely a place where creativity 00:02:34.830 --> 00:02:36.900 was rewarded in biology. 00:02:36.900 --> 00:02:39.567 (upbeat music)

Creativity break: what types of science jobs involve creativity?

https://www.youtube.com/watch?v=N34Vowgievg

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WEBVTT Kind: captions Language: en 00:00:01.201 --> 00:00:03.784 (upbeat music) 00:00:10.070 --> 00:00:13.750 - All science careers involve creativity. 00:00:13.750 --> 00:00:14.620 Think about it. 00:00:14.620 --> 00:00:17.010 We're asking and answering questions, 00:00:17.010 --> 00:00:19.690 and we're solving the world's problems. 00:00:19.690 --> 00:00:24.040 So the more creatively we can solve the world's problems, 00:00:24.040 --> 00:00:26.800 the more new ideas and concepts 00:00:26.800 --> 00:00:30.420 and approaches we can use to address the world's problems, 00:00:30.420 --> 00:00:31.600 the better off we'll be. 00:00:31.600 --> 00:00:33.550 - Creativity is the guiding force 00:00:33.550 --> 00:00:35.110 on the path to good science. 00:00:35.110 --> 00:00:37.570 So there isn't a science job out there 00:00:37.570 --> 00:00:40.090 that doesn't benefit from creativity. 00:00:40.090 --> 00:00:42.780 Like you can be an engineer, 00:00:42.780 --> 00:00:45.340 building more efficient transistors for tinier 00:00:45.340 --> 00:00:46.660 and tinier phones. 00:00:46.660 --> 00:00:48.060 You could be a climate scientist, 00:00:48.060 --> 00:00:50.950 figuring out how we can reduce our carbon footprint 00:00:50.950 --> 00:00:53.210 and save the world from climate catastrophe, 00:00:53.210 --> 00:00:55.370 or an agricultural researcher. 00:00:55.370 --> 00:00:58.010 Reducing efficient ways to feed the planet. 00:00:58.010 --> 00:01:00.550 Or maybe an entomologist like me. 00:01:00.550 --> 00:01:04.200 Understanding how relationships between organisms 00:01:04.200 --> 00:01:05.470 keep us all healthy. 00:01:05.470 --> 00:01:08.700 Creativity is important in all of these careers. 00:01:08.700 --> 00:01:09.950 - One really cool job is, 00:01:11.210 --> 00:01:13.740 is working for a science museum. 00:01:13.740 --> 00:01:16.080 And so the people who are like the 00:01:16.080 --> 00:01:18.622 the chief directors or bioscientist, 00:01:18.622 --> 00:01:21.930 or what have you for science museums usually have a biology 00:01:21.930 --> 00:01:25.160 or a science background of some kind, 00:01:25.160 --> 00:01:28.080 maybe you've have gone through even being a PhD 00:01:28.080 --> 00:01:29.833 or postdoctoral fellow. 00:01:31.967 --> 00:01:35.300 And their job is to design exhibits for, 00:01:35.300 --> 00:01:37.770 for visitors to museums 00:01:37.770 --> 00:01:42.770 and come up with engaging ways to share ideas in science. 00:01:42.800 --> 00:01:45.540 And so I see that's a really cool job 00:01:47.230 --> 00:01:49.230 that you might not immediately think of. 00:01:50.655 --> 00:01:52.427 (upbeat music)

Creativity break: how is creativity in biology changing the world?

https://www.youtube.com/watch?v=w8wR836X1q4

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WEBVTT Kind: captions Language: en 00:00:00.142 --> 00:00:02.725 (upbeat music) 00:00:03.608 --> 00:00:05.466 (logos pop) 00:00:05.466 --> 00:00:06.315 (screen whooshes) 00:00:06.315 --> 00:00:09.148 (keyboard clicks) 00:00:11.460 --> 00:00:12.820 - I think it's really exciting 00:00:12.820 --> 00:00:16.400 how biology and creativity have combined, 00:00:16.400 --> 00:00:21.400 particularly in the area of health and outcomes. 00:00:21.490 --> 00:00:24.910 And how do we help people with blindness? 00:00:24.910 --> 00:00:28.210 How do we help people who are paraplegic, 00:00:28.210 --> 00:00:31.970 where we can start to read the electrical activity 00:00:31.970 --> 00:00:35.624 of their intended movement and have a robot do that. 00:00:35.624 --> 00:00:38.310 So they can gain, you know, 00:00:38.310 --> 00:00:40.700 that activity again, 00:00:40.700 --> 00:00:44.060 and have that power in their lives again. 00:00:44.060 --> 00:00:46.020 I think that is a classic 00:00:46.020 --> 00:00:49.460 and beautiful example of the combination 00:00:49.460 --> 00:00:54.460 of biology and creativity making our lives better 00:00:54.500 --> 00:00:55.550 every single day 00:00:55.550 --> 00:00:58.640 - Butterflies use something called structural color 00:00:58.640 --> 00:01:01.850 which involves bending light to generate color instead 00:01:01.850 --> 00:01:03.370 of using a bunch of pigment. 00:01:03.370 --> 00:01:05.120 So it definitely saves the butterflies 00:01:05.120 --> 00:01:07.280 a bunch of energy in making that pigment. 00:01:07.280 --> 00:01:10.980 But now because of some observant and innovative scientists 00:01:10.980 --> 00:01:12.770 it's saving us energy too. 00:01:12.770 --> 00:01:14.520 It's being used in screens 00:01:14.520 --> 00:01:16.850 around the world to make them more efficient 00:01:16.850 --> 00:01:19.970 at projecting color, which reduces the carbon footprint 00:01:19.970 --> 00:01:22.570 as some of our most common electronics. 00:01:22.570 --> 00:01:25.620 And how about the creativity of using mRNA 00:01:25.620 --> 00:01:29.000 which is pretty much just biological text messages 00:01:29.000 --> 00:01:31.350 to give our bodies a heads up 00:01:31.350 --> 00:01:33.790 that they need to recognize dangerous viruses. 00:01:33.790 --> 00:01:36.540 It's the technology being used in some 00:01:36.540 --> 00:01:39.548 of our most innovative vaccines right now. 00:01:39.548 --> 00:01:40.748 (screen whooshes) 00:01:40.748 --> 00:01:43.232 (upbeat music)

Creativity break: what types of skills will help students innovate in biology?

https://www.youtube.com/watch?v=rF7yuIYELNU

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WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:02.583 (upbeat music) 00:00:11.270 --> 00:00:13.940 - I think it's going to be even more important 00:00:13.940 --> 00:00:18.940 to have the widest range of skillsets that you could have, 00:00:19.410 --> 00:00:24.410 so less specialization, more a jack-of-all-trades, 00:00:27.350 --> 00:00:32.350 including design, design thinking, design work, 00:00:33.220 --> 00:00:36.133 together with that programming experience, 00:00:37.840 --> 00:00:42.840 so that you can jump into the new technological advances 00:00:42.850 --> 00:00:44.790 that are being made every day. 00:00:44.790 --> 00:00:48.810 We're gonna be so much more in virtual reality, 00:00:48.810 --> 00:00:52.280 can you not just use it, but can you program it? 00:00:52.280 --> 00:00:55.990 - I think the most important ones will be curiosity 00:00:55.990 --> 00:00:58.750 and keen-eyed observational skills. 00:00:58.750 --> 00:01:01.810 See, curiosity fuels the question why, 00:01:01.810 --> 00:01:04.660 which is an essential part of every innovation, 00:01:04.660 --> 00:01:07.380 and keen observational skills allow us 00:01:07.380 --> 00:01:10.180 not to waste our effort reinventing the wheel. 00:01:10.180 --> 00:01:14.070 Life has already solved so many of the toughest problems 00:01:14.070 --> 00:01:16.140 that the world can possibly throw in it, 00:01:16.140 --> 00:01:19.500 so why not figure out how biology has overcome an obstacle 00:01:19.500 --> 00:01:21.341 and adapt or improve on that? 00:01:21.341 --> 00:01:23.924 (upbeat music)

Creativity break: how can students expand their creativity in biology?

https://www.youtube.com/watch?v=B-up-XLGQIA

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WEBVTT Kind: captions Language: en 00:00:00.311 --> 00:00:02.894 (bright music) 00:00:06.574 --> 00:00:09.657 (keyboard clacking) 00:00:11.310 --> 00:00:13.530 - I'd encourage every single one of you 00:00:13.530 --> 00:00:16.130 to spend some time immersed in a different culture 00:00:16.130 --> 00:00:18.830 or maybe even spend some time working 00:00:18.830 --> 00:00:20.650 in a totally different part of the world 00:00:20.650 --> 00:00:22.271 from where you grew up. 00:00:22.271 --> 00:00:23.170 And... 00:00:23.170 --> 00:00:25.810 It doesn't have to be quite that drastic. 00:00:25.810 --> 00:00:30.590 It could be as simple as investing in relationships 00:00:30.590 --> 00:00:32.520 with people from other parts of the world. 00:00:32.520 --> 00:00:33.780 And while you're at it, 00:00:33.780 --> 00:00:36.180 I'd encourage you to learn a different language. 00:00:37.086 --> 00:00:39.550 Both of those experiences, I think, 00:00:39.550 --> 00:00:41.240 will stretch your mind in ways 00:00:41.240 --> 00:00:44.660 that help you consider other possibilities. 00:00:44.660 --> 00:00:47.000 - Students can expand their creative 00:00:47.000 --> 00:00:48.780 and scientific skill sets 00:00:48.780 --> 00:00:51.780 by thinking beyond the classroom and beyond the textbook, 00:00:51.780 --> 00:00:52.870 using that information 00:00:52.870 --> 00:00:54.730 from classroom and from the textbook 00:00:54.730 --> 00:00:57.260 and from other formal information sources, 00:00:57.260 --> 00:01:00.880 and expanding that to learn more about both today's world 00:01:00.880 --> 00:01:03.360 and the world that you imagine for the future. 00:01:03.360 --> 00:01:05.140 That involves using those skills 00:01:05.140 --> 00:01:07.000 such as communication, and problem-solving, 00:01:07.000 --> 00:01:08.520 and critical thinking 00:01:08.520 --> 00:01:11.260 to wonder not just about what is already known, 00:01:11.260 --> 00:01:13.560 but to wonder about what is not yet known, 00:01:13.560 --> 00:01:18.560 which involves using creativity to think and to wonder. 00:01:19.270 --> 00:01:21.430 And that also means communicating with other people 00:01:21.430 --> 00:01:23.637 to see how wanna shape the world as well. 00:01:23.637 --> 00:01:26.220 (bright music)

Creativity break: how does creativity play a role in your everyday life?

https://www.youtube.com/watch?v=urs0Pep2Wdc

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WEBVTT Kind: captions Language: en 00:00:00.251 --> 00:00:02.751 (light music) 00:00:10.270 --> 00:00:13.946 - As we move forward, as scientists, as biologists, 00:00:13.946 --> 00:00:17.067 the old adage is true: 00:00:17.067 --> 00:00:22.010 A picture is worth a thousand words. 00:00:22.010 --> 00:00:27.010 So what is that image, that graph, that graphic, 00:00:27.510 --> 00:00:29.460 or even that imagery 00:00:30.454 --> 00:00:35.375 that really gets to the core of your idea. 00:00:35.375 --> 00:00:37.740 It almost gets to advertising. 00:00:37.740 --> 00:00:42.740 You want that image to stick in your listeners' minds 00:00:42.925 --> 00:00:47.280 that both lets them understand 00:00:47.280 --> 00:00:51.360 the undeniably complex concept that you're trying to convey 00:00:51.360 --> 00:00:53.654 but also makes it memorable 00:00:53.654 --> 00:00:58.430 and developing that skill to come up with that picture 00:00:58.430 --> 00:01:01.293 that is truly worth a thousand words 00:01:01.293 --> 00:01:05.472 is going to be the skill that we will all need 00:01:05.472 --> 00:01:07.030 going into the future. 00:01:07.030 --> 00:01:09.670 - Creativity plays a role in my life 00:01:09.670 --> 00:01:13.307 pretty much every single day by reminding me not to stop 00:01:13.307 --> 00:01:15.350 just because I've reached a setback, 00:01:15.350 --> 00:01:18.720 like hitting a wall as you're moving towards a goal 00:01:18.720 --> 00:01:20.926 doesn't have to be the end for that goal. 00:01:20.926 --> 00:01:23.609 To me it just means the path to success 00:01:23.609 --> 00:01:25.990 isn't gonna be quite as straightforward 00:01:25.990 --> 00:01:27.260 as I originally thought. 00:01:27.260 --> 00:01:29.180 Like the way around that wall 00:01:29.180 --> 00:01:32.550 may require me to climb over it, or tunnel under it, 00:01:32.550 --> 00:01:35.180 or maybe even dig straight through it. 00:01:35.180 --> 00:01:36.732 But if I'm creative enough, 00:01:36.732 --> 00:01:39.959 I can probably find a way to get to the other side. 00:01:39.959 --> 00:01:42.440 And this plays out for me in the lab 00:01:42.440 --> 00:01:44.710 literally every single day. 00:01:44.710 --> 00:01:47.737 It fuels a tenacity that can see you through things 00:01:47.737 --> 00:01:50.637 like graduate school, if you ever choose to go that route.

Creativity break: how do you get into your creative zone?

https://www.youtube.com/watch?v=SdzST7SD3ig

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WEBVTT Kind: captions Language: en 00:00:00.060 --> 00:00:02.643 (upbeat music) 00:00:10.550 --> 00:00:12.510 - I allow my brain to do the work 00:00:12.510 --> 00:00:14.800 to get into my creative zone. 00:00:14.800 --> 00:00:16.964 When I have a problem to resolve, 00:00:16.964 --> 00:00:18.550 sometimes I just sleep on it 00:00:18.550 --> 00:00:22.160 and I let my subconscious mind work 00:00:22.160 --> 00:00:26.000 through resolving problems and solving problems. 00:00:26.000 --> 00:00:28.310 Our brains are always at work 00:00:28.310 --> 00:00:32.950 like trying to defragment and break apart 00:00:32.950 --> 00:00:34.890 the things that we encounter. 00:00:34.890 --> 00:00:38.570 So I spend a little time thinking about 00:00:38.570 --> 00:00:41.340 how I can approach things creatively, 00:00:41.340 --> 00:00:43.270 and then I spend a little time 00:00:43.270 --> 00:00:45.070 not thinking about those things 00:00:45.070 --> 00:00:48.080 and allowing my brain and my subconscious mind 00:00:48.080 --> 00:00:51.290 to have an opportunity to do the work for me. 00:00:51.290 --> 00:00:53.820 A lot of times when I come back afterwards, 00:00:53.820 --> 00:00:56.560 I've got a great idea, I've got the answers, 00:00:56.560 --> 00:00:59.620 and I have new ways to solve and resolve things 00:00:59.620 --> 00:01:01.320 that I've been thinking about. 00:01:01.320 --> 00:01:03.930 - To get into my creative zone, I do something 00:01:03.930 --> 00:01:07.390 that I'd like to call productive procrastination. 00:01:07.390 --> 00:01:10.630 I start what I'm working on way before it's due, 00:01:10.630 --> 00:01:12.570 and then in fits and starts, 00:01:12.570 --> 00:01:17.520 I work while giving my mind permission to wander to things 00:01:17.520 --> 00:01:21.070 that absolutely are not on the agenda. 00:01:21.070 --> 00:01:25.480 It's encouraged some of my most creative experiences, 00:01:25.480 --> 00:01:28.470 some of my best songwriting, educational videos, 00:01:28.470 --> 00:01:30.010 and even scientific breakthroughs 00:01:30.010 --> 00:01:31.460 while I was supposed to be working 00:01:31.460 --> 00:01:33.980 on something totally unrelated. 00:01:33.980 --> 00:01:35.570 This won't work for everyone, 00:01:35.570 --> 00:01:37.250 but my mind is most creative 00:01:37.250 --> 00:01:39.883 when it's free to go on unplanned adventures. 00:01:40.770 --> 00:01:42.490 Good music also helps. 00:01:42.490 --> 00:01:46.260 A great playlist to me is worth its weight in gold. 00:01:46.260 --> 00:01:47.890 My playlists are special, 00:01:47.890 --> 00:01:52.300 because they only include instrumental music and songs 00:01:52.300 --> 00:01:54.600 in languages that I don't actually speak, 00:01:54.600 --> 00:01:56.120 so my thoughts don't get too pulled 00:01:56.120 --> 00:01:57.638 into the lyrics themselves. 00:01:57.638 --> 00:02:00.221 (upbeat music)

Creativity break: what are some new ways of thinking about problem solving?

https://www.youtube.com/watch?v=LOgjCaCn9_E

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WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:02.583 (upbeat music) 00:00:11.350 --> 00:00:15.010 - We have the opportunity to work together with a variety 00:00:15.010 --> 00:00:19.410 of different voices, colleagues from all over the world 00:00:19.410 --> 00:00:24.140 who have different strengths that they bring, 00:00:24.140 --> 00:00:25.940 different perspectives that they bring, 00:00:25.940 --> 00:00:28.870 about life, and about how the world operates, 00:00:28.870 --> 00:00:31.160 and only when we bring those voices together 00:00:31.160 --> 00:00:33.580 will we have a more complete picture 00:00:33.580 --> 00:00:36.040 about how the living world works. 00:00:36.040 --> 00:00:41.040 So in order to really solve the problems of the future, 00:00:41.680 --> 00:00:43.030 we're going to need to work together 00:00:43.030 --> 00:00:44.630 as a global community. 00:00:44.630 --> 00:00:46.780 - Problems are not solved in isolation. 00:00:46.780 --> 00:00:49.900 They're solved in collaborative groups with other people, 00:00:49.900 --> 00:00:52.360 and they're solved to be realistic. 00:00:52.360 --> 00:00:54.820 So you have to consider not just your own discipline 00:00:54.820 --> 00:00:58.790 or your own science, but also some economics, and ethics, 00:00:58.790 --> 00:01:00.800 and other things that relate to the real world 00:01:00.800 --> 00:01:03.940 to help you reach a real world, but sensible, solution. 00:01:03.940 --> 00:01:06.380 So it requires combining all those different ways 00:01:06.380 --> 00:01:09.560 of thinking, being communicative and problem solving 00:01:09.560 --> 00:01:10.990 and working with other people 00:01:10.990 --> 00:01:12.660 so that you can reach solutions 00:01:12.660 --> 00:01:13.990 that actually benefit the world, 00:01:13.990 --> 00:01:17.090 because some solutions are gonna be great on paper, 00:01:17.090 --> 00:01:19.910 but in practice, they aren't really practical. 00:01:19.910 --> 00:01:21.620 So that's why using new ways 00:01:21.620 --> 00:01:25.110 of thinking to solve problems is really important. 00:01:25.110 --> 00:01:28.223 - As an example, for me, in my PhD project, 00:01:29.860 --> 00:01:31.860 even though my background has been in biology, 00:01:31.860 --> 00:01:36.670 the problem that really captured my interest 00:01:36.670 --> 00:01:41.670 and that I wanted to pursue involves mechanics and physics. 00:01:42.100 --> 00:01:44.420 And so it required learning a lot 00:01:44.420 --> 00:01:48.650 of some deep theories and ideas in physics 00:01:48.650 --> 00:01:50.700 that I wouldn't have thought of before, 00:01:50.700 --> 00:01:52.610 and now I kinda approach, 00:01:52.610 --> 00:01:53.710 it sort of changed the way 00:01:53.710 --> 00:01:56.000 that I approach biological problems. 00:01:56.000 --> 00:01:59.240 Now I have this physics lens that I didn't have before, 00:01:59.240 --> 00:02:02.680 and that expands the possibilities 00:02:02.680 --> 00:02:04.220 of experiments I can think of, 00:02:04.220 --> 00:02:06.832 or hypotheses that I could have for how something works. 00:02:06.832 --> 00:02:09.499 (upbeat music)

Creativity break: how have you used creative communication to solve a problem?

https://www.youtube.com/watch?v=DAKmXK-qWJ8

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WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:02.667 (gentle music) 00:00:12.750 --> 00:00:15.880 - I've used creative communication to solve problems related 00:00:15.880 --> 00:00:19.290 to especially people learning different science. 00:00:19.290 --> 00:00:22.840 For example, in chemistry people sometimes have a hard time 00:00:22.840 --> 00:00:25.450 understanding subatomic particles 00:00:25.450 --> 00:00:29.310 and molecules and atoms and making those connections 00:00:29.310 --> 00:00:31.330 between quantities and numbers. 00:00:31.330 --> 00:00:33.120 So instead of jumping right into that 00:00:33.120 --> 00:00:34.840 which can be very difficult for people, 00:00:34.840 --> 00:00:37.130 I've learned to be creative and use analogies 00:00:37.130 --> 00:00:39.160 or relating that to something that is more accessible 00:00:39.160 --> 00:00:43.360 such as cooking or money or building something. 00:00:43.360 --> 00:00:45.210 And then when people can make the relation 00:00:45.210 --> 00:00:47.650 between something large and familiar, 00:00:47.650 --> 00:00:51.070 to something small or subatomic and unfamiliar 00:00:51.070 --> 00:00:53.980 it makes it easier for them to make those connections 00:00:53.980 --> 00:00:55.650 and build upon that knowledge. 00:00:55.650 --> 00:00:58.760 So several years ago I started making videos of myself 00:00:58.760 --> 00:01:01.810 explaining biology and entomology in language 00:01:01.810 --> 00:01:04.800 that was accessible and familiar to people my age 00:01:04.800 --> 00:01:07.610 and people who don't fit the stereotypical model 00:01:07.610 --> 00:01:08.970 of a scientist. 00:01:08.970 --> 00:01:11.670 It's a choice that I'm really glad that I made actually. 00:01:11.670 --> 00:01:15.140 I've received so much positive feedback about videos 00:01:15.140 --> 00:01:16.670 no more complicated than me 00:01:16.670 --> 00:01:18.390 holding a bug in front of a camera. 00:01:18.390 --> 00:01:21.679 And actually just like this, 00:01:21.679 --> 00:01:26.679 me literally holding a bug in front of a camera 00:01:27.040 --> 00:01:29.417 and explaining what makes a tick. 00:01:29.417 --> 00:01:31.893 Note to self, 00:01:31.893 --> 00:01:35.540 I should make a video about what makes ticks tick. 00:01:35.540 --> 00:01:36.373 That'd be pretty cool. 00:01:36.373 --> 00:01:38.090 Wait, sorry, that's neither here nor there. 00:01:38.090 --> 00:01:40.130 The point of what I'm saying is 00:01:40.130 --> 00:01:43.300 the choice not to excise my personality, 00:01:43.300 --> 00:01:45.640 the choice to bring all of my quirkiness 00:01:45.640 --> 00:01:49.190 into how I communicate is what seems to make the difference. 00:01:49.190 --> 00:01:52.801 A big part of being creative really can be just figuring out 00:01:52.801 --> 00:01:54.870 how to bring all of you 00:01:54.870 --> 00:01:56.923 to whatever it is that you choose to do. 00:01:56.923 --> 00:01:59.590 (gentle music)

Phishing attacks

https://www.youtube.com/watch?v=83VKm3aLq3I

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https://www.youtube.com/api/timedtext?v=83VKm3aLq3I&ei=uVWUZaLZH_KhhcIP87yYkA0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9D08F2E8810E2A194282E746B8007C898C00E28C.5BB05EF6C8D30C1F1CA8D52E791B7C0DF8CDB26C&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:02.300 - [Instructor] Let's say you get an email like this, 00:00:02.300 --> 00:00:04.780 where it looks like it is from PayPal. 00:00:04.780 --> 00:00:06.920 It says "Response required" really big, 00:00:06.920 --> 00:00:08.350 so this is a little bit scary. 00:00:08.350 --> 00:00:10.687 And it says, "Dear," you, 00:00:10.687 --> 00:00:14.007 "We emailed you a little while ago to ask you for your help 00:00:14.007 --> 00:00:16.820 "resolving an issue with your PayPal account." 00:00:16.820 --> 00:00:18.417 This seems really serious. 00:00:18.417 --> 00:00:21.047 "Your account is still temporarily limited 00:00:21.047 --> 00:00:22.797 "because we haven't heard from you. 00:00:22.797 --> 00:00:27.467 "We noticed some unusual login activity with your account. 00:00:27.467 --> 00:00:29.947 "Please check that no one has logged into your account 00:00:29.947 --> 00:00:30.900 "without your permission." 00:00:30.900 --> 00:00:32.050 This is scary: 00:00:32.050 --> 00:00:33.110 To help us with this 00:00:33.110 --> 00:00:35.760 and to see what you can and can't do with your account 00:00:35.760 --> 00:00:37.520 until the issue is resolved, 00:00:37.520 --> 00:00:41.620 log in to your account or go to the Resolution Center. 00:00:41.620 --> 00:00:44.540 As always, if you need help or have any questions, 00:00:44.540 --> 00:00:45.980 feel free to contact us. 00:00:45.980 --> 00:00:47.460 We're always here to help. 00:00:47.460 --> 00:00:49.930 Thank you for being a PayPal customer. 00:00:49.930 --> 00:00:51.750 Sincerely, PayPal. 00:00:51.750 --> 00:00:54.820 What would you do in this situation? 00:00:54.820 --> 00:00:57.120 Well, I think for a lot of us, our emotional response is, 00:00:57.120 --> 00:01:00.290 hey, PayPal, some of my money is involved, there. 00:01:00.290 --> 00:01:02.870 They're talking about other people maybe trying to log in. 00:01:02.870 --> 00:01:04.400 I definitely wanna resolve this. 00:01:04.400 --> 00:01:06.150 And just in the heat of the moment, 00:01:06.150 --> 00:01:07.790 you might click on this "log in," 00:01:07.790 --> 00:01:09.940 or you might go to the Resolution Center, 00:01:09.940 --> 00:01:14.460 and that might start you down a little bit of a scary path. 00:01:14.460 --> 00:01:17.410 Because even though this looks like PayPal, 00:01:17.410 --> 00:01:21.430 you really need to verify that it really is PayPal. 00:01:21.430 --> 00:01:23.490 And there are some clues here 00:01:23.490 --> 00:01:26.060 that make it clear that it is not PayPal. 00:01:26.060 --> 00:01:27.583 See if you can find those. 00:01:29.850 --> 00:01:33.430 Well, the biggest clue is up here on the email address. 00:01:33.430 --> 00:01:38.430 So, it says service@intl.paypal.com as its name, 00:01:38.770 --> 00:01:40.220 but when you look at the actual 00:01:40.220 --> 00:01:41.880 email address right over here, 00:01:41.880 --> 00:01:45.240 notice it actually isn't a PayPal email address. 00:01:45.240 --> 00:01:48.570 It says @outlook.com. 00:01:48.570 --> 00:01:52.350 So, this is a pretty good clue that this is not from PayPal. 00:01:52.350 --> 00:01:53.940 And so, what is this? 00:01:53.940 --> 00:01:58.090 Well, this is known as a phishing attack. 00:01:58.090 --> 00:02:00.400 Why is it called a phishing attack? 00:02:00.400 --> 00:02:03.270 Well, I think it's probably based on the idea 00:02:03.270 --> 00:02:05.610 that when you're trying to catch fish, 00:02:05.610 --> 00:02:07.290 you dangle some bait for the fish 00:02:07.290 --> 00:02:09.680 and you see which fish are going to bite. 00:02:09.680 --> 00:02:11.300 And so, this isn't exactly fishing. 00:02:11.300 --> 00:02:14.030 They spelled the "Fuh" sound P-H 00:02:14.030 --> 00:02:15.330 because what they're really doing 00:02:15.330 --> 00:02:17.630 is they're dangling some bait in front of you 00:02:17.630 --> 00:02:20.760 and see if you're going to metaphorically 00:02:20.760 --> 00:02:22.950 get your cheek cut by the fish hook 00:02:22.950 --> 00:02:25.780 or whatever happens to fish before they get pulled out. 00:02:25.780 --> 00:02:28.010 And how would that happen metaphorically? 00:02:28.010 --> 00:02:29.680 Well, when you click on this, 00:02:29.680 --> 00:02:34.680 it probably goes to this phishy company or person's website. 00:02:36.280 --> 00:02:39.180 And that website might look like PayPal, 00:02:39.180 --> 00:02:42.170 but it's not going to be paypal.com. 00:02:42.170 --> 00:02:44.800 It's going to be some other web address. 00:02:44.800 --> 00:02:47.730 And so, one way to avoid doing that beyond looking 00:02:47.730 --> 00:02:50.510 at that this is a phishy email address 00:02:50.510 --> 00:02:53.532 is that in some browsers or in some email readers, 00:02:53.532 --> 00:02:55.010 you can scroll over this 00:02:55.010 --> 00:02:57.280 and you'll see what the website would be. 00:02:57.280 --> 00:02:58.840 Or you can right click on that. 00:02:58.840 --> 00:03:01.000 You could, say, copy the URL 00:03:01.000 --> 00:03:02.590 and you could put that in a text document 00:03:02.590 --> 00:03:04.600 to see what the actual URL is. 00:03:04.600 --> 00:03:05.870 And it's very likely 00:03:05.870 --> 00:03:08.350 that that is not going to be a PayPal URL. 00:03:08.350 --> 00:03:10.040 In fact, I would guarantee you in this case 00:03:10.040 --> 00:03:11.360 it would not be. 00:03:11.360 --> 00:03:13.110 It would look like PayPal when you get there, 00:03:13.110 --> 00:03:15.400 and what they'll probably try to get you to do 00:03:15.400 --> 00:03:17.990 is type in your username and password 00:03:17.990 --> 00:03:19.850 for your PayPal account. 00:03:19.850 --> 00:03:21.420 Why is that valuable for them? 00:03:21.420 --> 00:03:24.180 Well, you just would have then given them your username 00:03:24.180 --> 00:03:26.610 and password for your PayPal account, 00:03:26.610 --> 00:03:29.950 which then they could use to steal money from you 00:03:29.950 --> 00:03:32.600 or to do something else to you. 00:03:32.600 --> 00:03:33.940 So, be very careful 00:03:33.940 --> 00:03:36.990 where you get these urgent emails or texts. 00:03:36.990 --> 00:03:38.857 I got a text recently saying that, 00:03:38.857 --> 00:03:41.457 "Your Amazon account has been compromised. 00:03:41.457 --> 00:03:43.747 "Click here fast in order to make sure 00:03:43.747 --> 00:03:45.820 "that no more fraud happens on your account." 00:03:45.820 --> 00:03:47.870 Well, it turns out that the URL, 00:03:47.870 --> 00:03:51.310 the web address there was not amazon.com. 00:03:51.310 --> 00:03:53.210 It was going to take me to a shady website, 00:03:53.210 --> 00:03:55.680 and that shady website looked a lot like Amazon. 00:03:55.680 --> 00:03:56.890 And so, if I acted really quickly, 00:03:56.890 --> 00:04:01.400 I would've given them my Amazon username and password. 00:04:01.400 --> 00:04:04.510 So, be on the lookout for these phishing attacks, 00:04:04.510 --> 00:04:07.890 and the main way to catch them is be skeptical of anything 00:04:07.890 --> 00:04:09.250 that's talking about fraud, 00:04:09.250 --> 00:04:12.267 about something that you would scare you and say, 00:04:12.267 --> 00:04:14.850 "Hey, do I really think this is happening?" 00:04:14.850 --> 00:04:18.020 And then, if you really think it might be happening, 00:04:18.020 --> 00:04:22.060 verify the email addresses, verify the web addresses 00:04:22.060 --> 00:04:25.190 that they're really coming from who they say they're from. 00:04:25.190 --> 00:04:29.160 And it doesn't matter if the name is @somethingpaypal.com. 00:04:29.160 --> 00:04:31.330 You have to look at the actual email address 00:04:31.330 --> 00:04:33.030 and it doesn't matter what it says here. 00:04:33.030 --> 00:04:35.510 It matters what the actual URL is 00:04:35.510 --> 00:04:40.010 that it clicks to to make sure that it isn't fishy. 00:04:40.010 --> 00:04:43.033 No pun intended, or actually, that pun was intended.

Tracking users on the Internet

https://www.youtube.com/watch?v=StoIE3hhSqA

vtt

https://www.youtube.com/api/timedtext?v=StoIE3hhSqA&ei=uVWUZbrVG4a5vdIPg_CE4Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=28AC916B9C425BD21F9A3719693FF8598665C72C.B2FE9EBBF9A4E65D1761205DDB5A7F1F015DB9F4&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:01.490 - So there's a bunch 00:00:01.490 --> 00:00:04.130 of reasons why a website might want to track you. 00:00:04.130 --> 00:00:05.420 And depending on your opinion, 00:00:05.420 --> 00:00:06.840 you might think some of these are reasonable 00:00:06.840 --> 00:00:09.460 and you might think some of them are unreasonable. 00:00:09.460 --> 00:00:10.450 Just to understand, 00:00:10.450 --> 00:00:12.730 imagine if you were to go to say Khan Academy 00:00:12.730 --> 00:00:14.060 and you were to do some work, 00:00:14.060 --> 00:00:15.610 well it might be nice that if you were 00:00:15.610 --> 00:00:17.720 to come back another day that, 00:00:17.720 --> 00:00:19.020 that work isn't lost. 00:00:19.020 --> 00:00:20.680 And so that might be a reason 00:00:20.680 --> 00:00:23.980 why you would want Khan Academy to know who you are. 00:00:23.980 --> 00:00:25.080 Now, there's a bunch 00:00:25.080 --> 00:00:27.200 of different ways that this could happen. 00:00:27.200 --> 00:00:28.340 The most obvious way is 00:00:28.340 --> 00:00:30.840 by having an account with a username and a password. 00:00:30.840 --> 00:00:32.980 So when you type in your username and password 00:00:32.980 --> 00:00:34.820 the site knows exactly who you are. 00:00:34.820 --> 00:00:36.820 It can retrieve your data from a database 00:00:36.820 --> 00:00:39.490 and then you can pick up right where you left off. 00:00:39.490 --> 00:00:41.300 That's probably the most obvious to people. 00:00:41.300 --> 00:00:44.410 And it's also the most obvious how to not be tracked 00:00:44.410 --> 00:00:46.410 in that way is that you log out. 00:00:46.410 --> 00:00:48.260 But just because you logged out or just 00:00:48.260 --> 00:00:50.940 because you don't have a username and password doesn't mean 00:00:50.940 --> 00:00:53.330 that you can't be tracked by a site. 00:00:53.330 --> 00:00:55.400 There's several other ways that can be tracked 00:00:55.400 --> 00:00:56.780 that you should know about 00:00:56.780 --> 00:00:59.910 and also know how to undo them if possible. 00:00:59.910 --> 00:01:03.080 Another way is leveraging something called cookies. 00:01:03.080 --> 00:01:06.200 Cookies, even if you don't have an account on a site, 00:01:06.200 --> 00:01:09.490 most web browsers are going to allow the website 00:01:09.490 --> 00:01:12.810 to place a little bit of text on your computer. 00:01:12.810 --> 00:01:14.360 So the browser, which is running 00:01:14.360 --> 00:01:16.260 on your computer is gonna place it, 00:01:16.260 --> 00:01:17.760 so that next time your browser goes 00:01:17.760 --> 00:01:19.480 to that site again, the site will say, 00:01:19.480 --> 00:01:22.130 oh this is the same person whose cookie I put there. 00:01:22.130 --> 00:01:24.060 And then there might that cookie might have a little bit 00:01:24.060 --> 00:01:26.430 of data associated with it and say, okay 00:01:26.430 --> 00:01:28.461 there could be some useful things. 00:01:28.461 --> 00:01:29.294 We can pick up where we left off. 00:01:29.294 --> 00:01:31.120 We can customize for what you were looking for. 00:01:31.120 --> 00:01:32.840 Or you might say that's a little bit creepy, 00:01:32.840 --> 00:01:34.570 that a site that I didn't get permission to 00:01:34.570 --> 00:01:35.880 is able to keep track of me. 00:01:35.880 --> 00:01:38.470 And so you might want to delete your cookies 00:01:38.470 --> 00:01:41.210 which your browser will allow you to do. 00:01:41.210 --> 00:01:44.410 Now cookies, as I saId, they have their benefits. 00:01:44.410 --> 00:01:45.243 This one of the reasons 00:01:45.243 --> 00:01:47.520 why you can often stay logged 00:01:47.520 --> 00:01:50.120 into a website because the website says, 00:01:50.120 --> 00:01:50.953 oh, this is a cookie. 00:01:50.953 --> 00:01:53.830 This is the person who keeps logging in. 00:01:53.830 --> 00:01:55.490 You might want the personalization 00:01:55.490 --> 00:01:56.820 of the advertisements 00:01:56.820 --> 00:01:59.280 or any other customizations without logging in. 00:01:59.280 --> 00:02:01.040 And that's where a cookie could be useful. 00:02:01.040 --> 00:02:03.710 But if you don't want it, of course, you can delete it. 00:02:03.710 --> 00:02:05.530 Now, another way that a website can keep track 00:02:05.530 --> 00:02:06.840 is your IP address. 00:02:06.840 --> 00:02:08.490 When your web browser 00:02:08.490 --> 00:02:11.090 which is running on your computer or on your phone 00:02:12.100 --> 00:02:13.540 wants to look at a website, 00:02:13.540 --> 00:02:15.100 it sends a request to that website, 00:02:15.100 --> 00:02:16.970 and then that request sends the data, 00:02:16.970 --> 00:02:18.400 sends the website back. 00:02:18.400 --> 00:02:20.400 And so in order to send the data back 00:02:20.400 --> 00:02:23.170 it needs an address for your phone or for your computer 00:02:23.170 --> 00:02:26.340 and that's going to be in the form of an IP address. 00:02:26.340 --> 00:02:29.610 Now you can imagine if that site knows your IP address 00:02:29.610 --> 00:02:31.350 and then if you were to come from the same device 00:02:31.350 --> 00:02:33.270 with the same IP address, again, it'll say, okay, 00:02:33.270 --> 00:02:34.820 it's at least the same device. 00:02:34.820 --> 00:02:36.220 Maybe it's the same person. 00:02:36.220 --> 00:02:38.810 And then they might be able to track you in that way. 00:02:38.810 --> 00:02:39.870 Once again, it might be 00:02:39.870 --> 00:02:42.030 for some good uses, like customization 00:02:42.030 --> 00:02:45.580 or maybe it's things that you aren't so comfortable with. 00:02:45.580 --> 00:02:48.020 Now, what gets extra interesting 00:02:48.020 --> 00:02:50.380 and might be useful or not useful, 00:02:50.380 --> 00:02:53.140 depending on your point of view is that it's not 00:02:53.140 --> 00:02:56.100 necessarily just your relationship with one website. 00:02:56.100 --> 00:02:59.380 For example, you might have an advertiser that puts cookies 00:02:59.380 --> 00:03:02.280 on a bunch of websites, and so can keep track 00:03:02.280 --> 00:03:04.740 of you as you go from site to site. 00:03:04.740 --> 00:03:07.520 And so then it's getting, at least for me, 00:03:07.520 --> 00:03:10.320 I don't like the fact that people can see 00:03:10.320 --> 00:03:12.800 how I'm moving around on the internet. 00:03:12.800 --> 00:03:15.230 Or I remember recently I was looking 00:03:15.230 --> 00:03:19.440 for a mountain bike and I did it on one eCommerce site. 00:03:19.440 --> 00:03:20.350 And then all of a sudden it seemed 00:03:20.350 --> 00:03:21.450 like the whole internet knew 00:03:21.450 --> 00:03:22.790 that I wanted to buy a mountain bike. 00:03:22.790 --> 00:03:24.220 I didn't end up buying a mountain bike. 00:03:24.220 --> 00:03:25.362 Now some of you might say, that's nice. 00:03:25.362 --> 00:03:27.670 You know, the internet knows I want a mountain bike. 00:03:27.670 --> 00:03:29.570 I'd like to keep being presented 00:03:29.570 --> 00:03:31.230 with ads on mountain bikes. 00:03:31.230 --> 00:03:32.670 Some of you might say, hey, that's not so cool. 00:03:32.670 --> 00:03:34.530 It was just, well, you know, a random search I did. 00:03:34.530 --> 00:03:35.363 And it's kind of weird 00:03:35.363 --> 00:03:37.250 that the internet is starting to build this profile of me 00:03:37.250 --> 00:03:40.110 of someone who might be in the market for mountain bikes. 00:03:40.110 --> 00:03:43.880 And so once again, deleting your cookies can go a long way 00:03:43.880 --> 00:03:45.020 to preventing that type of thing, 00:03:45.020 --> 00:03:46.620 if you're uncomfortable with it. 00:03:46.620 --> 00:03:49.430 And then IP addresses, that's a little bit harder to hide. 00:03:49.430 --> 00:03:51.710 Sometimes you have dynamic IP addresses 00:03:51.710 --> 00:03:55.190 sometimes it changes, but the clearest way 00:03:55.190 --> 00:03:57.060 of protecting your IP address is 00:03:57.060 --> 00:03:58.950 if you use something like a virtual private network 00:03:58.950 --> 00:04:02.450 which does get a little bit more complex. 00:04:02.450 --> 00:04:03.640 Now related to all of this, 00:04:03.640 --> 00:04:05.100 some of you also might be thinking 00:04:05.100 --> 00:04:06.890 about being tracked when you do a search. 00:04:06.890 --> 00:04:07.980 You might see that, 00:04:07.980 --> 00:04:10.170 hey, these suggested searches 00:04:10.170 --> 00:04:11.710 that the site is giving, 00:04:11.710 --> 00:04:14.010 it seems like it's kind of specific to me. 00:04:14.010 --> 00:04:16.080 And that's because in many cases it is. 00:04:16.080 --> 00:04:17.890 The search engine probably 00:04:17.890 --> 00:04:21.350 has placed cookies, or it's keeping with an IP address 00:04:21.350 --> 00:04:23.900 of things that you have searched for before. 00:04:23.900 --> 00:04:25.940 And the things that you have clicked on. 00:04:25.940 --> 00:04:27.410 And so it could use that maybe 00:04:27.410 --> 00:04:28.990 to give you different search results, 00:04:28.990 --> 00:04:31.430 maybe to change what the auto-complete is. 00:04:31.430 --> 00:04:34.450 It also might be keeping track of a search history. 00:04:34.450 --> 00:04:36.270 So the search history could be useful, 00:04:36.270 --> 00:04:37.150 if you wanna look 00:04:37.150 --> 00:04:39.340 at other sites that you have been to before 00:04:39.340 --> 00:04:40.910 or you might not want that around. 00:04:40.910 --> 00:04:45.190 You might not want the site or someone else 00:04:45.190 --> 00:04:47.500 who if you just happen to be using your computer 00:04:47.500 --> 00:04:49.130 to see what you've been searching for. 00:04:49.130 --> 00:04:51.410 So most browsers, sorry 00:04:51.410 --> 00:04:54.650 most search engines are going to let you delete that. 00:04:54.650 --> 00:04:56.403 So there's a lot more to it. 00:04:56.403 --> 00:04:59.540 This is just kind of the tip of the iceberg, 00:04:59.540 --> 00:05:02.150 but think about how you may or may not be tracked 00:05:02.150 --> 00:05:04.600 and think about how you may or may not want to be tracked. 00:05:04.600 --> 00:05:06.140 And good hygiene is, 00:05:06.140 --> 00:05:08.770 especially if you're at a public computer log out of things. 00:05:08.770 --> 00:05:11.720 That's also so other people can't use use your account, 00:05:11.720 --> 00:05:12.730 really be thoughtful about 00:05:12.730 --> 00:05:15.000 whether you even want to create an account for a site. 00:05:15.000 --> 00:05:16.820 Is this something that you really need? 00:05:16.820 --> 00:05:18.560 What are going to be the benefits for you? 00:05:18.560 --> 00:05:20.970 Think about whether you want to accept cookies? 00:05:20.970 --> 00:05:23.810 I would recommend deleting cookies pretty regularly. 00:05:23.810 --> 00:05:24.840 It might have some negatives. 00:05:24.840 --> 00:05:26.470 You might have to re-log into a few sites, 00:05:26.470 --> 00:05:28.550 but there's probably a lot of other shady sites 00:05:28.550 --> 00:05:31.740 that no longer can track what you're doing. 00:05:31.740 --> 00:05:33.720 But even if you do all of those things 00:05:33.720 --> 00:05:36.513 still be very careful and very conscientious.

Importance of Data Security

https://www.youtube.com/watch?v=fU4vsLeh1So

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en

WEBVTT Kind: captions Language: en 00:00:01.370 --> 00:00:03.610 - I'm going to make a bold prediction. 00:00:03.610 --> 00:00:07.350 You probably don't like people stealing your identity 00:00:07.350 --> 00:00:09.840 which allows them to steal your money. 00:00:09.840 --> 00:00:12.620 Or maybe tell the whole universe what you're up to 00:00:12.620 --> 00:00:14.800 and being able to track you and your family, 00:00:14.800 --> 00:00:16.800 and compromise your security. 00:00:16.800 --> 00:00:18.950 These don't feel like good things. 00:00:18.950 --> 00:00:21.780 And so, if that is true of you, it's true of me. 00:00:21.780 --> 00:00:23.330 I don't like any of those things. 00:00:23.330 --> 00:00:26.540 I wanna keep my private information private, 00:00:26.540 --> 00:00:29.460 then you should care about data security. 00:00:29.460 --> 00:00:32.020 And that's what we're going to do in this unit. 00:00:32.020 --> 00:00:32.910 You're gonna learn a lot 00:00:32.910 --> 00:00:35.470 about personally identifiable information. 00:00:35.470 --> 00:00:36.910 Your name is one example, 00:00:36.910 --> 00:00:39.070 but also things like your social security number, 00:00:39.070 --> 00:00:42.050 or things that are indirectly, personally identifiable 00:00:42.050 --> 00:00:44.630 like your address, or your phone number, 00:00:44.630 --> 00:00:46.420 why that's important. 00:00:46.420 --> 00:00:47.960 And then we're going to learn the ways 00:00:47.960 --> 00:00:50.100 that people are going to try to get ahold of it, 00:00:50.100 --> 00:00:51.670 and why they want to get ahold of it. 00:00:51.670 --> 00:00:54.430 Because they might wanna misrepresent you, 00:00:54.430 --> 00:00:57.180 or or publish things about you on the Internet, 00:00:57.180 --> 00:00:59.030 or control your presence on the internet, 00:00:59.030 --> 00:01:03.430 or steal money from you or from others that you care about. 00:01:03.430 --> 00:01:04.330 And then we're going to learn 00:01:04.330 --> 00:01:05.760 about ways to protect from those. 00:01:05.760 --> 00:01:08.110 A lot of that's going to be behavior change on your part 00:01:08.110 --> 00:01:09.890 to be a little bit more vigilant, 00:01:09.890 --> 00:01:13.360 but also technology ways of keeping your data secret, 00:01:13.360 --> 00:01:15.650 encrypting your data, authentication, 00:01:15.650 --> 00:01:18.530 making sure that the person who says they are who they are, 00:01:18.530 --> 00:01:20.530 are actually them. 00:01:20.530 --> 00:01:23.180 So enjoy this unit on data security. 00:01:23.180 --> 00:01:25.620 It isn't just interesting, which it is. 00:01:25.620 --> 00:01:28.400 It could save you a lot of money, 00:01:28.400 --> 00:01:31.023 a lot of pain, and a lot of embarrassment.

Personally Identifiable Information (PII)

https://www.youtube.com/watch?v=FwBKZOcn4yI

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en

WEBVTT Kind: captions Language: en 00:00:00.573 --> 00:00:01.710 - Hi everyone. 00:00:01.710 --> 00:00:03.360 Sal Khan here from Khan academy. 00:00:03.360 --> 00:00:06.250 My Social Security Number is 857, 00:00:06.250 --> 00:00:07.180 - 32 00:00:07.180 --> 00:00:08.133 - 5567. 00:00:10.600 --> 00:00:11.433 No, it's not. 00:00:11.433 --> 00:00:14.320 I wouldn't tell you my Social Security Number like that. 00:00:14.320 --> 00:00:15.153 And that's because 00:00:15.153 --> 00:00:20.153 it is personally identifiable information, or PII. 00:00:20.360 --> 00:00:22.630 And there's a reason why you want to keep that 00:00:22.630 --> 00:00:26.493 to yourself, or at least limit who has access to PII. 00:00:27.630 --> 00:00:31.950 Because if someone has access, they can expose your privacy, 00:00:31.950 --> 00:00:34.290 tell the world where you live, they could track you 00:00:34.290 --> 00:00:36.310 and they could tell the world what you've been up to, 00:00:36.310 --> 00:00:37.560 maybe when you should be working 00:00:37.560 --> 00:00:38.740 what websites you're visiting, 00:00:38.740 --> 00:00:43.380 or, even worse, potentially, they could steal your identity, 00:00:43.380 --> 00:00:44.790 take money out of your bank account, 00:00:44.790 --> 00:00:46.410 take a credit card in your name, 00:00:46.410 --> 00:00:48.493 do some other form of identity theft 00:00:48.493 --> 00:00:52.890 that could be embarrassing, or super costly. 00:00:52.890 --> 00:00:55.340 So, if you have some type of a service, 00:00:55.340 --> 00:00:57.850 either online or otherwise, that's asking for something 00:00:57.850 --> 00:00:59.650 like your Social Security Number, 00:00:59.650 --> 00:01:02.840 or your birthday, which might be a little bit more indirect, 00:01:02.840 --> 00:01:05.603 or your email address, or your phone number, 00:01:05.603 --> 00:01:07.430 you might ask why. 00:01:07.430 --> 00:01:09.230 Sometimes there's a legitimate reason 00:01:09.230 --> 00:01:10.197 why they need to know these things 00:01:10.197 --> 00:01:13.570 but many times, I'd argue even most of the time, 00:01:13.570 --> 00:01:15.350 there might not be a legitimate reason. 00:01:15.350 --> 00:01:16.900 And so you need to ask yourself, well 00:01:16.900 --> 00:01:18.075 what are they going to do with it? 00:01:18.075 --> 00:01:21.220 And if you don't feel comfortable giving that information, 00:01:21.220 --> 00:01:23.960 ask yourself, do you really need that service? 00:01:23.960 --> 00:01:26.200 So think seriously about your PII. 00:01:26.200 --> 00:01:28.640 Unfortunately, bad actors on the Internet are coming 00:01:28.640 --> 00:01:32.630 up with new ways of leveraging both direct PII, 00:01:32.630 --> 00:01:34.300 personally identifiable information 00:01:34.300 --> 00:01:35.700 like Social Security Numbers, 00:01:35.700 --> 00:01:38.360 even biometrics, even your name, 00:01:38.360 --> 00:01:41.760 and indirect measures, or indirect pieces of PII, 00:01:41.760 --> 00:01:46.430 like your birthday, or your address, or your email address, 00:01:46.430 --> 00:01:48.640 or your phone number, that can be put together 00:01:48.640 --> 00:01:51.070 to do shady things with your identity. 00:01:51.070 --> 00:01:53.333 So be very careful.

Lunar eclipses

https://www.youtube.com/watch?v=WXSHQK56Bfs

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en

WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.720 - [Narrator] Have you ever seen the full moon 00:00:01.720 --> 00:00:03.490 appear to change from this, 00:00:03.490 --> 00:00:05.490 to this, to this 00:00:05.490 --> 00:00:07.570 all in a couple hours? 00:00:07.570 --> 00:00:10.070 If so, you've witnessed a lunar eclipse. 00:00:10.070 --> 00:00:12.100 The word eclipse comes from a Greek word 00:00:12.100 --> 00:00:13.170 meaning "to leave." 00:00:13.170 --> 00:00:14.850 For centuries, people have marveled 00:00:14.850 --> 00:00:16.340 at how the full moon appears to leave 00:00:16.340 --> 00:00:17.820 during a lunar eclipse. 00:00:17.820 --> 00:00:19.770 The Incas believed that lunar eclipses happened 00:00:19.770 --> 00:00:21.820 when a giant jaguar ate the full moon. 00:00:21.820 --> 00:00:23.790 It turns out, lunar eclipses happen 00:00:23.790 --> 00:00:26.130 when the moon is covered by Earth's shadow. 00:00:26.130 --> 00:00:27.220 We can only see the moon 00:00:27.220 --> 00:00:28.960 because it reflects light from the sun. 00:00:28.960 --> 00:00:31.360 The moon doesn't generate any light of its own. 00:00:31.360 --> 00:00:33.730 The sun lights up half of the sphere of the moon. 00:00:33.730 --> 00:00:35.780 When Earth is between the sun and the moon, 00:00:35.780 --> 00:00:38.260 we can see the entire lit part of the moon. 00:00:38.260 --> 00:00:40.540 We call this the full moon. 00:00:40.540 --> 00:00:42.200 But sometimes during a full moon, 00:00:42.200 --> 00:00:44.620 Earth, the moon, and the sun all line up 00:00:44.620 --> 00:00:46.950 in such a way that Earth casts a shadow onto the moon. 00:00:46.950 --> 00:00:49.460 This creates a lunar eclipse. 00:00:49.460 --> 00:00:50.670 Lunar eclipses can be seen 00:00:50.670 --> 00:00:52.520 from anywhere on the night side of Earth. 00:00:52.520 --> 00:00:54.720 The two most dramatic types of lunar eclipses 00:00:54.720 --> 00:00:56.120 are total and partial. 00:00:56.120 --> 00:00:57.522 During a total lunar eclipse, 00:00:57.522 --> 00:01:00.100 Earth's shadow completely covers the moon. 00:01:00.100 --> 00:01:02.640 This means that no direct sunlight is reaching the moon. 00:01:02.640 --> 00:01:05.780 However, the moon is still visible during the eclipse. 00:01:05.780 --> 00:01:06.780 Why is this? 00:01:06.780 --> 00:01:08.820 As sunlight passes through our atmosphere, 00:01:08.820 --> 00:01:10.610 some of it gets bent slightly 00:01:10.610 --> 00:01:11.820 allowing it to reach the moon 00:01:11.820 --> 00:01:13.750 as indirect sunlight. 00:01:13.750 --> 00:01:16.180 Most of the light that gets bent is red or orange, 00:01:16.180 --> 00:01:18.120 meaning that the moon appears reddish orange 00:01:18.120 --> 00:01:19.480 during the eclipse. 00:01:19.480 --> 00:01:21.010 During a partial lunar eclipse, 00:01:21.010 --> 00:01:23.540 Earth's shadow only partially covers the moon. 00:01:23.540 --> 00:01:26.420 So some direct sunlight is still reaching the moon. 00:01:26.420 --> 00:01:28.850 Lunar eclipses only happen during a full moon 00:01:28.850 --> 00:01:30.840 since it's the only time in the moon's orbit 00:01:30.840 --> 00:01:32.950 where Earth is between the sun and the moon. 00:01:32.950 --> 00:01:35.570 And you might be wondering, "why isn't there a lunar eclipse 00:01:35.570 --> 00:01:37.010 during every full moon?" 00:01:37.010 --> 00:01:39.070 Well, the moon's orbit around Earth 00:01:39.070 --> 00:01:41.480 is tilted relative to Earth's orbit around the sun. 00:01:41.480 --> 00:01:42.420 This means that the moon 00:01:42.420 --> 00:01:45.600 often passes just above or just below Earth's shadow. 00:01:45.600 --> 00:01:47.600 Partial lunar eclipses happen when the sun, 00:01:47.600 --> 00:01:50.730 the moon, and Earth almost, but not quite exactly, 00:01:50.730 --> 00:01:53.360 line up so that the moon is only partially covered 00:01:53.360 --> 00:01:54.450 by Earth's shadow. 00:01:54.450 --> 00:01:56.880 Total lunar eclipses happen only when the sun, 00:01:56.880 --> 00:01:59.540 the moon, and Earth all line up precisely. 00:01:59.540 --> 00:02:01.900 So if you ever get to see a lunar eclipse, 00:02:01.900 --> 00:02:04.510 you can thank our planet for blocking the moon's sunlight 00:02:04.510 --> 00:02:06.760 and letting us enjoy the celestial spectacle.

Cellular respiration

https://www.youtube.com/watch?v=1RXk1NJpRDI

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en

WEBVTT Kind: captions Language: en 00:00:00.250 --> 00:00:01.770 - [Instructor] So let's say I was preparing 00:00:01.770 --> 00:00:03.890 to go on a long hike. 00:00:03.890 --> 00:00:06.720 Besides packing water, dressing for the weather 00:00:06.720 --> 00:00:08.060 and mapping my route, 00:00:08.060 --> 00:00:10.520 I'd probably also want to eat a snack 00:00:10.520 --> 00:00:13.450 before leaving to make sure I have enough energy 00:00:13.450 --> 00:00:14.550 for the hike. 00:00:14.550 --> 00:00:17.710 We as humans need food to nourish our bodies. 00:00:17.710 --> 00:00:20.880 But how exactly does that food give us energy? 00:00:20.880 --> 00:00:24.280 How does something like an apple or a piece of chocolate 00:00:24.280 --> 00:00:27.630 get converted into something our bodies can use? 00:00:27.630 --> 00:00:29.770 The answer to this question can be found 00:00:29.770 --> 00:00:32.630 in a process called cellular respiration. 00:00:32.630 --> 00:00:35.920 Which is how organisms get their energy from food. 00:00:35.920 --> 00:00:36.930 In other words, 00:00:36.930 --> 00:00:40.120 cellular respiration helps make life possible. 00:00:40.120 --> 00:00:42.250 It's happening right now in your cells 00:00:42.250 --> 00:00:43.290 and in mine, 00:00:43.290 --> 00:00:45.860 in my little brothers pet hamster cells 00:00:45.860 --> 00:00:48.760 and in the cells of the tree outside the window. 00:00:48.760 --> 00:00:50.900 It's providing all of us with the energy 00:00:50.900 --> 00:00:52.560 that we need to function. 00:00:52.560 --> 00:00:54.510 So let's dive into this process 00:00:54.510 --> 00:00:57.090 to find out more about how it works. 00:00:57.090 --> 00:01:00.700 Cellular respiration is a series of chemical reactions 00:01:00.700 --> 00:01:04.110 that happen in an organized way inside our cells. 00:01:04.110 --> 00:01:06.310 It's these chemical reactions that result 00:01:06.310 --> 00:01:10.400 in an overall release of energy that our bodies can use. 00:01:10.400 --> 00:01:11.740 Although cellular respiration 00:01:11.740 --> 00:01:15.240 involves many chemical reactions, this entire process 00:01:15.240 --> 00:01:17.740 for plants and animals can be summarized here 00:01:17.740 --> 00:01:19.380 by this equation. 00:01:19.380 --> 00:01:22.520 On the left side of this equation are the inputs; 00:01:22.520 --> 00:01:25.060 Glucose, which is a type of sugar, 00:01:25.060 --> 00:01:26.500 and oxygen. 00:01:26.500 --> 00:01:29.630 Glucose comes from our food and oxygen comes 00:01:29.630 --> 00:01:31.690 from the air we breathe. 00:01:31.690 --> 00:01:34.310 The right side of this equation shows the outputs, 00:01:34.310 --> 00:01:36.700 carbon dioxide and water. 00:01:36.700 --> 00:01:39.220 The air in the middle shows that during the process 00:01:39.220 --> 00:01:40.830 of cellular respiration, 00:01:40.830 --> 00:01:43.850 glucose and oxygen molecules are are broken apart 00:01:43.850 --> 00:01:46.060 and their atoms are rearranged 00:01:46.060 --> 00:01:49.130 to eventually form carbon dioxide and water. 00:01:49.130 --> 00:01:51.430 This whole process releases energy, 00:01:51.430 --> 00:01:55.020 similar to how firewood releases energy as it burns. 00:01:55.020 --> 00:01:59.010 Also, no atoms are lost during cellular respiration. 00:01:59.010 --> 00:02:01.700 You can see the same number of each type of atom 00:02:01.700 --> 00:02:04.320 on both sides of the arrow, for example, 00:02:04.320 --> 00:02:06.720 six carbon atoms on both sides. 00:02:06.720 --> 00:02:10.030 It's similar to how you could take apart a brick house 00:02:10.030 --> 00:02:13.650 and use those bricks to build something else, like a bridge. 00:02:13.650 --> 00:02:15.710 You're not throwing away any of the bricks, 00:02:15.710 --> 00:02:18.790 but instead you're creating something new out of them. 00:02:18.790 --> 00:02:22.100 So we know that cellular respiration involves a series 00:02:22.100 --> 00:02:23.650 of chemical reactions, 00:02:23.650 --> 00:02:26.720 but where in the cell do these steps happen? 00:02:26.720 --> 00:02:29.580 To find out, let's walk through the process together. 00:02:29.580 --> 00:02:32.010 After eating, your food is broken down 00:02:32.010 --> 00:02:34.870 into small molecules during digestion. 00:02:34.870 --> 00:02:37.670 These small molecules which include glucose 00:02:37.670 --> 00:02:39.520 can enter your cells. 00:02:39.520 --> 00:02:41.950 Then cellular respiration can begin. 00:02:41.950 --> 00:02:45.120 The first set of chemical reactions happen in the cytosol, 00:02:45.120 --> 00:02:47.860 which is the jelly-like fluid containing all 00:02:47.860 --> 00:02:49.110 of the cells organelles, 00:02:49.110 --> 00:02:51.840 and they involve glucose as an input. 00:02:51.840 --> 00:02:54.860 The rest of the reactions happen in mitochondria, 00:02:54.860 --> 00:02:58.380 with oxygen as an input and carbon dioxide 00:02:58.380 --> 00:03:00.380 and water as outputs. 00:03:00.380 --> 00:03:02.710 Together, these chemical reactions result 00:03:02.710 --> 00:03:05.600 in an overall release of energy. 00:03:05.600 --> 00:03:07.150 It might be a little mind boggling 00:03:07.150 --> 00:03:09.680 for you to think about how the food we eat provides 00:03:09.680 --> 00:03:11.130 the energy our bodies need 00:03:11.130 --> 00:03:13.630 to carry out all of lives processes. 00:03:13.630 --> 00:03:15.460 And I know it was for me. 00:03:15.460 --> 00:03:18.740 After all, it's not every day you take a bite of an apple 00:03:18.740 --> 00:03:20.860 and wonder how that apple's molecules 00:03:20.860 --> 00:03:23.270 are rearranged inside your body. 00:03:23.270 --> 00:03:24.680 What's important to know though, 00:03:24.680 --> 00:03:26.270 is that cellular respiration 00:03:26.270 --> 00:03:29.410 is the way our cells get usable energy. 00:03:29.410 --> 00:03:30.930 Through cellular respiration, 00:03:30.930 --> 00:03:32.880 you and I get the energy that we need 00:03:32.880 --> 00:03:34.670 to do the things we want to do, 00:03:34.670 --> 00:03:37.260 including accomplishing our goals. 00:03:37.260 --> 00:03:39.430 So, the next time you feel proud of your yourself 00:03:39.430 --> 00:03:43.090 for finishing a big hike or acing your biology quiz, 00:03:43.090 --> 00:03:45.883 make sure to thank your mitochondria.

Food and energy in organisms

https://www.youtube.com/watch?v=wPhjCn9kq5M

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https://www.youtube.com/api/timedtext?v=wPhjCn9kq5M&ei=uVWUZYH8Gc2Cp-oP78CJwAo&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=58D444EF53F301E13D10771C7D35A3A143BE80A2.D4924CE164175C0F373F609E5E9FBC26DF013FB3&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.140 --> 00:00:02.220 - [Instructor] Hey, quick question for you. 00:00:02.220 --> 00:00:04.670 You ever look at a person's baby pictures 00:00:04.670 --> 00:00:08.300 and wonder how people go from being small to, well, big? 00:00:08.300 --> 00:00:10.040 I mean, yes, I get it. 00:00:10.040 --> 00:00:12.450 People grow up, but here, I'm thinking more 00:00:12.450 --> 00:00:14.540 on the level of the atoms and molecules 00:00:14.540 --> 00:00:15.640 that make up the body 00:00:15.640 --> 00:00:19.090 because A, I'm a scientist and that's kind of what we do, 00:00:19.090 --> 00:00:21.560 and then also B, because after all, 00:00:21.560 --> 00:00:23.650 all the changes we see on these larger scales 00:00:23.650 --> 00:00:26.410 are just reflections of very many changes occurring 00:00:26.410 --> 00:00:28.360 on the molecular scale. 00:00:28.360 --> 00:00:30.790 And so if you think about it that way, 00:00:30.790 --> 00:00:33.040 then it's likely reasonable to assume 00:00:33.040 --> 00:00:35.230 that because the adult's body is bigger, 00:00:35.230 --> 00:00:38.020 it has more molecules and/or larger molecules 00:00:38.020 --> 00:00:39.200 than the baby's body. 00:00:39.200 --> 00:00:42.960 And so this means that there are some molecules in this baby 00:00:42.960 --> 00:00:46.200 and those molecules are interacting and combining 00:00:46.200 --> 00:00:48.890 with some other source of molecules in the world 00:00:48.890 --> 00:00:50.920 in order to become this adult. 00:00:50.920 --> 00:00:52.210 And generally speaking, 00:00:52.210 --> 00:00:55.200 the source of those molecules is going to be our diet, 00:00:55.200 --> 00:00:56.660 AKA our food. 00:00:56.660 --> 00:00:58.540 And to kind of understand this, 00:00:58.540 --> 00:01:00.690 we can actually make a comparison here 00:01:00.690 --> 00:01:03.360 between food and wood. 00:01:03.360 --> 00:01:05.330 So what I mean by that 00:01:05.330 --> 00:01:06.760 is that the molecules in food 00:01:06.760 --> 00:01:09.250 interact with the molecules on our bodies 00:01:09.250 --> 00:01:11.160 in two primary ways. 00:01:11.160 --> 00:01:14.720 The first is as a source of molecular building blocks, 00:01:14.720 --> 00:01:15.553 or in other words, 00:01:15.553 --> 00:01:18.690 molecules the body can use to build new structures. 00:01:18.690 --> 00:01:20.240 And the second is going to be 00:01:20.240 --> 00:01:22.360 as a source of molecules for fuel, 00:01:22.360 --> 00:01:26.560 much like a campfire or firewood, like what we have here. 00:01:26.560 --> 00:01:27.990 But in order to understand 00:01:27.990 --> 00:01:30.000 how and why this can happen, 00:01:30.000 --> 00:01:33.820 we need to briefly discuss the molecular basis of food. 00:01:33.820 --> 00:01:35.530 So what are the molecules in food? 00:01:35.530 --> 00:01:36.670 Let me introduce you. 00:01:36.670 --> 00:01:38.090 All right, 'cause generally speaking, 00:01:38.090 --> 00:01:41.520 food is made up of these three classes of molecules. 00:01:41.520 --> 00:01:43.750 First up are fats, 00:01:43.750 --> 00:01:45.550 then we've got sugars, 00:01:45.550 --> 00:01:48.230 and finally some protein. 00:01:48.230 --> 00:01:51.490 I'd imagine some of these sound reasonably familiar. 00:01:51.490 --> 00:01:53.760 These molecules are made basically 00:01:53.760 --> 00:01:55.440 from just a few elements. 00:01:55.440 --> 00:01:59.300 So this is color-coded and the gray balls are carbon. 00:01:59.300 --> 00:02:01.610 The white ones are hydrogen. 00:02:01.610 --> 00:02:02.600 Those are the big ones. 00:02:02.600 --> 00:02:04.030 So most of life's molecules 00:02:04.030 --> 00:02:06.350 are made mostly of carbon and hydrogen. 00:02:06.350 --> 00:02:09.040 But we've also got oxygen here in red 00:02:09.040 --> 00:02:10.740 and nitrogen in blue, 00:02:10.740 --> 00:02:12.630 those are the other two big ones. 00:02:12.630 --> 00:02:13.570 And every now and then, 00:02:13.570 --> 00:02:15.880 we'll also find small amounts of some other elements, 00:02:15.880 --> 00:02:18.210 like this sulfur here in yellow. 00:02:18.210 --> 00:02:20.110 But the super interesting part here 00:02:20.110 --> 00:02:23.050 is that these are actually the same exact elements 00:02:23.050 --> 00:02:26.020 that make up most of the cells in your body. 00:02:26.020 --> 00:02:27.500 So you may notice on this right-hand side 00:02:27.500 --> 00:02:30.380 the same colors is what we have on the left. 00:02:30.380 --> 00:02:33.930 So this is where the whole Molecular Lumber thing comes in. 00:02:33.930 --> 00:02:36.190 Our cells can take food 00:02:36.190 --> 00:02:38.880 and break it down into small building blocks 00:02:38.880 --> 00:02:40.680 and then use those building blocks 00:02:40.680 --> 00:02:43.130 in order to build new structures in our body. 00:02:43.130 --> 00:02:45.410 So is how we grow. 00:02:45.410 --> 00:02:48.000 This is how babies become adults. 00:02:48.000 --> 00:02:50.320 Turns out, we actually are what we eat. 00:02:50.320 --> 00:02:52.140 It's pretty amazing. 00:02:52.140 --> 00:02:54.090 All right, but before we get too excited, 00:02:54.090 --> 00:02:54.923 let's bring it in. 00:02:54.923 --> 00:02:56.880 So let's switch gears for a second here 00:02:56.880 --> 00:02:58.830 to talk about the other side of things 00:02:58.830 --> 00:03:02.170 because I told you before that food is like wood. 00:03:02.170 --> 00:03:04.930 And we can use wood to build new structures, sure. 00:03:04.930 --> 00:03:05.780 But when we need to, 00:03:05.780 --> 00:03:09.250 we can also burn wood to get energy. 00:03:09.250 --> 00:03:10.820 So we can start a campfire. 00:03:10.820 --> 00:03:13.250 And if we do, we know that we're gonna get some energy 00:03:13.250 --> 00:03:14.530 in the form of light, 00:03:14.530 --> 00:03:16.660 we'll get some energy in the form of heat, 00:03:16.660 --> 00:03:19.300 and maybe some other things like sound. 00:03:19.300 --> 00:03:21.440 And food is actually the same way, 00:03:21.440 --> 00:03:23.610 and so we can take those same food molecules 00:03:23.610 --> 00:03:25.980 that we broke down before to get building blocks 00:03:25.980 --> 00:03:30.710 and instead use them as fuel to generate cellular energy. 00:03:30.710 --> 00:03:33.020 And then we can use that cellular energy 00:03:33.020 --> 00:03:36.170 to fuel all of the building that we just talked about. 00:03:36.170 --> 00:03:39.500 And likewise, if our cells work together, which they do, 00:03:39.500 --> 00:03:42.290 they can use this energy to do things like running, 00:03:42.290 --> 00:03:46.190 thinking, and all the other things that we humans do. 00:03:46.190 --> 00:03:47.390 All right. 00:03:47.390 --> 00:03:49.620 Let's step back just one more time 00:03:49.620 --> 00:03:51.730 because what we'll see is that these two processes 00:03:51.730 --> 00:03:53.130 that we've just described, 00:03:53.130 --> 00:03:55.950 so food is lumber and food is fuel 00:03:55.950 --> 00:03:58.500 actually explain so much of life. 00:03:58.500 --> 00:04:00.100 So this is not just us. 00:04:00.100 --> 00:04:02.620 Every living thing on this planet is doing this. 00:04:02.620 --> 00:04:03.850 So you feed your dog 00:04:03.850 --> 00:04:07.293 to fuel his or her molecular construction projects as well. 00:04:08.450 --> 00:04:09.820 So right there and then, 00:04:09.820 --> 00:04:12.520 we've already kind of answered our question from before, 00:04:12.520 --> 00:04:14.060 which, reminder, was: 00:04:14.060 --> 00:04:16.830 how do people go from small to big? 00:04:16.830 --> 00:04:19.420 So what's happening is that this baby becomes an adult 00:04:19.420 --> 00:04:22.520 by eating food, milk, formula, gushy stuff, 00:04:22.520 --> 00:04:24.090 I don't know, whatever babies eat. 00:04:24.090 --> 00:04:25.700 And some of the molecules in that food 00:04:25.700 --> 00:04:28.580 will be used as fuel to generate energy, 00:04:28.580 --> 00:04:30.150 and then some of that energy 00:04:30.150 --> 00:04:32.550 will be used to combine food molecules 00:04:32.550 --> 00:04:34.500 with molecules in the baby 00:04:34.500 --> 00:04:37.690 to build up a larger baby, AKA an adult. 00:04:37.690 --> 00:04:39.410 All right, I hope that helps. 00:04:39.410 --> 00:04:40.370 Let's wrap it here. 00:04:40.370 --> 00:04:41.570 See you in the next one.

Fossils and rock layers

https://www.youtube.com/watch?v=3LObb5WxMdw

vtt

https://www.youtube.com/api/timedtext?v=3LObb5WxMdw&ei=uVWUZcCrGcXKp-oPrr26yAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6545852EDB8B1972DD857995076489FE715FF3DC.76A896707CFFC0320FCE39AC62E98080188F4959&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.033 --> 00:00:02.690 - [Instructor] Have you ever wanted to travel back in time? 00:00:02.690 --> 00:00:04.720 Would you go meet your younger self? 00:00:04.720 --> 00:00:07.130 Would you go and ride a dinosaur? 00:00:07.130 --> 00:00:09.750 Or would you meticulously create a timeline 00:00:09.750 --> 00:00:12.610 of the Earth's 4.6-billion-year long history 00:00:12.610 --> 00:00:14.780 based on major geological events? 00:00:14.780 --> 00:00:17.070 Even though geologists can't go back in time, 00:00:17.070 --> 00:00:19.240 they've been able to do just that. 00:00:19.240 --> 00:00:22.150 Their timeline is called geologic timescale 00:00:22.150 --> 00:00:24.000 and it breaks up all of Earth's history 00:00:24.000 --> 00:00:26.350 into units called eons and eras. 00:00:26.350 --> 00:00:28.540 And you may be wondering, "How can we map out 00:00:28.540 --> 00:00:30.720 what happened on Earth billions of years ago?" 00:00:30.720 --> 00:00:32.620 The answer is rocks. 00:00:32.620 --> 00:00:35.550 Geologists look for clues in sedimentary rock layers, 00:00:35.550 --> 00:00:37.520 which we call strata. 00:00:37.520 --> 00:00:40.240 The fossil record, which are the remains of organisms 00:00:40.240 --> 00:00:42.290 that have been preserved in rock layers 00:00:42.290 --> 00:00:45.750 can give us glimpses of creatures that breathe long ago. 00:00:45.750 --> 00:00:48.050 Also, the difference in mineral composition 00:00:48.050 --> 00:00:49.280 in different rock layers 00:00:49.280 --> 00:00:51.570 can tell geologists when a volcano erupted 00:00:51.570 --> 00:00:53.340 or an asteroid hit. 00:00:53.340 --> 00:00:55.380 But how did geologists know when one rock layer 00:00:55.380 --> 00:00:56.850 is older than another? 00:00:56.850 --> 00:00:58.720 Well, when sedimentary rocks form, 00:00:58.720 --> 00:01:01.690 they're deposited in layers, one on top of the other. 00:01:01.690 --> 00:01:04.460 So unless the layers are disturbed or turned over, 00:01:04.460 --> 00:01:05.670 the layers at the bottom 00:01:05.670 --> 00:01:08.000 are always older than the layers at the top. 00:01:08.000 --> 00:01:11.340 Geologists call this rule the Law of Superposition. 00:01:11.340 --> 00:01:14.140 So if a geologist finds a fossil of an ammonite 00:01:14.140 --> 00:01:17.250 in a layer of rock above a fossil of a Dunkleosteus, 00:01:17.250 --> 00:01:19.310 the scientists would know that the Dunkleosteus 00:01:19.310 --> 00:01:20.750 is older than the ammonite. 00:01:20.750 --> 00:01:23.200 This process is called relative dating 00:01:23.200 --> 00:01:25.470 because it helps scientists determine the relative ages 00:01:25.470 --> 00:01:27.540 of rock layers and fossils. 00:01:27.540 --> 00:01:30.010 But what does relative ages mean? 00:01:30.010 --> 00:01:31.850 Let's say that I told you my friend Ava 00:01:31.850 --> 00:01:33.130 is younger than her sister, 00:01:33.130 --> 00:01:34.560 but older than her cat. 00:01:34.560 --> 00:01:37.430 Then, I wouldn't be telling you Ava's exact age, 00:01:37.430 --> 00:01:41.290 but her relative age in relation to her sister and her cat. 00:01:41.290 --> 00:01:44.010 Let's take a look at another example of relative ages, 00:01:44.010 --> 00:01:45.630 this time, with rocks. 00:01:45.630 --> 00:01:47.890 Imagine that one day you found a big rock 00:01:47.890 --> 00:01:49.760 with many layers like this. 00:01:49.760 --> 00:01:52.070 Because the rock is a sedimentary rock 00:01:52.070 --> 00:01:54.420 and you remember the Law of Superposition, 00:01:54.420 --> 00:01:56.990 you know that the layers at the bottom are older 00:01:56.990 --> 00:01:59.940 and you know that the layers up here are younger. 00:01:59.940 --> 00:02:02.030 But what about this section of rock right here 00:02:02.030 --> 00:02:04.450 that slices through the other layers? 00:02:04.450 --> 00:02:07.740 Geologists would call this section an igneous intrusion 00:02:07.740 --> 00:02:10.980 since it was formed for molten rock that has cooled. 00:02:10.980 --> 00:02:12.980 This particular igneous intrusion 00:02:12.980 --> 00:02:14.300 isn't clearly on top of 00:02:14.300 --> 00:02:16.560 or below any of the sedimentary rock layers. 00:02:16.560 --> 00:02:19.230 So we can't use the Law of Superposition here. 00:02:19.230 --> 00:02:21.640 Luckily, geologists have figured out another rule 00:02:21.640 --> 00:02:24.370 called the law of crosscutting relationships. 00:02:24.370 --> 00:02:26.650 This rule says that when two geologic features cross 00:02:26.650 --> 00:02:27.770 or intersect, 00:02:27.770 --> 00:02:30.280 the feature that cuts through the other is younger, 00:02:30.280 --> 00:02:31.290 and this makes sense 00:02:31.290 --> 00:02:34.120 because you can't break something before it even exists. 00:02:34.120 --> 00:02:35.640 So since our igneous intrusion 00:02:35.640 --> 00:02:37.710 cuts through the layers of the sedimentary rock, 00:02:37.710 --> 00:02:40.540 we know that it must be even younger than the rock layers. 00:02:40.540 --> 00:02:43.360 And what about this fault or break over here? 00:02:43.360 --> 00:02:45.350 Well, since it slice through all the layers, 00:02:45.350 --> 00:02:46.880 as well as the igneous rock, 00:02:46.880 --> 00:02:48.810 the law of crosscutting relationships 00:02:48.810 --> 00:02:49.740 tells us that the faults 00:02:49.740 --> 00:02:52.680 must be the very youngest geologic feature here. 00:02:52.680 --> 00:02:54.840 Other pieces of evidence, like fossils, 00:02:54.840 --> 00:02:56.580 could be used for relative dating. 00:02:56.580 --> 00:02:59.010 For example, suppose a geologist found a rock 00:02:59.010 --> 00:03:01.410 containing fossils of extinct organisms 00:03:01.410 --> 00:03:04.550 and another rock that contained fossils of modern organisms. 00:03:04.550 --> 00:03:06.010 The geologist could then deduce 00:03:06.010 --> 00:03:08.820 that the rock with the extinct organisms is older. 00:03:08.820 --> 00:03:11.810 Certain kinds of fossils, called index fossils, 00:03:11.810 --> 00:03:13.570 are especially helpful when determining 00:03:13.570 --> 00:03:15.010 the relative age of a rock. 00:03:15.010 --> 00:03:17.230 Index fossils are fossils that are only found 00:03:17.230 --> 00:03:19.910 on a specific section of the geologic timescale. 00:03:19.910 --> 00:03:22.690 I always remember what an index fossil is like this. 00:03:22.690 --> 00:03:24.330 Just like I use my index finger 00:03:24.330 --> 00:03:26.230 to point to give directions, 00:03:26.230 --> 00:03:29.440 index fossils can point to when on the geologic timescale 00:03:29.440 --> 00:03:30.750 a rock was formed. 00:03:30.750 --> 00:03:33.160 So if a geologist finds the same index fossil 00:03:33.160 --> 00:03:35.230 in rock layers in two different rocks, 00:03:35.230 --> 00:03:37.150 they know that those rock layers must have been formed 00:03:37.150 --> 00:03:38.830 around the same time period, 00:03:38.830 --> 00:03:40.450 but fossils aren't the only thing 00:03:40.450 --> 00:03:43.540 that can help geologists figure out a rock's relative age. 00:03:43.540 --> 00:03:46.200 For example, if a geologist found two rock layers 00:03:46.200 --> 00:03:48.520 that contained evidence of the same geologic event, 00:03:48.520 --> 00:03:51.230 like a layer of ash from a major volcanic eruption, 00:03:51.230 --> 00:03:52.610 the geologists could deduce 00:03:52.610 --> 00:03:54.770 that those rock layers were made at the same time. 00:03:54.770 --> 00:03:56.710 Relative dating is how geologists figured out 00:03:56.710 --> 00:03:58.320 that Stegosauruses were extinct 00:03:58.320 --> 00:04:00.720 long before T-Rex's even existed. 00:04:00.720 --> 00:04:02.070 It also helped them figure out 00:04:02.070 --> 00:04:03.670 the first single cellular life 00:04:03.670 --> 00:04:06.270 formed about 3.8 billion years ago 00:04:06.270 --> 00:04:08.080 and the first multicellular life 00:04:08.080 --> 00:04:10.460 formed about 600 million years ago, 00:04:10.460 --> 00:04:13.300 and they figured out that modern humans didn't even exist 00:04:13.300 --> 00:04:15.360 until about 200,000 years ago, 00:04:15.360 --> 00:04:18.740 which is right at the very end of the geologic time scale. 00:04:18.740 --> 00:04:21.270 In other words, it took a really, really long time 00:04:21.270 --> 00:04:23.810 for life to evolve into what it looks like today. 00:04:23.810 --> 00:04:25.530 We, humans, are very young 00:04:25.530 --> 00:04:27.770 in the grand scheme of the Earth's history. 00:04:27.770 --> 00:04:29.260 Now, if you'll excuse me, 00:04:29.260 --> 00:04:31.540 I'm gonna go saddle and ride this Brontosaurus. 00:04:31.540 --> 00:04:33.014 Let's go, ginger snap! 00:04:33.014 --> 00:04:33.847 Hyah!

Phases of the moon

https://www.youtube.com/watch?v=f592IgRzq2E

vtt

https://www.youtube.com/api/timedtext?v=f592IgRzq2E&ei=uVWUZbr2F4e3mLAP7bmIsA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6D668A7420EDBE968D8F0E3427A14B5889AF0B.51A81C0CA85D3EC0ABF2FF59C60A6951678E3136&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:01.740 - [Narrator] Imagine that one day, 00:00:01.740 --> 00:00:04.650 all of the clocks and computers on Earth broke, 00:00:04.650 --> 00:00:06.840 and all the calendars disappeared. 00:00:06.840 --> 00:00:09.470 How would you keep track of how much time had passed? 00:00:09.470 --> 00:00:11.680 Well, you could look to the Moon. 00:00:11.680 --> 00:00:13.760 Humans have used the Moon to keep track of time 00:00:13.760 --> 00:00:15.290 for thousands of years. 00:00:15.290 --> 00:00:17.460 It isn't a coincidence that the word moon 00:00:17.460 --> 00:00:20.020 is related to the word month in old English. 00:00:20.020 --> 00:00:22.910 The Moon is Earth's only natural satellite. 00:00:22.910 --> 00:00:25.290 A natural satellite is a naturally occurring body 00:00:25.290 --> 00:00:26.840 that orbits a planet. 00:00:26.840 --> 00:00:28.490 Some of the planets in our solar system 00:00:28.490 --> 00:00:30.760 have more than 50 satellites or moons, 00:00:30.760 --> 00:00:32.600 but the Earth just has one. 00:00:32.600 --> 00:00:35.150 The Moon does not generate its own light. 00:00:35.150 --> 00:00:36.560 We can see the Moon from the Earth, 00:00:36.560 --> 00:00:39.130 because it is partially lit by the light from the sun. 00:00:39.130 --> 00:00:41.360 In fact, moonlight is just sunlight 00:00:41.360 --> 00:00:43.360 reflected from the Moon onto Earth. 00:00:43.360 --> 00:00:45.280 The Moon takes about 27 days 00:00:45.280 --> 00:00:47.110 to make a full orbit around Earth. 00:00:47.110 --> 00:00:49.530 And as it does, the lit part of the Moon 00:00:49.530 --> 00:00:51.940 appears to change shape to us here on Earth. 00:00:51.940 --> 00:00:56.310 These shapes are called the moon phases, or lunar phases. 00:00:56.310 --> 00:00:58.870 So why do we see different lunar phases? 00:00:58.870 --> 00:01:02.690 Well, the 27 days it takes the Moon to orbit the Earth once 00:01:02.690 --> 00:01:03.600 is the same amount of time 00:01:03.600 --> 00:01:06.050 it takes the Moon to rotate on its axis once. 00:01:06.050 --> 00:01:07.680 This means that the same side of the Moon 00:01:07.680 --> 00:01:09.170 is always facing us. 00:01:09.170 --> 00:01:11.210 At the same time, the sun always lights up 00:01:11.210 --> 00:01:12.750 half of the sphere of the Moon. 00:01:12.750 --> 00:01:14.970 However, the side of the Moon that's facing us 00:01:14.970 --> 00:01:16.590 isn't always the same part of the Moon 00:01:16.590 --> 00:01:17.930 that the sun lights up. 00:01:17.930 --> 00:01:19.928 This causes the Moon to appear to have different shapes, 00:01:19.928 --> 00:01:21.300 or faces in the sky, 00:01:21.300 --> 00:01:22.870 depending on the time of the month. 00:01:22.870 --> 00:01:25.330 Let's take a closer look at the Moon's phases. 00:01:25.330 --> 00:01:27.200 First, we have the new moon, 00:01:27.200 --> 00:01:29.360 which happens when the Moon is closest to the sun 00:01:29.360 --> 00:01:30.330 in its orbit. 00:01:30.330 --> 00:01:32.160 During this phase, the lit side of the Moon 00:01:32.160 --> 00:01:34.020 is completely facing away from Earth. 00:01:34.020 --> 00:01:36.040 So it looks like the Moon has disappeared. 00:01:36.040 --> 00:01:38.820 In a day or two, we'd be able to see a little sliver of moon 00:01:38.820 --> 00:01:40.410 in the sky. 00:01:40.410 --> 00:01:41.900 Over the next few days, 00:01:41.900 --> 00:01:44.660 the crescent moon will appear to get bigger and bigger. 00:01:44.660 --> 00:01:46.050 When the Moon appears to get bigger 00:01:46.050 --> 00:01:48.800 from one day to the next, we say that the Moon is waxing. 00:01:48.800 --> 00:01:49.780 So this phase of the Moon 00:01:49.780 --> 00:01:52.010 is called the waxing crescent moon. 00:01:52.010 --> 00:01:53.330 You might notice that sometimes 00:01:53.330 --> 00:01:55.680 we can still see the rest of the Moon in the shadow. 00:01:55.680 --> 00:01:58.450 This is because the Earth reflects sunlight onto the Moon, 00:01:58.450 --> 00:02:00.570 just like the Moon reflects light onto Earth. 00:02:00.570 --> 00:02:03.090 Eventually, the Moon appears to change shape so much 00:02:03.090 --> 00:02:04.710 that it isn't a crescent anymore, 00:02:04.710 --> 00:02:06.700 but a half circle in the sky. 00:02:06.700 --> 00:02:08.990 This is called a first quarter moon. 00:02:08.990 --> 00:02:10.080 There are two ways to think about 00:02:10.080 --> 00:02:12.250 why this phase is called a quarter moon. 00:02:12.250 --> 00:02:14.840 Even though it looks like the Moon is half illuminated, 00:02:14.840 --> 00:02:16.550 the Moon is a sphere. 00:02:16.550 --> 00:02:19.420 So we can only ever see half of the Moon from Earth. 00:02:19.420 --> 00:02:20.540 During a quarter moon, 00:02:20.540 --> 00:02:23.460 the Moon forms a right angle with Earth and the sun. 00:02:23.460 --> 00:02:25.450 This means that we a half lit portion 00:02:25.450 --> 00:02:27.460 of the half of the Moon that's always facing us. 00:02:27.460 --> 00:02:30.260 It's half of a half, so it's a quarter. 00:02:30.260 --> 00:02:31.950 Also, a first quarter moon 00:02:31.950 --> 00:02:33.950 occurs when the Moon is a quarter of the way through 00:02:33.950 --> 00:02:35.490 its new cycle. 00:02:35.490 --> 00:02:37.930 Next, there's the waxing gibbous moon. 00:02:37.930 --> 00:02:41.160 The word gibbous comes from the Latin word meaning humpback. 00:02:41.160 --> 00:02:43.880 Once the Moon is farthest from the sun in its orbit, 00:02:43.880 --> 00:02:46.350 the full sun lit side of the Moon faces Earth. 00:02:46.350 --> 00:02:48.610 We call this phase the full moon, 00:02:48.610 --> 00:02:51.000 but the Moon is not done yet. 00:02:51.000 --> 00:02:53.630 It's only finished half of the cycle. 00:02:53.630 --> 00:02:56.470 Next, we have the same phases, but in reverse. 00:02:56.470 --> 00:02:58.840 As the Moon appears to get smaller and smaller, 00:02:58.840 --> 00:03:00.520 we say that it's waning. 00:03:00.520 --> 00:03:02.500 The full Moon appears to shrink, 00:03:02.500 --> 00:03:04.900 and then we see a waning gibbous. 00:03:04.900 --> 00:03:06.810 Then there's the third quarter moon. 00:03:06.810 --> 00:03:08.700 This happens when the Moon is three quarters 00:03:08.700 --> 00:03:09.940 the way done with its cycle, 00:03:09.940 --> 00:03:11.580 and the Moon forms another right angle 00:03:11.580 --> 00:03:12.930 with the sun and the Earth. 00:03:12.930 --> 00:03:15.140 The Moon appears to shrink even more, 00:03:15.140 --> 00:03:17.520 and it becomes a waning crescent, 00:03:17.520 --> 00:03:20.550 and the cycle starts anew with another new moon. 00:03:20.550 --> 00:03:23.760 Even though the Moon completes an orbit every 27 days, 00:03:23.760 --> 00:03:27.810 the lunar phases actually repeat about every 29.5 days. 00:03:27.810 --> 00:03:29.833 This is because the Earth is revolving around the sun 00:03:29.833 --> 00:03:31.830 while the Moon completes its orbit. 00:03:31.830 --> 00:03:34.960 So the Moon has to travel a little extra to catch up. 00:03:34.960 --> 00:03:36.570 The Moon isn't just something beautiful 00:03:36.570 --> 00:03:37.740 to look at in the sky, 00:03:37.740 --> 00:03:40.010 or just an easy way to keep track of time. 00:03:40.010 --> 00:03:42.240 The Moon's gravity controls the tides, 00:03:42.240 --> 00:03:44.660 which are the rise and fall of water in oceans, 00:03:44.660 --> 00:03:46.180 lakes, and rivers. 00:03:46.180 --> 00:03:50.320 Tides allow for unique ecosystems, like tide pools to exist. 00:03:50.320 --> 00:03:52.400 And we can use the tides to create electricity, 00:03:52.400 --> 00:03:53.900 and tidal power plants. 00:03:53.900 --> 00:03:56.800 The Moon also helps keep Earth's access stable. 00:03:56.800 --> 00:03:59.130 Without it, our planet would wobble more dramatically 00:03:59.130 --> 00:04:01.370 on its axis over long periods of time, 00:04:01.370 --> 00:04:03.950 which would change up our weather and our seasons. 00:04:03.950 --> 00:04:05.230 So even though your calendar 00:04:05.230 --> 00:04:08.050 is pretty unlikely to spontaneously combust tomorrow, 00:04:08.050 --> 00:04:09.350 you could still thank the Moon 00:04:09.350 --> 00:04:11.240 for being such a stabilizing influence, 00:04:11.240 --> 00:04:12.953 and good companion to our planet.

Potential energy

https://www.youtube.com/watch?v=oGzwVYPxKjg

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https://www.youtube.com/api/timedtext?v=oGzwVYPxKjg&ei=uVWUZeHRGYGNvdIPvPit2A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245289&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D0EE4F600DFE64E8F75DCC13D171571C661EA961.BC26876762EFD8122BB3F3744FDD1E29DF009E78&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.330 --> 00:00:01.410 - [Narrator] Hello, everyone. 00:00:01.410 --> 00:00:03.960 Let's talk about potential energy. 00:00:03.960 --> 00:00:07.090 Potential energy is energy that is stored in an object, 00:00:07.090 --> 00:00:08.310 and this energy is related 00:00:08.310 --> 00:00:10.780 to the potential or the future possibility 00:00:10.780 --> 00:00:12.890 for an object to have a different type of energy, 00:00:12.890 --> 00:00:14.900 like kinetic energy for motion, 00:00:14.900 --> 00:00:17.310 that is converted from that potential energy. 00:00:17.310 --> 00:00:19.060 There are many kinds of potential energy, 00:00:19.060 --> 00:00:21.230 but they all arise from an object's relation 00:00:21.230 --> 00:00:23.703 to a position, or an original shape. 00:00:25.490 --> 00:00:26.520 So while in general, 00:00:26.520 --> 00:00:28.620 there are many different types of potential energy, 00:00:28.620 --> 00:00:30.786 there are several specific types that are very common. 00:00:30.786 --> 00:00:33.200 So, let's talk about these. 00:00:33.200 --> 00:00:34.770 Gravitational potential energy 00:00:34.770 --> 00:00:37.650 is the potential energy that an object with mass has 00:00:37.650 --> 00:00:40.290 due to the force of gravity from another object with mass, 00:00:40.290 --> 00:00:42.190 like say, the Earth. 00:00:42.190 --> 00:00:44.350 And in fact, we often use the surface of the Earth 00:00:44.350 --> 00:00:45.748 to compare an object's position with 00:00:45.748 --> 00:00:47.620 to see how much potential energy it has 00:00:47.620 --> 00:00:50.570 in the Earth's gravitational field. 00:00:50.570 --> 00:00:52.230 Gravity is an attractive force, 00:00:52.230 --> 00:00:53.810 so objects with mass want to move 00:00:53.810 --> 00:00:55.490 towards the surface of the Earth. 00:00:55.490 --> 00:00:57.110 If we move them further away, 00:00:57.110 --> 00:00:59.430 or opposite the direction of the gravitational force, 00:00:59.430 --> 00:01:02.150 we increase their gravitational potential energy. 00:01:02.150 --> 00:01:04.593 And the opposite is true if it gets closer. 00:01:05.910 --> 00:01:07.680 When an object is on the surface of Earth, 00:01:07.680 --> 00:01:09.970 we typically say it has no potential energy, 00:01:09.970 --> 00:01:12.320 but you could use any point to be this comparison 00:01:12.320 --> 00:01:15.180 where potential energy is zero. 00:01:15.180 --> 00:01:16.900 Consider a book on a bookshelf. 00:01:16.900 --> 00:01:18.570 If the book is on this shelf, 00:01:18.570 --> 00:01:22.330 we can use this shelf as the 0.4 potential energy. 00:01:22.330 --> 00:01:23.670 Moving it to a higher shelf 00:01:23.670 --> 00:01:26.070 would mean it has gravitational potential energy 00:01:26.070 --> 00:01:28.430 relative to that lower shelf, 00:01:28.430 --> 00:01:30.040 or relative to the floor 00:01:30.040 --> 00:01:32.490 if we want to use that as our comparison instead. 00:01:34.070 --> 00:01:36.500 Next, we have elastic potential energy, 00:01:36.500 --> 00:01:37.780 which is the potential energy 00:01:37.780 --> 00:01:40.790 some objects have due to their shape being changed. 00:01:40.790 --> 00:01:44.020 These types of objects are called elastic objects. 00:01:44.020 --> 00:01:46.540 Elastic objects are made of materials and designed, 00:01:46.540 --> 00:01:49.050 so they have internal or inside forces 00:01:49.050 --> 00:01:52.260 that try to return them to their original shape. 00:01:52.260 --> 00:01:55.120 One very common example of this is a spring. 00:01:55.120 --> 00:01:58.310 When you stretch or compress a spring, you change its shape. 00:01:58.310 --> 00:02:00.420 And the shape of the spring causes internal forces 00:02:00.420 --> 00:02:04.300 that try to return the spring to its original shape. 00:02:04.300 --> 00:02:05.797 Now electric potential energy, 00:02:05.797 --> 00:02:08.970 which is the potential energy a charged object has 00:02:08.970 --> 00:02:12.560 due to the electric force from another charged object. 00:02:12.560 --> 00:02:15.470 Opposite electric charges are attracted to one another, 00:02:15.470 --> 00:02:18.210 and similar electric charges are repelled. 00:02:18.210 --> 00:02:19.380 So the potential energy 00:02:19.380 --> 00:02:21.087 depends on what type of charges there are, 00:02:21.087 --> 00:02:23.810 and how far apart they are. 00:02:23.810 --> 00:02:25.500 Potential energy increases 00:02:25.500 --> 00:02:27.192 when the charges move opposite the direction 00:02:27.192 --> 00:02:28.710 of the electric force, 00:02:28.710 --> 00:02:33.030 for example, when two negative charges get closer together. 00:02:33.030 --> 00:02:35.250 Similarly, magnetic potential energy 00:02:35.250 --> 00:02:37.920 is the potential energy a magnetic object has 00:02:37.920 --> 00:02:41.140 due to the magnetic force from another magnet. 00:02:41.140 --> 00:02:44.210 Magnetic force causes similar poles to repel one another, 00:02:44.210 --> 00:02:46.290 and opposite poles to attract. 00:02:46.290 --> 00:02:49.180 And because magnets have north and south poles, 00:02:49.180 --> 00:02:51.110 the potential energy depends not only 00:02:51.110 --> 00:02:52.640 on the position within a field, 00:02:52.640 --> 00:02:55.470 but also the magnets orientation. 00:02:55.470 --> 00:02:57.830 Again, you could increase the potential energy 00:02:57.830 --> 00:03:00.010 by moving the magnets opposite the direction 00:03:00.010 --> 00:03:01.250 of the magnetic force. 00:03:01.250 --> 00:03:05.240 For example, by pulling apart a North Pole and a South Pole. 00:03:05.240 --> 00:03:07.900 All of these types of energy are due to different forces, 00:03:07.900 --> 00:03:10.400 and are calculated differently from different equations, 00:03:10.400 --> 00:03:11.830 which we won't cover here, 00:03:11.830 --> 00:03:14.570 but they are all potential energy. 00:03:14.570 --> 00:03:16.550 And these are just a few of the most common types 00:03:16.550 --> 00:03:18.940 of potential energy, but there are more. 00:03:18.940 --> 00:03:21.470 In summary, potential energy is the stored energy 00:03:21.470 --> 00:03:23.720 in an object due to its position, its properties, 00:03:23.720 --> 00:03:25.730 and the forces acting on it. 00:03:25.730 --> 00:03:26.890 Potential energy is measured 00:03:26.890 --> 00:03:29.290 relative to some comparison position or shape, 00:03:29.290 --> 00:03:32.050 and describes the potential for other forms of energy, 00:03:32.050 --> 00:03:35.630 commonly kinetic energy for motion, to exist. 00:03:35.630 --> 00:03:37.610 There are many forms of potential energy, 00:03:37.610 --> 00:03:41.100 including gravitational, elastic, magnetic, and electric. 00:03:41.100 --> 00:03:41.933 Thanks for watching, 00:03:41.933 --> 00:03:44.053 and I hope you learned a little bit of something.

Worked example: analyzing a generic food web

https://www.youtube.com/watch?v=vniXioPlsLA

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https://www.youtube.com/api/timedtext?v=vniXioPlsLA&ei=vlWUZcHdFda4vdIPoe298Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245294&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=678FE02C86CA5B2CECD0E0786C8E3173CAB330A5.7678EFAE7635D5AE1C8E15360E102CDEAD9E3F4C&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.550 --> 00:00:03.470 - [Narrator] What we have here is a diagram of a food web 00:00:03.470 --> 00:00:05.650 that shows us how matter and energy 00:00:05.650 --> 00:00:09.420 are transferred between organisms in an ecosystem. 00:00:09.420 --> 00:00:10.550 But it's a little bit abstract, 00:00:10.550 --> 00:00:12.370 they don't tell us what these organisms are. 00:00:12.370 --> 00:00:14.310 They just say organism one, organism two, 00:00:14.310 --> 00:00:16.950 organism three, and so forth. 00:00:16.950 --> 00:00:19.680 But even this gives us some information 00:00:19.680 --> 00:00:22.250 about which organism are the producers, 00:00:22.250 --> 00:00:25.120 the primary consumers, the secondary consumers, 00:00:25.120 --> 00:00:27.310 and the decomposers. 00:00:27.310 --> 00:00:30.240 So the first thing I want you to think about is 00:00:30.240 --> 00:00:35.020 which arrows show us going from producers, 00:00:35.020 --> 00:00:36.500 I'll write it like, 00:00:36.500 --> 00:00:39.860 to primary consumers? 00:00:39.860 --> 00:00:41.210 Pause the video and think about that. 00:00:41.210 --> 00:00:44.793 Which arrows show producers to primary consumers? 00:00:46.310 --> 00:00:48.320 All right, now in a food web, 00:00:48.320 --> 00:00:51.070 the giveaway that something is a producer 00:00:51.070 --> 00:00:53.990 is that it doesn't have arrows coming into it, 00:00:53.990 --> 00:00:56.360 it only has arrows coming out of it. 00:00:56.360 --> 00:01:01.210 And so organism one is a producer. 00:01:01.210 --> 00:01:05.730 Organism five is also a producer. 00:01:05.730 --> 00:01:07.890 Where are they getting their matter and energy from? 00:01:07.890 --> 00:01:10.330 Well, they're getting their matter from the environment 00:01:10.330 --> 00:01:13.970 and the energy, in most cases, is coming from the sun. 00:01:13.970 --> 00:01:16.350 And the things that eat the producers, 00:01:16.350 --> 00:01:18.350 those are primary consumers. 00:01:18.350 --> 00:01:20.720 So this is an arrow that goes from a producer 00:01:20.720 --> 00:01:22.310 to a primary consumer. 00:01:22.310 --> 00:01:24.520 This is an arrow that goes from a producer 00:01:24.520 --> 00:01:26.100 to a primary consumer. 00:01:26.100 --> 00:01:29.350 And this is an arrow that goes from a producer 00:01:29.350 --> 00:01:31.840 to a primary consumer. 00:01:31.840 --> 00:01:33.500 Now, with that out of the way, 00:01:33.500 --> 00:01:38.400 which arrows show us going from a primary consumer 00:01:39.290 --> 00:01:42.900 to a secondary consumer? 00:01:42.900 --> 00:01:45.440 Pause the video and think about that. 00:01:45.440 --> 00:01:47.670 Well, I just said that these things 00:01:47.670 --> 00:01:49.470 that are consuming the producers, 00:01:49.470 --> 00:01:52.930 these are primary, I'll just say P for primary, 00:01:52.930 --> 00:01:54.580 primary consumer. 00:01:54.580 --> 00:01:57.070 This is a primary consumer. 00:01:57.070 --> 00:02:00.320 This is a primary consumer, as well. 00:02:00.320 --> 00:02:02.350 Now secondary consumers are by definition 00:02:02.350 --> 00:02:04.120 things that aren't decomposers, 00:02:04.120 --> 00:02:06.620 but they're eating primary consumers. 00:02:06.620 --> 00:02:08.710 So they're going to have arrows coming in 00:02:08.710 --> 00:02:11.400 from primary consumers and out 00:02:11.400 --> 00:02:15.040 to either other secondary consumers or to decomposers. 00:02:15.040 --> 00:02:20.040 So organism three right over here is a secondary consumer. 00:02:20.540 --> 00:02:22.070 So we're going from a primary consumer 00:02:22.070 --> 00:02:23.140 to a secondary consumer. 00:02:23.140 --> 00:02:25.610 So this arrow is from a primary consumer 00:02:25.610 --> 00:02:27.530 to a secondary consumer. 00:02:27.530 --> 00:02:29.780 This arrow over here is interesting. 00:02:29.780 --> 00:02:32.260 It's a secondary consumer being consumed, 00:02:32.260 --> 00:02:33.790 but you can see that organism four 00:02:33.790 --> 00:02:35.900 only has arrows going into it, 00:02:35.900 --> 00:02:39.070 which is a pretty good clue that this is a decomposer. 00:02:39.070 --> 00:02:43.003 So I'm not going to call organism four a secondary, 00:02:43.920 --> 00:02:45.850 a secondary consumer. 00:02:45.850 --> 00:02:47.580 So let's keep going. 00:02:47.580 --> 00:02:50.960 What about the arrow that goes from organism six 00:02:50.960 --> 00:02:52.110 to organism seven? 00:02:52.110 --> 00:02:55.770 That looks like primary consumer to primary consumer. 00:02:55.770 --> 00:02:57.060 Well, it turns out that something can be 00:02:57.060 --> 00:03:00.260 both a primary consumer and a secondary consumer. 00:03:00.260 --> 00:03:03.010 So this is also a secondary consumer. 00:03:03.010 --> 00:03:06.230 Why, because it's eating a primary consumer 00:03:06.230 --> 00:03:07.830 and it's not a decomposer, 00:03:07.830 --> 00:03:09.470 so this is also another example 00:03:09.470 --> 00:03:11.600 of an arrow from a primary consumer 00:03:11.600 --> 00:03:14.230 to a secondary consumer. 00:03:14.230 --> 00:03:15.770 Last but not least, 00:03:15.770 --> 00:03:19.200 what are the arrows that go from a consumer, 00:03:19.200 --> 00:03:23.210 that go from a consumer, to a decomposer? 00:03:23.210 --> 00:03:25.330 And we already broke this down a little bit, 00:03:25.330 --> 00:03:27.340 no pun intended. 00:03:27.340 --> 00:03:29.880 Pause the video and try to think about that. 00:03:29.880 --> 00:03:32.290 Well, this is the only decomposer 00:03:32.290 --> 00:03:34.050 that's depicted in this diagram, 00:03:34.050 --> 00:03:37.420 and so this is going from a consumer to a decomposer, 00:03:37.420 --> 00:03:38.600 right over here. 00:03:38.600 --> 00:03:42.570 This is from a consumer to a decomposer, 00:03:42.570 --> 00:03:44.210 and that's all we have here. 00:03:44.210 --> 00:03:46.069 And to be clear, you don't have to go 00:03:46.069 --> 00:03:48.500 only from a consumer to decomposer. 00:03:48.500 --> 00:03:50.500 You could have gone from a producer 00:03:50.500 --> 00:03:51.880 straight to a decomposer. 00:03:51.880 --> 00:03:54.340 You could have arrows that look like that, as well, 00:03:54.340 --> 00:03:58.330 because if a plant dies and it gets decomposed, 00:03:58.330 --> 00:04:00.270 well, it's going to be, that matter and energy 00:04:00.270 --> 00:04:02.523 is going to be used by that decomposer.

Worked example: analyzing an ocean food web

https://www.youtube.com/watch?v=vGwhsG-4j-0

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https://www.youtube.com/api/timedtext?v=vGwhsG-4j-0&ei=vlWUZYqDHZnUxN8P7LqKEA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245294&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=3EE9C66C138E5068671E8C96122FE6428568FCA8.200F7E2C94C84829BC6139209A82AF9269FB8B1E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:01.950 - [Instructor] So this diagram right over here 00:00:01.950 --> 00:00:03.410 describes a food web. 00:00:03.410 --> 00:00:04.930 And a food web models 00:00:04.930 --> 00:00:07.910 how energy and matter moves in an ecosystem. 00:00:07.910 --> 00:00:10.340 And we're going to use this food web 00:00:10.340 --> 00:00:11.690 to answer some questions, 00:00:11.690 --> 00:00:14.400 to make sure we understand food webs. 00:00:14.400 --> 00:00:16.780 So the first thing I'm going to ask you is, 00:00:16.780 --> 00:00:21.000 what are the producers in this food web. 00:00:21.000 --> 00:00:25.433 Pause this video and see if you can figure this out. 00:00:26.610 --> 00:00:28.830 All right, now let's work through this together. 00:00:28.830 --> 00:00:30.780 The producers are the ones 00:00:30.780 --> 00:00:33.950 that can take matter in the ecosystem, in the environment, 00:00:33.950 --> 00:00:36.890 and energy from an outside source, usually the sun, 00:00:36.890 --> 00:00:39.470 in order to construct themselves 00:00:39.470 --> 00:00:42.290 and also in order to store that energy. 00:00:42.290 --> 00:00:44.210 And when you look at a food web, 00:00:44.210 --> 00:00:47.740 producers are going to have arrows pointed away from them. 00:00:47.740 --> 00:00:49.730 So they're getting their energy 00:00:49.730 --> 00:00:51.400 and their matter from the environment 00:00:51.400 --> 00:00:53.710 and then other people are going to consume them. 00:00:53.710 --> 00:00:55.940 And we're gonna talk about them in a little bit. 00:00:55.940 --> 00:00:59.960 But we can see here that the kelp is a producer. 00:00:59.960 --> 00:01:02.820 This is an aquatic ecosystem that we're looking at. 00:01:02.820 --> 00:01:04.270 But the kelp is a producer. 00:01:04.270 --> 00:01:06.290 There's no arrows going into it 00:01:06.290 --> 00:01:09.960 so it's using the sun and elements and atoms and molecules 00:01:09.960 --> 00:01:12.440 that it's finding in its environment in order to grow. 00:01:12.440 --> 00:01:16.030 And we can also see that's the case with the phytoplankton. 00:01:16.030 --> 00:01:19.150 It's also able to do photosynthesis, like the kelp, 00:01:19.150 --> 00:01:21.623 and capture that energy from the sun. 00:01:22.610 --> 00:01:27.610 Now, the next question I have is, where are the decomposers? 00:01:28.480 --> 00:01:31.653 Pause the video and try to answer that one. 00:01:32.970 --> 00:01:33.830 All right. 00:01:33.830 --> 00:01:36.150 Now you might remember decomposers, 00:01:36.150 --> 00:01:38.260 you can think about that's where a lot 00:01:38.260 --> 00:01:40.240 of the energy and the matter ends up, 00:01:40.240 --> 00:01:42.950 to be decomposed and then recycled again 00:01:42.950 --> 00:01:45.190 and be reused again by the producers. 00:01:45.190 --> 00:01:47.110 And if you're looking at a food web, 00:01:47.110 --> 00:01:48.210 these would-be organisms 00:01:48.210 --> 00:01:50.190 where all of the arrows point to them, 00:01:50.190 --> 00:01:52.750 but you don't have any arrows coming from them. 00:01:52.750 --> 00:01:55.650 And over here, it's clear that the bacteria, 00:01:55.650 --> 00:01:58.190 and there's many different species of bacteria 00:01:58.190 --> 00:02:00.100 or many different types of bacteria, 00:02:00.100 --> 00:02:03.970 but the bacteria here are the decomposers. 00:02:03.970 --> 00:02:05.740 Next, I am going to ask you 00:02:05.740 --> 00:02:08.747 about the primary consumers. 00:02:11.410 --> 00:02:14.363 Pause this video and see if you can identify them. 00:02:16.930 --> 00:02:19.700 Well, primary consumers are consumers 00:02:19.700 --> 00:02:22.370 that directly eat the producers. 00:02:22.370 --> 00:02:24.920 And so let's see, who is eating the kelp? 00:02:24.920 --> 00:02:27.530 You have have the sea urchin eating the kelp. 00:02:27.530 --> 00:02:29.890 You have the fish eating the kelp. 00:02:29.890 --> 00:02:31.600 Who's eating the phytoplankton? 00:02:31.600 --> 00:02:35.360 You have the zooplankton eating the phytoplankton. 00:02:35.360 --> 00:02:39.040 So these are primary consumers. 00:02:39.040 --> 00:02:42.780 Next, let's think about secondary consumers. 00:02:42.780 --> 00:02:44.033 Secondary. 00:02:45.180 --> 00:02:49.230 These are those that eat primary consumers. 00:02:49.230 --> 00:02:51.520 Pause the video and think about that. 00:02:51.520 --> 00:02:52.370 Well, let's think about 00:02:52.370 --> 00:02:55.060 who's eating these primary consumers. 00:02:55.060 --> 00:02:57.820 You have the otter. 00:02:57.820 --> 00:03:00.570 What's interesting is the fish is a primary consumer 00:03:00.570 --> 00:03:03.200 because it consumes kelp, which is a producer, 00:03:03.200 --> 00:03:06.610 but it also can consume another primary consumer. 00:03:06.610 --> 00:03:08.700 So, a fish, or the fish here, 00:03:08.700 --> 00:03:11.860 are both primary and secondary consumers. 00:03:11.860 --> 00:03:14.330 And then I think we are done. 00:03:14.330 --> 00:03:16.820 So you can see the general notions here. 00:03:16.820 --> 00:03:19.270 The producers have arrows going away from them 00:03:19.270 --> 00:03:20.640 but no arrows coming into them 00:03:20.640 --> 00:03:22.840 because they're getting their energy from the sun 00:03:22.840 --> 00:03:25.580 and they're using the matter in the ecosystem. 00:03:25.580 --> 00:03:29.330 Primary consumers are eating those producers, 00:03:29.330 --> 00:03:30.970 and you can see they have arrows going into them. 00:03:30.970 --> 00:03:34.760 And then they're eaten by other folks, secondary consumers, 00:03:34.760 --> 00:03:36.800 or those that eat the primary consumers. 00:03:36.800 --> 00:03:39.430 And then last but not least, you have the bacteria, 00:03:39.430 --> 00:03:43.230 which are decomposers, where the arrows all point to them 00:03:43.230 --> 00:03:44.810 and they continue to use that energy 00:03:44.810 --> 00:03:47.860 and then they take those nutrients, those molecules, 00:03:47.860 --> 00:03:49.790 and they put 'em back into the ecosystem 00:03:49.790 --> 00:03:51.633 so that it can be recycled again.

Matter and energy in food webs

https://www.youtube.com/watch?v=qIgL05zOx5U

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https://www.youtube.com/api/timedtext?v=qIgL05zOx5U&ei=vlWUZaO-KLiBhcIPxNOJ-AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245294&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A67D8538289612BE0D9D6561DDD6FB2012C4DFFD.27BA1AE68F3F41CEA5445AD59B489CA3541A43ED&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.840 --> 00:00:01.673 - [Narrator] In this video, 00:00:01.673 --> 00:00:03.160 we're gonna talk about food webs, 00:00:03.160 --> 00:00:04.760 which is really just a way 00:00:04.760 --> 00:00:07.600 of picturing how all of the matter, 00:00:07.600 --> 00:00:12.600 and how all of the energy flows inside of an ecosystem. 00:00:12.690 --> 00:00:14.050 Now, when I talk about matter, 00:00:14.050 --> 00:00:16.730 I'm talking about the atoms in an ecosystem, 00:00:16.730 --> 00:00:18.830 the molecules, when you look at your hand, 00:00:18.830 --> 00:00:20.750 it is made up of atoms. 00:00:20.750 --> 00:00:22.350 And it turns out that the matter 00:00:22.350 --> 00:00:24.400 is not created or destroyed, 00:00:24.400 --> 00:00:27.510 it's just recycled throughout an ecosystem. 00:00:27.510 --> 00:00:29.460 And we're going to see that in a second. 00:00:29.460 --> 00:00:31.083 And then when we talk about energy, 00:00:31.083 --> 00:00:33.549 it's the energy that your cells need to be alive, 00:00:33.549 --> 00:00:37.440 the energy you need to be alive, to not just exist, 00:00:37.440 --> 00:00:40.340 but to do things, to think, to move. 00:00:40.340 --> 00:00:43.690 And so this food web essentially describes that. 00:00:43.690 --> 00:00:45.620 As we've talked about in other videos, 00:00:45.620 --> 00:00:50.130 in most ecosystems, the great majority of the energy 00:00:50.130 --> 00:00:53.630 in an ecosystem comes from the sun. 00:00:53.630 --> 00:00:56.690 So what we have here is the sun produces energy. 00:00:56.690 --> 00:00:58.880 It travels to Earth, 00:00:58.880 --> 00:01:03.410 and then you have organisms, which we would call producers, 00:01:03.410 --> 00:01:07.230 that are able to take that light energy from the sun, 00:01:07.230 --> 00:01:11.060 and then take atoms and molecules from its environment, 00:01:11.060 --> 00:01:14.240 things like carbon dioxide in the air, 00:01:14.240 --> 00:01:17.090 things like water, and other nutrients. 00:01:17.090 --> 00:01:19.480 And it's able to construct itself 00:01:19.480 --> 00:01:21.670 using that energy from the sun. 00:01:21.670 --> 00:01:23.300 Now, when it constructs itself, 00:01:23.300 --> 00:01:25.370 it not only gives it structure, 00:01:25.370 --> 00:01:27.610 but it's also able to store energy. 00:01:27.610 --> 00:01:30.610 And right over here, we have several producers depicted. 00:01:30.610 --> 00:01:33.760 We have this tree here, which is able to do photosynthesis. 00:01:33.760 --> 00:01:36.600 We have the grass here that's able to do photosynthesis, 00:01:36.600 --> 00:01:38.020 and it's not just plants. 00:01:38.020 --> 00:01:39.250 You have things like algae, 00:01:39.250 --> 00:01:43.050 and other microorganisms that are able to be producers. 00:01:43.050 --> 00:01:45.030 But then we have things like this bunny, 00:01:45.030 --> 00:01:48.090 and this bunny is not able to harness energy 00:01:48.090 --> 00:01:50.140 from the sun by itself. 00:01:50.140 --> 00:01:53.780 In order for it to get its energy and its matter, 00:01:53.780 --> 00:01:56.220 it needs to eat one of these producers, 00:01:56.220 --> 00:01:58.370 probably some of this grass. 00:01:58.370 --> 00:02:01.330 And so we would call this bunny right over here, 00:02:01.330 --> 00:02:04.680 this rabbit, we would call it a consumer. 00:02:04.680 --> 00:02:05.810 And it is a consumer, 00:02:05.810 --> 00:02:08.840 you could think of it as both matter and energy. 00:02:08.840 --> 00:02:10.630 When it eats that plant, 00:02:10.630 --> 00:02:13.840 those atoms are then able to make up the bunny. 00:02:13.840 --> 00:02:15.114 It will poop out a little bit, 00:02:15.114 --> 00:02:18.360 so some of the matter might end up right over here. 00:02:18.360 --> 00:02:20.610 But then also there is energy 00:02:20.610 --> 00:02:22.650 that is stored in those molecules, 00:02:22.650 --> 00:02:25.860 and that rabbit can use that energy to exist and live, 00:02:25.860 --> 00:02:27.150 but as it does it, 00:02:27.150 --> 00:02:31.433 it does release some of the energy in the form of heat. 00:02:32.320 --> 00:02:34.890 And actually, even producers need to use energy 00:02:34.890 --> 00:02:35.723 in order to live. 00:02:35.723 --> 00:02:39.430 And as they do that, they also release heat. 00:02:39.430 --> 00:02:42.770 Now we have this fox, the fox is not a vegetarian. 00:02:42.770 --> 00:02:45.700 It does not eat, it does not eat trees. 00:02:45.700 --> 00:02:48.410 It likes to eat things like squirrels and bunnies, 00:02:48.410 --> 00:02:50.710 but big picture, it's not producing its own food. 00:02:50.710 --> 00:02:54.210 It's consuming food, so it also is a consumer. 00:02:54.210 --> 00:02:56.250 We can differentiate more in the future 00:02:56.250 --> 00:02:58.140 between things that eat plants, 00:02:58.140 --> 00:03:00.220 and things that eat other animals. 00:03:00.220 --> 00:03:01.440 And you can see in this food web, 00:03:01.440 --> 00:03:04.714 we draw an arrow from the thing that is being consumed 00:03:04.714 --> 00:03:07.090 to the thing that is doing the consuming. 00:03:07.090 --> 00:03:09.620 So a rabbit consumes a plant, 00:03:09.620 --> 00:03:12.660 and so the arrow goes from the plant to the rabbit. 00:03:12.660 --> 00:03:15.380 A fox consumes a rabbit or a squirrel, 00:03:15.380 --> 00:03:19.080 so an arrow goes from the rabbit or the squirrel to the fox. 00:03:19.080 --> 00:03:20.290 Now some of you might have noticed 00:03:20.290 --> 00:03:22.910 that we have these arrows that are pointing downward. 00:03:22.910 --> 00:03:25.040 And so let me scroll down a little bit. 00:03:25.040 --> 00:03:28.400 And we see these microorganisms, the worms, 00:03:28.400 --> 00:03:30.940 the fungi, the mushrooms right over here, 00:03:30.940 --> 00:03:34.070 and we call these decomposers. 00:03:34.070 --> 00:03:37.000 Now what decomposers are really doing 00:03:37.000 --> 00:03:38.380 is what what you would imagine, 00:03:38.380 --> 00:03:41.330 breaking down all of the things that might die, 00:03:41.330 --> 00:03:43.300 the poop that is falling down. 00:03:43.300 --> 00:03:47.600 And by doing that, it's continuing to recycle that matter. 00:03:47.600 --> 00:03:48.880 And when it decomposes, 00:03:48.880 --> 00:03:51.340 those atoms are released back into the soil, 00:03:51.340 --> 00:03:52.670 or the atmosphere, 00:03:52.670 --> 00:03:55.460 and then that can be reused by the producers. 00:03:55.460 --> 00:03:58.420 And once again, every organism in this food web 00:03:58.420 --> 00:04:00.990 is using some of the energy in order to exist, 00:04:00.990 --> 00:04:03.330 and do whatever it needs to do. 00:04:03.330 --> 00:04:05.900 And some of that energy is being released 00:04:05.900 --> 00:04:09.573 as heat in every single situation.

Photosynthesis in ecosystems

https://www.youtube.com/watch?v=_1U6uMmUJZU

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https://www.youtube.com/api/timedtext?v=_1U6uMmUJZU&ei=vlWUZai8KIachcIPoquZiAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245294&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7C556A9592EFECFD08C86142C2669981A843BFE7.70F15DA164015A4FA9630C377922C9153597F289&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.400 --> 00:00:01.233 - [Instructor] When you look at 00:00:01.233 --> 00:00:03.400 a rainforest ecosystem like this, 00:00:03.400 --> 00:00:05.660 one of the obvious questions may be, 00:00:05.660 --> 00:00:07.300 where do these plants come from? 00:00:07.300 --> 00:00:08.150 How do they grow? 00:00:08.150 --> 00:00:09.370 They're growing all the time, 00:00:09.370 --> 00:00:11.070 they're getting larger and larger and larger. 00:00:11.070 --> 00:00:13.990 Where does that mass, where does that matter come from? 00:00:13.990 --> 00:00:15.890 Pause this video and think about that. 00:00:17.120 --> 00:00:19.960 Well, you might already be guessing where it comes from. 00:00:19.960 --> 00:00:22.390 It might have something to do with photosynthesis, 00:00:22.390 --> 00:00:25.760 which we go into a lot of depth in other videos, 00:00:25.760 --> 00:00:30.210 but this is a process where you have carbon dioxide 00:00:30.210 --> 00:00:33.990 from the air in conjunction with water 00:00:33.990 --> 00:00:37.190 that primarily is coming from the soil, 00:00:37.190 --> 00:00:40.600 and it uses energy from the sun 00:00:40.600 --> 00:00:42.100 so I'll just draw that in, 00:00:42.100 --> 00:00:44.380 these yellow squiggles coming from the sun, 00:00:44.380 --> 00:00:46.290 in order to do two things. 00:00:46.290 --> 00:00:48.180 The plant is going to be building itself 00:00:48.180 --> 00:00:51.090 using the matter in the carbon dioxide and the water 00:00:51.090 --> 00:00:54.760 while also expelling oxygen as a byproduct. 00:00:54.760 --> 00:00:56.760 And this matter that the plant is able 00:00:56.760 --> 00:00:59.450 to take from its environment with photosynthesis 00:00:59.450 --> 00:01:02.220 is used to both become the structure of the plant 00:01:02.220 --> 00:01:05.590 and a store of energy in the form of sugars. 00:01:05.590 --> 00:01:07.440 Now, animals like you and me, 00:01:07.440 --> 00:01:10.700 we get our energy by then eating these plants. 00:01:10.700 --> 00:01:12.590 And how do we unlock that energy? 00:01:12.590 --> 00:01:15.410 Well, that's where this oxygen is really useful. 00:01:15.410 --> 00:01:16.900 That's why we need to breathe oxygen 00:01:16.900 --> 00:01:18.790 because by breathing the oxygen, 00:01:18.790 --> 00:01:21.780 we can essentially do photosynthesis in reverse, 00:01:21.780 --> 00:01:24.240 and we can break down this matter, 00:01:24.240 --> 00:01:27.000 these sugars, that we're getting from plants. 00:01:27.000 --> 00:01:29.050 So all of this biomass is coming 00:01:29.050 --> 00:01:31.400 from essentially water from the soil 00:01:31.400 --> 00:01:34.160 and carbon dioxide, and energy from the sun 00:01:34.160 --> 00:01:36.720 is used essentially put it together. 00:01:36.720 --> 00:01:38.190 There might be a few other nutrients 00:01:38.190 --> 00:01:40.980 that are also coming from the environment, like the soil, 00:01:40.980 --> 00:01:43.553 but primarily the water and the carbon dioxide.

Analog vs. digital signals

https://www.youtube.com/watch?v=PEYdn56pdcQ

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https://www.youtube.com/api/timedtext?v=PEYdn56pdcQ&ei=v1WUZZLhNqq9mLAPgaWr8Ak&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245295&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=BF6813DFCD18051D6D276D0665801753EADD6BF5.D538FC16052EE2C36DDBE6118F013A7FE49A30FA&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.140 --> 00:00:01.240 - [Narrator] In this video we're gonna think 00:00:01.240 --> 00:00:04.690 about analog versus digital signals. 00:00:04.690 --> 00:00:06.830 And one way to think about the difference 00:00:06.830 --> 00:00:10.810 is an analog signal is trying to reproduce 00:00:10.810 --> 00:00:13.330 exactly in some type of a signal 00:00:13.330 --> 00:00:17.130 what is going on while a digital signal is converting it, 00:00:17.130 --> 00:00:20.950 usually the ones and zeros which then can be converted back. 00:00:20.950 --> 00:00:22.480 So the first thing to realize 00:00:22.480 --> 00:00:24.980 is that almost any type of information, 00:00:24.980 --> 00:00:27.840 it might be how intense a certain color is 00:00:27.840 --> 00:00:31.690 or how bright it is or it might be a frequency of sound, 00:00:31.690 --> 00:00:34.830 all of that can be represented as numbers. 00:00:34.830 --> 00:00:36.190 So whether you're trying to transmit 00:00:36.190 --> 00:00:38.380 an analog signal or a digital signal 00:00:38.380 --> 00:00:41.530 it really is about how do you communicate numbers 00:00:41.530 --> 00:00:43.550 using some type of signal. 00:00:43.550 --> 00:00:46.360 And as an example, let's say that you are trying 00:00:46.360 --> 00:00:50.360 to communicate the number 24 to someone. 00:00:50.360 --> 00:00:53.643 Well, one way to do it is as an analog signal. 00:00:55.120 --> 00:00:57.350 You could have, as time goes on, 00:00:57.350 --> 00:01:00.460 maybe this is some type of voltage across a wire. 00:01:00.460 --> 00:01:01.930 And if you put that voltage 00:01:01.930 --> 00:01:03.500 right at what the other person 00:01:03.500 --> 00:01:07.190 receiving it could interpret it as 24, 00:01:07.190 --> 00:01:09.630 well then you would transmit it and they might, 00:01:09.630 --> 00:01:14.290 if they get this nice clean signal, see it as a 24. 00:01:14.290 --> 00:01:16.450 Now the problem with analog signals 00:01:16.450 --> 00:01:19.280 is what happens when you have interference. 00:01:19.280 --> 00:01:21.770 So let's say this is a really long wire 00:01:21.770 --> 00:01:23.180 that you're transmitting it over 00:01:23.180 --> 00:01:26.170 or you're transmitting it using radio waves, 00:01:26.170 --> 00:01:27.540 and there's a lot of bad weather 00:01:27.540 --> 00:01:29.110 or other types of interference. 00:01:29.110 --> 00:01:32.720 And so on the receiving end even though you transmit 00:01:32.720 --> 00:01:36.280 something that looks like this, that is a clear 24, 00:01:36.280 --> 00:01:38.740 the other person might get something like this. 00:01:38.740 --> 00:01:42.190 And so this isn't obvious that is a 24 anymore. 00:01:42.190 --> 00:01:44.610 It goes between 20 and 30, 00:01:44.610 --> 00:01:47.380 and this could be interpreted as static 00:01:47.380 --> 00:01:48.860 or a garbled up message 00:01:48.860 --> 00:01:50.570 or just doesn't sound as clean 00:01:50.570 --> 00:01:52.910 depending on what the 24 is trying to represent, 00:01:52.910 --> 00:01:54.510 or the image isn't as clear, 00:01:54.510 --> 00:01:57.690 if this is representing say the lightness 00:01:57.690 --> 00:02:00.010 or the brightness of a pixel. 00:02:00.010 --> 00:02:05.010 Now the other option is to convert that 24 into binary. 00:02:06.080 --> 00:02:11.080 So 24 can be represented in binary as 1 1 0 0 0. 00:02:13.160 --> 00:02:15.260 Now we have other videos on Khan Academy 00:02:15.260 --> 00:02:17.480 that explain how to convert back and forth 00:02:17.480 --> 00:02:20.830 between our decimal system that has 10 digits, 00:02:20.830 --> 00:02:23.820 zero through nine, and the binary system, 00:02:23.820 --> 00:02:26.310 which has two digits, zero and one. 00:02:26.310 --> 00:02:27.310 But in case you're curious, 00:02:27.310 --> 00:02:28.720 and you don't have to understand this 00:02:28.720 --> 00:02:30.910 to know the difference between analog and digital signals 00:02:30.910 --> 00:02:32.410 and when they might be useful, 00:02:32.410 --> 00:02:35.150 this first place is the ones place just as you're used to. 00:02:35.150 --> 00:02:37.020 But instead of this being the tens place, 00:02:37.020 --> 00:02:38.560 this is the twos place. 00:02:38.560 --> 00:02:40.150 Instead of this being the hundreds place, 00:02:40.150 --> 00:02:41.910 this is the forth place. 00:02:41.910 --> 00:02:44.530 Instead of this being the thousands place, 00:02:44.530 --> 00:02:46.300 this is the eights place. 00:02:46.300 --> 00:02:49.540 And instead of that being the ten thousandths place, 00:02:49.540 --> 00:02:51.550 that's the sixteens place. 00:02:51.550 --> 00:02:52.750 So one way to think about it, 00:02:52.750 --> 00:02:57.360 1 1 0 0 0 means 1/16 and 1/8. 00:02:57.360 --> 00:03:00.240 And if you add those together, you would get 24. 00:03:00.240 --> 00:03:02.633 What would that actually look like as a signal? 00:03:03.480 --> 00:03:05.640 Well, it could look something like this. 00:03:05.640 --> 00:03:07.450 Where the person interpreting it knows 00:03:07.450 --> 00:03:09.220 that over this first time period 00:03:09.220 --> 00:03:10.560 whatever voltage you're getting, 00:03:10.560 --> 00:03:12.350 that tells you your first digit, 00:03:12.350 --> 00:03:13.980 that over the next time, period 00:03:13.980 --> 00:03:16.420 whatever voltage you're getting tells you the second digit, 00:03:16.420 --> 00:03:18.090 and so on and so forth. 00:03:18.090 --> 00:03:22.540 So this would be 1 1 0 0 0. 00:03:22.540 --> 00:03:24.130 Now, why is this useful? 00:03:24.130 --> 00:03:25.620 Well, let's think about the situation 00:03:25.620 --> 00:03:28.750 where all of a sudden there's interference again. 00:03:28.750 --> 00:03:30.040 Now with the interference, 00:03:30.040 --> 00:03:35.040 you could still interpret this exactly as 1 1 0 0 0. 00:03:35.190 --> 00:03:37.080 Remember the person receiving the signal 00:03:37.080 --> 00:03:38.760 or the system receiving the signal 00:03:38.760 --> 00:03:39.850 is just trying to determine 00:03:39.850 --> 00:03:41.530 whether it's getting a one or a zero. 00:03:41.530 --> 00:03:44.800 So even though this is being perturbed right over here, 00:03:44.800 --> 00:03:46.750 it's clear that we are at a one. 00:03:46.750 --> 00:03:49.750 We know that it would not be a 0.9 or 1.1. 00:03:49.750 --> 00:03:52.040 It has to be either one or zero. 00:03:52.040 --> 00:03:55.890 So it's clear that over this part right over here, 00:03:55.890 --> 00:03:57.100 you're getting a one, 00:03:57.100 --> 00:03:59.550 and then over here you're getting three zero. 00:03:59.550 --> 00:04:03.620 So they would be able to interpret it as 1 1 0 0 0, 00:04:03.620 --> 00:04:06.153 which is once again exactly 24.

Absorption and reflection

https://www.youtube.com/watch?v=6uHk1Q-Qb8k

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https://www.youtube.com/api/timedtext?v=6uHk1Q-Qb8k&ei=vlWUZeqeO5yUvdIPwMmimAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245295&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1874F7E06FD54BF61ED3E66DBBFCF9D393AD8C0E.D682FE9D1A04DEA9012C23BF74519FC77766D36C&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.270 --> 00:00:02.060 - [Instructor] I'm showing you this beautiful picture 00:00:02.060 --> 00:00:05.490 of snow-capped mountains overlooking this Alpine Lake, 00:00:05.490 --> 00:00:08.360 because there's a lot of light moving around. 00:00:08.360 --> 00:00:10.130 Now, we're gonna talk about the different ways 00:00:10.130 --> 00:00:13.890 that light can interact with different media, 00:00:13.890 --> 00:00:17.480 but what I'm talking about can generally be true of waves. 00:00:17.480 --> 00:00:19.160 But focusing on light for a second, 00:00:19.160 --> 00:00:20.420 we've already talked about how, 00:00:20.420 --> 00:00:22.130 if we go from one medium to another, 00:00:22.130 --> 00:00:24.670 if we're transmitting from one medium to another, 00:00:24.670 --> 00:00:27.590 that the light can go through a medium. 00:00:27.590 --> 00:00:30.580 And as it goes to that boundary from one medium to another, 00:00:30.580 --> 00:00:32.140 its direction can change. 00:00:32.140 --> 00:00:34.060 And we talk about that in another video, 00:00:34.060 --> 00:00:36.020 and we call that refraction. 00:00:36.020 --> 00:00:38.090 We have refraction when we enter the material, 00:00:38.090 --> 00:00:40.790 and then we have more refraction when we get out. 00:00:40.790 --> 00:00:43.700 Now, there's other things that light can also do, 00:00:43.700 --> 00:00:46.060 and that's the focus of this video, 00:00:46.060 --> 00:00:48.570 reflection and absorption. 00:00:48.570 --> 00:00:49.800 Now you probably have a sense 00:00:49.800 --> 00:00:51.550 of what happens with reflection. 00:00:51.550 --> 00:00:54.080 We can see a reflection of the mountains 00:00:54.080 --> 00:00:55.600 in the lake right over here. 00:00:55.600 --> 00:00:57.990 And the reason why we can see the reflection 00:00:57.990 --> 00:00:59.540 of the mountains and the lake here 00:00:59.540 --> 00:01:03.070 is because light that is coming from this mountain 00:01:03.070 --> 00:01:07.670 is hitting the lake and then it is bouncing off of it, 00:01:07.670 --> 00:01:11.830 and then coming to an observer's eyeball right over here, 00:01:11.830 --> 00:01:15.180 and so they see the light that's coming from here, 00:01:15.180 --> 00:01:17.180 they see it as coming from over here, 00:01:17.180 --> 00:01:18.520 because it is bounced off. 00:01:18.520 --> 00:01:22.160 And so reflection is exactly that, light is coming in, 00:01:22.160 --> 00:01:24.210 it hits that other material, 00:01:24.210 --> 00:01:27.300 and then if it bounces off, that's reflection. 00:01:27.300 --> 00:01:30.320 Now, the other thing that light can do is get absorbed. 00:01:30.320 --> 00:01:33.610 Absorbed is when the material doesn't reflect any, 00:01:33.610 --> 00:01:35.340 it doesn't transmit any through it, 00:01:35.340 --> 00:01:37.020 if it's completely absorbing. 00:01:37.020 --> 00:01:40.070 And so that would be a situation like this. 00:01:40.070 --> 00:01:41.740 Now, the reality in the real world 00:01:41.740 --> 00:01:43.830 is we have oftentimes a little bit 00:01:43.830 --> 00:01:46.170 of all of the above happening. 00:01:46.170 --> 00:01:50.800 For example, when we look at this white snow up here, 00:01:50.800 --> 00:01:52.730 this is reflecting pretty well. 00:01:52.730 --> 00:01:55.150 So there's light that's coming from the sun, 00:01:55.150 --> 00:01:57.420 or maybe it's being reflected off of the clouds, 00:01:57.420 --> 00:01:59.030 or maybe it's getting through the clouds, 00:01:59.030 --> 00:02:02.320 and when it hits that snow, it gets reflected. 00:02:02.320 --> 00:02:03.950 Now, the reason why we don't see a reflection 00:02:03.950 --> 00:02:06.370 the way that we see in this lake right over here 00:02:06.370 --> 00:02:09.370 is the snow reflects it in all different directions, 00:02:09.370 --> 00:02:11.310 but the fact that it's that bright color, in fact, 00:02:11.310 --> 00:02:13.260 you might need sunglasses to look at the snow, 00:02:13.260 --> 00:02:15.270 just as much as you need to look at the sky, 00:02:15.270 --> 00:02:18.000 is that it's reflecting most of the light. 00:02:18.000 --> 00:02:20.690 But if you go down here where we see the trees, 00:02:20.690 --> 00:02:23.070 the same light from the sky is hitting it, 00:02:23.070 --> 00:02:25.840 but not as much light is coming back to our eye, 00:02:25.840 --> 00:02:28.530 and that's because this part of the mountain, 00:02:28.530 --> 00:02:31.260 it might be trees, it might be rock, it might be dirt, 00:02:31.260 --> 00:02:34.040 is absorbing more of the light, 00:02:34.040 --> 00:02:35.330 but it's still reflecting some. 00:02:35.330 --> 00:02:36.890 We can still see it a little bit. 00:02:36.890 --> 00:02:39.860 So this might be where most of it is getting absorbed, 00:02:39.860 --> 00:02:42.610 but a little bit of the light gets reflected, 00:02:42.610 --> 00:02:44.670 which we can see right over there. 00:02:44.670 --> 00:02:46.970 And if we think about the water right over here, 00:02:46.970 --> 00:02:49.160 some of the light is probably making it through 00:02:49.160 --> 00:02:51.720 and probably refracting as it does so. 00:02:51.720 --> 00:02:53.570 Some of it is getting absorbed 00:02:53.570 --> 00:02:55.210 as it makes its way through the water. 00:02:55.210 --> 00:02:56.470 If this was a really deep lake, 00:02:56.470 --> 00:02:58.770 when you get to the bottom, it could be very, very dark. 00:02:58.770 --> 00:03:00.180 And then, as we talked about, 00:03:00.180 --> 00:03:02.000 it looks like a good bit is reflecting. 00:03:02.000 --> 00:03:03.900 When we look at the image that we see in the lake, 00:03:03.900 --> 00:03:07.290 it looks almost as bright as the real thing. 00:03:07.290 --> 00:03:10.830 So as I said, this is happening all around you. 00:03:10.830 --> 00:03:13.380 In fact, when people make fancy computer graphics, 00:03:13.380 --> 00:03:16.190 they actually try to do exactly what the light would do 00:03:16.190 --> 00:03:19.590 in the real world to make an image for your eyes 00:03:19.590 --> 00:03:21.490 that look like the real world. 00:03:21.490 --> 00:03:23.150 And they're thinking exactly about this. 00:03:23.150 --> 00:03:24.960 How much gets through the substance? 00:03:24.960 --> 00:03:27.700 How much gets reflected, and how much gets absorbed? 00:03:27.700 --> 00:03:28.820 And as I mentioned, 00:03:28.820 --> 00:03:31.030 it's not just light waves that do this. 00:03:31.030 --> 00:03:33.923 Waves in general can do all of the above.

Wave transmission

https://www.youtube.com/watch?v=3fY-DB9D6uU

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en

WEBVTT Kind: captions Language: en 00:00:00.450 --> 00:00:02.050 - [Instructor] When we're talking about waves, 00:00:02.050 --> 00:00:06.650 transmission is when a wave passes from a material 00:00:06.650 --> 00:00:08.300 into another one. 00:00:08.300 --> 00:00:11.170 For example, here we have the sun, 00:00:11.170 --> 00:00:14.580 93 million miles away on average, 00:00:14.580 --> 00:00:17.390 and imagine the different materials 00:00:17.390 --> 00:00:20.260 that the light has to travel through from the sun 00:00:20.260 --> 00:00:24.320 to, say, hit one of these sand particles right over here. 00:00:24.320 --> 00:00:27.410 Think about what it needs to be transmitted through. 00:00:27.410 --> 00:00:30.780 What's going to travel through 93 million miles 00:00:30.780 --> 00:00:32.130 of the vacuum of space, 00:00:32.130 --> 00:00:34.270 and that's one of the amazing things about light waves 00:00:34.270 --> 00:00:35.430 is that they don't need a medium. 00:00:35.430 --> 00:00:38.660 They can travel through vacuum, through emptiness, 00:00:38.660 --> 00:00:41.510 but then it's gonna travel through several miles 00:00:41.510 --> 00:00:43.230 of Earth's atmosphere. 00:00:43.230 --> 00:00:44.800 So it's going to travel through several miles 00:00:44.800 --> 00:00:45.633 of Earth's atmosphere. 00:00:45.633 --> 00:00:48.321 It will hit these, the lenses of these sunglasses, 00:00:48.321 --> 00:00:50.880 the light will travel through the lenses of the sunglass, 00:00:50.880 --> 00:00:54.280 little sunglass has some width or some depth to it, 00:00:54.280 --> 00:00:56.570 and then it'll go out onto the other side 00:00:56.570 --> 00:00:59.790 and it will hit the sand right over here. 00:00:59.790 --> 00:01:01.340 Now, one thing you might realize 00:01:01.340 --> 00:01:05.600 is the amount of transmission and what gets transmitted 00:01:05.600 --> 00:01:08.270 is dependent on the wavelengths of the wave, 00:01:08.270 --> 00:01:10.030 in this case, the wavelengths of light, 00:01:10.030 --> 00:01:13.630 and also about the material that they are going through. 00:01:13.630 --> 00:01:16.240 So for example, these sunglasses right over here, 00:01:16.240 --> 00:01:20.100 many sunglasses try to keep out UV light, ultraviolet light, 00:01:20.100 --> 00:01:22.150 which is a higher frequency than visible light, 00:01:22.150 --> 00:01:24.010 but that's what causes sunburns 00:01:24.010 --> 00:01:26.440 and that can also damage your eyes. 00:01:26.440 --> 00:01:29.670 So those high frequencies are not making it through. 00:01:29.670 --> 00:01:32.990 And we can also see that this sunglass right over here, 00:01:32.990 --> 00:01:34.850 it kind of has an orange color, 00:01:34.850 --> 00:01:36.940 which means that things that are closer 00:01:36.940 --> 00:01:38.130 to that end of the spectrum, 00:01:38.130 --> 00:01:40.390 closer to the red, the oranges, and the yellows 00:01:40.390 --> 00:01:41.310 are getting through, 00:01:41.310 --> 00:01:44.030 which means that it's filtering out blue light. 00:01:44.030 --> 00:01:47.350 So the blue light, isn't getting transmitted through as much 00:01:47.350 --> 00:01:49.370 as say the red, orange, and yellow light 00:01:49.370 --> 00:01:52.370 and that's why we see this as red, orange, or yellow. 00:01:52.370 --> 00:01:53.203 And then, of course, 00:01:53.203 --> 00:01:55.390 the light will get to that sand particle. 00:01:55.390 --> 00:01:57.010 Now transmission, as I mentioned, 00:01:57.010 --> 00:01:59.310 it isn't just about light waves. 00:01:59.310 --> 00:02:00.280 We could talk about 00:02:00.280 --> 00:02:02.010 one of our other favorite types of waves, 00:02:02.010 --> 00:02:04.060 for example, sound waves. 00:02:04.060 --> 00:02:05.880 If you are in a room, 00:02:05.880 --> 00:02:08.210 you have probably experienced the fact 00:02:08.210 --> 00:02:10.930 that even if you were to close the door, 00:02:10.930 --> 00:02:13.230 and I do this a lot because I record a lot of videos. 00:02:13.230 --> 00:02:16.320 This is me in my little closet recording a video. 00:02:16.320 --> 00:02:19.040 This is a top view for what I'm doing right now. 00:02:19.040 --> 00:02:21.840 A lot of times my kids are in other parts of the house 00:02:21.840 --> 00:02:24.650 and they're making a lot of noise. 00:02:24.650 --> 00:02:26.020 And as we've talked about, 00:02:26.020 --> 00:02:28.920 sound waves are nothing but traveling pressure waves 00:02:28.920 --> 00:02:29.753 through the air. 00:02:29.753 --> 00:02:32.200 Those air particles are knocking one into another. 00:02:32.200 --> 00:02:33.840 But in order to make it to me, 00:02:33.840 --> 00:02:35.460 they need to get through that wall, 00:02:35.460 --> 00:02:36.430 and the way they do that 00:02:36.430 --> 00:02:39.280 is they get transmitted through that wall. 00:02:39.280 --> 00:02:41.800 So those air particles make the particles 00:02:41.800 --> 00:02:43.420 or make the atoms or the molecules 00:02:43.420 --> 00:02:46.450 in the walls start vibrating, they bump into each other, 00:02:46.450 --> 00:02:49.720 and then the particles on the other side of the wall 00:02:49.720 --> 00:02:52.400 will bump into the air in my little closet, 00:02:52.400 --> 00:02:55.000 and then we will have, once again, 00:02:55.000 --> 00:02:57.020 the sound waves make it to me. 00:02:57.020 --> 00:02:59.510 Now, the overall magnitude of sound, 00:02:59.510 --> 00:03:02.050 the volume of the sound, will likely be diminished 00:03:02.050 --> 00:03:04.440 and not all of the frequencies of the sound 00:03:04.440 --> 00:03:06.030 will be transmitted equally. 00:03:06.030 --> 00:03:08.140 Different frequencies of sound waves 00:03:08.140 --> 00:03:11.000 are better at traveling through certain materials, 00:03:11.000 --> 00:03:14.010 just as we talked about with light waves. 00:03:14.010 --> 00:03:15.930 So now when you look at the world around you, 00:03:15.930 --> 00:03:17.480 or you hear the world around you, 00:03:17.480 --> 00:03:19.270 or look at other types of waves, 00:03:19.270 --> 00:03:21.210 just think about how it's transmitting 00:03:21.210 --> 00:03:23.723 from one material into another.

Refraction in a glass of water

https://www.youtube.com/watch?v=sv8-y7N0Ryw

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https://www.youtube.com/api/timedtext?v=sv8-y7N0Ryw&ei=v1WUZb7YNfGnp-oPtuyS0A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245295&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C3889C69EE6FC332C9CC154D616EE68E63919CBE.85B511D8DF9C728348469DB3BF23ABC9D978E952&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.290 --> 00:00:01.800 - [Instructor] So something very interesting 00:00:01.800 --> 00:00:04.050 is clearly going on when we look at this pencil 00:00:04.050 --> 00:00:06.000 dipped in this cup of water. 00:00:06.000 --> 00:00:10.390 We would expect if maybe there was no water in this glass 00:00:10.390 --> 00:00:13.250 that we would just see the pencil continue straight down 00:00:13.250 --> 00:00:16.740 in a line that looks something like that. 00:00:16.740 --> 00:00:19.240 But that's clearly not what we are seeing. 00:00:19.240 --> 00:00:21.340 It looks like, once we fill it with water, 00:00:21.340 --> 00:00:22.830 at least to our eye, 00:00:22.830 --> 00:00:25.760 it looks like the pencil gets bent or broken 00:00:25.760 --> 00:00:27.500 or bent in some way. 00:00:27.500 --> 00:00:28.850 And this notion, 00:00:28.850 --> 00:00:31.790 you might have heard people call it refraction. 00:00:31.790 --> 00:00:34.490 But it's interesting thing about exactly why 00:00:34.490 --> 00:00:35.780 this is happening. 00:00:35.780 --> 00:00:37.580 And I'll give you a hint. 00:00:37.580 --> 00:00:40.170 This is all about the bending of light. 00:00:40.170 --> 00:00:42.700 And it's not just light that can get bent 00:00:42.700 --> 00:00:45.490 as it goes from one medium into another. 00:00:45.490 --> 00:00:48.463 It can be any kind of wave. 00:00:48.463 --> 00:00:51.100 So let's think about what's going on over here. 00:00:51.100 --> 00:00:52.760 So first, let's think about the part of the pencil 00:00:52.760 --> 00:00:54.370 that is above the water. 00:00:54.370 --> 00:00:56.360 So this part right over here, 00:00:56.360 --> 00:00:59.710 the light is actually reflecting off of this pencil, 00:00:59.710 --> 00:01:02.120 and then it's bouncing straight into our eye. 00:01:02.120 --> 00:01:03.970 So just imagine a path from this dot 00:01:03.970 --> 00:01:05.250 straight into your eye. 00:01:05.250 --> 00:01:07.980 Once again, from here, it's going straight into your eye. 00:01:07.980 --> 00:01:11.360 When we go over here, it still doesn't look too distorted. 00:01:11.360 --> 00:01:13.750 So you have light that's going straight to your eye. 00:01:13.750 --> 00:01:15.614 It's going through the side of the glass 00:01:15.614 --> 00:01:18.553 and then getting to your eye. 00:01:18.553 --> 00:01:20.120 But then once we get under the water, 00:01:20.120 --> 00:01:21.360 something's interesting. 00:01:21.360 --> 00:01:25.430 You would expect the point that would have been here 00:01:25.430 --> 00:01:27.340 would then go straight to your eye 00:01:27.340 --> 00:01:28.980 just like everything up here. 00:01:28.980 --> 00:01:30.730 But it turns out that that light, 00:01:30.730 --> 00:01:35.020 once it transitions from going from the water to the glass 00:01:35.020 --> 00:01:37.300 and then the air, it bends. 00:01:37.300 --> 00:01:40.630 So at the interface between the media, 00:01:40.630 --> 00:01:42.080 between those different materials 00:01:42.080 --> 00:01:43.620 that the light is traveling through, 00:01:43.620 --> 00:01:44.935 instead of going towards your eye, 00:01:44.935 --> 00:01:48.470 it gets bent, in this case to our left. 00:01:48.470 --> 00:01:50.850 And so that's why when we look straight on here, 00:01:50.850 --> 00:01:53.999 we don't see anything in this region right over here. 00:01:53.999 --> 00:01:56.516 But the light that was going 00:01:56.516 --> 00:02:00.610 from the pencil towards this part of the glass, 00:02:00.610 --> 00:02:02.250 which typically you would not see, 00:02:02.250 --> 00:02:04.070 that would have typically just gone straight 00:02:04.070 --> 00:02:06.250 in that direction and not hit your eye, 00:02:06.250 --> 00:02:08.600 well, now that is getting refracted. 00:02:08.600 --> 00:02:10.330 It's getting bent to the left 00:02:10.330 --> 00:02:12.860 so that now that light hits your eye. 00:02:12.860 --> 00:02:15.990 So that's why you see what looks like a broken pencil. 00:02:15.990 --> 00:02:19.120 It's all about the light getting bent 00:02:19.120 --> 00:02:22.550 as it exits the water and goes into the glass 00:02:22.550 --> 00:02:23.923 and then the air.

Mechanical waves and light

https://www.youtube.com/watch?v=3dGiR32OxE8

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WEBVTT Kind: captions Language: en 00:00:00.550 --> 00:00:02.870 - [Instructor] Let's talk about waves. 00:00:02.870 --> 00:00:05.360 So let's imagine that you were to take a string 00:00:05.360 --> 00:00:08.150 and attach it at one end to a wall, 00:00:08.150 --> 00:00:09.390 and then on the other end, 00:00:09.390 --> 00:00:11.700 you were to wiggle it up and down. 00:00:11.700 --> 00:00:14.280 Well, then you would have made a wave. 00:00:14.280 --> 00:00:17.690 You would see a pattern that looks like this. 00:00:17.690 --> 00:00:21.010 Now, what would be a good definition for a wave? 00:00:21.010 --> 00:00:24.610 Well, we could call it a traveling disturbance. 00:00:24.610 --> 00:00:26.130 Well, what does that mean? 00:00:26.130 --> 00:00:27.750 Well, we're disturbing the rope. 00:00:27.750 --> 00:00:30.180 If we didn't move it, if we just held it straight, 00:00:30.180 --> 00:00:32.360 it might look something like that, 00:00:32.360 --> 00:00:34.350 or it might just hang down a little bit, 00:00:34.350 --> 00:00:37.700 but clearly we are now moving it up and down, 00:00:37.700 --> 00:00:40.740 and those movements are disturbing that rope 00:00:40.740 --> 00:00:44.190 and that disturbance can move along that rope. 00:00:44.190 --> 00:00:46.200 Now, we see waves not just in ropes 00:00:46.200 --> 00:00:48.020 that are moving up and down. 00:00:48.020 --> 00:00:50.590 You have probably seen water waves. 00:00:50.590 --> 00:00:52.740 If you were to take a tank of water like this 00:00:52.740 --> 00:00:55.110 and if you were to start pressing on one end 00:00:55.110 --> 00:00:56.400 of the water here, 00:00:56.400 --> 00:00:59.760 you would see these wave forms that start. 00:00:59.760 --> 00:01:03.600 We can also see that with sound and sound waves. 00:01:03.600 --> 00:01:04.760 You might not realize it, 00:01:04.760 --> 00:01:07.000 but the sound of my voice right now 00:01:07.000 --> 00:01:09.700 is actually just a traveling compression, 00:01:09.700 --> 00:01:12.270 or disturbance in the air that is getting to your ear. 00:01:12.270 --> 00:01:13.860 And that little hairs in your ears 00:01:13.860 --> 00:01:16.980 can sense those changes in pressure from the air 00:01:16.980 --> 00:01:19.820 and your mind perceives that as sound. 00:01:19.820 --> 00:01:23.010 And once again, this is a traveling disturbance. 00:01:23.010 --> 00:01:24.740 You have particles that have high pressure, 00:01:24.740 --> 00:01:26.880 and then they knock into the particles next to them, 00:01:26.880 --> 00:01:29.090 that then knock into the particles next to them. 00:01:29.090 --> 00:01:31.430 So if you were to be able to observe this in slow motion, 00:01:31.430 --> 00:01:34.230 you would see these high pressure parts right over here 00:01:34.230 --> 00:01:36.450 could be traveling, say to the right. 00:01:36.450 --> 00:01:38.440 And even though this might be a pressure wave 00:01:38.440 --> 00:01:39.950 that's traveling through the air, 00:01:39.950 --> 00:01:41.530 we can represent it in a way 00:01:41.530 --> 00:01:43.530 that looks a lot like our first rope 00:01:43.530 --> 00:01:45.490 that we were moving up and down. 00:01:45.490 --> 00:01:48.720 Areas where things are high, in the sound example, 00:01:48.720 --> 00:01:49.740 that's high pressure, 00:01:49.740 --> 00:01:51.510 and you have areas where things are low, 00:01:51.510 --> 00:01:54.110 in the sound example, that is low pressure. 00:01:54.110 --> 00:01:56.880 Now, when we talk about waves, there are common properties. 00:01:56.880 --> 00:01:58.700 For example, we might wanna know, 00:01:58.700 --> 00:02:00.500 how much are we getting disturbed 00:02:00.500 --> 00:02:02.440 from what we would call the equilibrium? 00:02:02.440 --> 00:02:03.760 You could view that as maybe 00:02:03.760 --> 00:02:05.840 the middle state right over there. 00:02:05.840 --> 00:02:08.450 Well, if we're getting disturbed that much, 00:02:08.450 --> 00:02:10.500 we could call that the amplitude. 00:02:10.500 --> 00:02:13.280 That's how much we are going above 00:02:13.280 --> 00:02:15.610 or below that equilibrium. 00:02:15.610 --> 00:02:18.370 This would be the amplitude as well. 00:02:18.370 --> 00:02:20.720 We could think about how far is it 00:02:20.720 --> 00:02:22.870 from the same points on the wave. 00:02:22.870 --> 00:02:26.010 So if we go from one peak to another peak, 00:02:26.010 --> 00:02:28.870 well, we could call that the wavelength, 00:02:28.870 --> 00:02:31.770 and you could just do it from any one point on the wave 00:02:31.770 --> 00:02:33.840 that's just like it on the wave again. 00:02:33.840 --> 00:02:35.840 So that would be the same wavelength 00:02:35.840 --> 00:02:38.240 as our original wavelength right over there. 00:02:38.240 --> 00:02:41.720 You might hear the term frequency of a wave. 00:02:41.720 --> 00:02:43.450 And one way to think about that 00:02:43.450 --> 00:02:46.470 is if you were to just observe our original rope, 00:02:46.470 --> 00:02:47.407 and if you were to say, 00:02:47.407 --> 00:02:50.770 "How many times does it go all the way up, 00:02:50.770 --> 00:02:52.970 all the way down, and then back up. 00:02:52.970 --> 00:02:54.870 so it completes a full cycle? 00:02:54.870 --> 00:02:57.190 How many times can it do that in a second? 00:02:57.190 --> 00:02:59.760 If it does that five times in second, 00:02:59.760 --> 00:03:02.220 then someone might say it has a frequency 00:03:02.220 --> 00:03:04.650 of five cycles per second. 00:03:04.650 --> 00:03:07.000 Now, everything that we have just talked about, 00:03:07.000 --> 00:03:09.400 these are called mechanical waves. 00:03:09.400 --> 00:03:10.560 It's a special category, 00:03:10.560 --> 00:03:13.200 probably the ones that you will see most often. 00:03:13.200 --> 00:03:17.100 Now, mechanical waves need a medium to travel through. 00:03:17.100 --> 00:03:19.610 In the rope example, the medium was the rope. 00:03:19.610 --> 00:03:21.440 In the water example, it's the water. 00:03:21.440 --> 00:03:24.950 In the sound example, the medium is the air. 00:03:24.950 --> 00:03:28.060 Now, there are things that can be described as waves 00:03:28.060 --> 00:03:30.200 that don't need a medium. 00:03:30.200 --> 00:03:31.280 In particular, 00:03:31.280 --> 00:03:33.300 and this is kind of mind boggling, 00:03:33.300 --> 00:03:36.460 is that light can be considered a wave. 00:03:36.460 --> 00:03:39.340 If we think about the different frequencies of light, 00:03:39.340 --> 00:03:42.970 our brain perceives that as different colors. 00:03:42.970 --> 00:03:45.830 And if we think about the amplitude of light, 00:03:45.830 --> 00:03:49.150 our brain perceives that as the intensity of light, 00:03:49.150 --> 00:03:50.300 how bright it is. 00:03:50.300 --> 00:03:51.980 And even more mindblowing, 00:03:51.980 --> 00:03:54.780 visible light are just certain frequencies 00:03:54.780 --> 00:03:57.690 of what we would call electromagnetic waves. 00:03:57.690 --> 00:04:01.270 There's actually higher frequencies of electromagnetic waves 00:04:01.270 --> 00:04:03.470 that have all sorts of applications. 00:04:03.470 --> 00:04:05.290 You might have heard of ultraviolet light, 00:04:05.290 --> 00:04:07.770 or x-rays, or gamma rays. 00:04:07.770 --> 00:04:09.900 Similarly, there's lower wavelengths of light. 00:04:09.900 --> 00:04:12.770 You might have heard things like infrared, or radio waves. 00:04:12.770 --> 00:04:14.670 These are all just different frequencies 00:04:14.670 --> 00:04:17.903 of what's known as electromagnetic waves.

Kinetic energy

https://www.youtube.com/watch?v=QFDVhfYu8HU

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WEBVTT Kind: captions Language: en 00:00:00.200 --> 00:00:01.120 - [Instructor] Hello, everyone. 00:00:01.120 --> 00:00:04.050 Let's talk about kinetic energy. 00:00:04.050 --> 00:00:06.580 Now, kinetic might be an unfamiliar word, 00:00:06.580 --> 00:00:08.170 but it just comes from a Greek word 00:00:08.170 --> 00:00:10.050 that means of motion, 00:00:10.050 --> 00:00:13.920 so kinetic energy is energy from motion. 00:00:13.920 --> 00:00:16.760 Any massive object that is in motion then 00:00:16.760 --> 00:00:20.280 has kinetic energy, but how much? 00:00:20.280 --> 00:00:23.040 First, let's consider some comparisons. 00:00:23.040 --> 00:00:26.930 This nice rat family, papa, mama, brother, and sister 00:00:26.930 --> 00:00:29.270 are sitting down to dinner at a long table 00:00:29.270 --> 00:00:31.760 passing blocks of cheese back-and-forth. 00:00:31.760 --> 00:00:33.650 Papa rat asks for the cheddar cheese 00:00:33.650 --> 00:00:36.020 and there are two identical blocks. 00:00:36.020 --> 00:00:38.950 Brother rat pushes one and sister rat pushes the other, 00:00:38.950 --> 00:00:40.930 so that the second cheese is traveling 00:00:40.930 --> 00:00:43.320 twice as fast as the first cheese. 00:00:43.320 --> 00:00:44.770 Which piece of cheddar cheese 00:00:44.770 --> 00:00:47.633 do you think has more kinetic energy? 00:00:49.090 --> 00:00:51.990 Yes, it's the one going faster. 00:00:51.990 --> 00:00:55.080 Now, papa rat doesn't need both pieces of cheddar, 00:00:55.080 --> 00:00:57.360 so he eats one and sends one back, 00:00:57.360 --> 00:00:59.410 along with this small piece of Swiss 00:00:59.410 --> 00:01:02.150 that weighs half as much as the piece of cheddar. 00:01:02.150 --> 00:01:04.490 Papa rat has better manners than his children, 00:01:04.490 --> 00:01:07.660 so he sends them both back at the same speed. 00:01:07.660 --> 00:01:09.470 Which piece of cheese would you think 00:01:09.470 --> 00:01:11.333 has more kinetic energy now? 00:01:14.020 --> 00:01:16.770 Yes, the heavier or more massive object, 00:01:16.770 --> 00:01:20.100 in this case, the cheddar, will have more kinetic energy. 00:01:20.100 --> 00:01:22.380 Let's make it a little more complicated. 00:01:22.380 --> 00:01:24.120 Brother and sister rat are full, 00:01:24.120 --> 00:01:27.040 so they send the cheeses back for mama rat. 00:01:27.040 --> 00:01:29.340 Brother rat pushes the larger piece of cheddar 00:01:29.340 --> 00:01:31.990 and sister rat pushes the smaller piece of Swiss 00:01:31.990 --> 00:01:36.210 so that the Swiss is going twice as fast as the cheddar. 00:01:36.210 --> 00:01:38.673 Now, which cheese has more kinetic energy? 00:01:40.870 --> 00:01:44.440 In fact, it turns out that it's the Swiss in this scenario. 00:01:44.440 --> 00:01:47.570 Kinetic energy depends on both mass and speed, 00:01:47.570 --> 00:01:50.800 but the dependence on speed is stronger. 00:01:50.800 --> 00:01:53.110 This estimation of kinetic energy 00:01:53.110 --> 00:01:55.290 can be quantified in an equation 00:01:55.290 --> 00:01:58.170 that lets us calculate kinetic energy exactly. 00:01:58.170 --> 00:02:00.500 We said kinetic energy depends on the mass 00:02:00.500 --> 00:02:03.740 and the speed, which we'll write as V for velocity, 00:02:03.740 --> 00:02:07.440 so we can start with K E equals M times V. 00:02:07.440 --> 00:02:10.580 But we said that it depends more on the speed, 00:02:10.580 --> 00:02:14.020 so the velocity here is actually squared. 00:02:14.020 --> 00:02:16.830 This means that if an object's mass doubles, 00:02:16.830 --> 00:02:19.420 its kinetic energy also doubles, 00:02:19.420 --> 00:02:21.280 but if its speed doubles, 00:02:21.280 --> 00:02:24.160 the kinetic energy actually quadruples. 00:02:24.160 --> 00:02:26.180 And there's also a constant factor of 1/2 00:02:26.180 --> 00:02:27.530 at the beginning of the equation, 00:02:27.530 --> 00:02:29.380 but we won't go into the details of the math 00:02:29.380 --> 00:02:30.750 of deriving this today. 00:02:30.750 --> 00:02:33.370 So, this is the equation for kinetic energy, 00:02:33.370 --> 00:02:36.290 1/2 M V squared. 00:02:36.290 --> 00:02:39.340 Let's apply this equation to our cheesy example. 00:02:39.340 --> 00:02:42.384 Say the Swiss has a mass of .05 kilograms, 00:02:42.384 --> 00:02:45.510 which makes the cheddar's mass .1 kilograms. 00:02:45.510 --> 00:02:48.240 When both cheeses have the same speed, 00:02:48.240 --> 00:02:50.060 say two meters per second, 00:02:50.060 --> 00:02:53.642 the cheddar's kinetic energy is 1/2 times .1 kilograms, 00:02:53.642 --> 00:02:57.708 times two meters per second squared, which is .2 Joules. 00:02:57.708 --> 00:03:01.829 The Swiss's kinetic energy is 1/2 times .05 kilograms 00:03:01.829 --> 00:03:05.073 times two meters per second squared, which is .1 Joules, 00:03:05.073 --> 00:03:07.550 or half the kinetic energy of the cheddar. 00:03:07.550 --> 00:03:09.697 So we can see that at the same speed, 00:03:09.697 --> 00:03:11.677 the cheddar has more kinetic energy 00:03:11.677 --> 00:03:14.177 because it has more mass. 00:03:14.177 --> 00:03:17.293 But when the Swiss has a speed of four meters per second 00:03:17.293 --> 00:03:20.030 and the cheddar still has a speed of two meters per second, 00:03:20.030 --> 00:03:24.740 the Swiss's kinetic energy is now 1/2 times .05 kilograms 00:03:24.740 --> 00:03:29.560 times four meters per second squared, which is .4 Joules. 00:03:29.560 --> 00:03:31.480 So now, the kinetic energy of the Swiss 00:03:31.480 --> 00:03:33.900 is twice the kinetic energy of the cheddar. 00:03:33.900 --> 00:03:36.730 So we can see that even though the cheddar has more mass 00:03:36.730 --> 00:03:38.510 the Swiss has more kinetic energy 00:03:38.510 --> 00:03:41.080 because it's going faster. 00:03:41.080 --> 00:03:42.660 In summary, kinetic energy 00:03:42.660 --> 00:03:45.370 is the motion energy of an object. 00:03:45.370 --> 00:03:48.740 The equation for kinetic energy is 1/2 M V squared. 00:03:48.740 --> 00:03:52.060 So as mass increases, kinetic energy increases, 00:03:52.060 --> 00:03:55.530 like the more massive cheddar versus the Swiss, 00:03:55.530 --> 00:03:57.230 and as velocity increases, 00:03:57.230 --> 00:03:59.480 kinetic energy increases even more, 00:03:59.480 --> 00:04:03.040 like the speedy Swiss versus the slower cheddar. 00:04:03.040 --> 00:04:03.873 Thanks for watching, 00:04:03.873 --> 00:04:05.983 and I hope you learned a little bit of something.

Electromagnetism

https://www.youtube.com/watch?v=E77NeY5Zmk8

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WEBVTT Kind: captions Language: en 00:00:00.130 --> 00:00:01.380 - [Instructor] You know what a magnet is, 00:00:01.380 --> 00:00:05.180 but did you know that some magnets can be turned on and off? 00:00:05.180 --> 00:00:09.200 One type of temporary magnet is called an electromagnet. 00:00:09.200 --> 00:00:12.010 So what is electromagnetism? 00:00:12.010 --> 00:00:14.750 Well, the hint is in the name itself. 00:00:14.750 --> 00:00:17.520 Electro for electrical, 00:00:17.520 --> 00:00:21.260 and magnet for, well, magnet. 00:00:21.260 --> 00:00:23.670 Let's take a moment to look at the definition 00:00:23.670 --> 00:00:25.860 of what an electromagnet is. 00:00:25.860 --> 00:00:29.630 Electromagnets are materials that become magnets 00:00:29.630 --> 00:00:31.593 in the presence of electricity. 00:00:32.460 --> 00:00:34.320 But how does that even happen? 00:00:34.320 --> 00:00:35.380 Well, it turns out 00:00:35.380 --> 00:00:38.100 that electrically-charged particles in motion 00:00:38.100 --> 00:00:41.280 actually have small magnetic fields around them. 00:00:41.280 --> 00:00:45.530 So, if we run electricity through a wire, 00:00:45.530 --> 00:00:48.303 a magnetic field will be created around the wire. 00:00:49.160 --> 00:00:52.500 Now, we can control the strength of this magnetic field 00:00:52.500 --> 00:00:54.320 in a couple of ways. 00:00:54.320 --> 00:00:57.680 We can move more electric charges through the wire 00:00:57.680 --> 00:00:58.933 at a faster rate, 00:00:59.850 --> 00:01:03.313 and we do this by increasing the electrical current. 00:01:04.720 --> 00:01:08.800 The second way is to increase the density 00:01:08.800 --> 00:01:10.223 of the charged particles, 00:01:11.740 --> 00:01:16.010 and we can do this by looping the wire into a coil. 00:01:16.010 --> 00:01:18.110 This gives us more charged particles 00:01:18.110 --> 00:01:20.810 with magnetic fields in a small space, 00:01:20.810 --> 00:01:23.210 strengthening the magnetic force. 00:01:23.210 --> 00:01:26.150 The other thing we can control with electromagnets 00:01:26.150 --> 00:01:29.790 is the direction of the magnetic field, 00:01:29.790 --> 00:01:32.370 and we can do this by changing the direction 00:01:32.370 --> 00:01:34.170 of the electricity. 00:01:34.170 --> 00:01:37.400 So if we go back to this wire example from earlier 00:01:37.400 --> 00:01:38.760 and change the direction 00:01:38.760 --> 00:01:41.370 of the electricity running through that wire, 00:01:41.370 --> 00:01:45.500 well, the magnetic fields will also change direction. 00:01:45.500 --> 00:01:48.010 This makes electromagnets quite different 00:01:48.010 --> 00:01:49.890 from permanent magnets. 00:01:49.890 --> 00:01:51.510 So let's take a look at that 00:01:51.510 --> 00:01:55.933 and compare permanent magnets to electromagnets. 00:01:58.110 --> 00:02:00.630 Electromagnets are typically made 00:02:00.630 --> 00:02:03.210 of loops of wire and a coil. 00:02:03.210 --> 00:02:06.010 The wire is typically made of metal like copper 00:02:06.010 --> 00:02:07.840 and wrapped around pieces of metal 00:02:07.840 --> 00:02:10.680 like iron, nickel, or cobalt. 00:02:10.680 --> 00:02:12.980 This is different from a permanent magnet 00:02:12.980 --> 00:02:15.603 because permanent magnets don't need this wire. 00:02:16.820 --> 00:02:19.530 Permanent magnets also have fixed poles. 00:02:19.530 --> 00:02:23.140 You can't change the north and south poles on these magnets, 00:02:23.140 --> 00:02:25.900 but as we now know, for electromagnets, 00:02:25.900 --> 00:02:28.870 we can change these poles by changing the direction 00:02:28.870 --> 00:02:30.570 of the electrical current. 00:02:30.570 --> 00:02:33.450 So, if we have an electromagnet with a north and south pole 00:02:33.450 --> 00:02:34.440 that looks like this 00:02:34.440 --> 00:02:36.890 and a current flowing in this direction, 00:02:36.890 --> 00:02:38.860 well, we can change the poles 00:02:38.860 --> 00:02:40.633 and the direction of the current. 00:02:42.110 --> 00:02:45.050 Permanent magnets have a fixed strength, 00:02:45.050 --> 00:02:46.480 but we just talked about 00:02:46.480 --> 00:02:49.270 how we can change the strength of electromagnets, 00:02:49.270 --> 00:02:52.600 so electromagnets have adjustable strength. 00:02:52.600 --> 00:02:55.900 And finally, electromagnets need a power source 00:02:55.900 --> 00:02:58.130 in order to generate the electricity required 00:02:58.130 --> 00:03:00.140 to produce magnetic fields. 00:03:00.140 --> 00:03:03.240 Permanent magnets do not need a power source, 00:03:03.240 --> 00:03:06.550 but this means that we can also turn electromagnets 00:03:06.550 --> 00:03:07.690 on and off, 00:03:07.690 --> 00:03:10.030 which is pretty cool when you think about it. 00:03:10.030 --> 00:03:10.863 On the other hand, 00:03:10.863 --> 00:03:13.650 permanent magnets are always on. 00:03:13.650 --> 00:03:15.680 Now, you might be thinking 00:03:15.680 --> 00:03:19.220 if electrical charge can affect magnetism, 00:03:19.220 --> 00:03:23.060 can magnetism affect electrical charge? 00:03:23.060 --> 00:03:26.590 Absolutely, let's look at how we can do that. 00:03:26.590 --> 00:03:30.930 The only way to do this is by changing the magnetic field 00:03:30.930 --> 00:03:32.860 around the charged particles. 00:03:32.860 --> 00:03:36.070 This can be done by moving magnets closer 00:03:36.070 --> 00:03:38.650 or further away from the particles 00:03:38.650 --> 00:03:41.520 or by spinning the magnets. 00:03:41.520 --> 00:03:45.610 In fact, spinning magnets is how most of the electricity 00:03:45.610 --> 00:03:48.380 we use in cities and homes is generated. 00:03:48.380 --> 00:03:51.260 A turbine spins a magnet inside a coil 00:03:51.260 --> 00:03:52.890 to produce electricity, 00:03:52.890 --> 00:03:55.750 and since electromagnets need a power source, 00:03:55.750 --> 00:03:58.690 this turbine is powered by wind. 00:03:58.690 --> 00:04:00.870 So you can see why electromagnetism 00:04:00.870 --> 00:04:02.840 is an incredibly important force, 00:04:02.840 --> 00:04:06.160 and this isn't the only important application of it. 00:04:06.160 --> 00:04:09.330 We use electromagnets in all sorts of other applications, 00:04:09.330 --> 00:04:13.423 from motors to speakers and even medical scanners.

Fields

https://www.youtube.com/watch?v=JmIXAN9qBUw

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https://www.youtube.com/api/timedtext?v=JmIXAN9qBUw&ei=v1WUZa-KKqOivdIPuJ-LeA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245295&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=ABE7816D0E2BB8B0C5AE0FCF703EA85B8ED8E716.10EEE91AE85943B91CEF773BEE59638CE04C9E38&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:02.890 - If you hold a ball up in the air and let it go, 00:00:02.890 --> 00:00:05.890 you know it's going to fall, but why? 00:00:05.890 --> 00:00:08.190 Nothing is touching it once you let it go. 00:00:08.190 --> 00:00:10.330 How can there be a force on it? 00:00:10.330 --> 00:00:13.170 Well, this is because Earth's gravitational force 00:00:13.170 --> 00:00:17.210 is pulling the ball and gravity is a non-contact force. 00:00:17.210 --> 00:00:19.940 Non-contact forces don't have to touch an object 00:00:19.940 --> 00:00:21.710 to exert a force on it. 00:00:21.710 --> 00:00:24.840 Instead, these forces act over a region. 00:00:24.840 --> 00:00:27.100 So if an object is in that region, 00:00:27.100 --> 00:00:29.250 it will be affected by the force. 00:00:29.250 --> 00:00:32.720 In this case, the ball is in Earth's gravitational field, 00:00:32.720 --> 00:00:35.880 and so it feels an attractive force towards the Earth 00:00:35.880 --> 00:00:37.852 and the ball falls to the ground. 00:00:37.852 --> 00:00:41.350 Field forces include non-contact forces, 00:00:41.350 --> 00:00:45.518 such as electric, magnetic, 00:00:45.518 --> 00:00:49.270 and of course, gravitational forces. 00:00:49.270 --> 00:00:51.700 So since these forces are non-contact, 00:00:51.700 --> 00:00:54.340 they can exert a force on objects they aren't touching, 00:00:54.340 --> 00:00:55.960 but how do these objects know 00:00:55.960 --> 00:00:57.950 if there's a force between them? 00:00:57.950 --> 00:01:00.380 To explain these non-contact forces, 00:01:00.380 --> 00:01:02.490 scientists eventually developed the idea 00:01:02.490 --> 00:01:04.340 that these objects were surrounded by something 00:01:04.340 --> 00:01:05.513 called a field. 00:01:06.420 --> 00:01:08.230 So what is a field? 00:01:08.230 --> 00:01:10.860 A field extends through space from an object 00:01:10.860 --> 00:01:12.720 with certain physical properties. 00:01:12.720 --> 00:01:14.330 What are those? 00:01:14.330 --> 00:01:17.150 Well, for gravitational forces, 00:01:17.150 --> 00:01:19.650 these affect objects with mass. 00:01:19.650 --> 00:01:23.241 So any object with mass has a gravitational field 00:01:23.241 --> 00:01:27.360 surrounding it that points towards the object's center. 00:01:27.360 --> 00:01:29.430 The further you move away from the object, 00:01:29.430 --> 00:01:32.900 the less dense the field and weaker the field becomes. 00:01:32.900 --> 00:01:36.080 Electric forces effect charged objects. 00:01:36.080 --> 00:01:40.470 So an electric field surrounds any object with a net charge, 00:01:40.470 --> 00:01:44.469 and the direction of this field will depend on the charge. 00:01:44.469 --> 00:01:47.510 Magnetic fields will affect magnets 00:01:47.510 --> 00:01:50.173 and any other material with magnetic properties. 00:01:51.410 --> 00:01:55.136 Each spot on a field has two things associated with it: 00:01:55.136 --> 00:01:58.700 magnitude and direction. 00:01:58.700 --> 00:01:59.890 And these help us predict 00:01:59.890 --> 00:02:02.000 what forces objects will experience 00:02:02.000 --> 00:02:03.760 when they're in the field. 00:02:03.760 --> 00:02:07.530 So let's look at an example to help understand this. 00:02:07.530 --> 00:02:09.700 Say we have a planet. 00:02:09.700 --> 00:02:12.470 Now, the planet has a lot of mass 00:02:12.470 --> 00:02:14.490 so we know it's going to be surrounded 00:02:14.490 --> 00:02:16.159 by a gravitational field 00:02:16.159 --> 00:02:19.790 that points towards the center of the planet. 00:02:19.790 --> 00:02:21.780 I can draw these little field lines 00:02:21.780 --> 00:02:25.500 that show the direction of the field and its strength. 00:02:25.500 --> 00:02:27.400 As we move away from the planet, 00:02:27.400 --> 00:02:28.890 the field will start to weaken, 00:02:28.890 --> 00:02:32.470 and I'm going to represent that by a less dense field 00:02:32.470 --> 00:02:33.930 with these arrows. 00:02:33.930 --> 00:02:35.610 Now, let's say there's an asteroid 00:02:35.610 --> 00:02:38.120 moving near the planet in this direction. 00:02:38.120 --> 00:02:41.265 I know that the asteroid, as it's shown here, 00:02:41.265 --> 00:02:45.230 is in the outskirts of this planet's gravitational field. 00:02:45.230 --> 00:02:48.490 So it is going to feel some gravitational attraction 00:02:48.490 --> 00:02:49.690 towards the planet, 00:02:49.690 --> 00:02:52.960 which we can draw with this vector, Fg, 00:02:52.960 --> 00:02:55.340 which is force of gravity. 00:02:55.340 --> 00:02:57.210 Now, because it's attracted to the planet, 00:02:57.210 --> 00:03:00.310 the astroid will continue to move towards the planet. 00:03:00.310 --> 00:03:03.070 And the closer the asteroid gets to the planet, 00:03:03.070 --> 00:03:04.014 the stronger the field 00:03:04.014 --> 00:03:07.412 and the stronger the force of attraction it will feel. 00:03:07.412 --> 00:03:11.160 And so in this way, scientists can use fields 00:03:11.160 --> 00:03:13.410 to help predict behavior of objects 00:03:13.410 --> 00:03:16.060 experiencing non-contact forces. 00:03:16.060 --> 00:03:18.180 And all of this may sound kind of odd, 00:03:18.180 --> 00:03:21.269 but you probably already think about forces this way. 00:03:21.269 --> 00:03:23.910 For example, if we go back to the ball 00:03:23.910 --> 00:03:25.700 that you know is going to fall, 00:03:25.700 --> 00:03:28.430 you knew this because the force of gravity from Earth 00:03:28.430 --> 00:03:30.960 was going to pull the ball towards the Earth. 00:03:30.960 --> 00:03:33.430 But now you also know that that's because 00:03:33.430 --> 00:03:36.400 Earth's gravity is a field force. 00:03:36.400 --> 00:03:40.550 And so the ball is in the field of gravity for Earth 00:03:40.550 --> 00:03:43.950 and experiences an attractive gravitational force. 00:03:43.950 --> 00:03:46.842 So while fields may sound mysterious, 00:03:46.842 --> 00:03:51.842 they really just mean that a force is felt over a distance. 00:03:52.060 --> 00:03:54.625 Gravitational, electric, and magnetic forces 00:03:54.625 --> 00:03:56.400 are all field forces, 00:03:56.400 --> 00:03:58.241 which means they act over distance 00:03:58.241 --> 00:04:00.753 and can affect a lot of objects.

Magnetic forces

https://www.youtube.com/watch?v=Ikto_172Vak

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https://www.youtube.com/api/timedtext?v=Ikto_172Vak&ei=v1WUZeeYMYKUhcIPspOV0Aw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245295&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B047A2C1A211E71CD0DF4E703391C9CD7FFBE717.4B06CC1A637F91B74E3D6DC1F48385C20A76ACB6&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.350 - [Instructor] Let's talk about magnets 00:00:01.350 --> 00:00:03.310 and magnetic forces. 00:00:03.310 --> 00:00:05.690 Magnets are these neat objects that are able 00:00:05.690 --> 00:00:08.100 to attract metals like iron. 00:00:08.100 --> 00:00:10.310 Magnets are used in all sorts of things, 00:00:10.310 --> 00:00:13.650 from holding paper on your refrigerator, 00:00:13.650 --> 00:00:17.180 to computers, to compasses. 00:00:17.180 --> 00:00:20.490 So magnets can be used to stick things together, 00:00:20.490 --> 00:00:23.890 point us in the right direction, and even lift things, 00:00:23.890 --> 00:00:27.360 and they do this through magnetic forces. 00:00:27.360 --> 00:00:30.930 If you've handled two magnets, you felt magnetic forces, 00:00:30.930 --> 00:00:33.670 even when the magnets weren't touching each other. 00:00:33.670 --> 00:00:37.950 That's because magnetic forces are non-contact forces, 00:00:37.950 --> 00:00:40.660 which just means they can affect other objects 00:00:40.660 --> 00:00:42.210 they aren't even touching. 00:00:42.210 --> 00:00:46.560 Magnets will attract or repel each other, 00:00:46.560 --> 00:00:51.010 and this attraction or repulsion is a magnetic force. 00:00:51.010 --> 00:00:54.680 But magnetic forces don't affect everything the same way. 00:00:54.680 --> 00:00:56.820 Otherwise, a magnet would stick to you, 00:00:56.820 --> 00:00:58.640 not just a refrigerator. 00:00:58.640 --> 00:01:01.680 In this video, we're going to talk about the magnetic forces 00:01:01.680 --> 00:01:03.313 between two magnets. 00:01:04.200 --> 00:01:06.900 So why do magnet sometimes attract each other 00:01:06.900 --> 00:01:09.610 and other times repel each other? 00:01:09.610 --> 00:01:14.470 Well, this has to do with the orientation of the magnets. 00:01:14.470 --> 00:01:17.440 Orientation is really just a fancy word 00:01:17.440 --> 00:01:21.600 for how the magnets are positioned compared to one another. 00:01:21.600 --> 00:01:24.800 You see, it turns out that each magnet has a north 00:01:24.800 --> 00:01:26.910 and south pole, 00:01:26.910 --> 00:01:30.870 but what does this have to do with attraction or repulsion? 00:01:30.870 --> 00:01:33.570 Well, as you may have heard, opposites attract. 00:01:33.570 --> 00:01:37.490 So, if you face the north pole of one magnet 00:01:37.490 --> 00:01:41.430 to the south pole of another magnet, guess what? 00:01:41.430 --> 00:01:43.900 They will be attracted to each other. 00:01:43.900 --> 00:01:46.350 But if you turn one of those magnets around 00:01:46.350 --> 00:01:49.400 so that you have two north poles facing each other, 00:01:49.400 --> 00:01:50.940 they will repel. 00:01:50.940 --> 00:01:52.080 And the same thing would happen 00:01:52.080 --> 00:01:54.610 if it was two south pulse facing each other. 00:01:54.610 --> 00:01:58.630 So the direction of the magnetic force completely depends 00:01:58.630 --> 00:02:01.150 on the orientation of the magnets. 00:02:01.150 --> 00:02:03.850 Orientation, though, is just one thing 00:02:03.850 --> 00:02:05.710 that affects magnetic forces. 00:02:05.710 --> 00:02:08.420 The strength of magnetic forces depends 00:02:08.420 --> 00:02:10.130 on a couple of things. 00:02:10.130 --> 00:02:12.093 For one, distance. 00:02:13.040 --> 00:02:14.830 If you've ever held two magnets, 00:02:14.830 --> 00:02:17.930 you may have noticed that when you move them closer, 00:02:17.930 --> 00:02:20.310 they seem to almost jump together. 00:02:20.310 --> 00:02:23.260 Or if you try to push two light poles together, 00:02:23.260 --> 00:02:25.370 they get harder and harder to hold together 00:02:25.370 --> 00:02:27.050 the closer you get. 00:02:27.050 --> 00:02:30.740 This is because magnetic forces depend on distance. 00:02:30.740 --> 00:02:32.840 The closer the two magnets are together, 00:02:32.840 --> 00:02:34.770 the stronger the force between them. 00:02:34.770 --> 00:02:39.063 So, as the distance decreases, the force increases, 00:02:39.900 --> 00:02:41.970 but the farther away they are, 00:02:41.970 --> 00:02:44.130 the weaker the magnetic force is. 00:02:44.130 --> 00:02:48.610 So, distance increases; force decreases. 00:02:48.610 --> 00:02:50.340 The other big factor that affects 00:02:50.340 --> 00:02:52.330 how strong a magnetic force is... 00:02:52.330 --> 00:02:54.610 Well, the magnets themselves. 00:02:54.610 --> 00:02:56.550 Sub magnets are really weak, 00:02:56.550 --> 00:02:58.750 like a lot of refrigerator magnets. 00:02:58.750 --> 00:03:01.560 Others are so strong that even tiny ones 00:03:01.560 --> 00:03:04.460 can be almost impossible to pull apart. 00:03:04.460 --> 00:03:07.070 Some of these stronger magnets are even used 00:03:07.070 --> 00:03:10.630 to make high-speed trains levitate off the ground. 00:03:10.630 --> 00:03:14.410 And yes, this rectangle is supposed to be a train. 00:03:14.410 --> 00:03:16.830 While my drawing isn't amazing, 00:03:16.830 --> 00:03:20.553 the fact that magnetic forces can levitate a train is.

Gravitational forces

https://www.youtube.com/watch?v=atogJ2qw9Ko

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https://www.youtube.com/api/timedtext?v=atogJ2qw9Ko&ei=wFWUZdC1CY6Kp-oP4uq48AU&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=31F5C1452EAA38415450BF6A3D4938FB5822CFA4.EB74C8908407A457E5F0155CA8231D7DBF9EA6B4&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.130 --> 00:00:02.120 - [Instructor] When you hear the word gravity, 00:00:02.120 --> 00:00:04.430 you probably just think of things falling, 00:00:04.430 --> 00:00:06.610 like an apple from a tree. 00:00:06.610 --> 00:00:08.240 But did you know it's also the reason 00:00:08.240 --> 00:00:10.910 why your lamp is staying on the floor? 00:00:10.910 --> 00:00:13.000 That's because gravity is so much more 00:00:13.000 --> 00:00:14.730 than things falling down. 00:00:14.730 --> 00:00:17.089 Gravitational forces are these invisible forces 00:00:17.089 --> 00:00:20.260 that pull objects together. 00:00:20.260 --> 00:00:22.880 So gravitational force is actually attracting 00:00:22.880 --> 00:00:25.819 the lamp to the floor and these forces exist 00:00:25.819 --> 00:00:28.470 between all objects with mass. 00:00:28.470 --> 00:00:29.771 So let's write these key points out 00:00:29.771 --> 00:00:32.630 about gravitational forces, which I'm going 00:00:32.630 --> 00:00:34.403 to use GF to represent. 00:00:35.380 --> 00:00:38.720 We said they are attractive forces, 00:00:38.720 --> 00:00:43.720 and that they exist between all objects with mass. 00:00:44.630 --> 00:00:49.630 Objects with mass, to explain this, 00:00:50.100 --> 00:00:52.810 we first need to remember a couple of things. 00:00:52.810 --> 00:00:57.000 Mass is how much matter objects have, 00:00:57.000 --> 00:01:00.590 and matter is the stuff an object is made of. 00:01:00.590 --> 00:01:03.680 Any object with mass generates a gravitational pull. 00:01:03.680 --> 00:01:05.710 So, there is a gravitational force 00:01:05.710 --> 00:01:08.720 of attraction between every object. 00:01:08.720 --> 00:01:10.390 The amount of gravitational force 00:01:10.390 --> 00:01:14.223 between two objects will depend on two things: 00:01:15.420 --> 00:01:20.203 the masses of the two objects and the distance between them. 00:01:21.470 --> 00:01:23.950 The mass of each object is proportional 00:01:23.950 --> 00:01:26.130 to the gravitational force. 00:01:26.130 --> 00:01:29.550 This means that the more mass an object has 00:01:29.550 --> 00:01:31.993 the stronger it's gravitational force. 00:01:33.010 --> 00:01:36.470 And, now, we can understand why gravity makes things fall. 00:01:36.470 --> 00:01:39.380 The Earth has massive, literally. 00:01:39.380 --> 00:01:43.400 It's almost six septillion kilograms. 00:01:43.400 --> 00:01:48.080 That's a 6 with 24 zeros after it. 00:01:48.080 --> 00:01:50.573 So, it generates a huge attractive force. 00:01:51.720 --> 00:01:55.160 For comparison, my lamp is only one kilogram, 00:01:55.160 --> 00:01:57.630 which is why if I jump, I fall towards 00:01:57.630 --> 00:01:59.613 the Earth and not towards my lamp. 00:02:00.720 --> 00:02:03.070 But we said the mass of the object 00:02:03.070 --> 00:02:04.670 is just one factor affecting 00:02:04.670 --> 00:02:07.310 the strength of its gravitational force. 00:02:07.310 --> 00:02:10.040 The other is the distance between objects. 00:02:10.040 --> 00:02:12.450 The more distance between the objects 00:02:12.450 --> 00:02:14.993 the weaker the gravitational pull between them. 00:02:16.210 --> 00:02:18.680 For small objects without much mass, 00:02:18.680 --> 00:02:21.690 it doesn't take much distance for their gravitational forces 00:02:21.690 --> 00:02:25.023 between each other to be so weak that we don't notice them. 00:02:26.210 --> 00:02:28.030 For something like the Earth, you have 00:02:28.030 --> 00:02:31.560 to go really far away to not be affected 00:02:31.560 --> 00:02:34.100 by its gravitational force of attraction. 00:02:34.100 --> 00:02:39.100 I mean, look at the moon, it's almost 240,000 miles away, 00:02:39.900 --> 00:02:43.620 that's almost 400,000 kilometers away, 00:02:43.620 --> 00:02:46.970 and it still feels effects from Earth's gravity. 00:02:46.970 --> 00:02:50.060 That's why it's orbiting us, but since the moon 00:02:50.060 --> 00:02:53.830 is also a pretty massive object, we do experience 00:02:53.830 --> 00:02:57.320 the effects of its gravitational pull on the Earth. 00:02:57.320 --> 00:03:00.740 This is why we have tides, the moon's gravitational force 00:03:00.740 --> 00:03:03.080 will pull on Earth's water, which results 00:03:03.080 --> 00:03:05.073 in us having high and low tides. 00:03:06.100 --> 00:03:08.980 Now, you might be wondering if gravity can affect the moon, 00:03:08.980 --> 00:03:12.470 or cause tides, how can we even move around? 00:03:12.470 --> 00:03:14.230 Why aren't we just face planted on the ground 00:03:14.230 --> 00:03:17.280 because Earth's gravity is pulling us towards it? 00:03:17.280 --> 00:03:21.050 It turns out that actually gravity is a pretty weak force. 00:03:21.050 --> 00:03:23.270 We only even notice its effects when an object 00:03:23.270 --> 00:03:26.000 is massive, like planets or stars, 00:03:26.000 --> 00:03:28.150 and the gravitational force on you 00:03:28.150 --> 00:03:32.420 is way weaker than most forces you exert every day. 00:03:32.420 --> 00:03:35.490 In fact, every time you pick up a glass of water, 00:03:35.490 --> 00:03:38.490 you're overpowering the entire mass of Earth. 00:03:38.490 --> 00:03:39.553 How cool is that?

Action and reaction forces

https://www.youtube.com/watch?v=Hm7B-xXJ1uM

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https://www.youtube.com/api/timedtext?v=Hm7B-xXJ1uM&ei=wFWUZd-9Fsi-mLAP58Cj4Ag&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2D1010AAD3B3D14351523630153B9A7E0C5EDC23.5B69D508A7F74193051D671BBFD178E03D9F0ED4&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.300 --> 00:00:02.160 - [Lecturer] You've probably heard the phrase that 00:00:02.160 --> 00:00:03.530 for every force, 00:00:03.530 --> 00:00:06.340 there's an equal and opposite reaction force. 00:00:06.340 --> 00:00:10.200 And this is also known as Newton's third law of motion, 00:00:10.200 --> 00:00:14.240 but it's also one of the most misunderstood laws of physics. 00:00:14.240 --> 00:00:16.330 So that's why we're going to dig into it a little bit 00:00:16.330 --> 00:00:17.930 in this video. 00:00:17.930 --> 00:00:21.700 So I have two examples here where Newton's third law 00:00:21.700 --> 00:00:24.570 or this notion of an action and a reaction force 00:00:24.570 --> 00:00:25.960 is happening. 00:00:25.960 --> 00:00:27.960 So over here, you have this plane flying 00:00:27.960 --> 00:00:30.620 and the plane is able to move forward 00:00:30.620 --> 00:00:33.960 by pushing air particles through these jet engines. 00:00:33.960 --> 00:00:36.760 So these air particles are pushed outward 00:00:36.760 --> 00:00:41.280 at a very, very high velocity out the back of the engines. 00:00:41.280 --> 00:00:43.800 If you are to enlarge one of those air particles, 00:00:43.800 --> 00:00:46.790 let's say, this is this purple dot right over here. 00:00:46.790 --> 00:00:49.530 There is a force that is being exerted on it 00:00:49.530 --> 00:00:51.080 by the jet engine. 00:00:51.080 --> 00:00:55.240 And that force is going in that direction. 00:00:55.240 --> 00:00:58.700 So what is the equal and opposite reaction force? 00:00:58.700 --> 00:01:01.100 Well, the equal and opposite reaction force 00:01:01.100 --> 00:01:04.390 is not also are occurring on that molecule. 00:01:04.390 --> 00:01:07.320 It's what the molecule is doing to the plane. 00:01:07.320 --> 00:01:09.790 The equal and opposite reaction force 00:01:09.790 --> 00:01:11.813 is that the molecule is going to be pushing 00:01:11.813 --> 00:01:16.110 on the jet engine with an equal but an opposite force. 00:01:16.110 --> 00:01:18.670 So it's going to go in the opposite direction. 00:01:18.670 --> 00:01:22.380 And that's how the jet is able to accelerate forward 00:01:22.380 --> 00:01:25.190 by pushing on these particles and accelerating them 00:01:25.190 --> 00:01:27.530 backward by exerting a force on them. 00:01:27.530 --> 00:01:30.140 The equal and opposite force is the force 00:01:30.140 --> 00:01:31.210 that the particles, 00:01:31.210 --> 00:01:33.930 those molecules of air are exerting on the jet 00:01:33.930 --> 00:01:35.810 and moving it forward. 00:01:35.810 --> 00:01:39.380 The same thing here is going on with this rocket. 00:01:39.380 --> 00:01:42.280 You have some rocket fuel in there. 00:01:42.280 --> 00:01:43.210 It gets ignited. 00:01:43.210 --> 00:01:44.360 It explodes. 00:01:44.360 --> 00:01:46.070 And as it explodes, 00:01:46.070 --> 00:01:51.070 there's a force that exerts on those little molecules 00:01:51.170 --> 00:01:55.113 and that force is going in this direction. 00:01:56.290 --> 00:01:57.400 But as it does that, 00:01:57.400 --> 00:01:59.620 there's an equal and opposite force 00:01:59.620 --> 00:02:03.360 that the molecules are exerting on the rocket. 00:02:03.360 --> 00:02:06.950 The rocket is having a force acted on it, 00:02:06.950 --> 00:02:10.010 once again, equal and opposite. 00:02:10.010 --> 00:02:12.810 So it's important to realize that the reaction force 00:02:12.810 --> 00:02:14.680 is not on the same object. 00:02:14.680 --> 00:02:16.040 It's on the other object. 00:02:16.040 --> 00:02:19.700 If one object is putting an action force on another, 00:02:19.700 --> 00:02:22.200 then the second object is putting a reaction force 00:02:22.200 --> 00:02:23.580 on the first. 00:02:23.580 --> 00:02:26.730 The forces do not cancel out. 00:02:26.730 --> 00:02:28.480 It's also important to realize that 00:02:28.480 --> 00:02:31.000 both forces are generated in pairs 00:02:31.000 --> 00:02:33.490 and happen at the exact same time. 00:02:33.490 --> 00:02:35.320 There's no delay. 00:02:35.320 --> 00:02:37.720 We can look at other examples of this. 00:02:37.720 --> 00:02:40.620 This is a scenario that I would never want to be caught in 00:02:40.620 --> 00:02:42.010 being drifting through space. 00:02:42.010 --> 00:02:44.870 Now this astronaut here has some type of a rocket pack 00:02:44.870 --> 00:02:46.030 that might help him move around. 00:02:46.030 --> 00:02:49.170 But let's say that your rocket pack ran out of fuel 00:02:49.170 --> 00:02:51.160 and you're just drifting through space. 00:02:51.160 --> 00:02:54.563 How can you get back to your spaceship? 00:02:55.440 --> 00:02:57.710 Well, if you have a wrench or something on you 00:02:57.710 --> 00:02:59.150 that you can throw, 00:02:59.150 --> 00:03:01.683 if you can take that wrench, 00:03:03.070 --> 00:03:06.400 and if you can push that wrench in that direction, 00:03:06.400 --> 00:03:09.310 and let's say your spaceship is over here to the left. 00:03:09.310 --> 00:03:11.900 Well, the equal and opposite force is the force 00:03:11.900 --> 00:03:14.880 that the wrench is going to exert on you, the astronaut, 00:03:14.880 --> 00:03:17.840 and then it will push you in that direction 00:03:17.840 --> 00:03:20.160 and accelerate you in that direction. 00:03:20.160 --> 00:03:21.230 So that's a useful thing, 00:03:21.230 --> 00:03:23.930 if you're ever get caught drifting through space. 00:03:23.930 --> 00:03:25.820 But you could do an experiment right now. 00:03:25.820 --> 00:03:28.210 Press on the table in front of you. 00:03:28.210 --> 00:03:29.630 When you press on that table, 00:03:29.630 --> 00:03:32.660 you're clearly putting a force onto that table. 00:03:32.660 --> 00:03:35.660 If your table is soft, you will see it get compressed. 00:03:35.660 --> 00:03:38.880 But notice your finger itself is also getting compressed. 00:03:38.880 --> 00:03:40.380 And the whole reason why you can even feel that 00:03:40.380 --> 00:03:42.040 is because your finger is getting compressed. 00:03:42.040 --> 00:03:43.910 And that is the equal and opposite force 00:03:43.910 --> 00:03:46.740 that the table is putting on your finger. 00:03:46.740 --> 00:03:50.570 And this can happen at very, very large distances as well. 00:03:50.570 --> 00:03:53.350 The whole reason why the Moon is in orbit around the Earth 00:03:53.350 --> 00:03:56.330 is because there's a gravitational force 00:03:56.330 --> 00:03:59.260 of Earth's mass acting on the Moon. 00:03:59.260 --> 00:04:03.610 But there's an equal and opposite force of the Moon 00:04:03.610 --> 00:04:05.987 acting on Earth. 00:04:05.987 --> 00:04:08.510 And it's actually not that the Moon is rotating 00:04:08.510 --> 00:04:09.343 around the Earth. 00:04:09.343 --> 00:04:11.280 It's actually, they're both rotating around 00:04:11.280 --> 00:04:14.000 the center of mass of their combination, 00:04:14.000 --> 00:04:16.530 that just happens to be so much closer to Earth. 00:04:16.530 --> 00:04:18.440 It's actually within Earth's volume 00:04:18.440 --> 00:04:21.920 that it looks like the Moon is rotating around the Earth. 00:04:21.920 --> 00:04:24.230 And this isn't just celestial bodies. 00:04:24.230 --> 00:04:26.460 I weigh 165 pounds. 00:04:26.460 --> 00:04:30.000 That is the force that Earth is acting on me due to gravity, 00:04:30.000 --> 00:04:33.180 but it turns out that there's an equal and opposite force 00:04:33.180 --> 00:04:38.180 of 165 pounds that I am pulling on Earth with. 00:04:38.570 --> 00:04:40.050 So I will leave you there. 00:04:40.050 --> 00:04:41.200 Look around the world. 00:04:41.200 --> 00:04:42.700 This is happening everywhere. 00:04:42.700 --> 00:04:43.950 For every force, 00:04:43.950 --> 00:04:46.470 there's an equal and opposite reaction force. 00:04:46.470 --> 00:04:47.890 But they don't cancel out 00:04:47.890 --> 00:04:50.483 because they're acting on different bodies.

Net force

https://www.youtube.com/watch?v=fwDWJZkrtUE

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https://www.youtube.com/api/timedtext?v=fwDWJZkrtUE&ei=wFWUZcf2AYmPmLAPhvCQiAg&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=081E3B6004E52B7F56EFDA509AF0D12C5BBA4E7B.0C42C1695DFB7CB54AD4EB18CFD54564CB499348&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.560 --> 00:00:02.900 - [Instructor] Let's say that we are in deep space, 00:00:02.900 --> 00:00:05.100 and there is this asteroid here, 00:00:05.100 --> 00:00:07.590 that compared to us, is stationary, 00:00:07.590 --> 00:00:10.150 or relative to us is stationary. 00:00:10.150 --> 00:00:13.480 And what we wanna do is we wanna start to move it. 00:00:13.480 --> 00:00:18.480 So what we do is we attach a rocket to one side, 00:00:20.530 --> 00:00:22.540 and then we ignite that rocket, 00:00:22.540 --> 00:00:26.920 and it starts to send all this super-heated gas, 00:00:26.920 --> 00:00:30.130 all of these particles to the right. 00:00:30.130 --> 00:00:32.450 Well, what do you think that's going to do to the asteroid? 00:00:32.450 --> 00:00:37.120 Well, it's going to push on the asteroid in that direction. 00:00:37.120 --> 00:00:39.490 Or you could say it's going to exert a force 00:00:39.490 --> 00:00:40.570 on that asteroid. 00:00:40.570 --> 00:00:42.980 And we could show that force like this, 00:00:42.980 --> 00:00:45.190 where the strength of that force, 00:00:45.190 --> 00:00:49.420 or the magnitude of the force, is the length of this line. 00:00:49.420 --> 00:00:50.460 And then the direction, 00:00:50.460 --> 00:00:53.810 I will specify or show with that arrow. 00:00:53.810 --> 00:00:57.780 So fair enough, I will be pushing towards the left. 00:00:57.780 --> 00:00:59.310 And when I push to the left, 00:00:59.310 --> 00:01:01.870 it doesn't just start to move the asteroid to the left, 00:01:01.870 --> 00:01:05.330 it actually will accelerate the asteroid to the left. 00:01:05.330 --> 00:01:07.790 So the longer that this rocket is running, 00:01:07.790 --> 00:01:10.980 it's going to make the asteroid move to the left 00:01:10.980 --> 00:01:14.020 faster and faster and faster. 00:01:14.020 --> 00:01:15.800 But let's think about another example. 00:01:15.800 --> 00:01:19.360 Let's say that you and one of your friends, 00:01:19.360 --> 00:01:21.330 you have a little bit of miscommunication, 00:01:21.330 --> 00:01:23.820 and they went and put an identical rocket 00:01:23.820 --> 00:01:26.423 on this side of the asteroid. 00:01:27.330 --> 00:01:31.120 And y'all ignited it at the exact same time. 00:01:31.120 --> 00:01:34.370 So this one is going to push in the other direction. 00:01:34.370 --> 00:01:35.480 What do you think is going to happen 00:01:35.480 --> 00:01:38.130 if these happened at the exact same time? 00:01:38.130 --> 00:01:40.230 Even though there's now twice as much force 00:01:40.230 --> 00:01:41.900 being exerted on this asteroid, 00:01:41.900 --> 00:01:45.160 it's going in opposite directions, so they zero out, 00:01:45.160 --> 00:01:47.690 and so there's zero net force. 00:01:47.690 --> 00:01:51.270 And so this asteroid won't be accelerated at all. 00:01:51.270 --> 00:01:53.150 Now let's say that a third friend 00:01:53.150 --> 00:01:55.110 wanted to correct this situation, 00:01:55.110 --> 00:01:57.870 and this isn't necessarily the most efficient way to do it, 00:01:57.870 --> 00:02:02.270 but what they do is they put another identical rocket 00:02:02.270 --> 00:02:06.173 right over here, and let's say ignite that. 00:02:07.060 --> 00:02:08.423 Now what will happen? 00:02:09.290 --> 00:02:11.600 Well, now you had the original two forces 00:02:11.600 --> 00:02:13.220 that net out to each other. 00:02:13.220 --> 00:02:15.630 But now you have this also this new force, 00:02:15.630 --> 00:02:17.880 which I will make in purple, 'cause it's a purple rocket. 00:02:17.880 --> 00:02:22.880 And so that new force, you could draw like this, 00:02:23.630 --> 00:02:26.630 to show, all right, that will now be the net force, 00:02:26.630 --> 00:02:28.550 'cause you have the equivalent of two rockets 00:02:28.550 --> 00:02:29.800 going in the left direction, 00:02:29.800 --> 00:02:32.100 and one rocket going in the right direction. 00:02:32.100 --> 00:02:34.570 Or another way we could draw that is 00:02:34.570 --> 00:02:38.270 we have two rockets going in the left direction, 00:02:38.270 --> 00:02:41.150 so that would have a force that looks like this. 00:02:41.150 --> 00:02:43.380 And then we have one going in the right direction. 00:02:43.380 --> 00:02:46.000 And so if you were to net it out, 00:02:46.000 --> 00:02:48.450 this is equivalent to just having one rocket 00:02:48.450 --> 00:02:49.930 that we originally saw. 00:02:49.930 --> 00:02:52.460 That's equivalent to just going back 00:02:52.460 --> 00:02:54.770 to what we originally saw. 00:02:54.770 --> 00:02:57.610 So the important takeaway from this video 00:02:57.610 --> 00:03:00.680 is that it's not just about the force that's being applied. 00:03:00.680 --> 00:03:02.820 If you wanna think about how something 00:03:02.820 --> 00:03:05.400 might be accelerated, and in what direction, 00:03:05.400 --> 00:03:07.160 you need to think about the net force, 00:03:07.160 --> 00:03:10.503 because some of the forces could counteract each other.

Force, mass and acceleration

https://www.youtube.com/watch?v=YBErdKxFvUA

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WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:03.022 - So I have three different asteroids over here 00:00:03.022 --> 00:00:05.500 and they have different masses. 00:00:05.500 --> 00:00:08.920 And we'll talk a lot more about what mass means. 00:00:08.920 --> 00:00:10.618 But one way to think about it is, 00:00:10.618 --> 00:00:13.800 how much stuff there is there. 00:00:13.800 --> 00:00:15.320 There's other ways to think about it. 00:00:15.320 --> 00:00:17.920 And so let's say that this first asteroid 00:00:17.920 --> 00:00:22.880 is twice the mass of either of these two smaller ones. 00:00:22.880 --> 00:00:26.040 And these two smaller ones have the same mass. 00:00:26.040 --> 00:00:28.590 Now, we've attached the back of a rocket 00:00:28.590 --> 00:00:30.310 to each of these asteroids. 00:00:30.310 --> 00:00:32.729 In fact, this one over here has two rockets, 00:00:32.729 --> 00:00:33.900 and we're going to assume 00:00:33.900 --> 00:00:35.750 that all of the rockets are equivalent 00:00:35.750 --> 00:00:37.270 and we ignite them all. 00:00:37.270 --> 00:00:42.270 And so they all exert the same force each on the asteroid. 00:00:42.810 --> 00:00:43.740 So for example, 00:00:43.740 --> 00:00:48.740 we have a net force acting leftward on this large asteroid. 00:00:49.070 --> 00:00:53.700 We have the same net force acting on this smaller asteroid, 00:00:53.700 --> 00:00:55.380 also going to the left. 00:00:55.380 --> 00:00:57.329 And on this other smaller asteroid, 00:00:57.329 --> 00:01:02.150 we have two times that net force acting to the left. 00:01:02.150 --> 00:01:04.600 So what I want you to do is pause this video 00:01:04.600 --> 00:01:07.019 and think about which of these asteroids 00:01:07.019 --> 00:01:09.320 is going to be accelerated the most, 00:01:09.320 --> 00:01:10.720 and which of these asteroids 00:01:10.720 --> 00:01:12.803 is going to be accelerated the least. 00:01:14.520 --> 00:01:15.353 All right. 00:01:15.353 --> 00:01:20.110 So you might have an intuition that the larger the force, 00:01:20.110 --> 00:01:22.630 the more acceleration you might see. 00:01:22.630 --> 00:01:24.390 So let me write it like this. 00:01:24.390 --> 00:01:27.830 So you might get a sense that if you increase your force, 00:01:27.830 --> 00:01:31.430 that that's also going to increase your acceleration. 00:01:31.430 --> 00:01:34.620 And it does turn out that that is indeed the case. 00:01:34.620 --> 00:01:37.680 Now, the other notion that you might have 00:01:37.680 --> 00:01:40.260 is that the more of the stuff that there is, 00:01:40.260 --> 00:01:42.450 the more mass that you have, 00:01:42.450 --> 00:01:45.300 the harder it is to accelerate it. 00:01:45.300 --> 00:01:48.070 So if you're mass is larger, 00:01:48.070 --> 00:01:51.150 than your acceleration is lower. 00:01:51.150 --> 00:01:54.860 And it turns out that these things are all proportional. 00:01:54.860 --> 00:01:56.620 So for example, 00:01:56.620 --> 00:02:00.350 if we just compare these two masses right over here, 00:02:00.350 --> 00:02:02.890 they have the same net force acting on it. 00:02:02.890 --> 00:02:04.370 And I keep saying net force, 00:02:04.370 --> 00:02:06.410 that means you just net out all of the forces 00:02:06.410 --> 00:02:07.900 acting in a certain dimension. 00:02:07.900 --> 00:02:10.340 For example, if I had another identical rocket 00:02:10.340 --> 00:02:12.970 acting in the opposite direction, 00:02:12.970 --> 00:02:15.390 they would net out, and this asteroid right over here 00:02:15.390 --> 00:02:17.700 wouldn't be accelerated at all. 00:02:17.700 --> 00:02:19.480 But going back to our example here, 00:02:19.480 --> 00:02:22.050 we have the same net force 00:02:22.050 --> 00:02:24.410 acting on each of these asteroids. 00:02:24.410 --> 00:02:25.580 But the first asteroid 00:02:25.580 --> 00:02:28.530 has twice the mass of the second asteroid. 00:02:28.530 --> 00:02:31.030 So how do you think the accelerations will relate? 00:02:31.930 --> 00:02:34.080 Well, as you might imagine, 00:02:34.080 --> 00:02:36.530 the acceleration on the larger asteroid 00:02:36.530 --> 00:02:39.900 is going to be half the acceleration on this asteroid. 00:02:39.900 --> 00:02:41.330 Or another way to think about it, 00:02:41.330 --> 00:02:44.562 this asteroid is going to have twice the acceleration 00:02:44.562 --> 00:02:46.780 as this first asteroid. 00:02:46.780 --> 00:02:50.340 And that's because it has half the mass. 00:02:50.340 --> 00:02:53.880 And one way you can relate force, mass, and acceleration, 00:02:53.880 --> 00:02:56.161 and this is one of the most important equations 00:02:56.161 --> 00:02:57.940 in all of physics, 00:02:57.940 --> 00:02:59.210 is that force 00:02:59.210 --> 00:03:04.210 is going to be equal to mass times acceleration, 00:03:04.820 --> 00:03:06.560 or I could say the magnitude of the force 00:03:06.560 --> 00:03:07.890 is equal to the mass 00:03:07.890 --> 00:03:10.430 times the magnitude of the acceleration. 00:03:10.430 --> 00:03:12.870 So notice, in this example right over here, 00:03:12.870 --> 00:03:16.270 our forces are the same, but the masses are different. 00:03:16.270 --> 00:03:18.900 If I have half the mass as I have over here, 00:03:18.900 --> 00:03:21.480 I'm going to have twice the acceleration. 00:03:21.480 --> 00:03:23.340 And that might make intuitive sense 00:03:23.340 --> 00:03:25.490 if you've ever tried to apply the same force 00:03:25.490 --> 00:03:27.250 to something that has a small mass 00:03:27.250 --> 00:03:29.960 versus something that has a large mass. 00:03:29.960 --> 00:03:33.900 Now, if we compare these two asteroids, 00:03:33.900 --> 00:03:36.690 they have the same mass here, 00:03:36.690 --> 00:03:38.930 but the force here, the net force, 00:03:38.930 --> 00:03:41.680 acting in that left direction, is double. 00:03:41.680 --> 00:03:44.240 So if you double the force, don't change the mass. 00:03:44.240 --> 00:03:45.922 Well, then you're going to have twice the acceleration. 00:03:45.922 --> 00:03:49.680 So this is going to have twice the acceleration of this one, 00:03:49.680 --> 00:03:50.513 and this one's 00:03:50.513 --> 00:03:52.930 going to have twice the acceleration of that one. 00:03:52.930 --> 00:03:54.215 But the important thing to realize 00:03:54.215 --> 00:03:58.403 is how force, mass, and acceleration are connected.

Frames of reference

https://www.youtube.com/watch?v=ypQPSH1qkI4

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en

WEBVTT Kind: captions Language: en 00:00:00.150 --> 00:00:02.140 - [Instructor] When we make new discoveries 00:00:02.140 --> 00:00:04.330 we need to be able to share them with others. 00:00:04.330 --> 00:00:06.570 And the first thing we have to do is make sure 00:00:06.570 --> 00:00:08.620 everyone is on the same page. 00:00:08.620 --> 00:00:12.040 We do this by using units and frames of reference, 00:00:12.040 --> 00:00:14.740 which are also called reference frames. 00:00:14.740 --> 00:00:16.930 We talk about units in another video, 00:00:16.930 --> 00:00:20.360 so let's look at what a frame of reference is. 00:00:20.360 --> 00:00:23.390 Let's say this blue box thing is a car, 00:00:23.390 --> 00:00:26.290 and it's going 45 miles per hour. 00:00:26.290 --> 00:00:28.240 Someone standing on the side of the road 00:00:28.240 --> 00:00:31.690 would see it pass at 45 miles per hour. 00:00:31.690 --> 00:00:36.690 Now, if this yellow truck is going 40 miles per hour 00:00:37.570 --> 00:00:40.070 someone sitting in the yellow truck 00:00:40.070 --> 00:00:44.540 would observe the blue traveling at five miles per hour. 00:00:44.540 --> 00:00:47.180 How could the person on the side of the road 00:00:47.180 --> 00:00:50.350 see the blue car traveling at 45 miles per hour 00:00:50.350 --> 00:00:52.004 and a person in the yellow truck 00:00:52.004 --> 00:00:55.500 see the blue car moving at five miles per hour? 00:00:55.500 --> 00:00:57.330 This is because both observers 00:00:57.330 --> 00:01:00.230 are using different frames of reference. 00:01:00.230 --> 00:01:02.010 So let's go ahead and take a look at that, 00:01:02.010 --> 00:01:04.580 starting with the speed of the blue car. 00:01:04.580 --> 00:01:06.480 The person on the side of the road 00:01:06.480 --> 00:01:09.720 is using their frame of reference of being at rest. 00:01:09.720 --> 00:01:12.710 So relative to them, the blue car is moving 00:01:12.710 --> 00:01:15.060 at 45 miles per hour. 00:01:15.060 --> 00:01:17.140 To the person in this yellow truck, 00:01:17.140 --> 00:01:20.540 which remember is already going 40 miles per hour, 00:01:20.540 --> 00:01:23.433 the blue car is going five miles per hour. 00:01:24.470 --> 00:01:26.990 Now let's do the exact same thing 00:01:26.990 --> 00:01:29.550 for the speed of the yellow truck. 00:01:29.550 --> 00:01:31.900 So what is the speed of the yellow truck 00:01:31.900 --> 00:01:34.510 for the observer on the side of the road? 00:01:34.510 --> 00:01:35.833 It's 40 miles per hour. 00:01:37.270 --> 00:01:39.520 And what do you think the speed of the truck is 00:01:39.520 --> 00:01:43.203 for the person using their blue car as the reference frame? 00:01:44.570 --> 00:01:47.890 Well, the blue car is moving at 45 miles per hour, 00:01:47.890 --> 00:01:51.900 and the truck is only moving at 40 miles per hour. 00:01:51.900 --> 00:01:54.120 So the speed of the yellow truck 00:01:54.120 --> 00:01:56.580 is actually five miles per hour slower 00:01:56.580 --> 00:01:59.340 than this reference frame, because the blue car 00:01:59.340 --> 00:02:01.583 is already moving at 45 miles per hour. 00:02:02.570 --> 00:02:05.627 Now you might be thinking, "But wait, 00:02:05.627 --> 00:02:08.897 "the person on the side of the road isn't really at rest. 00:02:08.897 --> 00:02:12.330 "They're on the earth and the earth is moving." 00:02:12.330 --> 00:02:14.400 You're completely correct. 00:02:14.400 --> 00:02:17.670 The person is at rest with respect to the earth. 00:02:17.670 --> 00:02:20.500 And the earth is the most common frame of reference 00:02:20.500 --> 00:02:22.260 that we use. 00:02:22.260 --> 00:02:26.460 To an observer in space who is not rotating with the earth, 00:02:26.460 --> 00:02:29.830 the blue car is going 45 miles per hour, 00:02:29.830 --> 00:02:33.740 plus the speed of Earth's rotation. 00:02:33.740 --> 00:02:36.510 And this is why a frame of reference is so important. 00:02:36.510 --> 00:02:38.280 We just talked about one blue car 00:02:38.280 --> 00:02:40.490 having three different velocities 00:02:40.490 --> 00:02:43.160 depending what the frame of reference is. 00:02:43.160 --> 00:02:46.290 How would we communicate this to avoid confusion? 00:02:46.290 --> 00:02:49.470 Well, we state the reference frame we're using. 00:02:49.470 --> 00:02:52.970 The blue car is moving at five miles per hour 00:02:52.970 --> 00:02:57.970 with respect to, which I'll write as WRT, the yellow truck. 00:02:58.480 --> 00:03:00.300 This tells us that the yellow truck 00:03:00.300 --> 00:03:02.230 is our frame of reference. 00:03:02.230 --> 00:03:05.290 Or we could say that the yellow truck 00:03:05.290 --> 00:03:09.080 is moving at 40 miles per hour and the blue car 00:03:09.080 --> 00:03:12.483 at 45 miles per hour, with respect to the earth. 00:03:13.390 --> 00:03:16.140 That way everyone is on the same page, 00:03:16.140 --> 00:03:20.210 a page which, to be clear, is in a book that relative to me 00:03:20.210 --> 00:03:21.043 is at rest.

Units

https://www.youtube.com/watch?v=ID-ny-NOdxg

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en

WEBVTT Kind: captions Language: en 00:00:00.310 --> 00:00:02.010 - [Illustrator] Did you know that communication 00:00:02.010 --> 00:00:05.640 is actually one of the most important things in science? 00:00:05.640 --> 00:00:07.420 As we discover cool things, 00:00:07.420 --> 00:00:09.130 we need to be able to share them with others. 00:00:09.130 --> 00:00:11.700 And when we're talking about data and measurements 00:00:11.700 --> 00:00:13.270 with other scientists, 00:00:13.270 --> 00:00:15.820 we need to make sure we're on the same page. 00:00:15.820 --> 00:00:18.120 So how do we do that? 00:00:18.120 --> 00:00:21.460 Well, one of the ways is to use units. 00:00:21.460 --> 00:00:25.750 We use units whenever we talk about things like position, 00:00:25.750 --> 00:00:30.080 where an object is located, how long it is, it's mass, 00:00:30.080 --> 00:00:33.800 how much matter it's made up of or it's motion. 00:00:33.800 --> 00:00:35.173 How is that object moving? 00:00:36.300 --> 00:00:38.713 You probably hear units every day. 00:00:40.040 --> 00:00:42.290 For example, you've grown, 00:00:42.290 --> 00:00:45.410 let's say an inch and a half in the past year, 00:00:45.410 --> 00:00:50.410 or that tree over there is 25 feet tall. 00:00:51.040 --> 00:00:55.480 And maybe you went swimming in a 25 meter pool. 00:00:55.480 --> 00:00:59.190 And we're just gonna pretend that the pool is a rectangle 00:00:59.190 --> 00:01:01.480 because as you can tell from my tree, 00:01:01.480 --> 00:01:03.463 my artistic skills are not that great. 00:01:04.340 --> 00:01:07.410 Anyway, this brings up a super important point 00:01:07.410 --> 00:01:09.510 about why we use units. 00:01:09.510 --> 00:01:12.650 I just used three examples of length measurements 00:01:12.650 --> 00:01:17.650 with three different units, inches, feet, and meters. 00:01:17.780 --> 00:01:19.720 Imagine if I didn't attach a unit 00:01:19.720 --> 00:01:21.250 to any of these measurements, 00:01:21.250 --> 00:01:25.320 you grew one and a half, what? Meters? 00:01:25.320 --> 00:01:29.010 Whoa, one and a half hands. 00:01:29.010 --> 00:01:31.670 Well, whose hands? 00:01:31.670 --> 00:01:36.010 Your hands or my hands? 00:01:36.010 --> 00:01:39.420 Woof, well, pretend those are hands. 00:01:39.420 --> 00:01:44.010 Units let us know how much of a quantity there is. 00:01:44.010 --> 00:01:47.620 So a meter is always used to measure length 00:01:47.620 --> 00:01:50.580 and we know exactly how long a meter is. 00:01:50.580 --> 00:01:53.750 That way when we say something is two meters long, 00:01:53.750 --> 00:01:56.760 no one has to guess at how big that is. 00:01:56.760 --> 00:02:00.030 Any measurement or data point always needs to have a unit 00:02:00.030 --> 00:02:02.170 or else it's just a meaningless number. 00:02:02.170 --> 00:02:04.080 To avoid any confusion, 00:02:04.080 --> 00:02:07.890 in science we use what are called SI units. 00:02:07.890 --> 00:02:11.720 SI units are the International System. 00:02:11.720 --> 00:02:16.070 Could there be any more letters in this word system 00:02:16.070 --> 00:02:19.530 used by scientists all over the world. 00:02:19.530 --> 00:02:23.620 We'll use meters to describe position or length, 00:02:23.620 --> 00:02:25.780 kilograms for mass, 00:02:25.780 --> 00:02:28.630 and if we're talking about the motion of something, 00:02:28.630 --> 00:02:29.683 meters per second. 00:02:30.990 --> 00:02:35.260 And while this is the agreed upon scientific unit system, 00:02:35.260 --> 00:02:39.470 you should be aware that other systems do exist, 00:02:39.470 --> 00:02:43.060 which means things can very easily get very confusing 00:02:43.060 --> 00:02:44.960 if you forget your units. 00:02:44.960 --> 00:02:46.107 And you might be thinking, 00:02:46.107 --> 00:02:49.690 "Oh, come on, who mixes up units?' 00:02:49.690 --> 00:02:52.910 Well, it happens more often than you think, 00:02:52.910 --> 00:02:55.500 even rocket scientists have done it. 00:02:55.500 --> 00:02:58.430 I mean, a Mars Orbiter actually crashed 00:02:58.430 --> 00:03:00.830 due to a mix up in units. 00:03:00.830 --> 00:03:03.410 Now seriously, that actually happened, 00:03:03.410 --> 00:03:07.933 look it up and remember to use your units.

Meaning of absolute value

https://www.youtube.com/watch?v=zpln5ExhkyI

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https://www.youtube.com/api/timedtext?v=zpln5ExhkyI&ei=wFWUZbTRDPu5vdIPkuqDsAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C31249FBA98CADD0AB1B3D74318BBC4EBBF069B7.71499D72F7F4DAD772A2ABC704A2FCB616358DED&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.300 --> 00:00:01.133 - [Instructor] In this video, 00:00:01.133 --> 00:00:02.190 we're going to introduce ourselves 00:00:02.190 --> 00:00:04.230 to the idea of absolute value, 00:00:04.230 --> 00:00:09.100 which you can view as, how far are you from zero? 00:00:09.100 --> 00:00:10.970 So for example, 00:00:10.970 --> 00:00:14.270 let's say that we have a bunch of people living on a street. 00:00:14.270 --> 00:00:19.270 And let's say that we say that the school is at zero, 00:00:19.320 --> 00:00:22.030 and we could think about other people live. 00:00:22.030 --> 00:00:25.000 So let's say I live three miles 00:00:25.000 --> 00:00:27.920 to the right of the school, maybe that's east. 00:00:27.920 --> 00:00:30.600 So this is where I live. 00:00:30.600 --> 00:00:33.190 So that's me right over here. 00:00:33.190 --> 00:00:37.800 And that you live three miles to the left of the school. 00:00:37.800 --> 00:00:41.237 So this is where you would be, three miles to the left. 00:00:41.237 --> 00:00:44.370 Or maybe we could say that's to the west of the school. 00:00:44.370 --> 00:00:46.660 Now you could say that your position 00:00:46.660 --> 00:00:50.270 is at negative three miles relative to the school. 00:00:50.270 --> 00:00:52.810 And my position is at positive three miles 00:00:52.810 --> 00:00:54.290 relative to the school. 00:00:54.290 --> 00:00:55.680 But what we might care about 00:00:55.680 --> 00:00:58.770 is just how far are we from the school? 00:00:58.770 --> 00:01:00.060 And so there, you could say, 00:01:00.060 --> 00:01:03.760 well, we're each exactly three miles from the school. 00:01:03.760 --> 00:01:05.800 You're three miles from the school, 00:01:05.800 --> 00:01:08.520 and I am three miles from the school. 00:01:08.520 --> 00:01:12.460 And that's what absolute value is actually trying to get at. 00:01:12.460 --> 00:01:16.840 So for example, your position is negative three, 00:01:16.840 --> 00:01:19.730 but if we were to take the absolute value, 00:01:19.730 --> 00:01:23.730 which you denote by these two straight up down bars 00:01:23.730 --> 00:01:25.490 around the number, then we say, 00:01:25.490 --> 00:01:28.380 that's just going to be your distance from zero, 00:01:28.380 --> 00:01:31.100 which is just going to be three miles. 00:01:31.100 --> 00:01:31.933 Similarly, 00:01:33.360 --> 00:01:36.890 my position is at three miles, positive three miles. 00:01:36.890 --> 00:01:39.290 The absolute value of that is going to be, 00:01:39.290 --> 00:01:40.910 drum roll, please. 00:01:40.910 --> 00:01:43.500 It is going to be three as well. 00:01:43.500 --> 00:01:45.020 You might already see a pattern. 00:01:45.020 --> 00:01:47.530 If you're taking an absolute value of a negative number, 00:01:47.530 --> 00:01:49.950 you get the number without the negative. 00:01:49.950 --> 00:01:51.970 And if you take the absolute value of a positive number, 00:01:51.970 --> 00:01:54.260 it just equals itself again. 00:01:54.260 --> 00:01:56.990 But the reason why that is the case 00:01:56.990 --> 00:01:58.000 is because we're just saying, 00:01:58.000 --> 00:02:01.370 how far is that thing from zero? 00:02:01.370 --> 00:02:03.430 Let me give you another example. 00:02:03.430 --> 00:02:08.430 Let's say that we have some type of a cruise ship, 00:02:09.020 --> 00:02:11.550 and that's the water right over there. 00:02:11.550 --> 00:02:14.590 This is the cruise ship. 00:02:14.590 --> 00:02:16.000 Let me draw it. 00:02:16.000 --> 00:02:18.880 It's this big cruise ship, nice and big one, 00:02:18.880 --> 00:02:20.790 has water slides on it, and whatever else, 00:02:20.790 --> 00:02:23.060 whatever you would expect from a huge cruise ship. 00:02:23.060 --> 00:02:25.970 And let say, we think about the height 00:02:25.970 --> 00:02:28.020 of where the different floors are in the ship. 00:02:28.020 --> 00:02:29.680 And a natural place to think about 00:02:29.680 --> 00:02:32.890 is based on where the sea level is. 00:02:32.890 --> 00:02:35.770 So we call that height zero. 00:02:35.770 --> 00:02:40.770 Now there's this big waterfall pool type thing up here. 00:02:40.900 --> 00:02:44.250 Let's just say, it's a pool for simplicity, on the roof. 00:02:44.250 --> 00:02:49.250 And let's say that that is at an altitude of 80 feet. 00:02:49.610 --> 00:02:53.620 So we would call that at positive 80 feet. 00:02:53.620 --> 00:02:56.880 And let's say the engine room is right over here. 00:02:56.880 --> 00:02:58.550 And if you wanted to know its position, 00:02:58.550 --> 00:03:02.040 its height, well, it is going to be below zero, 00:03:02.040 --> 00:03:06.443 it's below sea level, let's say it's at negative 20 feet. 00:03:07.290 --> 00:03:09.340 So that would give you its position. 00:03:09.340 --> 00:03:11.960 One is 80 feet above the sea level, 00:03:11.960 --> 00:03:14.600 and then one is 20 feet below the sea level. 00:03:14.600 --> 00:03:17.260 But if you just wanted to know how far they are, 00:03:17.260 --> 00:03:18.930 well, you could take the absolute value. 00:03:18.930 --> 00:03:21.720 How far is that roof deck pool? 00:03:21.720 --> 00:03:24.040 Well, you take the absolute value of 80. 00:03:24.040 --> 00:03:26.610 You are going to get 80. 00:03:26.610 --> 00:03:30.650 How far is that engine room from zero? 00:03:30.650 --> 00:03:33.030 How far is it from sea level? 00:03:33.030 --> 00:03:36.773 Well, the absolute value of negative 20 is going to be 20.

Compare rational numbers using a number line

https://www.youtube.com/watch?v=6h0Wi8Dcd0E

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https://www.youtube.com/api/timedtext?v=6h0Wi8Dcd0E&ei=wFWUZavVGoudhcIPh-amwAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8EDDB4C319AA09AEFBE94935073A3ED07C8C9A9F.D9B2E3C97107563C7B6ED2F9D8F31574D4291255&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.300 --> 00:00:01.690 - [Sal] What we're gonna do in this video 00:00:01.690 --> 00:00:04.040 is get some practice comparing numbers, 00:00:04.040 --> 00:00:07.640 especially positive and negative numbers. 00:00:07.640 --> 00:00:10.250 So for each of these pairs of numbers, 00:00:10.250 --> 00:00:13.330 I want you to either write a less than sign 00:00:13.330 --> 00:00:14.760 or a greater than sign, 00:00:14.760 --> 00:00:16.580 or just think about which of these two 00:00:16.580 --> 00:00:18.880 is greater than the other. 00:00:18.880 --> 00:00:20.440 Pause this video and see if you can work 00:00:20.440 --> 00:00:22.003 through these four pairs. 00:00:22.920 --> 00:00:26.200 All right, now let's do it together. 00:00:26.200 --> 00:00:30.110 So let's first compare -7/4 to -3/4. 00:00:30.110 --> 00:00:31.450 And I'm going to try to do that 00:00:31.450 --> 00:00:34.890 by visualizing them on a number line. 00:00:34.890 --> 00:00:37.390 So let me draw a straighter line. 00:00:37.390 --> 00:00:38.950 There we go. 00:00:38.950 --> 00:00:40.530 Let's see, they're both negative, 00:00:40.530 --> 00:00:42.310 which means both to the left of zero. 00:00:42.310 --> 00:00:44.270 So I'll focus on the left of zero. 00:00:44.270 --> 00:00:46.640 So that's zero. 00:00:46.640 --> 00:00:47.473 And let's see, 00:00:47.473 --> 00:00:48.630 they're both given in fourths 00:00:48.630 --> 00:00:51.260 and we need to go all the way to 7/4, 00:00:51.260 --> 00:00:52.340 less than zero. 00:00:52.340 --> 00:00:54.970 So let me think of each of these as a fourth. 00:00:54.970 --> 00:00:58.920 So one, two, three, four. 00:00:58.920 --> 00:01:01.010 That would be -1. 00:01:01.010 --> 00:01:05.020 One, two, three, four. 00:01:05.020 --> 00:01:07.200 That would be -2 and that's enough for us, 00:01:07.200 --> 00:01:09.170 but I could keep going if I liked. 00:01:09.170 --> 00:01:13.790 Now, where is -7/4 on this number line? 00:01:13.790 --> 00:01:15.670 Well, I just said each of these is a fourth, 00:01:15.670 --> 00:01:19.590 so negative 1/4, 2/4, 3/4, 00:01:19.590 --> 00:01:23.700 4/4, 5/4, 6/4, 7/4. 00:01:23.700 --> 00:01:26.023 So this right over here is -7/4. 00:01:28.720 --> 00:01:32.082 And where is negative -3/4 on the number line? 00:01:32.082 --> 00:01:36.373 - 1/4, -2/4, -3/4. 00:01:37.850 --> 00:01:39.670 So which one is greater? 00:01:39.670 --> 00:01:42.240 Well, we can see that -3/4 00:01:42.240 --> 00:01:46.580 is to the right of -7/4. 00:01:46.580 --> 00:01:51.580 So -3/4 is greater or that -7/4 is less than -3/4. 00:01:53.010 --> 00:01:55.700 So I'll put a less than right over here. 00:01:55.700 --> 00:01:57.110 Let's do this next example. 00:01:57.110 --> 00:01:58.860 We're going to compare 0.6 to -1.8. 00:02:00.524 --> 00:02:02.270 If you haven't already given it a shot 00:02:02.270 --> 00:02:05.120 or if this previous example helped inspire something 00:02:05.120 --> 00:02:06.430 and you give it another shot, 00:02:06.430 --> 00:02:08.640 and then we'll do it together. 00:02:08.640 --> 00:02:11.493 So let's draw a number line again. 00:02:12.480 --> 00:02:17.480 And let me put zero right over here. 00:02:18.950 --> 00:02:20.620 That's 1. 00:02:20.620 --> 00:02:22.340 That's 2. 00:02:22.340 --> 00:02:24.700 This is -1. 00:02:24.700 --> 00:02:27.000 This is -2. 00:02:27.000 --> 00:02:29.500 And actually let me make half marks here, 00:02:29.500 --> 00:02:32.140 so we can get a little bit closer to thinking 00:02:32.140 --> 00:02:35.440 about where these two numbers sit on the number line. 00:02:35.440 --> 00:02:37.233 I'll start with 0.6. 00:02:38.440 --> 00:02:41.460 0.6 is you could view that as 6/10. 00:02:41.460 --> 00:02:42.990 It's a little bit more than 5/10. 00:02:42.990 --> 00:02:44.520 It's a little bit more than 1/2. 00:02:44.520 --> 00:02:47.220 So 0.6 is gonna be roughly right around here 00:02:47.220 --> 00:02:49.053 on our number line, 0.6. 00:02:50.230 --> 00:02:51.193 And where is -1.8? 00:02:53.230 --> 00:02:54.100 Well, it's negative. 00:02:54.100 --> 00:02:56.030 So it's going to be to the left of zero, 00:02:56.030 --> 00:02:58.220 and we're gonna go 1.8 to the left. 00:02:58.220 --> 00:02:59.950 So this is -1. 00:02:59.950 --> 00:03:02.090 This is -2, that's too far. 00:03:02.090 --> 00:03:03.660 This is -1.5. 00:03:03.660 --> 00:03:07.230 - 1.8 is going to be roughly, 00:03:07.230 --> 00:03:09.460 let me do this in this color, right over here. 00:03:09.460 --> 00:03:12.063 It's going to be roughly right over there, -1.8. 00:03:13.600 --> 00:03:16.173 And so you can see that it is left of 0.6 00:03:17.401 --> 00:03:18.742 on our number line. 00:03:18.742 --> 00:03:21.667 And so -1.8 is less than 0.6, 00:03:21.667 --> 00:03:24.000 or 0.6 is greater than -1.8. 00:03:26.900 --> 00:03:28.280 Let's do more examples here. 00:03:28.280 --> 00:03:30.670 Let's compare these two numbers. 00:03:30.670 --> 00:03:31.503 Well, once again, 00:03:31.503 --> 00:03:33.070 let me put them on a number line. 00:03:33.070 --> 00:03:34.300 And I wanna show you that the number line 00:03:34.300 --> 00:03:35.390 does not have to go left-right. 00:03:35.390 --> 00:03:37.260 It could go up-down. 00:03:37.260 --> 00:03:38.780 So let's try that. 00:03:38.780 --> 00:03:40.700 And I'll do it in a different color. 00:03:40.700 --> 00:03:44.480 So I'll make a line like this. 00:03:44.480 --> 00:03:48.160 And I am going to have, 00:03:48.160 --> 00:03:52.200 let's call this zero right over here. 00:03:52.200 --> 00:03:53.820 And so this is 1. 00:03:53.820 --> 00:03:55.990 This is 2. 00:03:55.990 --> 00:03:58.570 This is -1. 00:03:58.570 --> 00:04:01.600 This is -2. 00:04:01.600 --> 00:04:05.430 Now, where is 2 1/5 on the number line? 00:04:05.430 --> 00:04:08.980 So that is positive 1, positive 2. 00:04:08.980 --> 00:04:11.020 And then we're going to go about a fifth. 00:04:11.020 --> 00:04:14.710 So that'll get us roughly right over there. 00:04:14.710 --> 00:04:18.790 And then where is -1 1/10? 00:04:18.790 --> 00:04:21.875 Well, we're not gonna go below zero, so -1. 00:04:21.875 --> 00:04:25.270 And we're gonna go another 1/10 beyond that below zero. 00:04:25.270 --> 00:04:28.030 So it's gonna be roughly around there. 00:04:28.030 --> 00:04:31.070 So that is -1 1/10. 00:04:31.070 --> 00:04:36.070 And so we can see that -1 1/10 is less than positive 2 1/5, 00:04:36.830 --> 00:04:41.830 or positive 2 1/5 is greater than -1 1/10. 00:04:42.880 --> 00:04:46.850 Let's do one last example, comparing these two numbers here. 00:04:46.850 --> 00:04:51.160 And actually, I can extend this number line right over here, 00:04:51.160 --> 00:04:54.410 and I should be able to fit both of these numbers. 00:04:54.410 --> 00:04:56.050 So let me try to do that. 00:04:56.050 --> 00:04:57.920 So I'm going to extend it. 00:04:57.920 --> 00:05:01.490 This is -3 right over here. 00:05:01.490 --> 00:05:03.167 So where would -1.5 sit? 00:05:04.700 --> 00:05:07.554 Well, we're going below zero so that's a -1. 00:05:07.554 --> 00:05:09.920 - 1.5 would be another half, 00:05:09.920 --> 00:05:11.999 it'd be right in between -1 and -2. 00:05:11.999 --> 00:05:16.600 So -1.5 is right over there. 00:05:16.600 --> 00:05:19.230 And where would -2.5 be? 00:05:19.230 --> 00:05:22.860 Well, we go -1, -2, and then another half. 00:05:22.860 --> 00:05:25.073 So this right over here is -2.5. 00:05:27.650 --> 00:05:29.630 And we could see very clearly that -1.5 00:05:31.210 --> 00:05:32.800 is higher than -2.5, 00:05:34.010 --> 00:05:37.260 so it is also greater. 00:05:37.260 --> 00:05:38.173 And we're done.

Introduction to negative numbers

https://www.youtube.com/watch?v=u8UKdNdpkh4

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https://www.youtube.com/api/timedtext?v=u8UKdNdpkh4&ei=wFWUZfjTFYmYvdIPk4G6aA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5934A974EBA6C569483A4423DE11F9C225EBFDDA.9AC6660310D25739D1F272B0BAAE7B6E01D72812&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.860 --> 00:00:03.150 - [Instructor] In this video, we're gonna introduce ourself 00:00:03.150 --> 00:00:06.560 to the idea of negative numbers. 00:00:06.560 --> 00:00:10.210 Now you're already used to the idea of positive numbers. 00:00:10.210 --> 00:00:13.280 You just call them numbers, not positive (chuckles) numbers. 00:00:13.280 --> 00:00:14.810 And just to give you an example, 00:00:14.810 --> 00:00:16.620 I will draw a number line here. 00:00:16.620 --> 00:00:19.550 And this should all be review for you, 00:00:19.550 --> 00:00:23.160 so let me start at zero, 00:00:23.160 --> 00:00:25.760 and then this would be one. 00:00:25.760 --> 00:00:27.510 This would be two. 00:00:27.510 --> 00:00:29.490 This would be three. 00:00:29.490 --> 00:00:32.530 And you can think of these numbers, which you're used to, 00:00:32.530 --> 00:00:34.650 which we could call positive numbers, 00:00:34.650 --> 00:00:37.460 as how far we are above zero. 00:00:37.460 --> 00:00:41.650 One is one above zero. Two is two above zero. 00:00:41.650 --> 00:00:43.920 Now what do you think negative numbers are going to be? 00:00:43.920 --> 00:00:47.970 If positive numbers are how far we are above zero, 00:00:47.970 --> 00:00:52.250 then a negative number would be how far are we below zero. 00:00:52.250 --> 00:00:56.460 So for example, if I go one to the left on this number line, 00:00:56.460 --> 00:00:59.240 that would now get us to negative one. 00:00:59.240 --> 00:01:01.320 Positive one is one to the right. 00:01:01.320 --> 00:01:03.610 Negative one is one to the left. 00:01:03.610 --> 00:01:05.930 If I were to go another one to the left, 00:01:05.930 --> 00:01:09.920 I would get to negative two, and I could keep going. 00:01:09.920 --> 00:01:12.030 As many positive numbers there are, 00:01:12.030 --> 00:01:14.040 I can have the negative version of it. 00:01:14.040 --> 00:01:15.620 However far I am to the right, 00:01:15.620 --> 00:01:18.770 I could be that far to the left. 00:01:18.770 --> 00:01:19.730 Now some of you, 00:01:19.730 --> 00:01:22.550 especially if you live in very cold parts of the world, 00:01:22.550 --> 00:01:24.970 might have already experienced negative numbers 00:01:24.970 --> 00:01:26.420 in some way. 00:01:26.420 --> 00:01:29.930 For example, if you look at a thermometer, 00:01:29.930 --> 00:01:33.400 this has both a Celsius thermometer, right over here, 00:01:33.400 --> 00:01:34.870 and Fahrenheit. 00:01:34.870 --> 00:01:37.970 We know that you can get temperatures 00:01:37.970 --> 00:01:41.050 below zero degrees Celsius 00:01:41.050 --> 00:01:43.810 and temperatures below zero degrees Fahrenheit. 00:01:43.810 --> 00:01:46.140 On this thermometer, they just mark 00:01:46.140 --> 00:01:49.340 how far we are below zero with these red numbers, 00:01:49.340 --> 00:01:51.490 but really these are negative numbers. 00:01:51.490 --> 00:01:53.650 And we specify negative numbers 00:01:53.650 --> 00:01:57.700 by putting that negative sign right in front of it 00:01:57.700 --> 00:01:59.070 like that. 00:01:59.070 --> 00:02:02.300 So for example, 20 degrees Celsius 00:02:02.300 --> 00:02:04.640 is positive of 20 degrees Celsius 00:02:04.640 --> 00:02:07.640 is actually a pretty comfortable temperature, 00:02:07.640 --> 00:02:11.890 but negative 20 degrees Celsius, that is below, 00:02:11.890 --> 00:02:15.350 20 degrees Celsius below the freezing point of water, 00:02:15.350 --> 00:02:19.430 that is a very, very, very, very cold temperature. 00:02:19.430 --> 00:02:21.840 One is 20 degrees above zero. 00:02:21.840 --> 00:02:25.650 One is 20 degrees below zero. 00:02:25.650 --> 00:02:28.440 So a big picture, for any given number, 00:02:28.440 --> 00:02:30.030 there's a negative version of it. 00:02:30.030 --> 00:02:33.080 For example, this right over here would be positive six, 00:02:33.080 --> 00:02:35.700 and then you could have negative six. 00:02:35.700 --> 00:02:38.900 But negative six is six below zero 00:02:38.900 --> 00:02:42.060 or six left of the zero on the number line, 00:02:42.060 --> 00:02:46.240 while positive six is, of course, six above zero. 00:02:46.240 --> 00:02:48.540 So I will leave you there. 00:02:48.540 --> 00:02:49.373 You might be thinking, 00:02:49.373 --> 00:02:52.090 "Oh wow, this looks a lot like a subtraction sign. 00:02:52.090 --> 00:02:54.360 Maybe it is related to subtraction somehow." 00:02:54.360 --> 00:02:57.200 Or "How can I do addition and subtraction, 00:02:57.200 --> 00:02:59.750 multiplication and division with negative numbers?" 00:02:59.750 --> 00:03:03.083 And for that we will go to future videos.

Seasons

https://www.youtube.com/watch?v=0r9Lc7oYq5M

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https://www.youtube.com/api/timedtext?v=0r9Lc7oYq5M&ei=wFWUZdfGGKa9mLAP6MiQ0AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EC0AC31D76977C51D9908503580450839DF62929.73A1AA2FB57E2F48C0403CA900AEB1CDB36D6FE5&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.260 --> 00:00:01.850 - [Instructor] In this video, we're gonna think about 00:00:01.850 --> 00:00:04.230 why we have seasons on Earth, 00:00:04.230 --> 00:00:08.340 like summer and fall and winter and spring. 00:00:08.340 --> 00:00:10.530 Now, one theory that some folks might have 00:00:10.530 --> 00:00:12.150 is maybe it's due to the distance 00:00:12.150 --> 00:00:13.550 between the Earth and the sun. 00:00:13.550 --> 00:00:16.210 We know that the Earth orbits the sun, 00:00:16.210 --> 00:00:19.170 the sun is where the great majority of the heat 00:00:19.170 --> 00:00:22.100 and the energy on the surface of the Earth comes from. 00:00:22.100 --> 00:00:23.670 And maybe it's the case 00:00:23.670 --> 00:00:25.630 that there's certain times of year 00:00:25.630 --> 00:00:27.580 when we are further from the sun, 00:00:27.580 --> 00:00:29.320 and there's other times of year 00:00:29.320 --> 00:00:32.490 when we are closer to the sun. 00:00:32.490 --> 00:00:36.050 Well, this doesn't actually hold up to why we have seasons 00:00:36.050 --> 00:00:38.840 because first of all, when the Northern Hemisphere 00:00:38.840 --> 00:00:41.060 the top half of Earth has winter, 00:00:41.060 --> 00:00:44.090 the bottom hemisphere has summer and vice versa. 00:00:44.090 --> 00:00:46.820 So it can't just be due to the distance of the whole planet, 00:00:46.820 --> 00:00:48.270 it also turns out 00:00:48.270 --> 00:00:53.200 that when Earth is furthest from the sun is in July, 00:00:53.200 --> 00:00:55.710 which is in the middle of summer 00:00:55.710 --> 00:00:57.600 in the Northern Hemisphere, 00:00:57.600 --> 00:00:59.580 and when we are closest to the sun 00:00:59.580 --> 00:01:01.660 is actually in January 00:01:01.660 --> 00:01:04.540 which we know tends to be our colder season 00:01:04.540 --> 00:01:06.040 in the Northern Hemisphere. 00:01:06.040 --> 00:01:08.780 So distance to the sun does not hold up 00:01:08.780 --> 00:01:11.200 as to why we have seasons. 00:01:11.200 --> 00:01:14.030 The real reason why we have seasons 00:01:14.030 --> 00:01:16.840 is because of Earth's axial tilt, 00:01:16.840 --> 00:01:19.500 I guess you could say that or it's rotational tilt. 00:01:19.500 --> 00:01:21.630 Now this picture shows that tilt 00:01:21.630 --> 00:01:23.940 but before we go into it, I'd like to remind folks 00:01:23.940 --> 00:01:27.030 that this is nowhere near drawn at scale. 00:01:27.030 --> 00:01:30.800 The actual sun has a diameter over 100 times out of Earth, 00:01:30.800 --> 00:01:32.950 a million Earths can fit in the sun 00:01:32.950 --> 00:01:36.210 and the actual distance between the Earth and the sun 00:01:36.210 --> 00:01:40.160 is over 100 times the diameter between the sun and Earth. 00:01:40.160 --> 00:01:41.700 But going back to tilt 00:01:41.700 --> 00:01:44.680 and you could see that here in this picture, 00:01:44.680 --> 00:01:48.430 Earth's north pole does not point straight up 00:01:48.430 --> 00:01:52.340 from the plane of Earth's orbit around the sun. 00:01:52.340 --> 00:01:55.560 What do I mean by the plane of Earth's orbit around the sun? 00:01:55.560 --> 00:01:58.160 This red circle that you see, 00:01:58.160 --> 00:01:59.920 or this ellipse that you see, 00:01:59.920 --> 00:02:02.440 if you imagine that being on a surface 00:02:02.440 --> 00:02:04.330 of a table or a plane, 00:02:04.330 --> 00:02:06.010 that would be our orbital plane. 00:02:06.010 --> 00:02:07.810 And we can see that the north pole 00:02:07.810 --> 00:02:09.530 does not go straight up from that 00:02:09.530 --> 00:02:11.720 and the south pole does not go straight down, 00:02:11.720 --> 00:02:13.370 that actually we're looking 00:02:13.370 --> 00:02:17.620 at an angle of about 23.5 degrees. 00:02:17.620 --> 00:02:21.120 And that's the reason why we have the seasons. 00:02:21.120 --> 00:02:23.290 To understand why that is the case, 00:02:23.290 --> 00:02:25.510 let's imagine Earth when the Northern Hemisphere 00:02:25.510 --> 00:02:27.330 is most pointed towards the sun, 00:02:27.330 --> 00:02:29.310 which happens in late June. 00:02:29.310 --> 00:02:30.490 And so let me draw the equator 00:02:30.490 --> 00:02:32.630 to help us visualize this a little bit 00:02:32.630 --> 00:02:34.210 and let's compare that 00:02:34.210 --> 00:02:35.800 to when the Northern Hemisphere 00:02:35.800 --> 00:02:37.630 is most pointed away from the sun, 00:02:37.630 --> 00:02:39.650 which happens in late December. 00:02:39.650 --> 00:02:42.340 And so I will draw the equator again 00:02:42.340 --> 00:02:46.400 to help us visualize this. 00:02:46.400 --> 00:02:50.250 And let's pick a similar point in the Northern Hemisphere. 00:02:50.250 --> 00:02:53.550 So let's pick a point that's a little bit above the equator. 00:02:53.550 --> 00:02:54.920 So let's say that point 00:02:54.920 --> 00:02:58.410 and a comparable point in this scenario 00:02:58.410 --> 00:03:01.060 is going to be right over here. 00:03:01.060 --> 00:03:04.480 It's about that same distance above the equator. 00:03:04.480 --> 00:03:08.240 Notice, in late June in the Northern Hemisphere 00:03:08.240 --> 00:03:10.700 the sun is almost directly above 00:03:10.700 --> 00:03:12.910 this white point that we're seeing here. 00:03:12.910 --> 00:03:16.300 While in this scenario, the sun is at an angle. 00:03:16.300 --> 00:03:18.700 The surface of the Earth is more like this, 00:03:18.700 --> 00:03:22.420 so the sun's rays are coming at an angle. 00:03:22.420 --> 00:03:24.050 And if you think about it, 00:03:24.050 --> 00:03:25.050 think about the scenario, 00:03:25.050 --> 00:03:26.580 the difference between when the sun 00:03:26.580 --> 00:03:28.870 is directly bearing down on something, 00:03:28.870 --> 00:03:30.650 versus when it is coming at an angle. 00:03:30.650 --> 00:03:33.700 Let's say this is a side view of two surfaces. 00:03:33.700 --> 00:03:36.870 And the surface on the right has twice the surface area. 00:03:36.870 --> 00:03:38.900 You can see the side view has twice the length, 00:03:38.900 --> 00:03:41.820 so the surface area if you were to see it in 3D 00:03:41.820 --> 00:03:43.380 would be twice the surface area 00:03:43.380 --> 00:03:46.470 of what we have on the left here. 00:03:46.470 --> 00:03:48.400 But if you have the same amount of sun 00:03:48.400 --> 00:03:50.460 coming from the same direction, 00:03:50.460 --> 00:03:54.330 so here, let me just draw three sun rays here, 00:03:54.330 --> 00:03:55.300 this is just indicative 00:03:55.300 --> 00:03:58.810 and let me draw three sun rays here. 00:03:58.810 --> 00:04:01.280 Notice you have this same amount of energy 00:04:01.280 --> 00:04:03.760 but here you're hitting twice the surface area. 00:04:03.760 --> 00:04:06.360 So, the amount of energy per unit surface area 00:04:06.360 --> 00:04:09.660 is gonna be half as much in this scenario 00:04:09.660 --> 00:04:11.840 where the sun is coming at an angle 00:04:11.840 --> 00:04:14.130 versus this scenario where the sunlight 00:04:14.130 --> 00:04:17.870 is coming more directly on top of that point. 00:04:17.870 --> 00:04:19.970 And wherever you go in the Northern Hemisphere 00:04:19.970 --> 00:04:22.590 the angle is less direct in the winter 00:04:22.590 --> 00:04:24.260 than it is in the summer. 00:04:24.260 --> 00:04:25.640 Now there's also some effects 00:04:25.640 --> 00:04:27.700 on the amount of daylight you get. 00:04:27.700 --> 00:04:29.610 For example, in the summer, 00:04:29.610 --> 00:04:30.810 when the Northern Hemisphere 00:04:30.810 --> 00:04:33.220 is most tilted towards the Earth, 00:04:33.220 --> 00:04:35.500 in the north pole, you're gonna have constant daylight 00:04:35.500 --> 00:04:37.640 and the south pole you're gonna have constant nighttime. 00:04:37.640 --> 00:04:38.940 And then the opposite happens 00:04:38.940 --> 00:04:41.370 when the Northern Hemisphere is pointed away. 00:04:41.370 --> 00:04:43.530 And then when we think about spring and autumn 00:04:43.530 --> 00:04:45.030 in either hemisphere, 00:04:45.030 --> 00:04:46.890 you can see that the angle of Earth's rotation 00:04:46.890 --> 00:04:49.920 does not change from that 23.5 degrees, 00:04:49.920 --> 00:04:51.610 but in spring and autumn 00:04:51.610 --> 00:04:53.660 the Northern Hemisphere is not pointed 00:04:53.660 --> 00:04:55.360 to or away from the sun, 00:04:55.360 --> 00:04:57.500 it's kind of just pointed to the side. 00:04:57.500 --> 00:04:59.030 So in these two points, 00:04:59.030 --> 00:05:01.760 comparable points on the Northern or Southern hemisphere 00:05:01.760 --> 00:05:05.723 are seeing similar angles of the actual sunlight.

Comparing animal and plant cells

https://www.youtube.com/watch?v=HjC-eMiMDfo

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https://www.youtube.com/api/timedtext?v=HjC-eMiMDfo&ei=wFWUZaXrLYToxN8P8vGaGA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=50447746DB7BD9F463D9655010E5CE09226134C9.4A0A79107F872EFAE09EB014837BFAC05D7F06FF&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.190 --> 00:00:02.890 - [Instructor] So let's play a game of Spot the Difference. 00:00:02.890 --> 00:00:04.700 Now, if you were asked to spot the difference 00:00:04.700 --> 00:00:06.380 between these two pictures, 00:00:06.380 --> 00:00:09.060 you'd probably laugh and say, "That's too easy." 00:00:09.060 --> 00:00:11.720 Because it's obvious that this picture of a lion on the left 00:00:11.720 --> 00:00:14.020 is nowhere close to looking like the picture 00:00:14.020 --> 00:00:16.090 of a green fern plant on the right. 00:00:16.090 --> 00:00:17.860 What's more, a lion and a fern 00:00:17.860 --> 00:00:19.680 not only look completely different, 00:00:19.680 --> 00:00:21.930 they also function differently. 00:00:21.930 --> 00:00:24.920 But what if I told you that if we zoomed in really close 00:00:24.920 --> 00:00:27.610 and compared the lion's cells with the fern's cells, 00:00:27.610 --> 00:00:30.240 they'd actually share many similarities? 00:00:30.240 --> 00:00:33.620 An animal cell and a plant cell have several common features 00:00:33.620 --> 00:00:36.030 as well as a few key differences. 00:00:36.030 --> 00:00:39.000 In this video, we're going to spot the similarities 00:00:39.000 --> 00:00:41.540 and the differences between the two types of cells, 00:00:41.540 --> 00:00:44.440 and talk about their functions inside the cells. 00:00:44.440 --> 00:00:47.290 So, first off, let's take a look at some cell models. 00:00:47.290 --> 00:00:49.500 Here on the left is an animal cell, 00:00:49.500 --> 00:00:51.880 and on the right is a plant cell. 00:00:51.880 --> 00:00:53.970 First, let's try and identify the things 00:00:53.970 --> 00:00:57.110 that both animal and plant cells share in common. 00:00:57.110 --> 00:00:59.530 If you recall, both animal and plant cells 00:00:59.530 --> 00:01:00.750 have a cell membrane, 00:01:00.750 --> 00:01:03.000 which acts like a gate to control what enters 00:01:03.000 --> 00:01:04.420 and leaves the cell. 00:01:04.420 --> 00:01:05.870 Animal cells and plant cells 00:01:05.870 --> 00:01:09.320 also have this jelly-like substance called the cytosol, 00:01:09.320 --> 00:01:11.720 which contains organelles or small compartments 00:01:11.720 --> 00:01:14.410 with specific functions inside the cell. 00:01:14.410 --> 00:01:17.630 Animal and plant cells share several common organelles, 00:01:17.630 --> 00:01:22.470 two of which include the nucleus and the mitochondria. 00:01:22.470 --> 00:01:24.180 The nucleus within each cell type 00:01:24.180 --> 00:01:27.960 serves as an information database to store the cell's genes, 00:01:27.960 --> 00:01:32.010 while the mitochondria act as factories to break down sugars 00:01:32.010 --> 00:01:34.860 and release energy that the cells can use. 00:01:34.860 --> 00:01:37.030 So now that we've identified some features 00:01:37.030 --> 00:01:38.840 found in both kinds of cells, 00:01:38.840 --> 00:01:41.750 let's look closer to spot the fundamental differences 00:01:41.750 --> 00:01:44.030 between animal and plant cells. 00:01:44.030 --> 00:01:45.610 As you can see in this diagram, 00:01:45.610 --> 00:01:48.070 plant cells have an additional layer of material 00:01:48.070 --> 00:01:49.890 that surrounds the cell membrane. 00:01:49.890 --> 00:01:52.180 This is called a cell wall, 00:01:52.180 --> 00:01:55.390 which makes the plant cell more structured and stiff. 00:01:55.390 --> 00:01:56.930 Think of a celery stalk 00:01:56.930 --> 00:02:00.020 compared to a raw piece of chicken or fish. 00:02:00.020 --> 00:02:02.200 The animal muscle tissue is floppy 00:02:02.200 --> 00:02:04.300 while the celery stalk is firm. 00:02:04.300 --> 00:02:06.530 That's cell walls in action. 00:02:06.530 --> 00:02:08.810 Also, plant cells have these special organelles 00:02:08.810 --> 00:02:11.380 called chloroplasts, which are what give plants, 00:02:11.380 --> 00:02:14.150 like the fern we saw, their green color. 00:02:14.150 --> 00:02:16.380 Chloroplasts are the site of photosynthesis, 00:02:16.380 --> 00:02:18.100 which is how plants make their own food 00:02:18.100 --> 00:02:19.680 in the form of sugars. 00:02:19.680 --> 00:02:22.670 If the word sugar rings a bell, you're on the right track 00:02:22.670 --> 00:02:24.930 because I mentioned earlier that mitochondria 00:02:24.930 --> 00:02:27.910 are responsible for breaking down sugars. 00:02:27.910 --> 00:02:30.550 In plant cells, chloroplasts and mitochondria 00:02:30.550 --> 00:02:32.590 are like good buddies that help each other 00:02:32.590 --> 00:02:33.900 and work together. 00:02:33.900 --> 00:02:36.750 Chloroplasts make sugars through photosynthesis 00:02:36.750 --> 00:02:39.380 and mitochondria convert the sugars into energy 00:02:39.380 --> 00:02:42.110 that, ultimately, the plant can use. 00:02:42.110 --> 00:02:45.520 Both cell walls and chloroplasts are found in plant cells 00:02:45.520 --> 00:02:48.760 but not animal cells, such as the ones in you and me. 00:02:48.760 --> 00:02:52.570 And luckily for you and me, this means we aren't green. 00:02:52.570 --> 00:02:55.720 In summary, we just identified several similarities 00:02:55.720 --> 00:02:59.560 and differences in our comparison of animal and plant cells. 00:02:59.560 --> 00:03:02.430 While both cell types have a cell membrane, 00:03:02.430 --> 00:03:06.400 cytosol, a nucleus, and mitochondria, 00:03:06.400 --> 00:03:07.680 plant cells have a cell wall 00:03:07.680 --> 00:03:11.720 that makes them stiff and rigid, think about celery stalks, 00:03:11.720 --> 00:03:13.240 and they have chloroplasts, 00:03:13.240 --> 00:03:16.750 which makes sugars and give plants their green color. 00:03:16.750 --> 00:03:18.560 All of these are just a handful 00:03:18.560 --> 00:03:20.570 of the similarities and differences 00:03:20.570 --> 00:03:22.950 between plant and animal cells. 00:03:22.950 --> 00:03:25.080 As you go forward in your biology journey, 00:03:25.080 --> 00:03:27.910 you'll probably learn about a lot more. 00:03:27.910 --> 00:03:29.540 But the differences that we've covered 00:03:29.540 --> 00:03:32.560 are a big part of what makes plant and animal cells 00:03:32.560 --> 00:03:35.320 so distinct and unique from each other. 00:03:35.320 --> 00:03:38.430 These differences are why we don't see green lions 00:03:38.430 --> 00:03:41.270 that photosynthesize using chloroplasts 00:03:41.270 --> 00:03:45.980 or floppy raw veggies with cell membranes but no cell walls. 00:03:45.980 --> 00:03:48.330 - Now I hope that you have a clear understanding 00:03:48.330 --> 00:03:51.670 of the different cell parts in both animal and plant cells, 00:03:51.670 --> 00:03:53.890 and that spotting the differences between the two 00:03:53.890 --> 00:03:55.793 will be easy breezy.

Khan Academy Ed Talks with Ted Coe, PhD - Tuesday, March 15

https://www.youtube.com/watch?v=f9j9pK8BkzU

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WEBVTT Kind: captions Language: en 00:00:00.330 --> 00:00:04.010 - Hello and welcome to Ed Talks with Khan Academy. 00:00:04.010 --> 00:00:04.990 I'm Kristen DiCerbo, 00:00:04.990 --> 00:00:06.880 the Chief Learning Officer at Khan Academy. 00:00:06.880 --> 00:00:11.140 And today, I am looking forward to talking to Dr. Ted Coe, 00:00:11.140 --> 00:00:15.270 who is with NWEA, one of our key partners here. 00:00:15.270 --> 00:00:18.340 He is the Director of Content, Advocacy and Design. 00:00:18.340 --> 00:00:20.270 We're looking forward to talking about math 00:00:20.270 --> 00:00:22.330 and math learning today. 00:00:22.330 --> 00:00:25.250 Before we get started, I wanna remind you that Khan Academy 00:00:25.250 --> 00:00:29.180 is a nonprofit organization and relies on donations 00:00:29.180 --> 00:00:31.920 from folks like you to help us continue 00:00:31.920 --> 00:00:32.930 to be able to do our work. 00:00:32.930 --> 00:00:36.230 So if you go to khanacademy.org/donate, 00:00:36.230 --> 00:00:39.500 you'll find a place where you can help keep us supported 00:00:39.500 --> 00:00:43.250 and work in continuing our work, so thank you for that. 00:00:43.250 --> 00:00:47.710 I also want to acknowledge our corporate supporters 00:00:47.710 --> 00:00:49.980 who have come and helped us work 00:00:49.980 --> 00:00:53.580 through the COVID-19 crisis, including AT&T, 00:00:53.580 --> 00:00:56.290 General Motors, and Fastly. 00:00:56.290 --> 00:01:01.290 If you would like to listen to this conversation 00:01:02.310 --> 00:01:04.860 or any of our previous conversations, 00:01:04.860 --> 00:01:07.230 you can, wherever you get your podcasts, 00:01:07.230 --> 00:01:09.950 find Homeroom with Sal, The Podcast 00:01:09.950 --> 00:01:13.170 and you'll be able to listen wherever you prefer, 00:01:13.170 --> 00:01:17.580 at the gym, on your walks, doing the dishes. 00:01:17.580 --> 00:01:18.683 We hope you enjoy it. 00:01:19.780 --> 00:01:24.780 So without further ado, let me introduce Dr. Ted Coe. 00:01:25.080 --> 00:01:28.930 So he has over 25 years of experience as a teacher, 00:01:28.930 --> 00:01:31.690 professor, department chair, administrator, 00:01:31.690 --> 00:01:34.570 and a nonprofit director, basically weaving together 00:01:34.570 --> 00:01:37.510 perspectives about mathematics education. 00:01:37.510 --> 00:01:39.400 He has experience as a full-time 00:01:39.400 --> 00:01:40.980 high school mathematics teacher, 00:01:40.980 --> 00:01:43.120 community college faculty member, 00:01:43.120 --> 00:01:45.550 a mathematics chair at two community colleges, 00:01:45.550 --> 00:01:48.330 and an assistant dean at the university level. 00:01:48.330 --> 00:01:52.410 And I will say, as someone who is a graduate 00:01:52.410 --> 00:01:53.660 of Arizona State University, 00:01:53.660 --> 00:01:57.093 he is a fellow Sun Devil as well, welcome. 00:01:58.250 --> 00:02:00.773 - Thank you, thank you, glad to be here. 00:02:01.810 --> 00:02:03.150 - We are glad to have you. 00:02:03.150 --> 00:02:07.490 So first of all, tell us what your role is specifically. 00:02:07.490 --> 00:02:09.053 What do you do at NWEA? 00:02:10.155 --> 00:02:12.955 - This is an interesting question, right? 00:02:12.955 --> 00:02:16.910 The answer is, the title is Director of Content, 00:02:16.910 --> 00:02:19.550 Advocacy and Design for mathematics. 00:02:19.550 --> 00:02:21.660 And the interesting side to it is, 00:02:21.660 --> 00:02:23.740 well, I get to advocate for content. 00:02:23.740 --> 00:02:26.260 And so for many ways for me 00:02:26.260 --> 00:02:27.760 it's like this dream world to be in, 00:02:27.760 --> 00:02:30.710 where I get to kind of imagine the kinds of things 00:02:30.710 --> 00:02:32.570 that we wanna work on, how do we wanna grow, 00:02:32.570 --> 00:02:36.380 how do we want to move beyond a focus on assessment 00:02:36.380 --> 00:02:40.140 to teaching and learning and getting into the classroom 00:02:40.140 --> 00:02:43.410 and getting it, so it's envisioning these kinds of things. 00:02:43.410 --> 00:02:46.050 It's being able to work with different state and districts 00:02:46.050 --> 00:02:47.670 and get in there and roll up our sleeves 00:02:47.670 --> 00:02:49.890 and get our hands dirty trying to solve 00:02:49.890 --> 00:02:52.300 some pretty messy problems. 00:02:52.300 --> 00:02:55.090 So that's a lot of what I get to do. 00:02:55.090 --> 00:02:57.633 And so to me, it's great fun. 00:02:58.870 --> 00:03:01.550 - That's fantastic, how did you come to be in this role? 00:03:01.550 --> 00:03:04.773 What was your path that you took to end up here? 00:03:05.691 --> 00:03:10.543 - It was so bizarre, it's a crazy path, career path, 00:03:12.350 --> 00:03:14.430 started out as a high school teacher, 00:03:14.430 --> 00:03:17.310 things were going well, I loved high school teaching, 00:03:17.310 --> 00:03:19.380 highlight of the career, right? 00:03:19.380 --> 00:03:23.040 Then I ended up getting pulled over 00:03:23.040 --> 00:03:24.840 to one of the community colleges 00:03:24.840 --> 00:03:26.660 and I actually walked right in my first job 00:03:26.660 --> 00:03:29.600 in the community college system was as a chair 00:03:29.600 --> 00:03:30.900 at Rio Salado College 00:03:30.900 --> 00:03:32.530 in the Maricopa Community College District. 00:03:32.530 --> 00:03:36.100 So it was like this big sort of leap. 00:03:36.100 --> 00:03:38.890 I ended up switching over to another community college 00:03:38.890 --> 00:03:42.270 in the district, Scotts Dale and while I was there, 00:03:42.270 --> 00:03:46.810 I ended up being involved deeply in the mathematics 00:03:46.810 --> 00:03:48.790 around the whole community college system 00:03:48.790 --> 00:03:51.690 and kind of involved in the articulation conversations 00:03:51.690 --> 00:03:53.000 around the state and everything. 00:03:53.000 --> 00:03:57.580 And somewhere along that time the Park Consortium came along 00:03:57.580 --> 00:03:58.413 and you might remember this, 00:03:58.413 --> 00:03:59.960 this was in the early years of the common core 00:03:59.960 --> 00:04:01.860 and there were the two major consortium, 00:04:01.860 --> 00:04:03.660 Park and Smarter Balanced. 00:04:03.660 --> 00:04:07.790 And I was brought on to the Park side of the conversation. 00:04:07.790 --> 00:04:10.910 Arizona was one of the governing states at the time. 00:04:10.910 --> 00:04:11.743 And I was brought in 00:04:11.743 --> 00:04:14.090 as one of the higher ed content experts. 00:04:14.090 --> 00:04:16.080 And so I was dropped into this space all of a sudden, 00:04:16.080 --> 00:04:18.940 where I had been a college professor 00:04:18.940 --> 00:04:21.780 and high school teacher and now I was in this space, 00:04:21.780 --> 00:04:23.020 where it's like, we want your input 00:04:23.020 --> 00:04:25.300 on this multi-state assessment 00:04:25.300 --> 00:04:26.700 that's on these new standards. 00:04:26.700 --> 00:04:28.000 And so I'm like, "Well, let's read the standards, 00:04:28.000 --> 00:04:29.700 let's see what this is about." 00:04:29.700 --> 00:04:32.920 And I got really involved in it and so much, in fact 00:04:32.920 --> 00:04:36.250 that eventually Park split off of the group 00:04:36.250 --> 00:04:38.060 that was running it, which was called Achieve. 00:04:38.060 --> 00:04:41.150 And Achieve was the ones for the American Diploma Product, 00:04:41.150 --> 00:04:42.730 helped lead the common core and all that, 00:04:42.730 --> 00:04:44.800 and the next generation science standards. 00:04:44.800 --> 00:04:47.380 And so they only hired me to be their math director. 00:04:47.380 --> 00:04:52.290 And so for the years prior to coming into this space 00:04:52.290 --> 00:04:54.570 at NWEA where I've been for two years, 00:04:54.570 --> 00:04:56.990 I was the director of mathematics there and got to work all 00:04:56.990 --> 00:04:59.740 around the country with great folks everywhere. 00:04:59.740 --> 00:05:03.797 And really get to see how the policies worked out 00:05:03.797 --> 00:05:05.880 and the difficulties that people were encountering 00:05:05.880 --> 00:05:07.607 and trying to talk through some of those things 00:05:07.607 --> 00:05:09.497 and getting the chance to speak all over the country. 00:05:09.497 --> 00:05:11.507 It was great fun, it's been great fun 00:05:11.507 --> 00:05:15.760 and it's been it one surprise after the other. 00:05:15.760 --> 00:05:17.083 And here I am today. 00:05:18.160 --> 00:05:19.950 - Fantastic, that sounds great. 00:05:19.950 --> 00:05:23.373 So let's talk a little bit about teaching and leaning math. 00:05:24.320 --> 00:05:28.260 Historically, there's been all this discussion about, 00:05:28.260 --> 00:05:30.850 should we teach procedural skills? 00:05:30.850 --> 00:05:33.440 Should we teach conceptual understanding? 00:05:33.440 --> 00:05:37.260 And these wars about which one is more important 00:05:37.260 --> 00:05:38.140 and where these is, 00:05:38.140 --> 00:05:40.340 is that the right conversation to be having? 00:05:41.732 --> 00:05:44.270 - It's a tale as old as time, 00:05:44.270 --> 00:05:46.310 at least as old as my career has been, right? 00:05:46.310 --> 00:05:49.290 But there's always this tension in there. 00:05:49.290 --> 00:05:53.118 And so I've had to sit back and think to myself 00:05:53.118 --> 00:05:56.920 how would I describe teaching and learning mathematics 00:05:56.920 --> 00:05:58.950 after my 20 years of teaching? 00:05:58.950 --> 00:06:02.420 And I was like, "Well, how do I sum this up?" 00:06:02.420 --> 00:06:04.230 And it was somehow developed along the way, 00:06:04.230 --> 00:06:07.630 but it was this idea that look, part of what we do 00:06:07.630 --> 00:06:11.030 in mathematics is we teach these ways of doing 00:06:12.290 --> 00:06:13.780 and we want you to be able to do those 00:06:13.780 --> 00:06:16.190 but we also wanna make sure that you're picking up 00:06:16.190 --> 00:06:18.710 ways of thinking, and I'll give you an example of that 00:06:18.710 --> 00:06:22.440 in just a moment, that go alongside habits of thinking. 00:06:22.440 --> 00:06:25.260 So you have these ways of thinking sort of at a core 00:06:25.260 --> 00:06:28.620 that are bolstered by these habits of thinking 00:06:28.620 --> 00:06:32.710 that are then in turn really sort of brought, 00:06:32.710 --> 00:06:34.220 they come to the table in certain ways, 00:06:34.220 --> 00:06:36.500 through the ways of doing that allow you to go on 00:06:36.500 --> 00:06:39.580 and do something bigger with the mathematics. 00:06:39.580 --> 00:06:41.910 An example I use quite frequently 00:06:41.910 --> 00:06:43.970 is with this idea of ways of thinking. 00:06:43.970 --> 00:06:46.390 And I can ask a room full of adults this question 00:06:46.390 --> 00:06:47.837 and basically I say something like, 00:06:47.837 --> 00:06:52.210 "Hey, how many years was it from December 7th, 1941 00:06:53.730 --> 00:06:54.887 to December 7th, 2014?" 00:06:56.220 --> 00:06:57.790 That's how long I've been using this question. 00:06:57.790 --> 00:07:02.790 Okay, so December 7th 2014 and by and large 00:07:04.950 --> 00:07:08.010 you ask this to a room full of even adults, right? 00:07:08.010 --> 00:07:10.830 And people will sit there and they start chewing on 00:07:10.830 --> 00:07:12.782 an answer and they start, "Oh, what can I do? 00:07:12.782 --> 00:07:13.615 What can I do?" 00:07:13.615 --> 00:07:15.060 And they go through some mechanizations in their head 00:07:15.060 --> 00:07:15.977 and they might think, 00:07:15.977 --> 00:07:19.050 "Well, that's actually kind of a subtraction problem 00:07:19.050 --> 00:07:22.370 but I don't really need to use subtraction to get it," 00:07:22.370 --> 00:07:23.890 because in this case, I'm just trying 00:07:23.890 --> 00:07:26.660 to find this additive comparison and this gap, if you will, 00:07:26.660 --> 00:07:28.160 between the two numbers 00:07:28.160 --> 00:07:29.320 and there are different ways to do it. 00:07:29.320 --> 00:07:32.220 Maybe I wanna go from 1941 to 2000, cut it off, 00:07:32.220 --> 00:07:33.850 and then go from 2000 to 2014, 00:07:33.850 --> 00:07:35.910 or maybe I wanna take the whole thing. 00:07:35.910 --> 00:07:37.280 So starting in 1941, 00:07:37.280 --> 00:07:42.280 I wanna slide the whole thing back a year and start at 1940. 00:07:42.460 --> 00:07:44.760 Either way, all of these things are fair 00:07:44.760 --> 00:07:48.730 but the majority of the folks I asked that question, 00:07:48.730 --> 00:07:51.050 they don't answer it with the way of doing, 00:07:51.050 --> 00:07:53.790 they don't do the 15 steps of setting up the algorithm, 00:07:53.790 --> 00:07:55.940 borrowing, not giving back all that thing, 00:07:55.940 --> 00:07:58.699 putting the one, they don't do that, 00:07:58.699 --> 00:08:02.740 they bring ways of thinking to bear, right? 00:08:02.740 --> 00:08:03.580 - Yeah. 00:08:03.580 --> 00:08:07.300 - And I think maybe part of why we get into this mess 00:08:07.300 --> 00:08:11.020 is in the standards, we have the learning progressions 00:08:11.020 --> 00:08:15.030 and the learning progressions and with the ways of doing. 00:08:15.030 --> 00:08:17.660 And so it looks like the way of doing is the goal, 00:08:17.660 --> 00:08:20.230 but the way of doing is just one more thing, 00:08:20.230 --> 00:08:22.830 it's just one more piece, right? 00:08:22.830 --> 00:08:25.620 Yeah, so I really like to emphasize 00:08:25.620 --> 00:08:29.340 this idea of ways of thinking with regards to 00:08:29.340 --> 00:08:31.210 ways of thinking, ways of doing, habits of thinking, 00:08:31.210 --> 00:08:33.640 all of those things working together. 00:08:33.640 --> 00:08:36.130 'Cause if you have just one, the ways of doing, 00:08:36.130 --> 00:08:38.870 all you've got is a box of puzzle pieces 00:08:38.870 --> 00:08:40.723 when you're done with it, yeah. 00:08:41.606 --> 00:08:44.650 - Right, so I'm gonna keep going with the year example here 00:08:44.650 --> 00:08:48.240 to push on this, so my sister got married in 1997 00:08:48.240 --> 00:08:52.050 and I have to say, somehow never made this connection, 00:08:52.050 --> 00:08:53.667 but she said to me one day, 00:08:53.667 --> 00:08:55.190 "If you wanna know how long we've been married, 00:08:55.190 --> 00:08:57.360 you just take what current year it is in add three, 00:08:57.360 --> 00:08:58.713 because 1997 to 2003." 00:09:00.660 --> 00:09:03.757 Then I was like, "Oh yeah, why did I not think of that?" 00:09:03.757 --> 00:09:04.670 (Kristen laughing) 00:09:04.670 --> 00:09:09.140 So that's a way of doing it, so then that's one way, 00:09:09.140 --> 00:09:11.780 or is that how does that relate then to ways of thinking? 00:09:11.780 --> 00:09:15.680 And so are there many different ways you can do it 00:09:15.680 --> 00:09:17.320 and the ways of thinking around it? 00:09:17.320 --> 00:09:20.350 - Yes, the idea is that when I ask that question, 00:09:20.350 --> 00:09:23.030 there are so many different ways you could approach it. 00:09:23.030 --> 00:09:25.320 You could approach it with a way of doing 00:09:25.320 --> 00:09:26.530 and no harm, no foul. 00:09:26.530 --> 00:09:28.240 You could approach it with ways of thinking, 00:09:28.240 --> 00:09:30.170 but if all you have is the way of doing 00:09:30.170 --> 00:09:32.160 and you don't have those ways of thinking, 00:09:32.160 --> 00:09:34.830 then when you get to somewhere in real life, 00:09:34.830 --> 00:09:36.500 it doesn't illuminate. 00:09:36.500 --> 00:09:40.586 And a place where this happens is you can ask 00:09:40.586 --> 00:09:43.280 like where in real life, ask this to an adult, 00:09:43.280 --> 00:09:45.560 where in real life have you ever actually used 00:09:45.560 --> 00:09:47.013 division of fractions? 00:09:47.880 --> 00:09:49.820 And I'll be surprised if you actually get 00:09:49.820 --> 00:09:54.740 any valid answer back from anybody and why is that? 00:09:54.740 --> 00:09:57.130 Because if we reflect back to it, 00:09:57.130 --> 00:10:00.100 when we were taught the division of fractions, 00:10:00.100 --> 00:10:02.630 those of us who were of a certain age, right? 00:10:02.630 --> 00:10:04.780 We were caught a way of doing 00:10:04.780 --> 00:10:08.790 and it was totally disconnected from ways of thinking 00:10:08.790 --> 00:10:12.280 grounded in what does it mean to divide so that- 00:10:12.280 --> 00:10:16.180 - Yes, you were just taught the procedure, yeah. 00:10:16.180 --> 00:10:18.450 - Yeah and so you've got the procedure 00:10:18.450 --> 00:10:20.170 but you have no place to hang it, 00:10:20.170 --> 00:10:22.380 when it comes and shows up in real life. 00:10:22.380 --> 00:10:26.650 - Right, that totally makes sense, so if I'm a teacher 00:10:26.650 --> 00:10:29.710 how do I start thinking about encouraging 00:10:29.710 --> 00:10:31.103 these ways of thinking? 00:10:32.500 --> 00:10:34.513 - See, that's the tricky part, right? 00:10:35.526 --> 00:10:36.359 - Right? 00:10:36.359 --> 00:10:41.120 - Yeah, and so one really cool thing that happened 00:10:42.180 --> 00:10:43.980 in the last couple years, Peter Liljedahl 00:10:43.980 --> 00:10:47.050 came out with a book called "Building Thinking Classrooms." 00:10:47.050 --> 00:10:49.420 And I'm like, yes, yes, we're seeing 00:10:49.420 --> 00:10:52.460 this emphasis shifting to thinking, fantastic. 00:10:52.460 --> 00:10:56.623 Because at the same time my colleagues and I at NWEA 00:10:56.623 --> 00:11:00.030 have been trying to work on this idea 00:11:00.030 --> 00:11:02.850 of how can we get ways of thinking moving 00:11:02.850 --> 00:11:04.450 and talked about in classrooms 00:11:04.450 --> 00:11:06.810 in ways that are non-threatening, right? 00:11:06.810 --> 00:11:09.640 That feel safe to both teachers and students 00:11:09.640 --> 00:11:13.790 because there's awkwardness when we ask ourselves 00:11:13.790 --> 00:11:16.890 thinking questions, all of us have to stop and think, 00:11:16.890 --> 00:11:20.300 and with thinking comes vulnerability, right? 00:11:20.300 --> 00:11:24.170 So we actually built out some things 00:11:24.170 --> 00:11:26.860 called these formative conversation starters. 00:11:26.860 --> 00:11:29.300 And the role of the formative conversation starters 00:11:29.300 --> 00:11:33.250 is to basically help shape how you might enter into 00:11:33.250 --> 00:11:34.930 some of these kinds of conversations 00:11:34.930 --> 00:11:37.910 that are designed to focus on ways of thinking 00:11:39.420 --> 00:11:42.830 and then to do it in such a way that you also know 00:11:42.830 --> 00:11:46.760 what it is you're trying to listen for at the same time. 00:11:46.760 --> 00:11:48.470 So we've got these bins, 00:11:48.470 --> 00:11:50.920 these big ideas to nurture sense making 00:11:50.920 --> 00:11:54.300 and then we've got clusters of questions 00:11:54.300 --> 00:11:57.623 that unfold as you ask them and might lead 00:11:57.623 --> 00:12:01.010 to moments of cognitive dissonance or might lead to ahas 00:12:01.010 --> 00:12:04.217 or might lead to places where you step back and go, 00:12:04.217 --> 00:12:07.077 "I really do need to think more deeply about that." 00:12:08.115 --> 00:12:10.250 So there are different options to do it. 00:12:10.250 --> 00:12:14.302 You can put in classroom routines, you can build tools, 00:12:14.302 --> 00:12:16.213 like we're trying to build out. 00:12:17.830 --> 00:12:21.507 But the idea is what can we do to do that? 00:12:21.507 --> 00:12:24.590 All kinds of things, like Peter's got in his book, 00:12:24.590 --> 00:12:26.420 all kinds of options, 00:12:26.420 --> 00:12:29.670 as well as what I'm offering here today. 00:12:29.670 --> 00:12:32.100 - Yeah, so I like this idea of conversation starters. 00:12:32.100 --> 00:12:36.170 I think we're putting a link to them in the chat 00:12:36.170 --> 00:12:38.940 for folks that are following along. 00:12:38.940 --> 00:12:41.700 Can you give us some examples, what are some examples 00:12:41.700 --> 00:12:43.840 of what these are and how do they work? 00:12:43.840 --> 00:12:48.840 - Yeah, so, and sometimes the idea like with fractions, 00:12:51.410 --> 00:12:54.346 I might come out and we might start with a question like, 00:12:54.346 --> 00:12:56.280 well, what's a fraction? 00:12:56.280 --> 00:12:58.120 And then, well, the next question might be, 00:12:58.120 --> 00:13:01.470 well, is a fraction one number or two numbers? 00:13:01.470 --> 00:13:03.700 And just sit back and talk about it. 00:13:03.700 --> 00:13:06.350 Talk about what you think on that, all right? 00:13:06.350 --> 00:13:08.420 And then, well, what do you think of 00:13:08.420 --> 00:13:10.193 when you think of three eighths? 00:13:11.140 --> 00:13:14.170 Okay, what do you think of when you see eight thirds? 00:13:14.170 --> 00:13:16.840 'Cause if you're of three eighths as three out of eight, 00:13:16.840 --> 00:13:18.360 then eight thirds becomes something 00:13:18.360 --> 00:13:21.230 that's maybe a little tougher to think about. 00:13:21.230 --> 00:13:23.560 Another example would be a question that starts off 00:13:23.560 --> 00:13:27.840 with like, well, what does division do for us? 00:13:27.840 --> 00:13:29.210 And so you wanna sit back and you think about, 00:13:29.210 --> 00:13:31.110 well, what does division do for us? 00:13:31.110 --> 00:13:32.640 And then the next question would be 00:13:32.640 --> 00:13:36.280 not to do a division problem, but to ask a question like, 00:13:39.628 --> 00:13:42.620 without computing how can you think about a problem like 00:13:42.620 --> 00:13:44.090 10 divided by one half 00:13:45.250 --> 00:13:48.660 and to be able to go on to the next one. 00:13:48.660 --> 00:13:51.090 Well, then how would you think about negative 10 00:13:51.090 --> 00:13:53.060 divided by one half, right? 00:13:53.060 --> 00:13:56.720 And if your ways of thinking are consistent and robust, 00:13:56.720 --> 00:13:59.130 then your answers were sort of gel together 00:13:59.130 --> 00:14:02.610 but if you have fractures and if they're disjoint, 00:14:02.610 --> 00:14:04.220 then you kind of have to go back 00:14:04.220 --> 00:14:06.150 and kind of try to figure out, well, how do I get the, 00:14:06.150 --> 00:14:09.340 I know that my thinking should gel together with my answers 00:14:09.340 --> 00:14:12.110 to all of these things, what do I need to do? 00:14:12.110 --> 00:14:13.920 How do I need to accommodate the way I'm thinking 00:14:13.920 --> 00:14:16.390 in order to make these things work? 00:14:16.390 --> 00:14:18.050 From the teacher's perspective, 00:14:18.050 --> 00:14:21.470 we help provide what you might be listening for in these- 00:14:21.470 --> 00:14:23.087 - I was just gonna ask that. 00:14:23.087 --> 00:14:24.686 (Kristen laughing) 00:14:24.686 --> 00:14:26.620 Yeah, what are the things that you're looking for 00:14:26.620 --> 00:14:28.335 from the teacher's perspective? 00:14:28.335 --> 00:14:31.557 - Yeah, so like we know that we want fraction 00:14:31.557 --> 00:14:34.330 and we want students to be able to think of a fraction 00:14:34.330 --> 00:14:39.330 as a single number, as a point on the number line, right? 00:14:39.870 --> 00:14:43.940 But if I ask my students about fractions 00:14:43.940 --> 00:14:44.773 and they're saying, 00:14:44.773 --> 00:14:48.130 "Well, we're only thinking of it as two numbers." 00:14:48.130 --> 00:14:50.870 Then I'm talking about something as the teacher 00:14:50.870 --> 00:14:53.860 that's completely different from what they're hearing. 00:14:53.860 --> 00:14:56.420 And so it's this idea of getting these meanings 00:14:56.420 --> 00:14:58.960 out in the open so that we all know 00:14:58.960 --> 00:15:00.920 that we're talking about the same thing, 00:15:00.920 --> 00:15:03.660 so when I say fraction, you're thinking the same thing. 00:15:03.660 --> 00:15:05.540 Or when I talk about division, 00:15:05.540 --> 00:15:07.570 you've got a notion of thinking of it 00:15:07.570 --> 00:15:09.750 as a multiplicative comparison. 00:15:09.750 --> 00:15:11.930 Or you've got way of thinking about it in terms of 00:15:11.930 --> 00:15:14.210 how many copies of run thing are in another, 00:15:14.210 --> 00:15:17.690 or this time's as large as this thing, right? 00:15:17.690 --> 00:15:19.030 Which when you have those ways of thinking 00:15:19.030 --> 00:15:19.863 that a question like, 00:15:19.863 --> 00:15:21.530 how can you think of 10 divided by one half, 00:15:21.530 --> 00:15:24.610 doesn't become something that's out of bounds at all. 00:15:24.610 --> 00:15:26.320 It becomes something that you can already hang onto 00:15:26.320 --> 00:15:28.888 one of those previous existing meanings of division, 00:15:28.888 --> 00:15:32.370 if they're there, if you've got those ways of thinking. 00:15:32.370 --> 00:15:35.020 - Right, right, yeah, that makes sense. 00:15:35.020 --> 00:15:39.855 So do these starters work across ages and grade levels? 00:15:39.855 --> 00:15:42.190 Are there things that we need to be, 00:15:42.190 --> 00:15:43.957 what kinds of things can younger kids do 00:15:43.957 --> 00:15:47.460 and what kinds of things can older kids start to get? 00:15:47.460 --> 00:15:50.850 - So the interesting thing about them is the way, 00:15:50.850 --> 00:15:52.810 if you go download, maybe some people have already gone 00:15:52.810 --> 00:15:54.830 to download the documents just while we're sitting here. 00:15:54.830 --> 00:15:59.230 But you'll see the entry point into this is through an item, 00:15:59.230 --> 00:16:02.040 it's through a standard, but the idea is 00:16:02.040 --> 00:16:06.500 we've spent so many years unpacking standards, 00:16:06.500 --> 00:16:08.990 digging in and saying, let's look at this one standard. 00:16:08.990 --> 00:16:09.970 What we wanna do is say, 00:16:09.970 --> 00:16:12.630 we're only using this as the entry point, 00:16:12.630 --> 00:16:14.370 because what we wanna do is we wanna find out, 00:16:14.370 --> 00:16:17.270 what is all of the other mathematics that has to come in 00:16:17.270 --> 00:16:20.480 alongside it to help get through this. 00:16:20.480 --> 00:16:23.080 We tend to look at an item go, this is the standard. 00:16:23.080 --> 00:16:24.360 And then we say, well, if they get it wrong, 00:16:24.360 --> 00:16:25.193 then we wanna go back 00:16:25.193 --> 00:16:27.020 and go to that nearest connecting standard. 00:16:27.020 --> 00:16:29.130 What we're saying here is actually maybe you wanna go 00:16:29.130 --> 00:16:31.903 ask them about what's a fraction, right? 00:16:31.903 --> 00:16:32.951 - Right. 00:16:32.951 --> 00:16:35.090 - So let's go talk about what a fraction is. 00:16:35.090 --> 00:16:37.270 It might not be the nearest neighbor standard 00:16:37.270 --> 00:16:39.500 that's the issue, it could be some ways of thinking 00:16:39.500 --> 00:16:41.890 that endure and that goes back to your question 00:16:41.890 --> 00:16:43.570 about who are these for? 00:16:43.570 --> 00:16:47.390 Well, you can take the ones that we've got packaged 00:16:47.390 --> 00:16:48.770 in the third grade and ask them*8 00:16:48.770 --> 00:16:50.100 to seventh and eighth graders, 00:16:50.100 --> 00:16:53.450 because the ways of thinking are enduring, right? 00:16:53.450 --> 00:16:56.100 And so the ideas are, yes, they grow a little bit, 00:16:56.100 --> 00:16:58.230 but they endure and they grew out of these things, 00:16:58.230 --> 00:17:02.460 actually grew out of, are thinking about what could we help 00:17:02.460 --> 00:17:07.060 to provide teachers with as we move into this phase now, 00:17:07.060 --> 00:17:08.070 where students are coming with 00:17:08.070 --> 00:17:11.130 such uneven opportunities to learn. 00:17:11.130 --> 00:17:12.790 And philosophically I'd say, 00:17:12.790 --> 00:17:15.020 well, I can't just be focus on ways of doing. 00:17:15.020 --> 00:17:17.107 I have to be focusing some way on the ways of thinking 00:17:17.107 --> 00:17:20.320 and these habits of thinking that come alongside it. 00:17:20.320 --> 00:17:21.940 And so what could we do? 00:17:21.940 --> 00:17:23.540 That's where we ended up with this. 00:17:23.540 --> 00:17:26.970 So if you are a third grade teacher, 00:17:26.970 --> 00:17:28.140 you could probably pull stuff 00:17:28.140 --> 00:17:29.610 from the fourth and fifth grade. 00:17:29.610 --> 00:17:30.870 If you are a high school teacher, 00:17:30.870 --> 00:17:32.940 you can pull things from any grades, right? 00:17:32.940 --> 00:17:34.890 And they'll still be fair game 00:17:34.890 --> 00:17:36.480 because there're things to talk about, 00:17:36.480 --> 00:17:39.450 ideas that endure that go on and on. 00:17:39.450 --> 00:17:40.790 So if you're in high school, 00:17:40.790 --> 00:17:42.130 you might dig into the functions, 00:17:42.130 --> 00:17:43.330 you might dig into comparison, 00:17:43.330 --> 00:17:45.030 you might dig into operations. 00:17:45.030 --> 00:17:48.300 I hope you dig into proportional relationships. 00:17:48.300 --> 00:17:52.629 - Yes, so this whole conversation is making me think about 00:17:52.629 --> 00:17:55.580 something that we talk a lot about at Khan Academy which is, 00:17:55.580 --> 00:17:57.970 what Sal used to call Swiss cheese gaps 00:17:57.970 --> 00:18:00.520 but now everyone calls unfinished learning. 00:18:00.520 --> 00:18:04.370 Which is the idea that lots of folks 00:18:04.370 --> 00:18:07.870 didn't get some of those foundational concepts 00:18:07.870 --> 00:18:12.250 and when they were first presented and so try to then build 00:18:12.250 --> 00:18:14.490 the next level without those concepts, 00:18:14.490 --> 00:18:18.093 which is kinda the shaky foundation and it just keeps going. 00:18:19.010 --> 00:18:23.300 So it sounds like these conversation starters 00:18:23.300 --> 00:18:27.390 are starting to think about almost diagnosing in some ways, 00:18:27.390 --> 00:18:29.303 like do you have those- 00:18:30.140 --> 00:18:32.750 - Do you have the ways of thinking, right? 00:18:32.750 --> 00:18:37.140 The foundational ways of thinking which are, 00:18:37.140 --> 00:18:39.340 when you look at your state standards, 00:18:39.340 --> 00:18:41.990 you're going to see them kind of in there, 00:18:41.990 --> 00:18:43.620 but you might not see them as explicit 00:18:43.620 --> 00:18:45.470 as we're trying to call them out here. 00:18:45.470 --> 00:18:46.990 Like these are some core ones 00:18:46.990 --> 00:18:48.420 that you wanna keep coming back to. 00:18:48.420 --> 00:18:52.810 You wanna keep revisiting these and keep listening. 00:18:52.810 --> 00:18:55.870 And so the kinds of questions that we're putting out here, 00:18:55.870 --> 00:18:58.720 use them however you wanna use them, use them full class, 00:18:58.720 --> 00:19:00.990 use them one on one, use them in small groups, 00:19:00.990 --> 00:19:02.340 use them for turning talks, 00:19:04.340 --> 00:19:06.973 the idea is to sit back and listen. 00:19:08.791 --> 00:19:11.503 What we would point out is it's also not intended, 00:19:14.370 --> 00:19:17.680 there will be a teachable moment, it's not during this time 00:19:17.680 --> 00:19:19.910 because we wanna set up the culture in such a way that 00:19:19.910 --> 00:19:24.200 this is free, open up, tell me what you're thinking 00:19:24.200 --> 00:19:26.530 and it's not to correct, it's to listen. 00:19:26.530 --> 00:19:27.790 And what's interesting about that, right? 00:19:27.790 --> 00:19:29.760 Is if you keep asking more questions, 00:19:29.760 --> 00:19:31.950 you might realize that your first thoughts 00:19:31.950 --> 00:19:35.160 about what people like to call misconceptions 00:19:35.160 --> 00:19:36.630 could be completely wrong. 00:19:36.630 --> 00:19:40.088 That you've misconceived their misconceptions. 00:19:40.088 --> 00:19:41.160 (both laughing) 00:19:41.160 --> 00:19:42.690 I don't like using the word misconceptions 00:19:42.690 --> 00:19:45.560 'cause the students have the conceptions 00:19:45.560 --> 00:19:46.860 and this is all about, 00:19:46.860 --> 00:19:49.740 what conceptions might they have, right? 00:19:49.740 --> 00:19:51.930 Not what don't they have, what conceptions might they have? 00:19:51.930 --> 00:19:54.320 How are they thinking about these things? 00:19:54.320 --> 00:19:57.300 And let's build from that, that connects back very closely 00:19:57.300 --> 00:20:01.330 to Sal's house building analogy, right? 00:20:01.330 --> 00:20:02.647 - Yeah, right. 00:20:02.647 --> 00:20:04.870 - These are these foundational, 00:20:04.870 --> 00:20:06.500 it's more like these foundational threads 00:20:06.500 --> 00:20:08.550 that wind their way all the way through, 00:20:08.550 --> 00:20:12.910 not just on the bottom floor but you just keep continuing 00:20:12.910 --> 00:20:15.290 to strengthen them like the trunk of a tree, right? 00:20:15.290 --> 00:20:17.940 It just keeps getting stronger and stronger. 00:20:17.940 --> 00:20:20.810 - Yeah, absolutely, that totally makes sense. 00:20:20.810 --> 00:20:25.280 How do you think about the idea of mastery in this world? 00:20:25.280 --> 00:20:28.080 We talk a lot about mastery learning here 00:20:28.080 --> 00:20:31.370 and thinking it's easy when you're talking about skills 00:20:31.370 --> 00:20:33.500 and having mastery of skills, 00:20:33.500 --> 00:20:37.370 but mastery of some of these things is somewhat different. 00:20:37.370 --> 00:20:39.040 Is that even a valid concept? 00:20:39.040 --> 00:20:39.890 I don't know. 00:20:39.890 --> 00:20:43.256 - Yeah, it's so hard to say what is mastery. 00:20:43.256 --> 00:20:46.510 I mean, we always wanna draw a line 00:20:46.510 --> 00:20:48.521 for proficiency somewhere, right? 00:20:48.521 --> 00:20:49.354 - Right. 00:20:49.354 --> 00:20:50.820 - What it means to have learned something 00:20:50.820 --> 00:20:53.690 but in this mindset on the ways of thinking, 00:20:53.690 --> 00:20:55.690 it's like these are things that continue to grow 00:20:55.690 --> 00:20:57.963 and morph and evolve. 00:20:58.808 --> 00:21:03.410 And as I think about, well, how do we ever establish 00:21:03.410 --> 00:21:04.750 whether students have mastered this? 00:21:04.750 --> 00:21:07.570 I'm not sure that that's even the right type of question. 00:21:07.570 --> 00:21:09.760 But rather to just likely, it's just to keep on 00:21:09.760 --> 00:21:13.040 how is that scheme of building up in their minds 00:21:13.040 --> 00:21:17.110 as they continue to go and how can I leverage that 00:21:17.110 --> 00:21:19.290 to go on to that next place? 00:21:19.290 --> 00:21:21.810 - Right and you can think about how you would expect 00:21:21.810 --> 00:21:25.210 some of these answers to change as you learn new things, 00:21:25.210 --> 00:21:27.790 you're changing your ideas about what these are 00:21:27.790 --> 00:21:29.750 as you kind of move up through new skills 00:21:29.750 --> 00:21:32.670 and things you're developing, interesting. 00:21:32.670 --> 00:21:35.820 So we obviously do a lot with technology 00:21:35.820 --> 00:21:37.630 but we also wanna think about 00:21:37.630 --> 00:21:41.010 how teachers and technology work together. 00:21:41.010 --> 00:21:44.904 And so I'm interested in your thoughts about, 00:21:44.904 --> 00:21:47.680 the interplay between the two is I think about 00:21:47.680 --> 00:21:48.890 what you're talking about, 00:21:48.890 --> 00:21:50.570 things technology's never gonna be good 00:21:50.570 --> 00:21:53.160 at doing what you're talking about, that's like the thing 00:21:53.160 --> 00:21:55.130 that teachers need to be in classrooms. 00:21:55.130 --> 00:21:58.497 So I'm interested in your thoughts about how teachers 00:21:58.497 --> 00:22:00.747 and technology can work together to build on. 00:22:02.880 --> 00:22:06.730 - Yeah, so I'm happy to hear you see it that way 00:22:06.730 --> 00:22:08.516 'cause that's how I see it. 00:22:08.516 --> 00:22:12.993 It's that idea that computers, they're really good 00:22:16.070 --> 00:22:18.347 at helping with that way of doing things, right? 00:22:18.347 --> 00:22:19.480 - Right. 00:22:19.480 --> 00:22:22.110 - But to sort of put these complex 00:22:22.110 --> 00:22:23.460 ways of thinking together, 00:22:23.460 --> 00:22:26.436 I mean, that takes some time and working and developing 00:22:26.436 --> 00:22:31.436 and to me I see a very human side to that 00:22:31.818 --> 00:22:36.818 that would be very hard to capture with a computer system. 00:22:37.090 --> 00:22:41.695 So each can play a very important role, right? 00:22:41.695 --> 00:22:46.695 So the computers provide an here to foreseen access 00:22:51.840 --> 00:22:55.667 to content in ways that we've never seen before, right? 00:22:55.667 --> 00:22:58.200 And so building that up, but that next task is, 00:22:58.200 --> 00:23:02.130 well, how do we take that access that we've now shared, 00:23:02.130 --> 00:23:04.630 but how do we build in these kinds of things? 00:23:04.630 --> 00:23:07.960 What can we have the computers help to support us with 00:23:07.960 --> 00:23:10.850 when it comes to engaging in these kinds of conversations 00:23:10.850 --> 00:23:13.280 that will be able to help sort of listen to students 00:23:13.280 --> 00:23:16.620 and figure out exactly sort of what might the next move be 00:23:16.620 --> 00:23:19.570 based on ways of thinking, not necessarily just the ways 00:23:19.570 --> 00:23:21.850 of doing as you might see pointed out in standards 00:23:21.850 --> 00:23:24.043 and standards mappings, that kinda thing. 00:23:25.060 --> 00:23:26.900 - Yeah, absolutely. 00:23:26.900 --> 00:23:31.060 So another piece that we try to encourage 00:23:31.060 --> 00:23:33.700 is helping students become owners of their own learning 00:23:33.700 --> 00:23:37.130 and thinking about developing those metacognitive skills. 00:23:37.130 --> 00:23:39.170 Being able to understand what they know 00:23:39.170 --> 00:23:41.240 and evaluate and what they understand 00:23:41.240 --> 00:23:43.823 and need to learn and how those fit in. 00:23:44.660 --> 00:23:46.210 I'm interested in how you think about that 00:23:46.210 --> 00:23:48.930 and some of this framework too. 00:23:48.930 --> 00:23:52.220 - Yeah, well that might land in that habits space, right? 00:23:52.220 --> 00:23:54.870 Being able to reflect on and being honest with myself, 00:23:54.870 --> 00:23:56.630 am I making sense? 00:23:56.630 --> 00:24:00.243 In my own mind can I justify what I'm saying? 00:24:01.370 --> 00:24:04.573 Or am I just spouting things off? 00:24:05.910 --> 00:24:08.900 So maybe part of that is that you can 00:24:08.900 --> 00:24:13.560 with this type of approach you really do get the opportunity 00:24:13.560 --> 00:24:17.710 for the student to reflect by not correcting right away, 00:24:17.710 --> 00:24:20.080 by continuing to ask questions. 00:24:20.080 --> 00:24:22.530 You're providing the student opportunities to reflect 00:24:22.530 --> 00:24:27.150 and then maybe when it's done and then you sit down 00:24:27.150 --> 00:24:29.290 with the student and then you help them have 00:24:29.290 --> 00:24:31.320 some metacognitive reflection on it. 00:24:31.320 --> 00:24:33.620 What would you like to work on it? 00:24:33.620 --> 00:24:36.040 What questions did you answer that you felt like 00:24:36.040 --> 00:24:38.800 you wanted to take back or think through again, 00:24:38.800 --> 00:24:41.250 or think more about or learn more about, right? 00:24:41.250 --> 00:24:45.250 To help them spot where they need ways 00:24:45.250 --> 00:24:48.120 they wanted to strengthen their ways of thinking. 00:24:48.120 --> 00:24:49.120 - Yeah, that makes sense. 00:24:49.120 --> 00:24:53.450 I think that idea of helping of thinking about 00:24:54.930 --> 00:24:57.000 your confidence in your answers 00:24:57.000 --> 00:24:58.730 is something that we talk about too, 00:24:58.730 --> 00:25:01.710 like after students give answers having them think about, 00:25:01.710 --> 00:25:03.540 so how sure of you were with that answer 00:25:03.540 --> 00:25:04.520 and what did you know 00:25:04.520 --> 00:25:07.320 and didn't you know and I could see them doing it 00:25:07.320 --> 00:25:09.170 with this too, so asking students, 00:25:09.170 --> 00:25:12.178 what do you think a fraction is? 00:25:12.178 --> 00:25:15.310 And then how confident are you in that answer 00:25:15.310 --> 00:25:18.980 and where that fits in would be interesting to think about, 00:25:18.980 --> 00:25:20.730 yeah, definitely. 00:25:20.730 --> 00:25:25.700 So as you think about advising teachers on next steps, 00:25:25.700 --> 00:25:28.350 so they've had this conversation, 00:25:28.350 --> 00:25:30.610 what is the next thing they should do 00:25:30.610 --> 00:25:33.053 based on the information that they get? 00:25:34.210 --> 00:25:35.730 - Well, I think as you're listening, 00:25:35.730 --> 00:25:39.000 you're trying to interpret, right? 00:25:39.000 --> 00:25:40.500 What are you noticing? 00:25:40.500 --> 00:25:42.750 Work on those, what do you wanna notice 00:25:42.750 --> 00:25:45.150 with what the student's saying. 00:25:45.150 --> 00:25:50.150 Reflect back on it, the things that we're putting together 00:25:50.730 --> 00:25:52.080 around these, we've got some videos 00:25:52.080 --> 00:25:56.850 and it's very fun to sit and watch because you get to, 00:25:56.850 --> 00:25:58.420 if you watch it two or three times sometimes 00:25:58.420 --> 00:26:01.090 you'll get even more and more out of it. 00:26:01.090 --> 00:26:06.090 So it's, yeah, teachers, what could you do with these? 00:26:06.825 --> 00:26:09.733 (both laughing) 00:26:09.733 --> 00:26:12.300 I don't know, did I answer that okay or? 00:26:12.300 --> 00:26:14.760 - Yeah, so the idea, it's going to have, 00:26:14.760 --> 00:26:16.220 the teachers are gonna have to do 00:26:16.220 --> 00:26:21.220 some pretty good interpretation of what they're hearing 00:26:21.360 --> 00:26:24.130 and then think about based on that 00:26:24.130 --> 00:26:29.130 what are the understandings that they need to either fill in 00:26:29.480 --> 00:26:32.873 or move forward or what that looks like. 00:26:32.873 --> 00:26:37.050 - And it's also self-reflective. 00:26:37.050 --> 00:26:40.460 I mean, when we were putting these, they made all of us 00:26:40.460 --> 00:26:43.327 stop and think, we had to sit there and think, 00:26:43.327 --> 00:26:45.467 "Oh, how would we answer this?" 00:26:46.391 --> 00:26:50.000 'Cause basically we weren't putting questions down 00:26:50.000 --> 00:26:51.330 to get right or wrong answers. 00:26:51.330 --> 00:26:54.590 It's coming up with questions that uncover thinking 00:26:54.590 --> 00:26:56.490 and you don't have to ask right or wrong questions 00:26:56.490 --> 00:26:58.240 to uncover thinking. 00:26:58.240 --> 00:27:02.410 - Right, yeah, I think that's another piece 00:27:02.410 --> 00:27:07.410 in math education that we're coming to better understandings 00:27:08.330 --> 00:27:11.894 that math education isn't just about right and wrong answers 00:27:11.894 --> 00:27:12.820 and where things are. 00:27:12.820 --> 00:27:16.263 Math does have right and wrong answers to some things, but. 00:27:17.655 --> 00:27:21.070 - I'm not minimizing the need for right or wrong answers. 00:27:21.070 --> 00:27:22.310 But there's a time for that 00:27:22.310 --> 00:27:25.570 and there's a time for listening to thinking. 00:27:25.570 --> 00:27:29.370 - Yeah, that totally makes sense, excellent. 00:27:29.370 --> 00:27:31.550 So anything that you're excited about, 00:27:31.550 --> 00:27:32.670 I'll close on this question. 00:27:32.670 --> 00:27:35.210 Anything you're excited about in the coming couple of months 00:27:35.210 --> 00:27:36.963 that your team work is working on. 00:27:38.011 --> 00:27:43.011 - Oh yeah, so one of the things I'm working on, 00:27:46.150 --> 00:27:50.270 I just did a talk on this at South by Southwest last week 00:27:50.270 --> 00:27:53.260 and I called it mathematical rigor mortis, 00:27:53.260 --> 00:27:54.493 the quest for a cure. 00:27:56.146 --> 00:27:59.900 And it's this idea where when we sit back 00:27:59.900 --> 00:28:02.180 and we think about our field math teachers, 00:28:02.180 --> 00:28:07.000 we think about how many ways does math kill things, right? 00:28:07.000 --> 00:28:11.073 Math kills dreams, it kills joy, it kills progress. 00:28:12.762 --> 00:28:15.660 And also it also kills moving policy 00:28:15.660 --> 00:28:16.773 in the right directions 00:28:16.773 --> 00:28:19.980 and making changes at systemic levels. 00:28:19.980 --> 00:28:22.930 This things are so entrenched in the way that we do things, 00:28:22.930 --> 00:28:24.780 but I'm encouraged and I'm encouraged 00:28:24.780 --> 00:28:27.110 and I hope that the folks out there are encouraged 00:28:27.110 --> 00:28:29.980 that I think we're moving in the right direction 00:28:29.980 --> 00:28:32.530 to cure mathematical rigor mortis. 00:28:32.530 --> 00:28:35.780 And if you ever wanna reach out and talk to me about it, 00:28:35.780 --> 00:28:38.570 I'd love to go into that as well. 00:28:38.570 --> 00:28:40.550 But that's something I'm encouraged about 00:28:40.550 --> 00:28:42.850 is the sort of spaces and the things 00:28:42.850 --> 00:28:45.460 I'm seeing across the country to help address that. 00:28:45.460 --> 00:28:48.190 - And we had a question from Angel on YouTube, 00:28:48.190 --> 00:28:51.900 who's a student and wants to know how they can stay 00:28:51.900 --> 00:28:53.650 motivated when they're doing work. 00:28:53.650 --> 00:28:56.650 We hear this question a lot from folks 00:28:56.650 --> 00:28:58.800 who are needing to stay motivated to do their work. 00:28:58.800 --> 00:29:00.725 What do you think? 00:29:00.725 --> 00:29:05.725 - Oh, so maybe Angel and I hope this is helpful 00:29:08.240 --> 00:29:11.820 but if math is being presented to you 00:29:11.820 --> 00:29:14.720 as though it's the collection of puzzle pieces. 00:29:14.720 --> 00:29:16.100 That you're just shaking the box 00:29:16.100 --> 00:29:17.950 and you can kinda hear them rattling, 00:29:19.643 --> 00:29:20.980 the challenge would be to know that 00:29:20.980 --> 00:29:23.560 it does make a big, beautiful picture, 00:29:23.560 --> 00:29:25.280 that all of the pieces fit together, 00:29:25.280 --> 00:29:27.400 that no piece stands alone. 00:29:27.400 --> 00:29:30.860 And that if you find that encouraging 00:29:30.860 --> 00:29:34.190 then you can figure out how these pieces fit together, 00:29:34.190 --> 00:29:36.390 what's the story that's being told here. 00:29:36.390 --> 00:29:40.110 It's a great one and there are lots of places 00:29:40.110 --> 00:29:42.950 where you could go to help get some support on that as well. 00:29:42.950 --> 00:29:47.950 But don't let the current situations that you might be in, 00:29:49.170 --> 00:29:53.450 or these things that are happening all around us right now, 00:29:53.450 --> 00:29:57.490 don't let them destroy the joy that mathematics has for you. 00:29:57.490 --> 00:29:59.380 That would be my take. 00:29:59.380 --> 00:30:02.010 - I like it and putting together that puzzle 00:30:02.010 --> 00:30:04.700 could be a challenge, a fun challenge to undertake 00:30:04.700 --> 00:30:06.470 and to think through, excellent. 00:30:06.470 --> 00:30:09.040 - Yeah, but it's there, it's ready to be put together, 00:30:09.040 --> 00:30:11.203 but it gets put together in your own head. 00:30:12.370 --> 00:30:15.410 - Fantastic, well thank you so much for joining us today. 00:30:15.410 --> 00:30:16.950 It was a pleasure to talk to you 00:30:16.950 --> 00:30:19.550 and I hope some of our folks out there 00:30:19.550 --> 00:30:22.260 dive into those conversation starters. 00:30:22.260 --> 00:30:23.960 - Well, thank you, this was great.

Sexual and asexual reproduction

https://www.youtube.com/watch?v=IZ6EvH240iA

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https://www.youtube.com/api/timedtext?v=IZ6EvH240iA&ei=wFWUZaarGYOdxgKi0b2ABQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=425465C7046E3A8072EE756C7D893B159BE2A970.3BFA85211A573DDBDDCE61D920A438393099FCEF&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.170 --> 00:00:02.100 - [Narrator] The planet we live on is full 00:00:02.100 --> 00:00:05.150 of life and has been for billions of years. 00:00:05.150 --> 00:00:07.470 Living things on earth have existed for as long 00:00:07.470 --> 00:00:11.090 as they have, because life found a way to create life. 00:00:11.090 --> 00:00:12.520 Sounds crazy, right? 00:00:12.520 --> 00:00:13.840 To put it another way, 00:00:13.840 --> 00:00:16.240 living things found ways to reproduce, 00:00:16.240 --> 00:00:18.220 creating offspring that can then go on 00:00:18.220 --> 00:00:19.910 to reproduce themselves, 00:00:19.910 --> 00:00:22.410 but what exactly is reproduction? 00:00:22.410 --> 00:00:26.160 Well, reproduction is the process of making new organisms. 00:00:26.160 --> 00:00:28.730 This happens when parent organisms reproduce 00:00:28.730 --> 00:00:30.330 to form offspring. 00:00:30.330 --> 00:00:31.410 During reproduction, 00:00:31.410 --> 00:00:34.080 organisms pass their genetic information 00:00:34.080 --> 00:00:35.640 on to their offspring. 00:00:35.640 --> 00:00:38.040 This genetic information provides blueprints 00:00:38.040 --> 00:00:40.760 for how the offspring will grow and develop 00:00:40.760 --> 00:00:43.800 and it's how traits get passed on from one generation 00:00:43.800 --> 00:00:44.940 to the next. 00:00:44.940 --> 00:00:48.540 There are two main ways organisms on earth reproduce. 00:00:48.540 --> 00:00:52.960 This is through asexual reproduction or sexual reproduction. 00:00:52.960 --> 00:00:56.480 Let's start off by breaking down asexual reproduction first. 00:00:56.480 --> 00:00:59.870 In asexual reproduction, only one parent is involved 00:00:59.870 --> 00:01:01.670 in producing offspring. 00:01:01.670 --> 00:01:04.270 Due to this, the offspring will inherit all 00:01:04.270 --> 00:01:06.930 of their genes from that single parent. 00:01:06.930 --> 00:01:10.420 This means that asexual reproduction produces offspring 00:01:10.420 --> 00:01:13.240 that are genetically identical to their parent, 00:01:13.240 --> 00:01:17.200 or in other words, they have the same collection of genes. 00:01:17.200 --> 00:01:20.190 Various kinds of microorganisms, plants, 00:01:20.190 --> 00:01:23.540 and even animals are able to reproduce asexually. 00:01:23.540 --> 00:01:25.400 An example of asexual reproduction 00:01:25.400 --> 00:01:28.650 in microorganisms can be seen in bacteria. 00:01:28.650 --> 00:01:31.080 This is due to their use of a specific type 00:01:31.080 --> 00:01:34.270 of asexual reproduction called binary fission. 00:01:34.270 --> 00:01:35.450 During this process, 00:01:35.450 --> 00:01:38.800 a single bacteria cell grows, copies its genes, 00:01:38.800 --> 00:01:41.460 and divides into two identical cells, 00:01:41.460 --> 00:01:43.330 kind of like a copy machine. 00:01:43.330 --> 00:01:45.940 Plants are able to reproduce asexually too. 00:01:45.940 --> 00:01:48.580 For example, some plants grow their offspring off 00:01:48.580 --> 00:01:49.870 of themselves. 00:01:49.870 --> 00:01:51.820 In fact, in many succulents, 00:01:51.820 --> 00:01:55.370 you can see baby plants growing off of their parent plant. 00:01:55.370 --> 00:01:58.430 These babies have the same genes as their parent plant 00:01:58.430 --> 00:01:59.560 and can grow on their own 00:01:59.560 --> 00:02:01.980 if you remove them and plant them in soil. 00:02:01.980 --> 00:02:03.870 Finally, and interestingly, 00:02:03.870 --> 00:02:06.800 there are various animals that can reproduce asexually. 00:02:06.800 --> 00:02:10.720 One example is seen in starfish or sea stars. 00:02:10.720 --> 00:02:12.710 Some species of starfish can split 00:02:12.710 --> 00:02:16.610 into multiple parts that then grow into new starfish 00:02:16.610 --> 00:02:19.170 and, since they have the same genes, 00:02:19.170 --> 00:02:22.620 each new starfish is a clone of its original. 00:02:22.620 --> 00:02:25.160 Now that we've covered asexual reproduction, 00:02:25.160 --> 00:02:27.900 let's move on to sexual reproduction. 00:02:27.900 --> 00:02:30.640 Unlike asexual reproduction, sexual reproduction 00:02:30.640 --> 00:02:33.530 involves two parents producing an offspring together 00:02:33.530 --> 00:02:35.070 instead of one. 00:02:35.070 --> 00:02:36.010 This is important 00:02:36.010 --> 00:02:38.510 because it means that the offspring will inherit half 00:02:38.510 --> 00:02:40.160 of their genes from one parent 00:02:40.160 --> 00:02:42.820 and half of their genes from the other. 00:02:42.820 --> 00:02:46.230 Because of this, a sexual reproduction produces offspring 00:02:46.230 --> 00:02:47.980 that are genetically distinct 00:02:47.980 --> 00:02:49.250 or have a different combination 00:02:49.250 --> 00:02:51.830 of genes compared to either parent. 00:02:51.830 --> 00:02:54.740 With this, because of the way the genes are passed on, 00:02:54.740 --> 00:02:56.690 there are tons of different combinations 00:02:56.690 --> 00:02:59.960 of genes that can be received from the two parents. 00:02:59.960 --> 00:03:01.560 In other words, this means 00:03:01.560 --> 00:03:05.210 that sexual reproduction creates offspring that show a lot 00:03:05.210 --> 00:03:08.450 of genetic variation between their siblings. 00:03:08.450 --> 00:03:09.880 To better understand this, 00:03:09.880 --> 00:03:11.640 let's take a look at my own dogs. 00:03:11.640 --> 00:03:12.720 They're brother and sister, 00:03:12.720 --> 00:03:15.660 so they share the same parents, which I've drawn here. 00:03:15.660 --> 00:03:18.560 As you've probably noticed, my dogs look pretty different 00:03:18.560 --> 00:03:19.490 from each other. 00:03:19.490 --> 00:03:22.410 One of the most notable differences though is how one 00:03:22.410 --> 00:03:24.910 of them received genes from this parent 00:03:24.910 --> 00:03:26.780 that gave them markings above their eyes 00:03:26.780 --> 00:03:30.250 that kind of looked like eyebrows while the other did not. 00:03:30.250 --> 00:03:32.480 And while it's easy to spot genetic differences, 00:03:32.480 --> 00:03:34.100 like my dog's eyebrows, 00:03:34.100 --> 00:03:38.030 genetic variation goes way deeper than dog's fur. 00:03:38.030 --> 00:03:40.700 It's what makes sexual reproduced organisms 00:03:40.700 --> 00:03:43.020 genetically distinct from each other 00:03:43.020 --> 00:03:46.160 and gives the building blocks to who they are. 00:03:46.160 --> 00:03:48.340 And with that, you now know the difference 00:03:48.340 --> 00:03:51.390 between asexual and sexual reproduction. 00:03:51.390 --> 00:03:54.310 Let's do a quick overview of what you've learned today. 00:03:54.310 --> 00:03:57.230 Living organisms reproduce to create offspring 00:03:57.230 --> 00:04:00.770 through either asexual or sexual reproduction. 00:04:00.770 --> 00:04:03.870 Asexual reproduction involves only one parent 00:04:03.870 --> 00:04:07.900 meaning the parent and offspring will have identical genes. 00:04:07.900 --> 00:04:10.850 Sexual reproduction involves two parents 00:04:10.850 --> 00:04:13.750 and results in offspring that are genetically unique 00:04:13.750 --> 00:04:16.230 compared to either parent and this all goes 00:04:16.230 --> 00:04:18.620 to show how fantastically unique life 00:04:18.620 --> 00:04:19.930 on earth is. 00:04:19.930 --> 00:04:21.600 Though organisms may differ 00:04:21.600 --> 00:04:23.860 in the ways that they've been able to reproduce 00:04:23.860 --> 00:04:25.070 as seen in the examples 00:04:25.070 --> 00:04:29.300 between bacteria, succulents, starfish, and dogs, 00:04:29.300 --> 00:04:32.370 these organisms, as with all living things, 00:04:32.370 --> 00:04:35.160 share the ability to create more life 00:04:35.160 --> 00:04:36.830 just as all life has shared 00:04:36.830 --> 00:04:39.153 for billions of years here on this planet.

Organism growth and the environment

https://www.youtube.com/watch?v=XEkafr12Wd8

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https://www.youtube.com/api/timedtext?v=XEkafr12Wd8&ei=wFWUZbjuKu-2mLAPlJaZ6Ak&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D59D46B9CF770D59FE307B25F455874355E311.7C3C3190464BB9BFB39D3D80DD4A3D31BC65455F&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.400 --> 00:00:01.760 - [Instructor] Hey, have you ever seen 00:00:01.760 --> 00:00:03.120 this kind of plant before? 00:00:03.120 --> 00:00:04.660 It's called a dandelion. 00:00:04.660 --> 00:00:07.970 If you live in a tropical climate, it might be unfamiliar, 00:00:07.970 --> 00:00:10.010 but if you live in a more temperate zone, 00:00:10.010 --> 00:00:13.080 you'll probably recognize it as it's a very common plant. 00:00:13.080 --> 00:00:16.410 Dandelions make yellow flowers that develop into balls 00:00:16.410 --> 00:00:19.990 of these fluffy white seed heads that fly off the plant. 00:00:19.990 --> 00:00:22.070 This can happen by a gust of wind, 00:00:22.070 --> 00:00:23.560 by animals spreading them, 00:00:23.560 --> 00:00:26.180 or even by someone blowing on the plant. 00:00:26.180 --> 00:00:28.750 When this happens, it seeds fly into the air 00:00:28.750 --> 00:00:31.430 and land on new spots on the ground. 00:00:31.430 --> 00:00:34.140 From there, the seeds can grow into new dandelions, 00:00:34.140 --> 00:00:36.720 starting the whole cycle over. 00:00:36.720 --> 00:00:39.180 But why do dandelions do this? 00:00:39.180 --> 00:00:41.330 Why do they turn into puff balls? 00:00:41.330 --> 00:00:43.010 Why are they yellow? 00:00:43.010 --> 00:00:44.700 If they don't have brains, 00:00:44.700 --> 00:00:48.320 how do they seem to know when to release their seeds? 00:00:48.320 --> 00:00:51.140 These are all complicated questions. 00:00:51.140 --> 00:00:53.090 But to begin answering them, 00:00:53.090 --> 00:00:56.440 we can talk about what influences the growth and development 00:00:56.440 --> 00:01:00.670 of dandelions and in turn all living things. 00:01:00.670 --> 00:01:04.110 So what determines how a dandelion will grow? 00:01:04.110 --> 00:01:07.070 Its genes and its environment. 00:01:07.070 --> 00:01:09.980 Let's take a moment to review what genes are. 00:01:09.980 --> 00:01:12.370 Genes make up the hereditary material 00:01:12.370 --> 00:01:14.540 inside an organism cells. 00:01:14.540 --> 00:01:16.170 Genes provide the information 00:01:16.170 --> 00:01:18.510 about what traits an organism has. 00:01:18.510 --> 00:01:22.490 So the reason that our dandelion has yellow pedals 00:01:22.490 --> 00:01:24.640 and develops fluffy white seed heads 00:01:24.640 --> 00:01:27.040 lies within its genes. 00:01:27.040 --> 00:01:30.450 Any influence genes have on the way an organism grows 00:01:30.450 --> 00:01:32.550 is called a genetic factor. 00:01:32.550 --> 00:01:35.750 So if one dandelion has more seeds than another 00:01:35.750 --> 00:01:39.320 as a result of which version of a certain gene it has, 00:01:39.320 --> 00:01:41.450 we can say that the difference in seed number 00:01:41.450 --> 00:01:43.780 is due to a genetic factor. 00:01:43.780 --> 00:01:46.800 The other major influence on how a dandelion grows 00:01:46.800 --> 00:01:48.510 is its environment. 00:01:48.510 --> 00:01:51.280 But what makes up an organism's environment? 00:01:51.280 --> 00:01:53.410 The environment is the set of conditions 00:01:53.410 --> 00:01:56.610 an organism is exposed to during its life. 00:01:56.610 --> 00:01:59.100 For a dandelion, this includes temperature, 00:01:59.100 --> 00:02:01.460 how much light and water it gets, 00:02:01.460 --> 00:02:03.900 and which nutrients are present in the soil 00:02:03.900 --> 00:02:05.330 where it grows. 00:02:05.330 --> 00:02:09.310 Any influence the environment has on an organism's growth 00:02:09.310 --> 00:02:11.990 is called an environmental factor. 00:02:11.990 --> 00:02:15.520 So if one dandelion plant is exposed to more sunlight 00:02:15.520 --> 00:02:18.750 than another and grows bigger, as a result, 00:02:18.750 --> 00:02:20.720 we can say that the difference is due 00:02:20.720 --> 00:02:23.310 to an environmental factor. 00:02:23.310 --> 00:02:25.750 But plants aren't the only living organisms 00:02:25.750 --> 00:02:28.230 that are motivated by these factors. 00:02:28.230 --> 00:02:32.540 Animals are also influenced by their genes and environment. 00:02:32.540 --> 00:02:34.900 For example, let's look at dogs. 00:02:34.900 --> 00:02:38.810 Dogs come in many different shapes, sizes, colors, 00:02:38.810 --> 00:02:41.410 and each have their own unique features. 00:02:41.410 --> 00:02:43.870 We can see this when looking at different breeds, 00:02:43.870 --> 00:02:47.130 like pugs which are small with squishy faces, 00:02:47.130 --> 00:02:48.410 and golden retrievers, 00:02:48.410 --> 00:02:52.010 which are large with flowing locks of golden fur. 00:02:52.010 --> 00:02:53.980 These traits are largely determined 00:02:53.980 --> 00:02:56.680 by which genes each breed of dog has, 00:02:56.680 --> 00:03:00.380 or in other words, by genetic factors. 00:03:00.380 --> 00:03:04.360 But dogs are also influenced by environmental factors too. 00:03:04.360 --> 00:03:07.180 For instance, how much food they get as they grow 00:03:07.180 --> 00:03:09.170 helps determine their size, 00:03:09.170 --> 00:03:11.420 and what they learn from other dogs, 00:03:11.420 --> 00:03:14.390 and from people help determine their behaviors. 00:03:14.390 --> 00:03:17.200 Like when you teach your dog a new trick. 00:03:17.200 --> 00:03:19.570 And now you know how organisms are influenced 00:03:19.570 --> 00:03:21.440 by genetics and their environment 00:03:21.440 --> 00:03:24.210 when it comes to growth and development. 00:03:24.210 --> 00:03:27.130 Let's do a quick review of what you've learned today. 00:03:27.130 --> 00:03:29.040 First, there are two main factors 00:03:29.040 --> 00:03:31.300 that influence an organism's growth, 00:03:31.300 --> 00:03:35.000 these are genetic and environmental factors. 00:03:35.000 --> 00:03:38.010 Genetic factors are the genes the organism gets 00:03:38.010 --> 00:03:40.090 from its parent or parents. 00:03:40.090 --> 00:03:42.477 While environmental factors are the conditions 00:03:42.477 --> 00:03:46.080 and organism is exposed to as it grows. 00:03:46.080 --> 00:03:48.600 These factors show that all living organisms 00:03:48.600 --> 00:03:53.040 have a couple things in common even dogs and dandelions. 00:03:53.040 --> 00:03:55.610 So while our interactions with them may differ 00:03:55.610 --> 00:03:58.020 like how you can't teach a dandelion to sit 00:03:58.020 --> 00:03:59.900 like you can with a dog, 00:03:59.900 --> 00:04:02.810 both organisms experience growth and development 00:04:02.810 --> 00:04:05.483 through their own unique genes and environments.

Sensory processing and the brain

https://www.youtube.com/watch?v=fMrz3L9bMsI

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https://www.youtube.com/api/timedtext?v=fMrz3L9bMsI&ei=wFWUZdyFOY6QhcIPtNCz-A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245297&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=AB8E89C1040806E0709EC53FB2A769470B6A2733.8089C447011EA74B26B12FBC2BF6532F93CB1107&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.200 --> 00:00:02.070 - [Narrator] As humans, we have a lot of senses 00:00:02.070 --> 00:00:04.920 that we put to use on a regular basis. 00:00:04.920 --> 00:00:09.500 They include sight, smell, taste, touch, and hearing. 00:00:09.500 --> 00:00:12.640 But have you ever wondered how it all works? 00:00:12.640 --> 00:00:15.940 How do you look at a beautiful painting in an art museum, 00:00:15.940 --> 00:00:18.840 or smell the rain outside on a stormy day, 00:00:18.840 --> 00:00:20.660 or feel that your favorite pair of socks 00:00:20.660 --> 00:00:22.510 are still a little damp, 00:00:22.510 --> 00:00:25.120 and need another cycle in the dryer? 00:00:25.120 --> 00:00:27.180 How does that information make its way 00:00:27.180 --> 00:00:30.240 from our sensory organs to our brains? 00:00:30.240 --> 00:00:33.580 Well, the answer lies in the nervous system. 00:00:33.580 --> 00:00:35.284 If you remember, our bodies are made up 00:00:35.284 --> 00:00:38.800 of multiple complex organ systems that work together 00:00:38.800 --> 00:00:41.910 to perform all different kinds of functions. 00:00:41.910 --> 00:00:45.070 Today, let's talk specifically about the nervous system, 00:00:45.070 --> 00:00:46.820 which is an organ system that allows us 00:00:46.820 --> 00:00:50.540 to sense and respond to our environment. 00:00:50.540 --> 00:00:53.341 To begin, the nervous system contains specialized cells 00:00:53.341 --> 00:00:56.550 and cell parts, called sensory receptors, 00:00:56.550 --> 00:00:59.610 which are able to pick up signals from the environment. 00:00:59.610 --> 00:01:01.760 These signals are called stimuli, 00:01:01.760 --> 00:01:04.970 or stimulus if you're talking about just one. 00:01:04.970 --> 00:01:07.890 Stimuli can come in many different forms. 00:01:07.890 --> 00:01:11.820 For instance, mechanical stimuli are physical in nature, 00:01:11.820 --> 00:01:15.570 and are involved with our senses of touch and hearing. 00:01:15.570 --> 00:01:16.910 You can strum a guitar, 00:01:16.910 --> 00:01:19.360 feeling the strings against your fingertips, 00:01:19.360 --> 00:01:21.900 and listening to the unique tones it produces 00:01:21.900 --> 00:01:23.600 as the strings vibrate. 00:01:23.600 --> 00:01:26.430 Those are all mechanical stimuli. 00:01:26.430 --> 00:01:28.900 Chemical stimuli are made up of molecules, 00:01:28.900 --> 00:01:32.390 and are involved with our senses of smell and taste. 00:01:32.390 --> 00:01:34.020 To illustrate an example, 00:01:34.020 --> 00:01:37.860 imagine eating a tasty bowl of chicken noodle soup. 00:01:37.860 --> 00:01:40.500 As you spoon mouthfuls of soup into your mouth, 00:01:40.500 --> 00:01:42.634 your taste and olfactory receptors 00:01:42.634 --> 00:01:44.234 are flooded with molecules 00:01:44.234 --> 00:01:47.690 that signal the qualities of the food you're eating. 00:01:47.690 --> 00:01:50.610 These molecular signals are chemical stimuli. 00:01:50.610 --> 00:01:51.810 And in this case, 00:01:51.810 --> 00:01:53.680 the molecules from the chicken noodle soup 00:01:53.680 --> 00:01:56.410 convey that the food you're eating is savory, 00:01:56.410 --> 00:01:58.800 and extremely delicious. 00:01:58.800 --> 00:02:01.220 Lastly, electromagnetic stimuli 00:02:01.220 --> 00:02:02.950 are involved with our sense of sight, 00:02:02.950 --> 00:02:06.140 and include the light that comes into our eyes every day. 00:02:06.140 --> 00:02:08.070 The sunlight that makes you squint, 00:02:08.070 --> 00:02:10.600 the traffic lights you see on the street, 00:02:10.600 --> 00:02:13.520 and the vibrant and diverse colors all around you. 00:02:13.520 --> 00:02:14.762 These are just a few examples 00:02:14.762 --> 00:02:18.660 of electromagnetic stimuli in the form of light. 00:02:18.660 --> 00:02:23.210 So then what happens after sensory receptors detect stimuli? 00:02:23.210 --> 00:02:26.410 Well, once a sensory receptor receives the information, 00:02:26.410 --> 00:02:29.430 it passes this information along nerve cells. 00:02:29.430 --> 00:02:31.440 Here's a picture of a nerve cell, 00:02:31.440 --> 00:02:33.313 which is specialized to transmit information 00:02:33.313 --> 00:02:36.300 in the form of electrical signals. 00:02:36.300 --> 00:02:39.420 These signals are transmitted along nerves to the brain, 00:02:39.420 --> 00:02:41.710 which is then responsible for processing, 00:02:41.710 --> 00:02:43.740 or organizing sensory information 00:02:43.740 --> 00:02:46.100 from different sensory receptors. 00:02:46.100 --> 00:02:48.080 After processing the information, 00:02:48.080 --> 00:02:49.407 the brain can elicit a response, 00:02:49.407 --> 00:02:52.610 and also store the information in the form of a memory 00:02:52.610 --> 00:02:54.140 for future use. 00:02:54.140 --> 00:02:55.940 For example, imagine you're playing catch 00:02:55.940 --> 00:02:57.830 with friends in a park. 00:02:57.830 --> 00:02:59.829 Your sensory receptors pick up information 00:02:59.829 --> 00:03:02.470 as you watch the ball come towards you, 00:03:02.470 --> 00:03:04.670 and feel the wind on your skin. 00:03:04.670 --> 00:03:05.758 Signals from these receptors 00:03:05.758 --> 00:03:08.670 travel along nerve cells to your brain, 00:03:08.670 --> 00:03:11.640 where all these different signals are organized. 00:03:11.640 --> 00:03:13.640 Then your brain elicits a response, 00:03:13.640 --> 00:03:16.040 such as moving to just the right spot, 00:03:16.040 --> 00:03:18.370 and putting your hands out to catch the ball. 00:03:18.370 --> 00:03:20.640 And the brain also stores a memory, 00:03:20.640 --> 00:03:22.260 perhaps remembering playing catch 00:03:22.260 --> 00:03:25.810 as a fun activity that you'd wanna do again. 00:03:25.810 --> 00:03:27.821 You can almost think of this flow of information 00:03:27.821 --> 00:03:31.670 from a stimulus to sensing, to processing, 00:03:31.670 --> 00:03:35.230 and finally, to eliciting a response or storing information, 00:03:35.230 --> 00:03:37.660 like a complex relay race. 00:03:37.660 --> 00:03:41.400 Sensory receptors pick up message in the form of stimuli, 00:03:41.400 --> 00:03:45.110 and pass this information along to nerves, and to the brain. 00:03:45.110 --> 00:03:47.522 Only in this relay, the end result at the finish line 00:03:47.522 --> 00:03:51.630 is a response to the stimulus and information storage. 00:03:51.630 --> 00:03:52.760 So to summarize, 00:03:52.760 --> 00:03:55.270 today, we talked about how our bodies sense, 00:03:55.270 --> 00:03:57.210 and respond to the environment. 00:03:57.210 --> 00:04:00.110 Information is transferred from a stimulus 00:04:00.110 --> 00:04:02.880 to a sensory receptor, to nerve cells, 00:04:02.880 --> 00:04:06.350 and finally to the brain, where processing occurs. 00:04:06.350 --> 00:04:08.210 Whether we're aware of it or not, 00:04:08.210 --> 00:04:12.400 our nervous system is working at rapid-fire speed every day 00:04:12.400 --> 00:04:14.170 to provide us with the information 00:04:14.170 --> 00:04:16.810 our bodies need to sense what's in our environment, 00:04:16.810 --> 00:04:18.223 and thrive in it.

Writing fraction division story problems

https://www.youtube.com/watch?v=UEna8ZEy6k4

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https://www.youtube.com/api/timedtext?v=UEna8ZEy6k4&ei=wFWUZdHBMoqhp-oP7paXIA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245296&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=19CB28FD3D9EB39190D52AFF8A41FEDF48BB3E25.462C61F7C3993E5E74B0988DDCC7479F6B7B6DA4&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.180 --> 00:00:04.100 - [Instructor] We're told that Darryl spent 24 1/4 hours 00:00:04.100 --> 00:00:06.610 writing a chapter of a novel. 00:00:06.610 --> 00:00:11.090 And then they ask us, what are some things that 24 1/4 00:00:11.090 --> 00:00:16.090 divided by 3/4 could represent in this context? 00:00:16.290 --> 00:00:18.090 So my understanding of this 00:00:18.090 --> 00:00:21.280 is they really just want us to be a little bit creative 00:00:21.280 --> 00:00:24.610 about what division by a fraction 00:00:24.610 --> 00:00:28.270 could represent in a given context. 00:00:28.270 --> 00:00:31.190 So, well, one, I encourage you to pause your video 00:00:31.190 --> 00:00:34.100 and think about that a little bit before I think about it. 00:00:34.100 --> 00:00:39.100 But one thing I think about is, well, if I took 24 1/4, 00:00:39.340 --> 00:00:43.280 and if I were to divide it into chunks of 3/4 of an hour 00:00:43.280 --> 00:00:47.140 because this is in hours, how many chunks would I have? 00:00:47.140 --> 00:00:52.080 So this could represent, let's say that he spent, 00:00:52.080 --> 00:00:55.280 he spent 45 minutes, 00:00:55.280 --> 00:00:57.140 which is the same thing of 3/4 of an hour, 00:00:57.140 --> 00:01:00.950 3/4 hours, of an hour, I should say, 00:01:00.950 --> 00:01:05.950 3/4 of an hour each day. 00:01:08.710 --> 00:01:13.710 How many days, how many days did it take him, did it take? 00:01:19.990 --> 00:01:24.670 And then you could evaluate this, 24 1/4 divided by 3/4. 00:01:24.670 --> 00:01:27.480 We've talked about how to evaluate that in other videos. 00:01:27.480 --> 00:01:29.270 So that's one context. 00:01:29.270 --> 00:01:34.270 Another one could be some type of a comparison. 00:01:34.470 --> 00:01:36.520 So let's say that 24 1/4 00:01:36.520 --> 00:01:41.250 is 3/4 of the amount of time 00:01:41.250 --> 00:01:43.950 that he spent doing something else. 00:01:43.950 --> 00:01:47.630 So let's say, so this is now a completely different context. 00:01:47.630 --> 00:01:48.640 I'm gonna put a line here. 00:01:48.640 --> 00:01:50.460 I'll do it in a different color just to make it clear 00:01:50.460 --> 00:01:52.030 it's a different context. 00:01:52.030 --> 00:01:55.860 So another one could be to justify doing this division, 00:01:55.860 --> 00:02:00.720 he spent 3/4 as long writing, 00:02:03.230 --> 00:02:08.230 writing as he spent illustrating, 00:02:10.120 --> 00:02:12.713 illustrating the chapter. 00:02:14.390 --> 00:02:15.630 And so then the question 00:02:15.630 --> 00:02:18.380 is how long did he spend illustrating? 00:02:18.380 --> 00:02:23.380 How long did he spend illustrating? 00:02:27.510 --> 00:02:29.030 Now, I really want you to think about this one. 00:02:29.030 --> 00:02:31.900 My brain, actually, this one takes a little bit longer 00:02:31.900 --> 00:02:34.280 for my brain to process. 00:02:34.280 --> 00:02:35.240 But when you think about it, 00:02:35.240 --> 00:02:38.280 if you divide by a fraction that is less than one, 00:02:38.280 --> 00:02:39.700 you're gonna get a number larger 00:02:39.700 --> 00:02:41.600 than the one that you're dealing with. 00:02:41.600 --> 00:02:43.410 Or another way to think about it, 00:02:43.410 --> 00:02:47.600 the time spent illustrating, time illustrating, 00:02:47.600 --> 00:02:48.870 I'll write it like this, 00:02:48.870 --> 00:02:52.330 the time illustrating times 3/4 00:02:52.330 --> 00:02:55.030 should be equal to the time spent writing 00:02:55.030 --> 00:02:57.280 because it says he spent, 00:02:57.280 --> 00:03:00.110 or he spent, I forgot to write that, 00:03:00.110 --> 00:03:03.550 he spent 3/4 as long writing as he spent illustrating. 00:03:03.550 --> 00:03:05.430 So time illustrating times 3/4 00:03:05.430 --> 00:03:08.810 should be time writing or 24 1/4. 00:03:08.810 --> 00:03:12.530 So if something times 3/4 is equal to 24 1/4, 00:03:12.530 --> 00:03:17.530 then 24 1/4 divided by 3/4 00:03:18.090 --> 00:03:23.090 should be equal to time illustrating. 00:03:23.710 --> 00:03:26.240 So these are the two contexts that I can think of 00:03:26.240 --> 00:03:27.170 that might make sense, 00:03:27.170 --> 00:03:29.220 but you might be able to think of others.

Area with fraction division example

https://www.youtube.com/watch?v=6K6tQulp-x8

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https://www.youtube.com/api/timedtext?v=6K6tQulp-x8&ei=wVWUZfHWA4fpxN8PntuTyAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245297&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=C263D90BEB4D9D5981DD9CB6DAFFB530FD86C4EE.C5ECE4354AD790A151A4A6003A94D66922760518&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.540 --> 00:00:02.840 - [Instructor] We're told a yoga mat is 3/5 of a meter wide. 00:00:02.840 --> 00:00:06.620 It has an area of 1 and 2/25 square meters. 00:00:06.620 --> 00:00:09.250 What is the length of the mat? 00:00:09.250 --> 00:00:12.100 Well, we know that length times width 00:00:12.100 --> 00:00:14.260 is going to give you area, 00:00:14.260 --> 00:00:16.070 or another way of thinking about it, 00:00:16.070 --> 00:00:19.040 if the product of two numbers gives you a third number, 00:00:19.040 --> 00:00:20.170 if you take that third number 00:00:20.170 --> 00:00:21.720 and divide it by one of these, 00:00:21.720 --> 00:00:22.700 you're going to get the other one. 00:00:22.700 --> 00:00:23.770 So another way of thinking about it 00:00:23.770 --> 00:00:28.770 is length would be the same thing as area divided by width. 00:00:29.460 --> 00:00:32.200 So we're trying to figure out the length here. 00:00:32.200 --> 00:00:34.550 We have the area, we have the width. 00:00:34.550 --> 00:00:37.980 So our length is going to be 1 and 2/25, 00:00:37.980 --> 00:00:42.980 1 and 2/25 divided by 3/5. 00:00:44.730 --> 00:00:46.970 Now this is going to be the same thing as, 00:00:46.970 --> 00:00:49.320 let me write this as an improper fraction, 00:00:49.320 --> 00:00:52.430 it's gonna be easier to do some arithmetic with it. 00:00:52.430 --> 00:00:57.430 So one is the same thing as 25/25, plus 2/25, 00:00:58.030 --> 00:01:03.030 this is 27/25 divided by 3/5. 00:01:05.630 --> 00:01:07.590 And we've already talked about how this is saying 00:01:07.590 --> 00:01:11.250 how many 3/5 can fit into 27/25. 00:01:11.250 --> 00:01:13.860 And we've given the intuition why this is the same thing 00:01:13.860 --> 00:01:18.860 as just multiplying 27/25 times the reciprocal of 3/5, 00:01:21.030 --> 00:01:24.230 which is 5/3. 00:01:24.230 --> 00:01:26.270 And so this is going to be equal to, 00:01:26.270 --> 00:01:28.300 and actually I'm gonna factor this out a little bit 00:01:28.300 --> 00:01:30.340 to simplify things a bit. 00:01:30.340 --> 00:01:34.110 27 is 3 x 3 x 3. 00:01:34.110 --> 00:01:36.910 25 is 5 x 5. 00:01:36.910 --> 00:01:38.120 So this is going to be equal to, 00:01:38.120 --> 00:01:40.980 in our numerator we're gonna have 3 x 3 x 3 x 5. 00:01:40.980 --> 00:01:45.250 3 x 3 x 3 x 5. 00:01:45.250 --> 00:01:49.220 And then in our denominator we're gonna have 5 x 5 x 3. 00:01:49.220 --> 00:01:52.290 5 x 5 x 3. 00:01:52.290 --> 00:01:55.310 And then we can reduce this a little bit. 00:01:55.310 --> 00:01:56.670 We can divide both the numerator 00:01:56.670 --> 00:01:58.180 and the denominator by five. 00:01:58.180 --> 00:01:59.470 We can divide both the numerator 00:01:59.470 --> 00:02:01.290 and the denominator by three. 00:02:01.290 --> 00:02:06.290 So in the numerator, we're gonna 3 x 3, which is 9/5. 00:02:06.680 --> 00:02:09.820 So this is all going to be equal to 9/5. 00:02:09.820 --> 00:02:13.380 So the yoga mat is 3/5 of a meter wide 00:02:13.380 --> 00:02:16.690 and 9/5 of a meter long. 00:02:16.690 --> 00:02:19.320 Now let's make sure that this makes sense. 00:02:19.320 --> 00:02:21.030 So I'm gonna make a grid. 00:02:21.030 --> 00:02:26.030 So this right over here is 1/5 of a meter. 00:02:26.998 --> 00:02:29.050 1/5 of a meter in that dimension 00:02:29.050 --> 00:02:33.600 and 1/5 of a meter in that dimension. 00:02:33.600 --> 00:02:38.600 And then we can see, well, if this is 1/5 of a meter, 00:02:38.840 --> 00:02:43.840 then the width right over here is 3/5 of a meter. 00:02:44.125 --> 00:02:47.810 Our length right over here, we have 1, 2, 3, 4, 00:02:47.810 --> 00:02:50.670 5, 6, 7, 8, 9, fifths. 00:02:50.670 --> 00:02:52.780 It is 9/5. 00:02:52.780 --> 00:02:56.900 Now each of these units, what is its area? 00:02:56.900 --> 00:03:01.750 Well, it is 1/25 meter squared. 00:03:01.750 --> 00:03:03.530 And how many of these do we have? 00:03:03.530 --> 00:03:07.810 Well, we can see, we have three rows of nine, 00:03:07.810 --> 00:03:11.350 which is 27 of these 25ths, 00:03:11.350 --> 00:03:14.280 so we're gonna have 27/25 square meters, 00:03:14.280 --> 00:03:17.833 which is the same thing as 1 and 2/5 square meters.

Decimal multiplication place value

https://www.youtube.com/watch?v=hdKDVDjUHhs

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WEBVTT Kind: captions Language: en 00:00:00.620 --> 00:00:02.280 - [Instructor] This is an exercise from Khan Academy. 00:00:02.280 --> 00:00:04.750 It tells us that the product 75 times 61 00:00:04.750 --> 00:00:08.110 is equal to 4,575. 00:00:08.110 --> 00:00:10.545 Use a previous fact to evaluate as a decimal. 00:00:10.545 --> 00:00:11.734 This right over here, 00:00:11.734 --> 00:00:15.900 7.5 times 0.061. 00:00:15.900 --> 00:00:19.110 Pause this video and see if you can have a go at it. 00:00:19.110 --> 00:00:21.280 All right, now let's do this together. 00:00:21.280 --> 00:00:23.110 So the first thing that you might realize 00:00:23.110 --> 00:00:28.110 is that 7.5 is the same thing as 75 00:00:28.290 --> 00:00:31.770 divided by 10. 00:00:31.770 --> 00:00:33.890 And 0.061, 00:00:33.890 --> 00:00:37.010 this is 61 thousandths. 00:00:37.010 --> 00:00:42.010 This right over here is the same thing as 61 00:00:42.180 --> 00:00:45.770 divided by 1,000 00:00:45.770 --> 00:00:49.140 and we're gonna take the product of these two things. 00:00:49.140 --> 00:00:51.530 Another way we could write this, 00:00:51.530 --> 00:00:53.540 75 divided by 10, 00:00:53.540 --> 00:00:54.450 this is the same thing 00:00:54.450 --> 00:00:57.490 as 75 over 10 00:00:57.490 --> 00:00:59.100 and I'm gonna take the product of that, 00:00:59.100 --> 00:01:03.490 and 61 thousandths, 61 divided by 1,000. 00:01:03.490 --> 00:01:08.490 So that would be 61/1,000. 00:01:09.130 --> 00:01:10.240 Now, when we look at it, 00:01:10.240 --> 00:01:11.380 either of these ways, 00:01:11.380 --> 00:01:13.430 well actually, I'll do both of them at the same time. 00:01:13.430 --> 00:01:14.430 You could change the order 00:01:14.430 --> 00:01:16.120 of the multiplication and the division here. 00:01:16.120 --> 00:01:19.800 So you could start with 75 times 61, 00:01:19.800 --> 00:01:22.760 75 times 61, 00:01:22.760 --> 00:01:24.923 and then divide that by 10, 00:01:26.160 --> 00:01:29.790 and then divide that by 1,000. 00:01:29.790 --> 00:01:32.020 You could do it that way 00:01:32.020 --> 00:01:34.130 or you could look right over here 00:01:34.130 --> 00:01:35.380 and say, all right, 00:01:35.380 --> 00:01:36.820 if I'm taking this product, 00:01:36.820 --> 00:01:39.970 my numerator is going to be 75 times 61, 00:01:39.970 --> 00:01:42.230 75 times 61. 00:01:42.230 --> 00:01:44.690 And then, my denominator 00:01:44.690 --> 00:01:48.000 is going to be 10 times 1,000 00:01:48.000 --> 00:01:49.380 which is essentially the same thing 00:01:49.380 --> 00:01:51.210 as dividing by 10, 00:01:51.210 --> 00:01:53.170 and then dividing by 1,000. 00:01:53.170 --> 00:01:57.220 And of course, that is going to be 10,000. 00:01:57.220 --> 00:02:00.900 Now on the left-hand side, right over here, 00:02:00.900 --> 00:02:04.420 they told us what this is, it's 4,575. 00:02:04.420 --> 00:02:05.440 So it's 4,575 00:02:07.590 --> 00:02:08.920 divided by 10, 00:02:08.920 --> 00:02:10.310 and then divided by 1,000. 00:02:10.310 --> 00:02:11.470 Well, if I divide by 10, 00:02:11.470 --> 00:02:13.150 and then I divide by 1,000, 00:02:13.150 --> 00:02:17.240 that's equivalent to dividing by 10,000. 00:02:17.240 --> 00:02:21.303 This is dividing by 10,000 00:02:22.480 --> 00:02:23.530 and you could see that over here. 00:02:23.530 --> 00:02:25.140 We're dividing by 10,000 00:02:25.140 --> 00:02:26.480 as well right over here. 00:02:26.480 --> 00:02:29.040 And the 75 times 61, 00:02:29.040 --> 00:02:32.850 this is 4,575. 00:02:32.850 --> 00:02:35.130 Now they want us to evaluate it as a decimal. 00:02:35.130 --> 00:02:37.080 We've now expressed it as a fraction 00:02:37.080 --> 00:02:39.720 and I still haven't fully evaluated this yet. 00:02:39.720 --> 00:02:41.030 So we really wanna think 00:02:41.030 --> 00:02:44.631 about this as 4,575 ten thousandths 00:02:44.631 --> 00:02:46.630 and you can see that very explicitly here. 00:02:46.630 --> 00:02:50.350 There's 4,575 ten thousandths. 00:02:50.350 --> 00:02:52.260 So how do we write that? 00:02:52.260 --> 00:02:55.680 Well, if I have a decimal right over here, 00:02:55.680 --> 00:02:57.450 that's the tenths place. 00:02:57.450 --> 00:02:59.510 This is the hundredths, 00:02:59.510 --> 00:03:02.820 thousandths, ten-thousandths place. 00:03:02.820 --> 00:03:05.140 So we have this many ten thousandths, 00:03:05.140 --> 00:03:09.410 4,575 ten thousandths 00:03:10.290 --> 00:03:11.300 and we're done. 00:03:11.300 --> 00:03:16.193 So this is gonna be 0.4575. 00:03:16.193 --> 00:03:19.360 Now I know what some of you might be thinking. 00:03:19.360 --> 00:03:21.700 Hey, I learned a technique 00:03:21.700 --> 00:03:23.710 where if I'm taking the product of two numbers, 00:03:23.710 --> 00:03:25.790 I could take the product of those two numbers, 00:03:25.790 --> 00:03:27.020 or if I'm taking the product of two numbers 00:03:27.020 --> 00:03:28.260 that are decimals, 00:03:28.260 --> 00:03:31.280 I could remove the decimals from them essentially, 00:03:31.280 --> 00:03:32.140 take their product 00:03:32.140 --> 00:03:34.240 which they actually gave us right over here. 00:03:34.240 --> 00:03:36.360 And then, count how many digits to the right 00:03:36.360 --> 00:03:38.540 of the decimal there were in our original numbers. 00:03:38.540 --> 00:03:42.190 So we have one, two, three, 00:03:42.190 --> 00:03:46.410 four digits to the right of the decimal. 00:03:46.410 --> 00:03:48.212 And so what I do is I then move, 00:03:48.212 --> 00:03:50.020 I then make sure that there's four digits 00:03:50.020 --> 00:03:52.030 to the right of the decimal in the product. 00:03:52.030 --> 00:03:53.500 And so I would say, okay, 00:03:53.500 --> 00:03:55.970 one, two, three, four, that looks good 00:03:55.970 --> 00:03:57.660 and I've gotten the same answer 00:03:57.660 --> 00:03:59.380 a lot faster than we just did it. 00:03:59.380 --> 00:04:01.810 Well, whole reason why I just did it the way I did 00:04:01.810 --> 00:04:04.240 is to show you why that works. 00:04:04.240 --> 00:04:07.160 When we take the product of the two numbers 00:04:07.160 --> 00:04:08.590 without the decimals, 00:04:08.590 --> 00:04:10.170 we're essentially ignoring the fact 00:04:10.170 --> 00:04:12.530 that the original product was dividing by 10 00:04:12.530 --> 00:04:14.290 and dividing by 1,000, 00:04:14.290 --> 00:04:16.390 and that's because we had one digit 00:04:16.390 --> 00:04:17.960 behind to the right of the decimal here, 00:04:17.960 --> 00:04:20.350 and we had three digits to the right of the decimal there. 00:04:20.350 --> 00:04:23.000 And so later after we take the product, 00:04:23.000 --> 00:04:25.700 we have to go and then actually take that product 00:04:25.700 --> 00:04:27.260 and divide by 10, 00:04:27.260 --> 00:04:28.490 and divide by 1,000 00:04:28.490 --> 00:04:30.290 or divide by 10,000. 00:04:30.290 --> 00:04:32.900 So that's why you can then just say, all right, well now, 00:04:32.900 --> 00:04:34.630 we originally had four digits to the right, 00:04:34.630 --> 00:04:36.460 so we still have to have four digits 00:04:36.460 --> 00:04:38.160 to the right of the decimal point.

Noble’s Story

https://www.youtube.com/watch?v=Zbir-vpwX7Q

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en

WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:01.810 - That was one of the best days of my life. 00:00:01.810 --> 00:00:03.180 Honestly, like signing day, 00:00:03.180 --> 00:00:05.270 just knew that all the hard work that I had put 00:00:05.270 --> 00:00:07.280 into this dream final paid off. 00:00:07.280 --> 00:00:09.940 I'm Noble. I'm a freshman at Brown University. 00:00:09.940 --> 00:00:11.420 I play receiver on the football team. 00:00:11.420 --> 00:00:14.280 It became apparent to me that when I got to high school 00:00:14.280 --> 00:00:16.220 that if I wanted to achieve the goals 00:00:16.220 --> 00:00:18.012 of going Division One football 00:00:18.012 --> 00:00:19.800 and going to school in the Ivy League, 00:00:19.800 --> 00:00:22.180 that I needed to improve on my SAT scores. 00:00:22.180 --> 00:00:25.170 A lot of people like my peers have test anxiety. 00:00:25.170 --> 00:00:27.390 First time I took it, I got a 1210. 00:00:27.390 --> 00:00:29.510 I knew I needed to improve if I wanted to get 00:00:29.510 --> 00:00:31.420 to a level of school that I'd envisioned. 00:00:31.420 --> 00:00:34.330 So, I dug into Khan Academy a lot. 00:00:34.330 --> 00:00:37.860 I took advantage of the option to upload your SAT scores 00:00:37.860 --> 00:00:40.050 to Khan Academy, and it would give you feedback 00:00:40.050 --> 00:00:41.540 on things you needed to work on. 00:00:41.540 --> 00:00:44.030 I definitely took a lot of stress off of my shoulders 00:00:44.030 --> 00:00:45.140 and like having the confidence 00:00:45.140 --> 00:00:47.460 that I could truly go into this test and perform 00:00:47.460 --> 00:00:49.900 to the standards that I wanted. By using Khan Academy 00:00:49.900 --> 00:00:53.318 I was able to improve my SAT score by 210 points. 00:00:53.318 --> 00:00:54.900 I was able to get a 1420, 00:00:54.900 --> 00:00:56.860 and that was a score that got me accepted in the Brown. 00:00:56.860 --> 00:00:58.240 Definitely would say it's life changing. 00:00:58.240 --> 00:01:00.010 I set my life on trajectory 00:01:00.010 --> 00:01:01.360 that wouldn't have been available 00:01:01.360 --> 00:01:02.960 if I didn't have access to Khan Academy. 00:01:02.960 --> 00:01:04.700 Whether you're upper class or lower class, 00:01:04.700 --> 00:01:06.717 or anywhere you fall in between those, 00:01:06.717 --> 00:01:08.770 and it's free and available for everyone. 00:01:08.770 --> 00:01:11.120 And that's, I can't stress that enough. 00:01:11.120 --> 00:01:14.030 I wanna leave a message that anything is possible. 00:01:14.030 --> 00:01:16.760 I definitely think the best beginning spot would be 00:01:16.760 --> 00:01:17.810 through Khan Academy.

Dividing a whole number by a fraction with reciprocal

https://www.youtube.com/watch?v=G7c0CBLWVfs

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https://www.youtube.com/api/timedtext?v=G7c0CBLWVfs&ei=xFWUZfaMKYK5mLAPtLWl2AI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=53B28FAA08980FD4B5EEF65FE74A522E76FB4504.4550D1198DC9B5C5D54C7692A43CB37A32279A82&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.180 --> 00:00:02.010 - [Instructor] In this video, we're gonna do an example 00:00:02.010 --> 00:00:03.480 that gives us a little bit of practice 00:00:03.480 --> 00:00:05.960 to think about what does it mean to divide by a fraction? 00:00:05.960 --> 00:00:06.860 So if we wanna figure out 00:00:06.860 --> 00:00:09.500 what eight divided by 7/5 is, 00:00:09.500 --> 00:00:12.170 but we're gonna break it down into two steps. 00:00:12.170 --> 00:00:14.410 First of all, we're gonna use these visuals here 00:00:14.410 --> 00:00:19.000 to think about how many groups of 7/5 are in one. 00:00:19.000 --> 00:00:20.110 Or another way of thinking about it 00:00:20.110 --> 00:00:24.100 is how these 7/5 are in a whole? 00:00:24.100 --> 00:00:27.000 So pause this video, and just think about this first part. 00:00:28.100 --> 00:00:31.600 All right, so let's look at 7/5. 00:00:31.600 --> 00:00:36.600 7/5 is everything from here, all the way to there. 00:00:37.360 --> 00:00:40.730 And then one is this. 00:00:40.730 --> 00:00:44.520 So how many 7/5 are in one? 00:00:44.520 --> 00:00:45.730 Well, you can see that one, 00:00:45.730 --> 00:00:50.120 which is the same thing as 5/5, is less than 7/5. 00:00:50.120 --> 00:00:53.560 So it's actually going to be a fraction of a 7/5 00:00:53.560 --> 00:00:57.090 that is one, or that is in one. 00:00:57.090 --> 00:00:59.500 And you can see what that fraction is. 00:00:59.500 --> 00:01:02.750 One is what fraction of 7/5. 00:01:02.750 --> 00:01:04.270 Well, if you look at the fifths, 00:01:04.270 --> 00:01:08.760 7/5 is of course seven of them, and a whole is 5/5, 00:01:08.760 --> 00:01:13.760 so five of the 7/5 make a whole. 00:01:13.760 --> 00:01:17.980 So the answer right over here is 5/7. 00:01:17.980 --> 00:01:22.980 5/7 of a 7/5 is equal to one. 00:01:23.460 --> 00:01:25.400 You can also see this right over here. 00:01:25.400 --> 00:01:28.460 If you take each of these to be a fifth, 00:01:28.460 --> 00:01:31.720 each of these to be a fifth, 00:01:31.720 --> 00:01:36.720 then this whole bar is equal to 7/5. 00:01:36.760 --> 00:01:39.080 And the blue part is equal to one. 00:01:39.080 --> 00:01:41.630 So how many 7/5 are in the blue part? 00:01:41.630 --> 00:01:45.520 Well, we can see it's 5/7 of the whole bar. 00:01:45.520 --> 00:01:48.020 Once again, 5/7 of the whole bar. 00:01:48.020 --> 00:01:48.992 So we can also think about this 00:01:48.992 --> 00:01:53.350 as one divided by 7/5. 00:01:53.350 --> 00:01:57.190 This is another way of saying how many 7/5 are in one, 00:01:57.190 --> 00:01:59.820 or how many groups of 7/5 are in one? 00:01:59.820 --> 00:02:02.890 And this is equal to 5/7, 00:02:02.890 --> 00:02:04.610 which we've learned in other videos 00:02:04.610 --> 00:02:06.590 is the reciprocal of 7/5. 00:02:06.590 --> 00:02:09.800 The numerator and the denominator is swapped. 00:02:09.800 --> 00:02:14.150 So now what is eight divided by 7/5 going to be? 00:02:14.150 --> 00:02:17.960 Well, if one divided by 7/5 is 5/7, 00:02:17.960 --> 00:02:21.540 or if you have 5/7 of a 7/5, 00:02:21.540 --> 00:02:22.950 of a 7/5 in one, 00:02:22.950 --> 00:02:25.260 I know the oral language gets a little bit confusing. 00:02:25.260 --> 00:02:28.350 Well, you're going to have eight times that many in eight. 00:02:28.350 --> 00:02:29.860 So this is going to be the same thing 00:02:29.860 --> 00:02:34.510 as eight times, we could do it this way, 00:02:34.510 --> 00:02:39.030 eight times one, divided by 7/5. 00:02:39.030 --> 00:02:41.960 Or you could just view this as eight times 00:02:41.960 --> 00:02:46.910 the reciprocal of 7/5, which is five over seven. 00:02:48.150 --> 00:02:50.900 And we've learned how to multiply this before. 00:02:50.900 --> 00:02:54.130 Eight times 5/7 is going to be equal 00:02:54.130 --> 00:02:58.170 to 40/7, and we're done. 00:02:58.170 --> 00:03:00.280 You could obviously also write that as a mixed number 00:03:00.280 --> 00:03:05.253 if you like, this would be the same thing as 5 5/7. 00:03:06.890 --> 00:03:10.000 So the big picture is when we think about 00:03:10.000 --> 00:03:13.030 how many of a fraction are in one, 00:03:13.030 --> 00:03:14.140 that's the same thing as saying, 00:03:14.140 --> 00:03:16.240 what's one divided by that fraction? 00:03:16.240 --> 00:03:17.980 As you see visually here, 00:03:17.980 --> 00:03:20.330 you essentially get the reciprocal of that fraction. 00:03:20.330 --> 00:03:22.970 And so if you take any other number other than one 00:03:22.970 --> 00:03:24.350 divided by that fraction, 00:03:24.350 --> 00:03:25.652 you're essentially just gonna multiply it 00:03:25.652 --> 00:03:30.000 by that reciprocal, because it's that number times one. 00:03:30.000 --> 00:03:32.120 So when you divide by that fraction, 00:03:32.120 --> 00:03:34.683 it's that number times the reciprocal.

Area of quadrilateral with 2 parallel sides

https://www.youtube.com/watch?v=uEIoh8uWs1U

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https://www.youtube.com/api/timedtext?v=uEIoh8uWs1U&ei=xFWUZZ-DELqpp-oP4eSDsAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=5364DD41DE8CAC66F09C87193D4E6F3B47237D5B.69AAE8E8FE3588652055A4388BDE99416CFE82F0&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:02.140 - [Instructor] What we're going to try to do in this video 00:00:02.140 --> 00:00:04.430 is find the area of this figure. 00:00:04.430 --> 00:00:05.930 And we can see it's a quadrilateral. 00:00:05.930 --> 00:00:08.740 It has 1, 2, 3, 4 sides. 00:00:08.740 --> 00:00:11.180 And we know that this side and this side 00:00:11.180 --> 00:00:13.570 that they're parallel to each other. 00:00:13.570 --> 00:00:16.160 You can see that they both form right angles 00:00:16.160 --> 00:00:18.080 with this dotted line. 00:00:18.080 --> 00:00:21.063 So pause this video and see if you can find the area. 00:00:22.930 --> 00:00:23.763 All right. 00:00:23.763 --> 00:00:25.590 Now, if you had a little bit of trouble with that 00:00:25.590 --> 00:00:27.160 I'll give you a hint. 00:00:27.160 --> 00:00:29.350 What if we were to take this quadrilateral 00:00:29.350 --> 00:00:32.220 and divide it into two triangles? 00:00:32.220 --> 00:00:35.470 So let me do this in a color that you are likely to see. 00:00:35.470 --> 00:00:39.120 So if I were to draw a line like this 00:00:39.120 --> 00:00:43.670 it now divides the quadrilateral into two triangles. 00:00:43.670 --> 00:00:47.630 If I were to take this triangle right over here 00:00:47.630 --> 00:00:50.660 I could take it out and reorient it, 00:00:50.660 --> 00:00:54.990 so it looks something like this, 00:00:54.990 --> 00:00:59.290 where the base has length 8, 00:00:59.290 --> 00:01:03.220 and then the height right over here, the height 00:01:03.220 --> 00:01:06.070 this has length 5. 00:01:06.070 --> 00:01:07.720 So that would be that triangle. 00:01:07.720 --> 00:01:10.890 And then, this triangle over here 00:01:10.890 --> 00:01:13.230 if you were to take it out and reorient it a little bit 00:01:13.230 --> 00:01:14.440 it could look like this, 00:01:14.440 --> 00:01:16.220 where the base is 4, 00:01:16.220 --> 00:01:19.990 and the triangle looks something like, 00:01:19.990 --> 00:01:21.270 looks something like this. 00:01:21.270 --> 00:01:24.290 So the base is 4, 00:01:24.290 --> 00:01:27.240 and then the height is going to be 5. 00:01:27.240 --> 00:01:30.680 So this height right over here, this height, 00:01:30.680 --> 00:01:32.290 we notice this is a right angle. 00:01:32.290 --> 00:01:34.630 So from here to here, which is the same thing 00:01:34.630 --> 00:01:37.560 as from here to right over here, 00:01:37.560 --> 00:01:39.080 we know that this is 5. 00:01:39.080 --> 00:01:41.470 So that's my fairly big hint to you, 00:01:41.470 --> 00:01:44.540 if you know how to find the area of a triangle. 00:01:44.540 --> 00:01:49.540 The area of a triangle we know is 1/2 base times height. 00:01:50.140 --> 00:01:51.700 So the area of this one right over here 00:01:51.700 --> 00:01:56.700 is gonna be 1/2 times 8 times 5. 00:01:57.040 --> 00:01:58.840 And the area of this one over here 00:01:58.840 --> 00:02:02.480 is going to be 1/2 times the base, 00:02:02.480 --> 00:02:07.470 which is 4 times the height, which is 5. 00:02:07.470 --> 00:02:09.480 And we could evaluate each of these, 00:02:09.480 --> 00:02:10.840 or we could just add them together. 00:02:10.840 --> 00:02:12.580 That the area of the entire thing 00:02:12.580 --> 00:02:16.960 is going to be 1/2 times this base right over here 00:02:16.960 --> 00:02:21.690 which is 8, times the height, which is 5, 00:02:21.690 --> 00:02:26.690 plus 1/2 times this side, 00:02:27.500 --> 00:02:30.640 you could do that as the other base, times 4 00:02:30.640 --> 00:02:33.400 times that same height, times 5. 00:02:33.400 --> 00:02:35.260 And obviously, you could just evaluate this 00:02:35.260 --> 00:02:38.330 or we could see some interesting things about it. 00:02:38.330 --> 00:02:40.440 We could express this as well 00:02:40.440 --> 00:02:45.440 if we were to factor out 1/2 and the 5 here. 00:02:45.520 --> 00:02:48.403 This could be rewritten as 1/2, 00:02:49.740 --> 00:02:54.250 1/2 times 8 plus 4, 00:02:54.250 --> 00:02:58.110 8 plus 4. 00:02:58.110 --> 00:03:03.110 And then, all of that, all of that times 5 right over here. 00:03:03.830 --> 00:03:05.770 And so, another way you could think about it is 00:03:05.770 --> 00:03:08.670 the average of the length of these two bases. 00:03:08.670 --> 00:03:11.220 You could view this as base 1 and base 2, 00:03:11.220 --> 00:03:12.730 you multiply that times the height 00:03:12.730 --> 00:03:15.710 and you have the area of this quadrilateral. 00:03:15.710 --> 00:03:16.970 Well, what's that going to be? 00:03:16.970 --> 00:03:19.344 8 plus 4 is 12. 00:03:19.344 --> 00:03:22.810 1/2 times 12, this is all going to be 6. 00:03:22.810 --> 00:03:27.560 6 times 5 is going to be equal to 30 square units. 00:03:27.560 --> 00:03:28.393 You could have figured it out here too. 00:03:28.393 --> 00:03:32.570 1/2 times 8 is 4, times 5 is 20. 00:03:32.570 --> 00:03:35.230 And then, this would've been 1/2 times 4 is 2, 00:03:35.230 --> 00:03:36.470 times 5 is 10. 00:03:36.470 --> 00:03:40.323 20 plus 10 is 30 square units once again.

Competition, predation, and mutualism

https://www.youtube.com/watch?v=S65RR_pEyPw

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https://www.youtube.com/api/timedtext?v=S65RR_pEyPw&ei=xFWUZaOLJNGMvdIPm_yq4Ao&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=43D11FE9C44BFF57A9233615EAB3A234DF6C4938.6ECE2AF125E0B0370E4FF660AAA564BDB4221689&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.770 --> 00:00:02.430 - [Instructor] All across ecosystems, 00:00:02.430 --> 00:00:05.940 we know that organisms interact in specific ways 00:00:05.940 --> 00:00:07.880 and scientists use special words 00:00:07.880 --> 00:00:11.000 to describe these types of interaction, 00:00:11.000 --> 00:00:14.990 competition, predation and mutualism. 00:00:14.990 --> 00:00:16.900 So let's first talk about competition 00:00:16.900 --> 00:00:19.590 which we have already talked about in other videos. 00:00:19.590 --> 00:00:22.210 In this picture here, do you see competition? 00:00:22.210 --> 00:00:24.110 Pause this video and think about that. 00:00:25.350 --> 00:00:27.710 Well, one limited resource 00:00:27.710 --> 00:00:30.830 that these animals need to survive is water. 00:00:30.830 --> 00:00:33.090 There's only a limited amount in this watering hole 00:00:33.090 --> 00:00:36.140 over here and so you could imagine there is competition 00:00:36.140 --> 00:00:38.650 not just amongst the members of a population 00:00:38.650 --> 00:00:40.520 let's say between the zebra 00:00:40.520 --> 00:00:43.090 but also between members of different species, 00:00:43.090 --> 00:00:45.630 between different populations in a community. 00:00:45.630 --> 00:00:48.580 The zebras are not just competing for water with each other 00:00:48.580 --> 00:00:50.160 but also with these antelope 00:00:50.160 --> 00:00:52.880 or with these buffalo over here. 00:00:52.880 --> 00:00:54.840 There might also be competition for food. 00:00:54.840 --> 00:00:57.140 It doesn't seem like there's a lot of grass to eat 00:00:57.140 --> 00:01:00.460 for all of these animals that like to graze on grass. 00:01:00.460 --> 00:01:03.220 So now let's move on to predation. 00:01:03.220 --> 00:01:07.200 Predation is when one organism eats another organism 00:01:07.200 --> 00:01:09.320 usually to its own benefit. 00:01:09.320 --> 00:01:11.930 Do you see any predation happening here? 00:01:11.930 --> 00:01:13.370 Well, we don't see any of these animals 00:01:13.370 --> 00:01:14.670 chasing and killing each other. 00:01:14.670 --> 00:01:17.250 There might be other animals like lions offscreen 00:01:17.250 --> 00:01:20.280 that might hunt and kill and eat these animals 00:01:20.280 --> 00:01:21.350 right over here 00:01:21.350 --> 00:01:23.670 but we know that these animals do eat grass 00:01:23.670 --> 00:01:26.470 and as I said, it's not just about hunting 00:01:26.470 --> 00:01:29.640 and killing and eating from one animal to another. 00:01:29.640 --> 00:01:31.480 It could be one organism to another. 00:01:31.480 --> 00:01:33.550 So the eating of the grass by these animals 00:01:33.550 --> 00:01:36.570 could actually be considered a form of predation 00:01:36.570 --> 00:01:38.980 especially if it kills the grass. 00:01:38.980 --> 00:01:42.190 A more obvious form of predation is this brown bear here 00:01:42.190 --> 00:01:45.540 that has gotten the salmon out of this river. 00:01:45.540 --> 00:01:49.340 It is clearly hunting and killing the salmon for its benefit 00:01:49.340 --> 00:01:51.090 and it is likely that each of these bears 00:01:51.090 --> 00:01:52.940 are in competition with other bears 00:01:52.940 --> 00:01:55.360 for this limited resource. 00:01:55.360 --> 00:01:56.710 So last but not least, 00:01:56.710 --> 00:01:59.590 let's think a little bit about mutualism. 00:01:59.590 --> 00:02:02.610 Mutualism happens when two organisms benefit 00:02:02.610 --> 00:02:04.363 from interacting with each other. 00:02:05.200 --> 00:02:07.620 Right over here, we have these starlings 00:02:07.620 --> 00:02:10.020 that actually hang out on this buffalo 00:02:10.020 --> 00:02:13.830 and pick lice and ticks off the buffalo's fur. 00:02:13.830 --> 00:02:16.337 This is mutualism because both parties benefit. 00:02:16.337 --> 00:02:18.310 The starlings are able to get food 00:02:18.310 --> 00:02:20.760 and the buffalo no longer have these parasites, 00:02:20.760 --> 00:02:23.280 these things that are living off of the buffalo 00:02:23.280 --> 00:02:25.520 sucking its blood out of its body 00:02:25.520 --> 00:02:28.280 and also probably not itching as much. 00:02:28.280 --> 00:02:30.120 Now, based on how I just described it, 00:02:30.120 --> 00:02:32.260 there's not just mutualism here. 00:02:32.260 --> 00:02:33.760 There's also predation 00:02:33.760 --> 00:02:35.980 because these birds are actually hunting 00:02:35.980 --> 00:02:39.750 and killing the lice and the ticks on the buffalo's body. 00:02:39.750 --> 00:02:41.880 Now, related to being a predator is another word 00:02:41.880 --> 00:02:43.190 known as being a parasite 00:02:43.190 --> 00:02:45.050 and that's what the lice and the ticks are doing 00:02:45.050 --> 00:02:47.150 where they're sucking the blood of the buffalo 00:02:47.150 --> 00:02:48.780 but they're not considered predators. 00:02:48.780 --> 00:02:51.860 They're more parasites because they don't kill the buffalo. 00:02:51.860 --> 00:02:54.530 They're just taking some resources away from it. 00:02:54.530 --> 00:02:55.560 So I'll leave you there. 00:02:55.560 --> 00:02:57.130 I encourage you when you look at nature, 00:02:57.130 --> 00:02:58.490 when you go to a park next time, 00:02:58.490 --> 00:03:00.570 when you go watch a documentary, 00:03:00.570 --> 00:03:02.960 I encourage you to think about how competition, 00:03:02.960 --> 00:03:06.730 predation and mutualism is happening in an ecosystem 00:03:06.730 --> 00:03:08.980 that you are seeing or that you're a part of.

Resources and population growth

https://www.youtube.com/watch?v=i5uF5inpY7s

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WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:02.280 - [Instructor] So we have a picture here of these animals 00:00:02.280 --> 00:00:03.570 at a watering hole. 00:00:03.570 --> 00:00:07.940 And my question to you is why don't we see more animals? 00:00:07.940 --> 00:00:10.640 There's clearly enough space for more animals, 00:00:10.640 --> 00:00:12.470 and we also know that if we focus 00:00:12.470 --> 00:00:15.510 on any one of these populations, say zebra, 00:00:15.510 --> 00:00:19.960 that every one zebra can have far more than one offspring 00:00:19.960 --> 00:00:21.020 in their lifetime. 00:00:21.020 --> 00:00:22.540 And that not only that, 00:00:22.540 --> 00:00:24.167 but those offspring can then have offspring, 00:00:24.167 --> 00:00:25.350 and so on and so forth. 00:00:25.350 --> 00:00:27.050 So it seems like over time, 00:00:27.050 --> 00:00:29.470 these zebra should just be able to keep multiplying 00:00:29.470 --> 00:00:31.150 until they fill up all of this land, 00:00:31.150 --> 00:00:32.630 similar for the buffalo, 00:00:32.630 --> 00:00:34.310 similar for the antelope. 00:00:34.310 --> 00:00:36.030 Why don't we see that? 00:00:36.030 --> 00:00:38.730 Pause this video and think about that. 00:00:38.730 --> 00:00:42.350 So let's start by thinking about what any organism, 00:00:42.350 --> 00:00:44.370 or a population of organisms, 00:00:44.370 --> 00:00:47.890 or a community of populations need to survive. 00:00:47.890 --> 00:00:50.590 Most animals that live on the surface, like these animals, 00:00:50.590 --> 00:00:52.700 need air, especially oxygen. 00:00:52.700 --> 00:00:54.980 Plants need carbon dioxide from the air. 00:00:54.980 --> 00:00:57.840 They need water. 00:00:57.840 --> 00:01:01.810 They need a source of energy, which I will call food, 00:01:01.810 --> 00:01:03.840 or I could say it's energy here, 00:01:03.840 --> 00:01:05.610 because it's not always in the form of food 00:01:05.610 --> 00:01:07.310 as we might recognize it. 00:01:07.310 --> 00:01:09.570 And I guess if we think really basically, 00:01:09.570 --> 00:01:12.400 they need space in which to exist. 00:01:12.400 --> 00:01:13.690 Now, as I mentioned, 00:01:13.690 --> 00:01:16.700 there seems to be a lot of space here for the animals, 00:01:16.700 --> 00:01:19.080 so that doesn't seem to be the resource 00:01:19.080 --> 00:01:21.880 that is limiting their growth. 00:01:21.880 --> 00:01:24.010 So let's rule that out here. 00:01:24.010 --> 00:01:25.540 Now, it's also clear that it seems like there's 00:01:25.540 --> 00:01:27.410 a fairly large amount of air here, 00:01:27.410 --> 00:01:30.320 more than enough air for these populations to grow, 00:01:30.320 --> 00:01:32.590 so that doesn't seem to be a resource 00:01:32.590 --> 00:01:34.970 that's somehow putting a maximum on how many 00:01:34.970 --> 00:01:36.610 of these organisms there are. 00:01:36.610 --> 00:01:39.450 It does not look like a limited resource, 00:01:39.450 --> 00:01:42.060 or a limiting resource. 00:01:42.060 --> 00:01:43.860 Now, what about water? 00:01:43.860 --> 00:01:45.820 Well, water does seem interesting here, 00:01:45.820 --> 00:01:47.980 because this watering hole does not seem 00:01:47.980 --> 00:01:48.970 like it's very deep. 00:01:48.970 --> 00:01:51.630 It does not seem like there's a lot of water here. 00:01:51.630 --> 00:01:55.350 So this one could be what we would call a limited resource 00:01:55.350 --> 00:01:57.180 that is limiting population. 00:01:57.180 --> 00:01:58.970 Maybe if they had more and more offspring, 00:01:58.970 --> 00:02:00.810 there just wouldn't be enough water 00:02:00.810 --> 00:02:02.800 for any member of a population, 00:02:02.800 --> 00:02:04.880 and then of course the populations would be competing 00:02:04.880 --> 00:02:05.790 with each other as well, 00:02:05.790 --> 00:02:09.170 because they all need the same water to drink. 00:02:09.170 --> 00:02:10.900 Now, what about food? 00:02:10.900 --> 00:02:13.110 Well, you might recognize that zebra, 00:02:13.110 --> 00:02:15.320 or antelope, or buffalo, 00:02:15.320 --> 00:02:17.070 they tend to graze on grasses, 00:02:17.070 --> 00:02:19.450 and there are some grasses over here, 00:02:19.450 --> 00:02:21.700 but we also see that a lot of the grass is dead 00:02:21.700 --> 00:02:22.780 or dried out, 00:02:22.780 --> 00:02:25.480 and there's just a lot of areas with dirt here. 00:02:25.480 --> 00:02:27.710 So it looks like the food and energy 00:02:27.710 --> 00:02:30.739 is also a limiting resource. 00:02:30.739 --> 00:02:32.470 And we have to remind ourselves there's populations 00:02:32.470 --> 00:02:33.720 of different types of grasses, 00:02:33.720 --> 00:02:35.550 and why aren't they spreading more? 00:02:35.550 --> 00:02:37.030 Well, from the perspective of a plant, 00:02:37.030 --> 00:02:39.630 it looks like the air and space is for sure abundant, 00:02:39.630 --> 00:02:42.130 and even energy in the form of sunlight 00:02:42.130 --> 00:02:44.120 is abundant based on this picture, 00:02:44.120 --> 00:02:46.840 so it's probably water is the limited resource, 00:02:46.840 --> 00:02:48.640 which is keeping us from having more plants 00:02:48.640 --> 00:02:50.790 and grasses in this picture. 00:02:50.790 --> 00:02:53.740 We can imagine a scenario in which it rains a lot. 00:02:53.740 --> 00:02:56.510 There's a lot of water, water is abundant, 00:02:56.510 --> 00:02:59.680 then all of the different types of populations of grasses 00:02:59.680 --> 00:03:01.050 are able to expand, 00:03:01.050 --> 00:03:03.650 and then there's more than enough food and water 00:03:03.650 --> 00:03:06.470 for these animals to keep reproducing. 00:03:06.470 --> 00:03:09.370 In that case, space might become an issue. 00:03:09.370 --> 00:03:11.070 But the important thing to realize here 00:03:11.070 --> 00:03:15.410 is that all organisms need resources in order to survive 00:03:15.410 --> 00:03:18.160 and in order to multiply and reproduce. 00:03:18.160 --> 00:03:20.670 Populations of many different species are often competing 00:03:20.670 --> 00:03:21.670 for those resources. 00:03:21.670 --> 00:03:22.950 Like the water here, 00:03:22.950 --> 00:03:24.490 that will tend to put a limit 00:03:24.490 --> 00:03:27.040 on how much these populations can grow. 00:03:27.040 --> 00:03:29.770 And the limit on one population can affect another. 00:03:29.770 --> 00:03:31.620 As we said, if you had more water, 00:03:31.620 --> 00:03:32.830 you could have more grass, 00:03:32.830 --> 00:03:35.000 which will allow them for more food and energy 00:03:35.000 --> 00:03:37.083 for these other populations.

Populations, communities, and ecosystems

https://www.youtube.com/watch?v=xzINev2Bd8s

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https://www.youtube.com/api/timedtext?v=xzINev2Bd8s&ei=xFWUZaPDFLiBhcIPxNOJ-AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=870B67ACE284D46E5F717326F51E858DC09EC737.70EBA0E4C538A171BD990C2F7EE6F70E3523120F&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.170 --> 00:00:01.700 - [Instructor] In biology, it's useful 00:00:01.700 --> 00:00:03.350 to have some shared language 00:00:03.350 --> 00:00:06.500 so we can communicate and describe the world around us 00:00:06.500 --> 00:00:09.580 in ways that we can all understand together. 00:00:09.580 --> 00:00:11.650 So here, we're going to talk about populations, 00:00:11.650 --> 00:00:13.570 communities, and ecosystems. 00:00:13.570 --> 00:00:17.060 And as we will see, these are all related ideas. 00:00:17.060 --> 00:00:21.420 So first of all, a population is talking about the members 00:00:21.420 --> 00:00:24.110 of a specific species in an area. 00:00:24.110 --> 00:00:26.710 So for example, in this picture, 00:00:26.710 --> 00:00:29.540 we have a population of zebra. 00:00:29.540 --> 00:00:32.970 I have one zebra there, one zebra there, 00:00:32.970 --> 00:00:35.090 there might be some others that we can't see. 00:00:35.090 --> 00:00:36.580 In fact, there are likely to be. 00:00:36.580 --> 00:00:40.560 So, these are each members of a population of zebra. 00:00:40.560 --> 00:00:43.060 Now, we have other populations in this picture. 00:00:43.060 --> 00:00:45.380 We have a population of buffalo. 00:00:45.380 --> 00:00:48.240 These three are members of that population. 00:00:48.240 --> 00:00:50.580 We have a population of antelope. 00:00:50.580 --> 00:00:53.420 In fact, there is a bunch of antelope in this picture. 00:00:53.420 --> 00:00:55.630 So, we have many members of that population. 00:00:55.630 --> 00:00:58.080 We even see some animals here in the background. 00:00:58.080 --> 00:01:00.500 I can't quite make out what they are, 00:01:00.500 --> 00:01:02.560 but that could be a different population. 00:01:02.560 --> 00:01:04.010 Let's say if those are elephants, 00:01:04.010 --> 00:01:06.230 they might be elephants the way I see them, 00:01:06.230 --> 00:01:09.030 but that could be members of a population of elephants. 00:01:09.030 --> 00:01:13.350 So if that is a population, what is a community? 00:01:13.350 --> 00:01:16.840 Well, a community is all of the living species 00:01:16.840 --> 00:01:19.030 that live in the same area. 00:01:19.030 --> 00:01:21.060 So, we have a community of animals 00:01:21.060 --> 00:01:24.770 that is made up of populations of buffalo, 00:01:24.770 --> 00:01:27.770 of zebra, and of antelope. 00:01:27.770 --> 00:01:30.560 And I wanna make clear that the populations 00:01:30.560 --> 00:01:31.930 or when we're talking about the communities, 00:01:31.930 --> 00:01:33.550 we're not necessarily just talking 00:01:33.550 --> 00:01:36.050 about large animals like this. 00:01:36.050 --> 00:01:38.940 We could be talking about populations of mosquitoes. 00:01:38.940 --> 00:01:41.470 We could be talking about populations of fish in this pond, 00:01:41.470 --> 00:01:42.740 if there are any fish. 00:01:42.740 --> 00:01:45.400 We could have a population of a certain species of plant. 00:01:45.400 --> 00:01:47.380 And likewise, when we're talking about communities, 00:01:47.380 --> 00:01:48.330 we're talking about collectively 00:01:48.330 --> 00:01:50.890 all of the living organisms together. 00:01:50.890 --> 00:01:54.560 Now, last but not least, what would be an ecosystem then? 00:01:54.560 --> 00:01:57.540 Well, an ecosystem is all of the living organisms 00:01:57.540 --> 00:01:59.870 plus all of the non-living things. 00:01:59.870 --> 00:02:01.920 So, the ecosystem that we see here 00:02:01.920 --> 00:02:03.700 would also include the water, 00:02:03.700 --> 00:02:05.370 it would also include the dirt, 00:02:05.370 --> 00:02:07.370 it would also include the air. 00:02:07.370 --> 00:02:09.930 And organisms like those that we see right here 00:02:09.930 --> 00:02:12.430 are constantly interacting with both the living 00:02:12.430 --> 00:02:15.040 and nonliving parts of their environment. 00:02:15.040 --> 00:02:17.560 These interactions are how organisms get food, 00:02:17.560 --> 00:02:20.070 shelter, water, and warmth. 00:02:20.070 --> 00:02:22.880 These interactions are how organisms survive 00:02:22.880 --> 00:02:24.420 and produce offspring. 00:02:24.420 --> 00:02:26.070 So, let's get a little bit more practice 00:02:26.070 --> 00:02:30.110 with this idea of populations, communities, and ecosystems. 00:02:30.110 --> 00:02:32.760 And we will do that by looking at this picture 00:02:32.760 --> 00:02:34.050 right over here. 00:02:34.050 --> 00:02:36.060 Pause this video and think about 00:02:36.060 --> 00:02:38.073 what are the populations here? 00:02:40.260 --> 00:02:41.700 Well, you might not know the name 00:02:41.700 --> 00:02:43.160 of all these different types of fish, 00:02:43.160 --> 00:02:44.790 but you can see that there's a population 00:02:44.790 --> 00:02:47.870 of this gold-colored fish right over here. 00:02:47.870 --> 00:02:51.910 There's also another population of this blue-colored fish. 00:02:51.910 --> 00:02:54.130 We could keep looking for other populations. 00:02:54.130 --> 00:02:58.120 It looks like there's a population of this silver-colored 00:02:58.120 --> 00:03:01.100 or I guess long-ish silver fish right over here. 00:03:01.100 --> 00:03:02.740 But once again, it's not just the fish. 00:03:02.740 --> 00:03:04.180 There's a population of coral, 00:03:04.180 --> 00:03:06.140 there's populations of microorganisms 00:03:06.140 --> 00:03:08.210 that we can't see here. 00:03:08.210 --> 00:03:12.050 The community would be all of these living organisms 00:03:12.050 --> 00:03:13.400 that live close to each other. 00:03:13.400 --> 00:03:15.730 And we'll see, sometimes they compete with each other, 00:03:15.730 --> 00:03:17.460 sometimes they eat each other, 00:03:17.460 --> 00:03:18.810 but sometimes they help each other, 00:03:18.810 --> 00:03:20.930 Or sometimes they don't matter that much to each other. 00:03:20.930 --> 00:03:23.640 And we'll study that in a lot more detail. 00:03:23.640 --> 00:03:26.950 And then the ecosystem includes all of the above 00:03:26.950 --> 00:03:31.950 plus the water, plus the oxygen that is in the water, 00:03:32.080 --> 00:03:35.650 plus the sand at the bottom of the ocean. 00:03:35.650 --> 00:03:37.000 So, I'll leave you there. 00:03:37.000 --> 00:03:38.750 Hopefully, you now have a sense 00:03:38.750 --> 00:03:40.400 of what biologists are talking about 00:03:40.400 --> 00:03:42.260 when they talk about populations, 00:03:42.260 --> 00:03:44.513 communities, and ecosystems.

Photosynthesis in organisms

https://www.youtube.com/watch?v=_BLShUdXbN4

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https://www.youtube.com/api/timedtext?v=_BLShUdXbN4&ei=xFWUZaCcEv7XxN8PyKCVsAk&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=963C846FE5DD8263429E1B4C2396D5A58CD0E769.314B86B0F6B8731FCD2A1FF8AD46A1C0154E2930&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.440 - [Narrator] Hey, I'm gonna let you in 00:00:01.440 --> 00:00:03.040 on a little secret of mine. 00:00:03.040 --> 00:00:05.200 I love gardening. 00:00:05.200 --> 00:00:07.730 In fact, I have a huge garden with apples, 00:00:07.730 --> 00:00:10.000 blueberries, pumpkins, and tomatoes. 00:00:10.000 --> 00:00:13.630 I give my plants micronutrients, and maybe some fertilizer. 00:00:13.630 --> 00:00:15.430 But I don't give them food in the same way 00:00:15.430 --> 00:00:19.180 that I would give my dog who eats multiple times a day. 00:00:19.180 --> 00:00:21.490 With plants, I just put them in the soil, 00:00:21.490 --> 00:00:24.240 water them regularly, and watch them grow. 00:00:24.240 --> 00:00:25.470 How do they do it? 00:00:25.470 --> 00:00:28.140 Well, they use a process called photosynthesis. 00:00:28.140 --> 00:00:30.790 Photosynthesis is a scientific term to describe 00:00:30.790 --> 00:00:33.330 how certain living things use energy from sunlight 00:00:33.330 --> 00:00:34.890 to live and grow. 00:00:34.890 --> 00:00:37.180 Many different kinds of plants, algae, 00:00:37.180 --> 00:00:40.010 and various single-celled organisms are able to carry out 00:00:40.010 --> 00:00:41.820 this amazing process. 00:00:41.820 --> 00:00:45.090 Today, let's describe photosynthesis using tomatoes. 00:00:45.090 --> 00:00:46.960 So here you see a young tomato plant, 00:00:46.960 --> 00:00:48.970 similar to the ones I have in my own garden. 00:00:48.970 --> 00:00:51.290 Let's name it Planty. 00:00:51.290 --> 00:00:52.300 First, let's start off 00:00:52.300 --> 00:00:54.780 by looking at Planty's immediate surroundings. 00:00:54.780 --> 00:00:57.270 The soil Planty is growing in contains water 00:00:57.270 --> 00:01:00.120 and the air surrounding Planty contains molecules 00:01:00.120 --> 00:01:01.590 of carbon dioxide. 00:01:01.590 --> 00:01:04.760 These two compounds are the starting materials or inputs 00:01:04.760 --> 00:01:08.100 that Planty needs in order to carry out photosynthesis. 00:01:08.100 --> 00:01:10.330 Now, let's take a look at the weather forecast. 00:01:10.330 --> 00:01:12.650 Well, it looks like it's gonna be a sunny day today. 00:01:12.650 --> 00:01:14.260 So when the sun shines on the earth, 00:01:14.260 --> 00:01:16.620 it sends out energy in the form of light. 00:01:16.620 --> 00:01:18.620 This energy is essential for Planty 00:01:18.620 --> 00:01:20.900 to be able to carry out photosynthesis. 00:01:20.900 --> 00:01:23.020 Next, let's take a closer look at Planty, 00:01:23.020 --> 00:01:26.060 because Planty's cells are hiding a secret of their own. 00:01:26.060 --> 00:01:28.810 Inside Planty's cells are microscopic structures 00:01:28.810 --> 00:01:31.180 that help Planty carry out photosynthesis. 00:01:31.180 --> 00:01:33.690 These structures are called chloroplasts. 00:01:33.690 --> 00:01:36.330 Chloroplasts contain green pigment molecules 00:01:36.330 --> 00:01:37.600 called chlorophyll. 00:01:37.600 --> 00:01:39.580 It is actually within these molecules 00:01:39.580 --> 00:01:41.880 that the sun's energy is captured for use 00:01:41.880 --> 00:01:43.310 during photosynthesis. 00:01:43.310 --> 00:01:45.560 Interestingly, chlorophyll is where leaves get 00:01:45.560 --> 00:01:46.730 their green color. 00:01:46.730 --> 00:01:49.270 To help you remember, think of chlorophyll like this: 00:01:49.270 --> 00:01:52.550 chloro means green and phyll means leaf. 00:01:52.550 --> 00:01:55.600 So when you put them together, you get green leaf. 00:01:55.600 --> 00:01:58.760 Okay, so now we know that carbon dioxide, water, 00:01:58.760 --> 00:02:01.880 and sunlight are required for photosynthesis to occur. 00:02:01.880 --> 00:02:04.310 And we know that in plants like Planty, 00:02:04.310 --> 00:02:06.740 photosynthesis happens in the chloroplast 00:02:06.740 --> 00:02:08.580 with the help of chlorophyll. 00:02:08.580 --> 00:02:10.580 Next, let's take a look at what happens 00:02:10.580 --> 00:02:13.370 during the process of photosynthesis itself. 00:02:13.370 --> 00:02:15.670 When the sunlight reaches Planty's chloroplast, 00:02:15.670 --> 00:02:18.190 its energy is used to rearrange the atoms 00:02:18.190 --> 00:02:20.810 in the carbon dioxide and water molecules 00:02:20.810 --> 00:02:23.080 through a series of chemical reactions. 00:02:23.080 --> 00:02:24.670 The outputs of these reactions 00:02:24.670 --> 00:02:27.310 are oxygen molecules and sugars. 00:02:27.310 --> 00:02:30.030 These sugars are vital to Planty's survival 00:02:30.030 --> 00:02:32.690 because they are used as a source of chemical energy 00:02:32.690 --> 00:02:34.800 that helps Planty live and grow. 00:02:34.800 --> 00:02:37.050 In other words, they're Planty's food. 00:02:37.050 --> 00:02:38.280 Planty can do a few things 00:02:38.280 --> 00:02:40.790 with the sugars made during photosynthesis. 00:02:40.790 --> 00:02:42.000 It can break the sugars down 00:02:42.000 --> 00:02:44.200 to get usable energy right away, 00:02:44.200 --> 00:02:47.210 or it can store the sugar molecules for later use. 00:02:47.210 --> 00:02:49.310 If Planty stores the sugar molecules, 00:02:49.310 --> 00:02:52.140 it can then use them as a source of energy in the future. 00:02:52.140 --> 00:02:53.830 This means that Planty can grow 00:02:53.830 --> 00:02:55.900 even when the sun isn't shining. 00:02:55.900 --> 00:02:58.170 Planty can also use the sugar molecules 00:02:58.170 --> 00:03:00.750 to build larger molecules such as cellulose 00:03:00.750 --> 00:03:03.230 that make up the structure of Planty itself. 00:03:03.230 --> 00:03:06.240 In this way, Planty can grow bigger and bigger 00:03:06.240 --> 00:03:08.350 with very little help from me; 00:03:08.350 --> 00:03:11.130 all thanks to the process of photosynthesis. 00:03:11.130 --> 00:03:13.370 Planty's other output, oxygen, 00:03:13.370 --> 00:03:15.310 is released into the atmosphere. 00:03:15.310 --> 00:03:18.390 This is really cool because it provides organisms 00:03:18.390 --> 00:03:22.060 in the ecosystem, including us, with oxygen. 00:03:22.060 --> 00:03:25.330 So thanks Planty and other photosynthetic organisms 00:03:25.330 --> 00:03:28.130 for giving us the oxygen we need to breathe. 00:03:28.130 --> 00:03:31.000 And that, my friends, is photosynthesis. 00:03:31.000 --> 00:03:32.350 So next time you're in a garden, 00:03:32.350 --> 00:03:33.830 I want you to think about this. 00:03:33.830 --> 00:03:37.480 All the plant structures you can see, such as stems, leaves, 00:03:37.480 --> 00:03:39.560 and even the fruits and vegetables that we eat 00:03:39.560 --> 00:03:42.100 are made up mostly of the atoms that were once a part 00:03:42.100 --> 00:03:44.740 of the starting materials of photosynthesis. 00:03:44.740 --> 00:03:46.490 With the help of a little sunlight, 00:03:46.490 --> 00:03:49.410 the plants made their own food and grew bigger, 00:03:49.410 --> 00:03:51.380 taking CO2 out of the atmosphere 00:03:51.380 --> 00:03:54.560 and releasing oxygen back in for us to breathe. 00:03:54.560 --> 00:03:57.140 And on that note, I think I should go outside 00:03:57.140 --> 00:03:59.200 and give my own garden some water. 00:03:59.200 --> 00:04:00.053 See you later.

Plant reproductive success

https://www.youtube.com/watch?v=nJIRCDipw7o

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https://www.youtube.com/api/timedtext?v=nJIRCDipw7o&ei=xFWUZYXtL6COvdIPtJq8uAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=7E6152BB728028158FA6B5DF58745C4EAD858166.18C8E428AC888A618E7123A02FD83D0CBA494659&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.380 --> 00:00:01.270 - [Instructor] We've already talked 00:00:01.270 --> 00:00:04.280 about reproductive success in other videos. 00:00:04.280 --> 00:00:07.240 It's related to the number of offspring 00:00:07.240 --> 00:00:10.180 an organism can have in its lifetime. 00:00:10.180 --> 00:00:11.630 And so in this video, 00:00:11.630 --> 00:00:14.030 we're going to think about strategies 00:00:14.030 --> 00:00:18.000 that plants will use for reproductive success. 00:00:18.000 --> 00:00:21.170 A plant that has more surviving offspring 00:00:21.170 --> 00:00:24.640 has a higher reproductive success. 00:00:24.640 --> 00:00:26.970 So one major strategy that plants use 00:00:26.970 --> 00:00:30.540 to increase their chances of reproduction 00:00:30.540 --> 00:00:34.680 is by leveraging animals for pollination. 00:00:34.680 --> 00:00:36.640 You have seen pollination. 00:00:36.640 --> 00:00:38.840 This is a picture of a bee gathering nectar 00:00:38.840 --> 00:00:42.210 from this flower, but as it gathers that nectar, 00:00:42.210 --> 00:00:44.630 pollen also gets attached to that bee. 00:00:44.630 --> 00:00:47.500 So as that bee goes from flower to flower, 00:00:47.500 --> 00:00:50.460 from plant to plant, it's able to pollinate, 00:00:50.460 --> 00:00:52.920 it's able to take pollen from one plant 00:00:52.920 --> 00:00:54.660 and give it to another plant, 00:00:54.660 --> 00:00:57.740 allowing for that genetic mixing to occur 00:00:57.740 --> 00:01:01.410 and also to then have more plant reproduction. 00:01:01.410 --> 00:01:04.340 Now, once a plant is able to reproduce, 00:01:04.340 --> 00:01:06.440 we also need to think about how viable 00:01:06.440 --> 00:01:08.320 its offspring are going to be. 00:01:08.320 --> 00:01:10.700 Are they in conditions where they are likely 00:01:10.700 --> 00:01:14.890 to succeed in living and then reproducing themselves? 00:01:14.890 --> 00:01:17.130 And here, a common strategy, 00:01:17.130 --> 00:01:20.350 or at least a category of strategies that plants use 00:01:20.350 --> 00:01:24.380 are known as seed dispersal. 00:01:24.380 --> 00:01:27.130 And it's really just trying to get the seeds 00:01:27.130 --> 00:01:28.910 in as many places as possible, 00:01:28.910 --> 00:01:32.030 potentially far away from the plant itself, 00:01:32.030 --> 00:01:34.290 to increase the chances that more of the seeds 00:01:34.290 --> 00:01:36.800 are going to be in places that are nutrient rich, 00:01:36.800 --> 00:01:38.600 where they can survive. 00:01:38.600 --> 00:01:41.800 And once again, you have likely seen this. 00:01:41.800 --> 00:01:45.880 This is a dandelion plant and when a strong wind blows, 00:01:45.880 --> 00:01:48.210 these dandelion seeds catch the wind 00:01:48.210 --> 00:01:49.210 because they have these structures 00:01:49.210 --> 00:01:51.120 which are not that aerodynamic, 00:01:51.120 --> 00:01:54.300 which pull the seeds along and can transport them 00:01:54.300 --> 00:01:56.440 for even miles and miles. 00:01:56.440 --> 00:01:59.280 Many of these seeds aren't going to end up in useful places, 00:01:59.280 --> 00:02:00.650 but some of them might, 00:02:00.650 --> 00:02:02.600 and they might be in places where 00:02:02.600 --> 00:02:06.070 the future dandelion offspring are more likely to survive 00:02:06.070 --> 00:02:08.435 and then reproduce themselves. 00:02:08.435 --> 00:02:11.593 But seed dispersal also gets the help of animals. 00:02:12.490 --> 00:02:15.000 This right over here is a picture of a bird 00:02:15.000 --> 00:02:16.840 eating fruit from a plant. 00:02:16.840 --> 00:02:20.190 And as that bird flies away and munches on that fruit, 00:02:20.190 --> 00:02:22.060 that seed might be dispersed, 00:02:22.060 --> 00:02:25.330 it might be thrown down hundreds of yards 00:02:25.330 --> 00:02:28.100 or even miles away from the original plant. 00:02:28.100 --> 00:02:30.380 In many cases, you might eat a fruit, 00:02:30.380 --> 00:02:32.880 and I am saying you, because we do this ourselves. 00:02:32.880 --> 00:02:35.610 You might eat, say, a watermelon or a papaya 00:02:35.610 --> 00:02:38.430 and a couple of seeds go down while you ate it. 00:02:38.430 --> 00:02:41.130 And then later on, you or some other animal 00:02:41.130 --> 00:02:44.470 might poop it someplace where it might be a good place 00:02:44.470 --> 00:02:48.560 for that watermelon plant or that papaya plant to grow. 00:02:48.560 --> 00:02:49.770 So this was just an overview 00:02:49.770 --> 00:02:52.430 of some of the strategies that plants use, 00:02:52.430 --> 00:02:55.400 but it's important to realize that throughout nature, 00:02:55.400 --> 00:02:58.940 we see this idea of reproductive success 00:02:58.940 --> 00:03:01.880 over and over again, and in animals' behaviors 00:03:01.880 --> 00:03:04.080 or strategies for reproductive success, 00:03:04.080 --> 00:03:09.080 and here we saw plants' strategies for reproductive success.

Animal behavior and offspring success

https://www.youtube.com/watch?v=txrCIhujs0g

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https://www.youtube.com/api/timedtext?v=txrCIhujs0g&ei=xFWUZZWFErO5mLAPiq2-mA8&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=D82E111E38CED201604A84DCA3C716DE97B293BB.6E7BCF0E8A4A7EEB6A8CC4F7427B227E98712BF8&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.500 --> 00:00:04.500 - Let's talk a little bit about reproductive success, 00:00:04.500 --> 00:00:08.415 which is related to the number of surviving offspring 00:00:08.415 --> 00:00:11.670 that an animal has during its lifetime. 00:00:11.670 --> 00:00:14.690 An animal that has more surviving offspring 00:00:14.690 --> 00:00:17.378 has a higher reproductive success. 00:00:17.378 --> 00:00:19.781 Now, there's two broad categories 00:00:19.781 --> 00:00:21.905 of traits or behaviors 00:00:21.905 --> 00:00:24.990 that might drive reproductive success. 00:00:24.990 --> 00:00:28.350 One might be behaviors that increase the chances 00:00:28.350 --> 00:00:30.970 of an animal producing offspring. 00:00:30.970 --> 00:00:33.060 And we know that most animals that we study, 00:00:33.060 --> 00:00:37.010 not all, but most, reproduce via sexual reproduction. 00:00:37.010 --> 00:00:37.860 To do that, 00:00:37.860 --> 00:00:41.300 they need to mate with an individual of the opposite sex. 00:00:41.300 --> 00:00:44.379 And that's why you see things like peacocks, 00:00:44.379 --> 00:00:48.070 where these very elaborate feathers are a way 00:00:48.070 --> 00:00:51.130 of signaling to members of the opposite sex, 00:00:51.130 --> 00:00:55.760 the peahens, that this peacock here has favorable traits, 00:00:55.760 --> 00:00:59.200 is attractive to the peahen, has good health, 00:00:59.200 --> 00:01:00.980 which signals to the peahen 00:01:00.980 --> 00:01:02.750 that by reproducing with this peacock, 00:01:02.750 --> 00:01:06.180 they're more likely to have reproductive success. 00:01:06.180 --> 00:01:07.390 They'll have healthier offspring, 00:01:07.390 --> 00:01:09.450 which are more likely to survive, 00:01:09.450 --> 00:01:12.340 which are more likely to then go on and reproduce. 00:01:12.340 --> 00:01:14.790 And then assuming that animals are able to mate 00:01:14.790 --> 00:01:16.166 and able to reproduce, 00:01:16.166 --> 00:01:19.358 another behavior that you will see amongst animals 00:01:19.358 --> 00:01:21.420 that will increase the chances 00:01:21.420 --> 00:01:22.765 that their offspring will survive, 00:01:22.765 --> 00:01:25.029 and then be able to reproduce themselves 00:01:25.029 --> 00:01:27.350 is parental care, 00:01:27.350 --> 00:01:30.695 or behaviors that protect offspring from predators. 00:01:30.695 --> 00:01:33.640 You see that throughout the animal kingdom. 00:01:33.640 --> 00:01:36.330 Here are some emperor penguins taking care 00:01:36.330 --> 00:01:39.110 of their young baby penguin. 00:01:39.110 --> 00:01:42.540 Here is a mother grizzly bear taking care of her bears. 00:01:42.540 --> 00:01:46.320 And here the parental care might be helping them find food, 00:01:46.320 --> 00:01:48.660 giving them food, training them, 00:01:48.660 --> 00:01:50.780 protecting them from other predators 00:01:50.780 --> 00:01:52.510 or from competitors in some way. 00:01:52.510 --> 00:01:54.970 And this isn't just amongst bears, and penguins, 00:01:54.970 --> 00:01:56.990 and potentially peacocks and peahens. 00:01:56.990 --> 00:01:59.780 It's all in service to, at least in some level, 00:01:59.780 --> 00:02:01.833 reproductive success.

Earth's changing climate

https://www.youtube.com/watch?v=z9xKxciHgo8

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https://www.youtube.com/api/timedtext?v=z9xKxciHgo8&ei=xFWUZceDF_nXxN8P0ra8gAI&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6C81092496B3722AA6B3F3825952AB96B1139293.7E3CFBE93DF2601B6F157D550A0DC26B65E07007&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:01.250 - [Narrator] Have you ever tried to imagine 00:00:01.250 --> 00:00:03.760 what the world was like in the distant past? 00:00:03.760 --> 00:00:06.390 Maybe you'd like to explore the age of the dinosaurs 00:00:06.390 --> 00:00:08.790 when the earth was much hotter than it was today. 00:00:08.790 --> 00:00:09.850 Perhaps you'd prefer 00:00:09.850 --> 00:00:12.340 when temperatures dropped too much colder than today. 00:00:12.340 --> 00:00:14.900 You could track a mammoth alongside our early ancestors 00:00:14.900 --> 00:00:17.740 who evolved around the end of the last ice age. 00:00:17.740 --> 00:00:19.730 We know about all of these ancient climate trends 00:00:19.730 --> 00:00:20.760 because scientists learned 00:00:20.760 --> 00:00:23.290 how to estimate them using evidence from ice cores, 00:00:23.290 --> 00:00:25.363 tree rings, and other natural phenomena. 00:00:26.230 --> 00:00:28.050 We now know that for most of human history, 00:00:28.050 --> 00:00:29.190 people could expect a pattern 00:00:29.190 --> 00:00:30.500 that looks something like this graph 00:00:30.500 --> 00:00:33.160 from the National Aeronautics and Space Administration 00:00:33.160 --> 00:00:35.330 which shows how temperatures changed each year 00:00:35.330 --> 00:00:37.120 in comparison to this line, 00:00:37.120 --> 00:00:39.500 which represents the average global annual temperature 00:00:39.500 --> 00:00:42.300 from 1880 to 1899. 00:00:42.300 --> 00:00:45.210 When we look at the time period between 1880 and 1940, 00:00:45.210 --> 00:00:47.450 we can see that some years temperatures would be higher 00:00:47.450 --> 00:00:49.770 than this average, some years they would be lower, 00:00:49.770 --> 00:00:51.130 but they generally swing back 00:00:51.130 --> 00:00:53.080 to a pretty comfortable state. 00:00:53.080 --> 00:00:54.450 Around the 1950s, though, 00:00:54.450 --> 00:00:56.060 the global average temperature began to climb 00:00:56.060 --> 00:00:57.850 to unprecedented levels. 00:00:57.850 --> 00:00:59.820 Our ancient temperature records never showed 00:00:59.820 --> 00:01:01.680 such a sudden increase. 00:01:01.680 --> 00:01:04.220 When we look at the time period from 1950 to today, 00:01:04.220 --> 00:01:05.560 we can see that while temperatures 00:01:05.560 --> 00:01:07.120 still swing back down some years, 00:01:07.120 --> 00:01:08.960 these colder years are still much hotter 00:01:08.960 --> 00:01:11.320 than the average temperatures in the past. 00:01:11.320 --> 00:01:13.700 Researchers noticed a change in the concentration 00:01:13.700 --> 00:01:16.120 of greenhouse gases in the Earth's atmosphere. 00:01:16.120 --> 00:01:17.760 These greenhouse gases trap heat 00:01:17.760 --> 00:01:19.140 from the sun in our atmosphere, 00:01:19.140 --> 00:01:21.480 similar to how a greenhouse allows sunlight 00:01:21.480 --> 00:01:22.830 to pass through its glass walls 00:01:22.830 --> 00:01:25.490 but prevents the heat it creates from leaving. 00:01:25.490 --> 00:01:27.800 This greenhouse effect is what keeps our planet warm 00:01:27.800 --> 00:01:29.430 and habitable enough for life. 00:01:29.430 --> 00:01:31.920 However, the amount of one particular greenhouse gas 00:01:31.920 --> 00:01:34.960 was rising, carbon dioxide or CO2. 00:01:34.960 --> 00:01:37.880 CO2 is naturally one of the most notable greenhouse gases 00:01:37.880 --> 00:01:38.970 besides water vapor, 00:01:38.970 --> 00:01:41.620 but we can also release CO2 by burning wood 00:01:41.620 --> 00:01:43.760 or fossil fuels like coal and oil. 00:01:43.760 --> 00:01:46.390 Over time, humans have increasingly relied on these fuels 00:01:46.390 --> 00:01:48.900 to power things like planes, cars, and trains 00:01:48.900 --> 00:01:51.200 as well as to generate electricity. 00:01:51.200 --> 00:01:52.740 As a result of these human activities, 00:01:52.740 --> 00:01:55.040 more CO2 is being released into the atmosphere 00:01:55.040 --> 00:01:56.280 than ever before, 00:01:56.280 --> 00:01:58.370 much more than is normally released by the Earth 00:01:58.370 --> 00:02:00.210 and at a much faster rate. 00:02:00.210 --> 00:02:02.460 The increasingly heavy blanket of greenhouse gases 00:02:02.460 --> 00:02:04.240 is trapping excess heat in our atmosphere 00:02:04.240 --> 00:02:05.510 rather than allowing more of it 00:02:05.510 --> 00:02:07.430 to radiate into space as normal. 00:02:07.430 --> 00:02:09.900 This is what's causing Earth's average temperature 00:02:09.900 --> 00:02:11.650 to rise beyond what scientists would expect 00:02:11.650 --> 00:02:13.690 based on historical patterns. 00:02:13.690 --> 00:02:14.880 While scientists once referred 00:02:14.880 --> 00:02:16.510 to this process as global warming, 00:02:16.510 --> 00:02:19.910 most now prefer the more general term, climate change. 00:02:19.910 --> 00:02:21.930 A world that's a little bit warmer on average 00:02:21.930 --> 00:02:23.530 might not seem like such a big deal, 00:02:23.530 --> 00:02:25.340 but we've learned that even a small shift 00:02:25.340 --> 00:02:26.740 in the planet's natural processes 00:02:26.740 --> 00:02:29.360 can have drastic consequences. 00:02:29.360 --> 00:02:31.320 When studying the early signs of climate change, 00:02:31.320 --> 00:02:33.190 scientists predicted that as cold places 00:02:33.190 --> 00:02:35.010 like North and South Pole got warmer, 00:02:35.010 --> 00:02:36.600 the ice would begin to melt. 00:02:36.600 --> 00:02:39.110 All of that frozen water suddenly flowing into the oceans 00:02:39.110 --> 00:02:40.460 would cause sea levels to rise, 00:02:40.460 --> 00:02:43.340 which would affect the planet's weather system. 00:02:43.340 --> 00:02:45.070 Have you heard all the news about weird weather 00:02:45.070 --> 00:02:46.410 in the past few years? 00:02:46.410 --> 00:02:49.020 Snow in places that's usually warm and dry, 00:02:49.020 --> 00:02:52.060 or drought in places that are usually cold and rainy, 00:02:52.060 --> 00:02:54.860 huge fires during extremely hot summers, 00:02:54.860 --> 00:02:58.570 severe storms battering coastlines and flooding cities. 00:02:58.570 --> 00:03:00.770 Many of these natural hazards used to be somewhat rare, 00:03:00.770 --> 00:03:02.480 but now they're becoming more common, 00:03:02.480 --> 00:03:05.020 exactly as climate scientists predicted. 00:03:05.020 --> 00:03:07.440 People have relied on relatively consistent weather patterns 00:03:07.440 --> 00:03:08.350 for generations, 00:03:08.350 --> 00:03:09.730 so they aren't prepared to adapt 00:03:09.730 --> 00:03:11.870 to these changes in their local environment. 00:03:11.870 --> 00:03:13.560 Communities that are already feeling the effects 00:03:13.560 --> 00:03:14.930 of climate change are worried 00:03:14.930 --> 00:03:16.130 that they're gonna lose their homes, 00:03:16.130 --> 00:03:19.193 their livelihoods, or their sources of food and water. 00:03:20.500 --> 00:03:21.940 Scientists are working on technologies 00:03:21.940 --> 00:03:23.820 that can help us remove some of the excess CO2 00:03:23.820 --> 00:03:24.710 from the atmosphere, 00:03:24.710 --> 00:03:27.470 but in the meantime they recommend that we emit less CO2 00:03:27.470 --> 00:03:28.650 in the first place. 00:03:28.650 --> 00:03:29.790 This would allow us to limit 00:03:29.790 --> 00:03:31.780 how much the global average temperature increases, 00:03:31.780 --> 00:03:33.200 giving communities time to adapt 00:03:33.200 --> 00:03:35.170 to changes in their surroundings. 00:03:35.170 --> 00:03:36.520 Of course, it's complicated 00:03:36.520 --> 00:03:38.570 to change the way our societies work. 00:03:38.570 --> 00:03:40.140 To help reduce CO2 emissions, 00:03:40.140 --> 00:03:41.610 you may see some people advocating 00:03:41.610 --> 00:03:43.210 for tweaking individual behaviors, 00:03:43.210 --> 00:03:44.670 like eating plant-based diets 00:03:44.670 --> 00:03:47.420 or using low carbon transportation methods. 00:03:47.420 --> 00:03:49.810 You may see others saying that since large organizations 00:03:49.810 --> 00:03:52.230 in highly populated countries emit the most CO2, 00:03:52.230 --> 00:03:53.160 we need to push them 00:03:53.160 --> 00:03:56.050 to make more wide raging institutional changes. 00:03:56.050 --> 00:03:57.750 As someone who works in environmental science, 00:03:57.750 --> 00:03:59.880 I know that sorting through all of these different facts 00:03:59.880 --> 00:04:03.170 and opinions on climate change can be overwhelming. 00:04:03.170 --> 00:04:04.990 It's difficult to think about living in a world 00:04:04.990 --> 00:04:06.140 that may be very different 00:04:06.140 --> 00:04:08.210 from what I've always known in the past. 00:04:08.210 --> 00:04:09.250 I've found it helpful 00:04:09.250 --> 00:04:12.030 to both adopt simple sustainable habits in my own life, 00:04:12.030 --> 00:04:13.820 while also seeking out community groups 00:04:13.820 --> 00:04:15.490 that work on bigger initiatives. 00:04:15.490 --> 00:04:17.100 It's easier to imagine the future 00:04:17.100 --> 00:04:19.510 when you help others to shape it. 00:04:19.510 --> 00:04:21.950 Now that we've taken some time to think about Earth's past 00:04:21.950 --> 00:04:23.880 and what's happening to it in the present, 00:04:23.880 --> 00:04:26.150 try looking towards the future of our planet. 00:04:26.150 --> 00:04:27.850 What is your ideal future? 00:04:27.850 --> 00:04:29.800 And how can you help to make it happen?

Weathering and erosion

https://www.youtube.com/watch?v=xWWOHttrkWI

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https://www.youtube.com/api/timedtext?v=xWWOHttrkWI&ei=xFWUZeeMItiLp-oPipqV8As&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=1EA38B3B44ED516E6120814B538D5EDDE416FEE0.4D2DA41A684C00AD0ADA132C57D7E587DFF8A7F3&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.380 --> 00:00:02.250 - [Instructor] Growing up in Southern Idaho, 00:00:02.250 --> 00:00:05.450 one of my favorite places to visit was Swan Falls, 00:00:05.450 --> 00:00:08.710 a gorgeous canyon formed by the snake river. 00:00:08.710 --> 00:00:11.400 All throughout my childhood, I remember scrambling 00:00:11.400 --> 00:00:13.430 over the boulders down in this canyon 00:00:13.430 --> 00:00:16.560 and playing in the cool water at the edge of the river. 00:00:16.560 --> 00:00:18.800 Over thousands and thousands of years, 00:00:18.800 --> 00:00:21.690 water slowly eroded away rock and sediment. 00:00:21.690 --> 00:00:26.660 Water made this canyon and water forms many landscapes, 00:00:26.660 --> 00:00:30.900 including valleys, ravines, cliffs, coastlines, 00:00:30.900 --> 00:00:34.940 all of these were largely shaped and affected by water. 00:00:34.940 --> 00:00:37.670 And given that water covers most of the earth, 00:00:37.670 --> 00:00:39.990 or over 70% of it, 00:00:39.990 --> 00:00:43.430 it's no surprise that water also shapes the earth. 00:00:43.430 --> 00:00:45.310 Water is a powerful force. 00:00:45.310 --> 00:00:47.390 It can literally wash away soil 00:00:47.390 --> 00:00:49.900 and carve away rock bit by bit, 00:00:49.900 --> 00:00:53.570 which scientists describe through two separate processes. 00:00:53.570 --> 00:00:57.490 When water breaks rocks apart, it's called weathering. 00:00:57.490 --> 00:01:00.830 And when water carries away surface soil, sediments, 00:01:00.830 --> 00:01:03.683 and that broken down rock it's called erosion. 00:01:04.810 --> 00:01:07.550 Erosion by water starts with rain. 00:01:07.550 --> 00:01:09.320 During a rain storm the impact 00:01:09.320 --> 00:01:11.710 of raindrops is actually powerful enough 00:01:11.710 --> 00:01:15.730 to dislodge soil particles and damage soil structure. 00:01:15.730 --> 00:01:18.380 This is called mechanical weathering. 00:01:18.380 --> 00:01:20.460 As rainwater starts to accumulate, 00:01:20.460 --> 00:01:22.640 it can erode a landscape by moving soil 00:01:22.640 --> 00:01:24.880 and rock particles, called sediment, 00:01:24.880 --> 00:01:27.480 away from their original location. 00:01:27.480 --> 00:01:31.280 And as water flows down the slope of hills and mountains, 00:01:31.280 --> 00:01:34.180 it transports sediment along with it. 00:01:34.180 --> 00:01:36.750 Eventually water gathers into small streams 00:01:36.750 --> 00:01:40.460 and then rivers, carrying more and more sediment. 00:01:40.460 --> 00:01:44.320 In fact, through erosion, water carries away billions 00:01:44.320 --> 00:01:47.540 of tons of sediment to the oceans every year. 00:01:47.540 --> 00:01:50.590 Plant roots and vegetation can hold soil in place 00:01:50.590 --> 00:01:53.190 and prevent or slow soil erosion. 00:01:53.190 --> 00:01:56.000 But if soil has nothing to hold it down, 00:01:56.000 --> 00:01:58.643 water can erode away soil very quickly. 00:02:00.460 --> 00:02:02.710 As the volume of water increases, 00:02:02.710 --> 00:02:05.290 so does its power of erosion. 00:02:05.290 --> 00:02:08.320 In turn, a large river can erode more soil 00:02:08.320 --> 00:02:11.320 and rock quicker than a small river can. 00:02:11.320 --> 00:02:13.050 The speed of the water flow 00:02:13.050 --> 00:02:15.630 also affects its erosional power. 00:02:15.630 --> 00:02:19.900 Simply put, faster moving water can carry more sediment. 00:02:19.900 --> 00:02:22.940 This relationship is one reason why fast moving water 00:02:22.940 --> 00:02:25.500 causes more erosion than the same volume 00:02:25.500 --> 00:02:27.460 of slow moving water. 00:02:27.460 --> 00:02:31.190 A great example of water erosion in relation to speed 00:02:31.190 --> 00:02:34.330 is that of meandering rivers and Oxbow lakes. 00:02:34.330 --> 00:02:38.130 You know, the weird horseshoe looking lake in this image. 00:02:38.130 --> 00:02:41.310 Let's take a look at how these Oxbow lakes form. 00:02:41.310 --> 00:02:43.560 The current of the water is fastest 00:02:43.560 --> 00:02:45.730 on the outside of the bend. 00:02:45.730 --> 00:02:48.410 In turn, these are the areas where water tends 00:02:48.410 --> 00:02:50.630 to erode away the river bank. 00:02:50.630 --> 00:02:53.680 Conversely, the current of the water is slowest 00:02:53.680 --> 00:02:55.510 on the inside of a bend. 00:02:55.510 --> 00:02:58.600 Here, the water slows down so much that some 00:02:58.600 --> 00:03:01.370 of the sediment that is being carried is dropped, 00:03:01.370 --> 00:03:02.920 or deposited. 00:03:02.920 --> 00:03:04.863 This is called sedimentation. 00:03:05.740 --> 00:03:08.200 Over time, through erosion and deposition, 00:03:08.200 --> 00:03:09.900 an Oxbow lake will form, 00:03:09.900 --> 00:03:12.050 which is eventually cut off from the river. 00:03:13.330 --> 00:03:15.070 Chemical weathering as another way 00:03:15.070 --> 00:03:16.990 that water can break rocks, 00:03:16.990 --> 00:03:19.720 such as when acids in water dissolve certain types 00:03:19.720 --> 00:03:21.300 of rocks and minerals. 00:03:21.300 --> 00:03:24.040 Over time, flowing water can dissolve the minerals 00:03:24.040 --> 00:03:27.020 and rocks on or under the surface. 00:03:27.020 --> 00:03:29.470 This chemical weathering can cause sinkholes, 00:03:29.470 --> 00:03:31.630 caves, and cliffs to form. 00:03:31.630 --> 00:03:33.540 Certain rocks like limestone 00:03:33.540 --> 00:03:36.430 are especially vulnerable to erosion. 00:03:36.430 --> 00:03:39.280 In particular, limestone easily erodes due 00:03:39.280 --> 00:03:41.280 to carbonic acid and rainwater, 00:03:41.280 --> 00:03:44.530 which forms when carbon dioxide, or CO2, 00:03:44.530 --> 00:03:46.980 from the atmosphere dissolves in water. 00:03:46.980 --> 00:03:49.250 In turn limestone erosion can produce 00:03:49.250 --> 00:03:50.933 intricate cave systems. 00:03:53.050 --> 00:03:55.030 Along beaches and the ocean front, 00:03:55.030 --> 00:03:58.140 coastal erosion breaks up and wears away rock. 00:03:58.140 --> 00:04:00.450 As waves sweep in over and over, 00:04:00.450 --> 00:04:03.103 they cause rock to weather away and break off. 00:04:05.970 --> 00:04:08.570 Going back to the Snake River and Swan Falls, 00:04:08.570 --> 00:04:12.089 I can see examples of weathering and erosion all around me. 00:04:12.089 --> 00:04:15.090 I look to the cliffs which have been slowly carved away 00:04:15.090 --> 00:04:18.920 by the Snake River over time to reveal this amazing valley, 00:04:18.920 --> 00:04:22.460 which was formed by weathering and water erosion. 00:04:22.460 --> 00:04:24.930 Water erosion is incredibly powerful 00:04:24.930 --> 00:04:28.380 and although it can be destructive by removing soil 00:04:28.380 --> 00:04:31.630 and rock over thousands and thousands of years, 00:04:31.630 --> 00:04:33.480 water erosion is also responsible 00:04:33.480 --> 00:04:34.820 for creating the beautiful 00:04:34.820 --> 00:04:37.643 and spectacular landscapes that we enjoy today.

The rock cycle

https://www.youtube.com/watch?v=rmH4W92eHVM

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https://www.youtube.com/api/timedtext?v=rmH4W92eHVM&ei=xFWUZb-LFKyDp-oPvsCy0AQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=08EE705CA3D44222956DCEECCF029B8F708CF2CD.0EC4C63F725DBD4A9C573E17809674E86559416E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.170 --> 00:00:01.100 - [Instructor] Have you ever tried 00:00:01.100 --> 00:00:03.490 to hold a staring contest with a rock? 00:00:03.490 --> 00:00:06.500 If you did, you might not have expected that all that time 00:00:06.500 --> 00:00:08.370 you were staring at one of the sneakiest 00:00:08.370 --> 00:00:10.470 shape-shifters in the world. 00:00:10.470 --> 00:00:13.570 No, rocks don't shapeshift into unicorns, 00:00:13.570 --> 00:00:16.530 but they do change shape and composition. 00:00:16.530 --> 00:00:18.450 Sometimes they change quickly, 00:00:18.450 --> 00:00:20.110 like when an interrupting volcano 00:00:20.110 --> 00:00:22.340 launches molten rock into the air. 00:00:22.340 --> 00:00:24.290 And sometimes they change slowly, 00:00:24.290 --> 00:00:26.400 like when a rock is heated and compressed 00:00:26.400 --> 00:00:29.770 in the earth for thousands to millions of years. 00:00:29.770 --> 00:00:31.480 When geologists stare at a rock, 00:00:31.480 --> 00:00:33.760 they can figure out the rocks composition 00:00:33.760 --> 00:00:36.280 and tell the story of how it was created. 00:00:36.280 --> 00:00:40.130 And it turns out rocks can be made in many different ways. 00:00:40.130 --> 00:00:42.930 When put it the right combination of heat and pressure, 00:00:42.930 --> 00:00:45.460 rocks can become molten and liquid. 00:00:45.460 --> 00:00:48.480 When this molten rock cools and becomes solid, 00:00:48.480 --> 00:00:50.960 we call the rock it makes igneous rock. 00:00:50.960 --> 00:00:53.420 This term comes from the Latin word igneus, 00:00:53.420 --> 00:00:56.250 which means fiery or burning hot. 00:00:56.250 --> 00:00:59.930 Igneous rocks make up more than 90% of the Earth's crust. 00:00:59.930 --> 00:01:02.630 One common kind of igneous rock is granite, 00:01:02.630 --> 00:01:04.620 which you've probably seen in bridges, 00:01:04.620 --> 00:01:06.560 buildings, and countertops. 00:01:06.560 --> 00:01:09.390 Another kind of igneous rock is obsidian, 00:01:09.390 --> 00:01:11.290 which is smooth and glassy, 00:01:11.290 --> 00:01:13.740 and is sometimes used to make knife weights. 00:01:13.740 --> 00:01:16.260 Both of these rocks were made of molten rock. 00:01:16.260 --> 00:01:18.425 So why do they look so different? 00:01:18.425 --> 00:01:21.120 Well, granite was made from magma, 00:01:21.120 --> 00:01:22.940 which is molten rock that exists 00:01:22.940 --> 00:01:24.560 below the surface of the earth. 00:01:24.560 --> 00:01:27.280 Magma tends to cool slowly underground, 00:01:27.280 --> 00:01:28.840 which gives time for the elements in it 00:01:28.840 --> 00:01:30.490 to form large crystals. 00:01:30.490 --> 00:01:32.909 And this obsidian rock was made from lava, 00:01:32.909 --> 00:01:36.250 which is molten rock that flows above the ground. 00:01:36.250 --> 00:01:38.220 Lava tends to cool quickly, 00:01:38.220 --> 00:01:41.010 which causes the rocks it forms like obsidian, 00:01:41.010 --> 00:01:42.960 tuff smaller crystals. 00:01:42.960 --> 00:01:44.520 I always remember the difference 00:01:44.520 --> 00:01:46.690 between magma and lava like this. 00:01:46.690 --> 00:01:48.860 I keep my lava lamp above the ground, 00:01:48.860 --> 00:01:50.940 just like lava is above the ground. 00:01:50.940 --> 00:01:53.330 If I buried my lava lamp in the ground, 00:01:53.330 --> 00:01:55.390 then I can call it a magma lamp. 00:01:55.390 --> 00:01:58.980 Once an igneous rock is created, its journey isn't over. 00:01:58.980 --> 00:02:00.320 The rock might begin to change 00:02:00.320 --> 00:02:02.000 through a process called weathering. 00:02:02.000 --> 00:02:05.850 This is when water, weather, wind, and other physical forces 00:02:05.850 --> 00:02:07.100 chip away at a rock 00:02:07.100 --> 00:02:09.170 and cause little pieces to break off. 00:02:09.170 --> 00:02:12.090 These little particles are called sediments. 00:02:12.090 --> 00:02:13.640 The sediment from our igneous rock 00:02:13.640 --> 00:02:16.060 can be moved around by wind and water. 00:02:16.060 --> 00:02:17.804 This is called erosion. 00:02:17.804 --> 00:02:20.900 Eventually, the sediment will settle down somewhere. 00:02:20.900 --> 00:02:23.410 Maybe at the bottom of an ocean or a lake, 00:02:23.410 --> 00:02:26.120 and it might join other sediment from other rocks, 00:02:26.120 --> 00:02:28.430 crushed up shells, and plant matter. 00:02:28.430 --> 00:02:31.570 And over time, this sediment will become a rock. 00:02:31.570 --> 00:02:33.140 Rocks that are formed from sediments 00:02:33.140 --> 00:02:35.946 are called, you guessed it, sedimentary rocks. 00:02:35.946 --> 00:02:37.960 But how does sedimentary goop 00:02:37.960 --> 00:02:40.290 at the bottom of the lake become a rock? 00:02:40.290 --> 00:02:43.350 Well, it goes through a process called lithification. 00:02:43.350 --> 00:02:45.650 Lith comes from the Greek word for stone. 00:02:45.650 --> 00:02:48.690 So you can think of this process as stonification. 00:02:48.690 --> 00:02:52.120 The first step of lithification is called deposition. 00:02:52.120 --> 00:02:54.950 This is when sediment is deposited in a new location 00:02:54.950 --> 00:02:57.342 and it spreads out to form a layer. 00:02:57.342 --> 00:02:59.690 As more and more layers are created, 00:02:59.690 --> 00:03:02.473 the layers underneath them become squished together. 00:03:03.430 --> 00:03:05.470 This is called compaction. 00:03:05.470 --> 00:03:07.640 When water moves to the layers of sediment, 00:03:07.640 --> 00:03:10.160 it can carry dissolve minerals with it. 00:03:10.160 --> 00:03:11.750 The water can leave these minerals 00:03:11.750 --> 00:03:13.430 in between the sediment particles, 00:03:13.430 --> 00:03:15.800 which makes everything stick together. 00:03:15.800 --> 00:03:19.650 This cementing of sediment is called cementation. 00:03:19.650 --> 00:03:22.320 Limestone is a sedimentary rock that is made with sediment 00:03:22.320 --> 00:03:24.950 that contains a lot of calcium carbonate in it 00:03:24.950 --> 00:03:26.930 goes through lithification. 00:03:26.930 --> 00:03:29.280 But once the sedimentary rock has been created, 00:03:29.280 --> 00:03:31.430 it doesn't mean that it is done changing. 00:03:31.430 --> 00:03:34.570 Sometimes a rock is squeezed or heated so much 00:03:34.570 --> 00:03:37.720 that the minerals inside it actually change composition. 00:03:37.720 --> 00:03:40.200 It is now a metamorphic rock. 00:03:40.200 --> 00:03:42.440 You might've heard of the word metamorphosis, 00:03:42.440 --> 00:03:44.040 which describes when something changes 00:03:44.040 --> 00:03:46.180 from one form and structure to another. 00:03:46.180 --> 00:03:48.700 Like when a caterpillar turns into a butterfly. 00:03:48.700 --> 00:03:51.920 Metamorphic rocks are made when igneous, sedimentary, 00:03:51.920 --> 00:03:53.746 or even other metamorphic rocks 00:03:53.746 --> 00:03:57.790 change form and structure because of heat and pressure. 00:03:57.790 --> 00:04:00.070 For example, when the sedimentary rock, limestone, 00:04:00.070 --> 00:04:02.030 gets put under a lot of heat and pressure, 00:04:02.030 --> 00:04:03.690 it can turn into marble, 00:04:03.690 --> 00:04:06.850 but metamorphic rocks still may not be done changing. 00:04:06.850 --> 00:04:09.970 Rocks can actually keep on changing forever. 00:04:09.970 --> 00:04:12.926 Igneous and metamorphic rocks can become sedimentary rocks 00:04:12.926 --> 00:04:15.330 if they're broken apart into sediments 00:04:15.330 --> 00:04:17.060 and go through lithification. 00:04:17.060 --> 00:04:19.850 And metamorphic rocks and sedimentary rocks 00:04:19.850 --> 00:04:22.210 can become igneous rocks when they are melted 00:04:22.210 --> 00:04:23.280 and then cools. 00:04:23.280 --> 00:04:25.530 And igneous rocks and sedimentary rocks 00:04:25.530 --> 00:04:27.110 can become metamorphic rocks 00:04:27.110 --> 00:04:29.320 when they're exposed to high heat and pressure. 00:04:29.320 --> 00:04:31.600 This is called the rock cycle. 00:04:31.600 --> 00:04:34.310 So maybe next time you get the chance to stare at a rock. 00:04:34.310 --> 00:04:36.630 See if you can figure out whether it's igneous, 00:04:36.630 --> 00:04:38.680 metamorphic, or sedimentary. 00:04:38.680 --> 00:04:40.410 And when rocks changed so much, 00:04:40.410 --> 00:04:42.663 who knows what kind of rock it'll be next.

The water cycle

https://www.youtube.com/watch?v=r2dnUvP1JgM

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https://www.youtube.com/api/timedtext?v=r2dnUvP1JgM&ei=xFWUZYOFFMebhcIPjJ-66A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=EEACFBA1C9CEDBAAAA5B5F5A8FA90F39244532D5.E6F19E9BE2C7E8BEB9B1B6B5785CAF16079BBA3C&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.360 --> 00:00:02.360 - [Instructor] Did you know that the water you drink 00:00:02.360 --> 00:00:05.540 is actually the same water that dinosaurs drank 00:00:05.540 --> 00:00:08.810 over 65 million years ago? 00:00:08.810 --> 00:00:10.350 It might be hard to believe 00:00:10.350 --> 00:00:14.070 but your water is actually really, really old. 00:00:14.070 --> 00:00:18.080 In fact, water on Earth is much older than the dinosaurs. 00:00:18.080 --> 00:00:20.300 Scientists estimate that the water on Earth 00:00:20.300 --> 00:00:24.000 is at least 4.6 billion years old. 00:00:24.000 --> 00:00:26.520 And the amount of water on Earth today, 00:00:26.520 --> 00:00:29.460 in lakes, rivers, oceans, glaciers, 00:00:29.460 --> 00:00:32.190 even under the ground and up in the clouds, 00:00:32.190 --> 00:00:33.600 it's about the same as it was 00:00:33.600 --> 00:00:35.980 millions and millions of years ago. 00:00:35.980 --> 00:00:38.220 That's because water is recycled. 00:00:38.220 --> 00:00:40.583 It just gets used again and again. 00:00:41.580 --> 00:00:43.690 And that brings us to the water cycle, 00:00:43.690 --> 00:00:46.170 which is how water continuously moves 00:00:46.170 --> 00:00:49.590 from the ground to the atmosphere and back again. 00:00:49.590 --> 00:00:53.890 And as water moves through the cycle, it changes form. 00:00:53.890 --> 00:00:56.870 In fact, water is the only substance on Earth 00:00:56.870 --> 00:00:59.530 that naturally exists in three states, 00:00:59.530 --> 00:01:02.180 solid, liquid, and gas. 00:01:02.180 --> 00:01:05.160 Have you seen water in all of its different states? 00:01:05.160 --> 00:01:07.420 Maybe on a hot day, you'll add some ice, 00:01:07.420 --> 00:01:09.470 which is water in its solid state, 00:01:09.470 --> 00:01:11.380 to a glass of liquid water. 00:01:11.380 --> 00:01:13.620 Or maybe when you take out some food 00:01:13.620 --> 00:01:15.460 that you've heated in the microwave, 00:01:15.460 --> 00:01:17.830 you'll see steam coming off of the food, 00:01:17.830 --> 00:01:20.913 which is water in its gas state as water vapor. 00:01:21.820 --> 00:01:23.010 When you think of water, 00:01:23.010 --> 00:01:25.720 you might think of the wide open ocean. 00:01:25.720 --> 00:01:29.710 Over 95% of all the water on Earth is in the ocean, 00:01:29.710 --> 00:01:33.150 so this is a great place to start with the water cycle. 00:01:33.150 --> 00:01:35.960 Here, energy from the sun warms up water 00:01:35.960 --> 00:01:37.690 on the surface of the ocean 00:01:37.690 --> 00:01:40.260 enough to turn it into water vapor. 00:01:40.260 --> 00:01:42.730 This is called evaporation. 00:01:42.730 --> 00:01:44.890 This water vapor is less dense, 00:01:44.890 --> 00:01:47.690 meaning it's lighter, than liquid water, 00:01:47.690 --> 00:01:50.770 so it rises up and up into the atmosphere. 00:01:50.770 --> 00:01:53.440 However, as the water vapor rises, 00:01:53.440 --> 00:01:56.000 the temperature in the atmosphere cools. 00:01:56.000 --> 00:01:58.290 In turn, the water vapor condenses 00:01:58.290 --> 00:02:00.670 into tiny liquid water droplets, 00:02:00.670 --> 00:02:03.770 or, as we see them, clouds. 00:02:03.770 --> 00:02:06.210 This is called condensation. 00:02:06.210 --> 00:02:10.540 Air currents then move these clouds all around the Earth. 00:02:10.540 --> 00:02:14.180 As a cloud collects more and more liquid water droplets, 00:02:14.180 --> 00:02:16.330 the water may be released from the cloud, 00:02:16.330 --> 00:02:17.820 pulled down by gravity, 00:02:17.820 --> 00:02:19.840 and then return to the ocean or land 00:02:19.840 --> 00:02:22.050 as precipitation, like rain. 00:02:22.050 --> 00:02:23.780 If it's really cold, though, 00:02:23.780 --> 00:02:27.230 the water drops may crystallize and become snow. 00:02:27.230 --> 00:02:28.940 The snow will fall to the ground 00:02:28.940 --> 00:02:31.070 and eventually melt back into a liquid 00:02:31.070 --> 00:02:34.880 and run off into a lake or river, pulled down by gravity, 00:02:34.880 --> 00:02:36.970 which flows back into the ocean 00:02:36.970 --> 00:02:39.253 where the whole process starts over again. 00:02:40.150 --> 00:02:43.090 But that's just one path water can take 00:02:43.090 --> 00:02:44.600 through the water cycle. 00:02:44.600 --> 00:02:47.130 It's like a choose your own adventure. 00:02:47.130 --> 00:02:50.320 Instead of snow melting and running off into a river, 00:02:50.320 --> 00:02:53.670 the snow could become part of an icy cold glacier 00:02:53.670 --> 00:02:56.430 and stay there for a long, long time, 00:02:56.430 --> 00:02:58.660 for thousands of years. 00:02:58.660 --> 00:03:02.870 Or rain can seep into the ground and become groundwater, 00:03:02.870 --> 00:03:05.860 where it's then absorbed by plant roots. 00:03:05.860 --> 00:03:08.260 In turn, through transpiration, 00:03:08.260 --> 00:03:10.090 the water absorbed by the plants 00:03:10.090 --> 00:03:12.550 can transition to water vapor 00:03:12.550 --> 00:03:14.550 and leave directly through the leaves 00:03:14.550 --> 00:03:17.150 via tiny holes called stomata 00:03:17.150 --> 00:03:18.913 and return to the atmosphere. 00:03:19.850 --> 00:03:23.250 Or instead of being absorbed by plant roots, 00:03:23.250 --> 00:03:27.030 the groundwater can work its way to an underground aquifer 00:03:27.030 --> 00:03:29.953 or a lake, river, or even the ocean. 00:03:31.040 --> 00:03:33.770 There are many different paths for water 00:03:33.770 --> 00:03:37.350 and the water cycle can be very complicated. 00:03:37.350 --> 00:03:41.060 But it really comes down to something very simple. 00:03:41.060 --> 00:03:42.700 The amount of water on Earth 00:03:42.700 --> 00:03:44.670 stays pretty constant over time 00:03:44.670 --> 00:03:46.860 and moves from place to place, 00:03:46.860 --> 00:03:49.520 sometimes transitioning between phases, 00:03:49.520 --> 00:03:52.570 depending on things like weather, geography, 00:03:52.570 --> 00:03:54.693 solar energy, and gravity. 00:03:55.770 --> 00:03:59.220 Now, we know that water is essential to life on Earth 00:03:59.220 --> 00:04:02.300 and fresh water is an especially limited resource 00:04:02.300 --> 00:04:04.620 for a growing world population. 00:04:04.620 --> 00:04:07.560 Changes in the water cycle can impact everyone 00:04:07.560 --> 00:04:09.990 through the economy, energy production, 00:04:09.990 --> 00:04:13.740 health, recreation transportation, agriculture, 00:04:13.740 --> 00:04:15.980 and of course drinking water. 00:04:15.980 --> 00:04:18.550 And that's why understanding the water cycle 00:04:18.550 --> 00:04:20.350 is so important. 00:04:20.350 --> 00:04:22.270 That, and it's pretty cool to know 00:04:22.270 --> 00:04:25.220 that you drink the same water as dinosaurs did. 00:04:25.220 --> 00:04:26.303 Until next time.

Earth's place in the universe

https://www.youtube.com/watch?v=Pv0Re0YEEq0

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en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:01.230 - [Narrator] Hello, everyone. 00:00:01.230 --> 00:00:02.690 Today, we are going to be talking about 00:00:02.690 --> 00:00:05.420 Earth's place in space. 00:00:05.420 --> 00:00:07.490 So for as long as there have been humans, 00:00:07.490 --> 00:00:09.240 we've been looking up at the stars, 00:00:09.240 --> 00:00:12.660 and wondering about our place in the universe. 00:00:12.660 --> 00:00:15.480 Our understanding about this has improved over time, 00:00:15.480 --> 00:00:17.410 and we have developed models 00:00:17.410 --> 00:00:21.320 that can help us understand something as vast as space. 00:00:21.320 --> 00:00:25.320 Now, models are just a way of representing a system of ideas 00:00:25.320 --> 00:00:29.260 that help us identify and understand patterns that we see. 00:00:29.260 --> 00:00:31.540 Models are a tool that can explain, 00:00:31.540 --> 00:00:35.690 and predict what we see in the world and space around us. 00:00:35.690 --> 00:00:39.330 And as we gain new information, we can update our models. 00:00:39.330 --> 00:00:42.220 So what kind of model might we construct 00:00:42.220 --> 00:00:46.660 about how Earth interacts with other bodies in the universe? 00:00:46.660 --> 00:00:48.260 To begin with, every day, 00:00:48.260 --> 00:00:51.730 we can see the sun rise in the east, and set in the west, 00:00:51.730 --> 00:00:55.230 and other objects in the sky follow a similar pattern. 00:00:55.230 --> 00:00:57.470 It was logical then for early models 00:00:57.470 --> 00:01:00.350 to consider the Earth as a stationary object, 00:01:00.350 --> 00:01:03.800 around which all of the universe revolves. 00:01:03.800 --> 00:01:06.350 This is called a geocentric model, 00:01:06.350 --> 00:01:09.720 geo for Earth, and centric for center. 00:01:09.720 --> 00:01:12.090 And this geocentric model was quite good 00:01:12.090 --> 00:01:14.580 at explaining a lot of the things that we see in the sky, 00:01:14.580 --> 00:01:18.070 like the apparent motion of the sun and the stars. 00:01:18.070 --> 00:01:21.670 But there were issues with this geocentric model. 00:01:21.670 --> 00:01:24.740 For example, the motions of other planets in the sky. 00:01:24.740 --> 00:01:27.910 A planet like Jupiter might sometimes move backwards 00:01:27.910 --> 00:01:29.460 in the opposite direction, 00:01:29.460 --> 00:01:31.420 which isn't really very well explained 00:01:31.420 --> 00:01:33.770 by this geocentric model. 00:01:33.770 --> 00:01:36.650 Now, when a model doesn't match our observations like this, 00:01:36.650 --> 00:01:39.790 we can add new pieces to improve the model. 00:01:39.790 --> 00:01:42.310 So astronomers working with the geocentric model 00:01:42.310 --> 00:01:44.500 did this by adding smaller cycles 00:01:44.500 --> 00:01:47.820 within the planets' orbits around the Earth. 00:01:47.820 --> 00:01:50.900 Adding these cycles did help match the geocentric model 00:01:50.900 --> 00:01:52.430 to the observations, 00:01:52.430 --> 00:01:54.280 but there were many of these cycles required, 00:01:54.280 --> 00:01:56.010 and there wasn't a good explanation 00:01:56.010 --> 00:01:57.470 for why these cycles existed. 00:01:57.470 --> 00:01:59.850 And there wasn't very much reasoning for them, 00:01:59.850 --> 00:02:01.522 and they made the model very complicated, 00:02:01.522 --> 00:02:03.563 and not particularly useful. 00:02:04.580 --> 00:02:06.720 Let's pause and talk a little bit about motion, 00:02:06.720 --> 00:02:09.343 specifically apparent versus actual. 00:02:10.470 --> 00:02:11.970 Imagine you're sitting in a car, 00:02:11.970 --> 00:02:13.750 and driving through a forest. 00:02:13.750 --> 00:02:16.380 To your perspective, as you look out the window, 00:02:16.380 --> 00:02:18.980 the trees seem to be whizzing by, 00:02:18.980 --> 00:02:21.300 but trees, of course, are rooted to the ground. 00:02:21.300 --> 00:02:22.840 It's actually you that are moving 00:02:22.840 --> 00:02:25.060 relative to the surface of the Earth. 00:02:25.060 --> 00:02:29.380 This is the difference between apparent and actual motion. 00:02:29.380 --> 00:02:32.050 So back to our geocentric model. 00:02:32.050 --> 00:02:34.710 Another way to explain some of the issues 00:02:34.710 --> 00:02:36.470 with a model like the geocentric model, 00:02:36.470 --> 00:02:39.480 besides adding evermore complicated features to it, 00:02:39.480 --> 00:02:42.410 is to in fact, just come up with a new model. 00:02:42.410 --> 00:02:43.970 And this is what astronomers did. 00:02:43.970 --> 00:02:44.961 The new model that was proposed 00:02:44.961 --> 00:02:49.563 to replace the geocentric model was the heliocentric model. 00:02:50.652 --> 00:02:53.750 In this model, the Earth and all the other planets 00:02:53.750 --> 00:02:56.400 actually revolve around the sun. 00:02:56.400 --> 00:02:58.480 Helio means sun. 00:02:58.480 --> 00:03:01.220 This heliocentric model didn't need complicated 00:03:01.220 --> 00:03:02.400 and unexplained cycles 00:03:02.400 --> 00:03:05.220 to explain the way the other planets moved across the sky. 00:03:05.220 --> 00:03:08.610 It was an expected outcome of the planets' orbits. 00:03:08.610 --> 00:03:09.930 Now you may be wondering, 00:03:09.930 --> 00:03:12.130 in this model, the sun is stationary. 00:03:12.130 --> 00:03:13.560 So why does it seem to be 00:03:13.560 --> 00:03:16.190 moving across the Earth's sky each day? 00:03:16.190 --> 00:03:18.480 This is actually also easily explained, 00:03:18.480 --> 00:03:20.160 because the motion of the sun in the sky 00:03:20.160 --> 00:03:23.760 is not actual motion, it is apparent motion. 00:03:23.760 --> 00:03:26.370 Not only is the Earth revolving around the sun, 00:03:26.370 --> 00:03:28.010 revolving means orbiting, 00:03:28.010 --> 00:03:31.020 but the Earth is also spinning on its own axis. 00:03:31.020 --> 00:03:32.670 And so as the surface of the Earth 00:03:32.670 --> 00:03:34.610 moves with its spinning motion, 00:03:34.610 --> 00:03:38.400 it makes it appear as if the sun is moving across the sky. 00:03:38.400 --> 00:03:39.690 The spinning of the Earth 00:03:39.690 --> 00:03:41.790 actually explains why celestial objects 00:03:41.790 --> 00:03:44.790 appear to rise and set over the course of a day, 00:03:44.790 --> 00:03:46.890 while the revolution, or orbit, 00:03:46.890 --> 00:03:49.470 around the sun explains the motion of those objects 00:03:49.470 --> 00:03:51.170 over the course of a year. 00:03:51.170 --> 00:03:53.910 It's important to remember that while the heliocentric model 00:03:53.910 --> 00:03:55.700 does a better job of explaining 00:03:55.700 --> 00:03:57.180 and predicting our solar system, 00:03:57.180 --> 00:04:00.770 which is what we want models to do, it is still a model, 00:04:00.770 --> 00:04:03.940 and not a perfect recreation of reality. 00:04:03.940 --> 00:04:06.110 For example, while the heliocentric model 00:04:06.110 --> 00:04:08.320 considers the sun as stationary, 00:04:08.320 --> 00:04:10.950 we know now that the sun is actually just one star 00:04:10.950 --> 00:04:14.090 of many billions orbiting the center of our own galaxy. 00:04:14.090 --> 00:04:17.060 And so the sun, along with the rest of the solar system, 00:04:17.060 --> 00:04:19.290 is in fact, moving. 00:04:19.290 --> 00:04:20.640 To summarize, in this video, 00:04:20.640 --> 00:04:22.610 we talked about how we can use models 00:04:22.610 --> 00:04:25.110 to help us understand what we see in the sky, 00:04:25.110 --> 00:04:27.670 and Earth's place in space. 00:04:27.670 --> 00:04:28.890 As we learn more, 00:04:28.890 --> 00:04:30.100 we improve our models, 00:04:30.100 --> 00:04:32.170 and we can develop new ones that do a better job 00:04:32.170 --> 00:04:33.870 of explaining our observations, 00:04:33.870 --> 00:04:35.730 and predicting the world around us, 00:04:35.730 --> 00:04:37.690 such as the change from a geocentric model 00:04:37.690 --> 00:04:40.020 to a heliocentric model. 00:04:40.020 --> 00:04:42.420 The Earth then is a planet that orbits the sun, 00:04:42.420 --> 00:04:44.450 like the other planets of the solar system. 00:04:44.450 --> 00:04:46.960 And the sun appears to move across the sky, 00:04:46.960 --> 00:04:50.300 because the Earth spins on its axis. 00:04:50.300 --> 00:04:51.133 Thanks for watching, 00:04:51.133 --> 00:04:53.463 and I hope you learned a little bit of something.

Organization in the human body

https://www.youtube.com/watch?v=YE2peDF4Zqg

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WEBVTT Kind: captions Language: en 00:00:00.290 --> 00:00:01.410 - [Instructor] Have you ever thought about 00:00:01.410 --> 00:00:04.260 how incredible the human body is? 00:00:04.260 --> 00:00:06.210 For example, just to name a few things 00:00:06.210 --> 00:00:08.220 that your body's already been doing today. 00:00:08.220 --> 00:00:11.220 You are using your lungs to take breaths in and out, 00:00:11.220 --> 00:00:13.430 your heart's beating without stopping. 00:00:13.430 --> 00:00:16.100 And your brain is coordinating your body's functions, 00:00:16.100 --> 00:00:20.040 and at the same time, helping you understand this video. 00:00:20.040 --> 00:00:22.600 All these body parts are made up of cells, 00:00:22.600 --> 00:00:26.560 which as you might remember, are the smallest units of life. 00:00:26.560 --> 00:00:29.330 And it's so amazing that trillions of cells, 00:00:29.330 --> 00:00:31.870 without thoughts or intentions of their own, 00:00:31.870 --> 00:00:33.620 can come together to form something 00:00:33.620 --> 00:00:36.340 as complex as the human body. 00:00:36.340 --> 00:00:38.460 To help us understand how this occurs, 00:00:38.460 --> 00:00:41.560 we have to understand how the body is organized. 00:00:41.560 --> 00:00:45.170 The human body has a hierarchical organization, 00:00:45.170 --> 00:00:47.510 meaning it's made up of nested layers, 00:00:47.510 --> 00:00:50.150 each one more complex than the last. 00:00:50.150 --> 00:00:54.110 In this case, four different layers make up this hierarchy. 00:00:54.110 --> 00:00:56.510 Cells, which make up tissues. 00:00:56.510 --> 00:00:58.630 Tissues, which make up organs. 00:00:58.630 --> 00:01:01.080 Organs, which make up organ systems. 00:01:01.080 --> 00:01:04.150 And finally organ systems, which help the human body 00:01:04.150 --> 00:01:06.040 function as a whole. 00:01:06.040 --> 00:01:08.290 So let's start with cells and tissues. 00:01:08.290 --> 00:01:10.570 Cells are the smallest unit of life, 00:01:10.570 --> 00:01:13.250 and the most basic level of organization 00:01:13.250 --> 00:01:14.800 in the human body. 00:01:14.800 --> 00:01:18.740 In the human body, not all cells look or work the same. 00:01:18.740 --> 00:01:20.810 Instead, they're specialized 00:01:20.810 --> 00:01:22.850 to carry out different functions. 00:01:22.850 --> 00:01:26.960 After cells, the next level of organization is tissues. 00:01:26.960 --> 00:01:31.790 A tissue is a collection of similar, specialized cells. 00:01:31.790 --> 00:01:34.840 And all of the cells that make up a tissue are like a team. 00:01:34.840 --> 00:01:38.100 They work together to ensure the tissue works properly. 00:01:38.100 --> 00:01:40.550 For instance, this image shows a section 00:01:40.550 --> 00:01:42.650 of the type of epithelial tissue 00:01:42.650 --> 00:01:45.140 that lines the inside of your mouth. 00:01:45.140 --> 00:01:48.950 This particular tissue is made up of epithelial cells, 00:01:48.950 --> 00:01:51.330 which are specialized to help protect your mouth 00:01:51.330 --> 00:01:52.920 from wear and tear. 00:01:52.920 --> 00:01:55.740 So the next time you're eating a pointy tortilla chip, 00:01:55.740 --> 00:02:00.030 remember how important this epithelial tissue is. 00:02:00.030 --> 00:02:03.240 Next up are organs and organ systems. 00:02:03.240 --> 00:02:06.570 So organs are structures that are made up of multiple 00:02:06.570 --> 00:02:09.530 different types of tissues, which all work together 00:02:09.530 --> 00:02:11.320 to help the organ function. 00:02:11.320 --> 00:02:14.970 And an organ system is a group of organs that work together 00:02:14.970 --> 00:02:18.280 to carry out complex functions for the body. 00:02:18.280 --> 00:02:21.410 For instance, the lungs shown here in the diagram 00:02:21.410 --> 00:02:23.870 are made up of several tissue types 00:02:23.870 --> 00:02:26.920 that help them expand and contract. 00:02:26.920 --> 00:02:29.690 These tissue types include epithelial tissue, 00:02:29.690 --> 00:02:32.490 which is the same type of tissue we talked about earlier 00:02:32.490 --> 00:02:35.640 in the mouth, and connective tissue. 00:02:35.640 --> 00:02:38.170 And these tissues work together so that the lungs 00:02:38.170 --> 00:02:41.100 can carry out their role in the respiratory system, 00:02:41.100 --> 00:02:43.380 which is the organ system that allows us 00:02:43.380 --> 00:02:45.470 to respire or breathe. 00:02:45.470 --> 00:02:49.040 The respiratory system is made up of multiple organs, 00:02:49.040 --> 00:02:51.650 including the lungs, the trachea, 00:02:51.650 --> 00:02:53.890 the nose and the diaphragm. 00:02:53.890 --> 00:02:55.820 When we breathe, our diaphragm 00:02:55.820 --> 00:02:58.670 which is this muscle right here, contracts. 00:02:58.670 --> 00:03:01.080 Air is pulled through our nose and trachea, 00:03:01.080 --> 00:03:02.810 and into our lungs. 00:03:02.810 --> 00:03:06.540 Here, gas exchange happens and our bodies take in oxygen 00:03:06.540 --> 00:03:08.770 and get rid of carbon dioxide. 00:03:08.770 --> 00:03:12.340 Then our diaphragm relaxes and we exhale. 00:03:12.340 --> 00:03:15.050 The respiratory system, and other organ systems 00:03:15.050 --> 00:03:17.730 in the body, carry out specific functions 00:03:17.730 --> 00:03:19.910 that work together to keep us alive. 00:03:19.910 --> 00:03:23.820 And they do this mostly without us even realizing it. 00:03:23.820 --> 00:03:26.190 So it might get a little tricky to remember 00:03:26.190 --> 00:03:30.500 how all four levels of organization cells, tissues, 00:03:30.500 --> 00:03:33.490 organs and organ systems relate to each other. 00:03:33.490 --> 00:03:35.870 I like to think of these four different levels, 00:03:35.870 --> 00:03:37.740 almost like the Russian nesting dolls 00:03:37.740 --> 00:03:39.710 that fit one inside another. 00:03:39.710 --> 00:03:42.630 With cells being the smallest doll on the inside. 00:03:42.630 --> 00:03:46.640 So cells make up tissues. Tissues make up organs. 00:03:46.640 --> 00:03:49.680 And organs make up organ systems. 00:03:49.680 --> 00:03:51.640 All of these components come together 00:03:51.640 --> 00:03:54.060 to make up the human body. 00:03:54.060 --> 00:03:56.680 So I hope you've learned more about how our body's 00:03:56.680 --> 00:04:00.290 organization helps us thrive and stay alive. 00:04:00.290 --> 00:04:03.750 So now use your brain to tell your muscular system 00:04:03.750 --> 00:04:07.180 to move your arm and give yourself a pat on the back. 00:04:07.180 --> 00:04:09.490 Because your body and its organized 00:04:09.490 --> 00:04:12.893 hierarchical system is really awesome.

Cell parts and their functions

https://www.youtube.com/watch?v=TVxtlfUwIY0

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https://www.youtube.com/api/timedtext?v=TVxtlfUwIY0&ei=xFWUZcibFbuJp-oPrp6j8AY&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8702CF890ACCB17494B7C790D9823A4BADC64DC9.43DB165319A25670BBBE4CAAADDB5A2CA78C128E&key=yt8&lang=en&name=Default&fmt=vtt

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WEBVTT Kind: captions Language: en 00:00:00.130 --> 00:00:02.200 - [Instructor] So let's imagine this scenario. 00:00:02.200 --> 00:00:03.210 It's cold outside 00:00:03.210 --> 00:00:05.830 and we want to make a nice hot bowl 00:00:05.830 --> 00:00:07.550 of chicken noodle soup. 00:00:07.550 --> 00:00:10.200 Well, we'd probably need to get the ingredients first. 00:00:10.200 --> 00:00:11.860 We need some chicken bones 00:00:11.860 --> 00:00:14.930 to give the broth that distinct chicken flavor, 00:00:14.930 --> 00:00:18.090 some noodles to add that starchy component, 00:00:18.090 --> 00:00:21.050 carrots and onions to give some sweetness and color. 00:00:21.050 --> 00:00:24.170 And of course, salt and pepper to provide seasoning. 00:00:24.170 --> 00:00:26.040 All of these ingredients would come together 00:00:26.040 --> 00:00:27.580 to make our chicken noodle soup 00:00:27.580 --> 00:00:30.530 the comfort food that so many people love, 00:00:30.530 --> 00:00:32.950 but this video is supposed to be about cells. 00:00:32.950 --> 00:00:34.460 You know, those tiny things 00:00:34.460 --> 00:00:36.670 that make up all living things on earth. 00:00:36.670 --> 00:00:40.030 So why am I telling you about chicken soup? 00:00:40.030 --> 00:00:42.790 Well, just like how each ingredient in chicken soup 00:00:42.790 --> 00:00:45.930 adds something unique to the soup's overall flavor 00:00:45.930 --> 00:00:48.230 and texture, a cell's different parts 00:00:48.230 --> 00:00:50.720 add something unique and necessary 00:00:50.720 --> 00:00:53.410 for the overall functioning of the cell. 00:00:53.410 --> 00:00:55.790 So, let's take a look at some of the structures 00:00:55.790 --> 00:00:58.560 inside a cell and see how their functions come together 00:00:58.560 --> 00:01:03.050 to allow cells to carry out all the processes of life. 00:01:03.050 --> 00:01:04.890 So let's explore the parts of a cell 00:01:04.890 --> 00:01:06.830 starting with the cell's surface. 00:01:06.830 --> 00:01:09.690 Cells are separated from their outside environment 00:01:09.690 --> 00:01:11.730 by a cell membrane. 00:01:11.730 --> 00:01:14.250 You can think of the cell membrane like a fortress gate, 00:01:14.250 --> 00:01:18.020 because it regulates what comes into and out of the cell, 00:01:18.020 --> 00:01:19.400 and contained within the cell 00:01:19.400 --> 00:01:22.350 is a jelly-like substance that fills out the cell 00:01:22.350 --> 00:01:24.660 and contains its internal parts, 00:01:24.660 --> 00:01:27.110 this jelly and all the structures within it 00:01:27.110 --> 00:01:29.790 make up the cell cytoplasm. 00:01:29.790 --> 00:01:31.020 Unlike chicken soup, 00:01:31.020 --> 00:01:32.730 the cell parts in the cytoplasm 00:01:32.730 --> 00:01:34.300 are not just floating around. 00:01:34.300 --> 00:01:36.760 Instead, they're organized and held in place 00:01:36.760 --> 00:01:39.280 by an internal structural network. 00:01:39.280 --> 00:01:41.790 Some of the parts contained within the cytoplasm 00:01:41.790 --> 00:01:43.760 are called organelles. 00:01:43.760 --> 00:01:46.180 So what exactly are organelles? 00:01:46.180 --> 00:01:48.880 Well, organelles are small compartments in the cell 00:01:48.880 --> 00:01:51.700 that have different structures and functions. 00:01:51.700 --> 00:01:54.740 The word organelle basically means, mini organ. 00:01:54.740 --> 00:01:57.910 And just like how our bodies are made up of different organs 00:01:57.910 --> 00:02:00.350 that work together to help us stay alive, 00:02:00.350 --> 00:02:02.890 cells contain different organelles that work together 00:02:02.890 --> 00:02:05.670 to get things done inside the cell. 00:02:05.670 --> 00:02:08.570 For example, these jellybean shaped organelles here 00:02:08.570 --> 00:02:10.830 are little energy producing factories 00:02:10.830 --> 00:02:12.730 called mitochondria. 00:02:12.730 --> 00:02:15.230 So mitochondria use chemical reactions 00:02:15.230 --> 00:02:17.110 to break down sugar molecules 00:02:17.110 --> 00:02:19.160 in order to release energy that the cell 00:02:19.160 --> 00:02:21.270 can use for other tasks. 00:02:21.270 --> 00:02:24.460 Another really amazing organelle is the nucleus. 00:02:24.460 --> 00:02:27.790 You can think of the nucleus as the information database 00:02:27.790 --> 00:02:28.690 of the cell. 00:02:28.690 --> 00:02:32.290 It contains DNA which includes the cell's genes. 00:02:32.290 --> 00:02:34.290 Genes are special instructions 00:02:34.290 --> 00:02:37.163 that the cell uses to carry out its functions. 00:02:38.550 --> 00:02:40.600 Moving over to a plant cell, 00:02:40.600 --> 00:02:44.420 we can see these green organelles called chloroplasts. 00:02:44.420 --> 00:02:48.020 You might remember that plants carry out photosynthesis. 00:02:48.020 --> 00:02:51.160 Well, chloroplasts are the organelle's responsible 00:02:51.160 --> 00:02:52.610 for this process. 00:02:52.610 --> 00:02:55.810 Plants need food to live, just like animals do. 00:02:55.810 --> 00:02:58.080 And chloroplasts use photosynthesis 00:02:58.080 --> 00:03:01.640 to produce sugars that plant cells use as food. 00:03:01.640 --> 00:03:04.590 Plant cells also have a layer outside their cell membrane 00:03:04.590 --> 00:03:05.680 called the cell wall, 00:03:05.680 --> 00:03:08.270 which helps provide structure for the cell. 00:03:08.270 --> 00:03:11.320 So as you can see, there are so many different parts 00:03:11.320 --> 00:03:12.930 that make up a single cell. 00:03:12.930 --> 00:03:15.740 There are many, many organelles present in cells, 00:03:15.740 --> 00:03:19.010 way more than the handful I mentioned in this video. 00:03:19.010 --> 00:03:20.810 And what's even more mind blowing 00:03:20.810 --> 00:03:23.640 is that these diagrams are only simplified versions 00:03:23.640 --> 00:03:25.840 of what cells actually look like. 00:03:25.840 --> 00:03:27.210 And just to give you an idea, 00:03:27.210 --> 00:03:30.600 here's a picture of what a real cell looks like. 00:03:30.600 --> 00:03:32.160 So when we're talking about cells 00:03:32.160 --> 00:03:34.290 and using these diagrams as references, 00:03:34.290 --> 00:03:37.330 keep in mind that these pictures are only simplified models 00:03:37.330 --> 00:03:38.970 of the real thing. 00:03:38.970 --> 00:03:40.750 To wrap up this video on cell parts, 00:03:40.750 --> 00:03:44.100 let's revisit our delicious bowl of chicken noodle soup 00:03:44.100 --> 00:03:45.800 that I mentioned at the beginning. 00:03:45.800 --> 00:03:47.160 Each ingredient that we added 00:03:47.160 --> 00:03:49.510 had a unique function that contributed 00:03:49.510 --> 00:03:51.980 to the soup's taste and texture. 00:03:51.980 --> 00:03:54.500 And similarly, our cell's ingredients, 00:03:54.500 --> 00:03:56.560 its organelles and structures, 00:03:56.560 --> 00:03:58.790 each contribute a unique function 00:03:58.790 --> 00:04:00.210 that helps the cell carry out 00:04:00.210 --> 00:04:02.690 all the tasks necessary for life. 00:04:02.690 --> 00:04:04.680 So the next time you find yourself 00:04:04.680 --> 00:04:06.690 in front of a bowl of noodle soup, 00:04:06.690 --> 00:04:10.110 just imagine that you're eating one enormous cell. 00:04:10.110 --> 00:04:12.823 Now, isn't that something to noodle on?

Cells and Organisms

https://www.youtube.com/watch?v=Uiqro5TUyLA

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https://www.youtube.com/api/timedtext?v=Uiqro5TUyLA&ei=xFWUZfjrI4v6mLAP9IizoAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6C7C20B55AFCB91771EFC6D29D574AB31DD1704D.7894FDA268F42A4816C2F6D9F2D92295EED63182&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.010 - [Narrator] Hi, everyone. 00:00:01.010 --> 00:00:01.843 In this video, 00:00:01.843 --> 00:00:03.170 we are going to be talking about 00:00:03.170 --> 00:00:06.060 one of the most fascinating and complex features 00:00:06.060 --> 00:00:08.630 of life on Earth, cells. 00:00:08.630 --> 00:00:09.610 But before we do, 00:00:09.610 --> 00:00:12.920 I'd like to take us way back to when I was a little kid. 00:00:12.920 --> 00:00:14.650 Now I know that for me, at least, 00:00:14.650 --> 00:00:17.100 I had a great time playing with toy building blocks, 00:00:17.100 --> 00:00:18.920 and creating things out of them. 00:00:18.920 --> 00:00:21.940 I used blocks of different shapes and sizes 00:00:21.940 --> 00:00:24.350 to make all kinds of things like houses, 00:00:24.350 --> 00:00:27.750 cars, even spaceships, and airplanes. 00:00:27.750 --> 00:00:28.700 You're probably thinking, 00:00:28.700 --> 00:00:31.120 what does this have to do with cells? 00:00:31.120 --> 00:00:34.200 Well, cells are considered the building blocks of life. 00:00:34.200 --> 00:00:37.290 Like my blocks, cells can come in a variety of shapes, 00:00:37.290 --> 00:00:39.570 and they have different features too. 00:00:39.570 --> 00:00:41.240 They can also stand alone, 00:00:41.240 --> 00:00:43.920 or they can come together to build something larger. 00:00:43.920 --> 00:00:47.930 So let's dive deeper into this fascinating topic of cells. 00:00:47.930 --> 00:00:49.978 So all living things, or organisms, 00:00:49.978 --> 00:00:52.650 like you, me, your pet dog, 00:00:52.650 --> 00:00:55.280 the birds in the sky, the fish in the sea, 00:00:55.280 --> 00:00:59.980 all organisms are made of these basic units called cells. 00:00:59.980 --> 00:01:03.960 Take this moss plant, for example, if we zoom way in, 00:01:03.960 --> 00:01:07.700 we can see that it's actually made up of many smaller units. 00:01:07.700 --> 00:01:09.890 These units are cells. 00:01:09.890 --> 00:01:12.510 Each cell contains a flurry of activity, 00:01:12.510 --> 00:01:13.858 as it works to carry out the functions 00:01:13.858 --> 00:01:16.500 that keep the organism alive. 00:01:16.500 --> 00:01:19.780 In fact, cells are the smallest unit that can carry out 00:01:19.780 --> 00:01:22.400 all the tasks necessary for life. 00:01:22.400 --> 00:01:25.890 For instance, all cells can take up nutrients and water, 00:01:25.890 --> 00:01:28.700 get rid of waste, use energy, 00:01:28.700 --> 00:01:30.241 and interact with the things around them 00:01:30.241 --> 00:01:32.500 in their environment. 00:01:32.500 --> 00:01:35.250 These functions, plus many others that cells carry out, 00:01:35.250 --> 00:01:37.680 are what make life possible. 00:01:37.680 --> 00:01:39.240 There are many different kinds of cells. 00:01:39.240 --> 00:01:40.618 For instance, take a look at these cells 00:01:40.618 --> 00:01:43.050 that make up an onion's outer skin, 00:01:43.050 --> 00:01:45.060 or these really cool red blood cells, 00:01:45.060 --> 00:01:47.120 or even these bacterial cells. 00:01:47.120 --> 00:01:49.840 This type of bacteria is called e-coli, 00:01:49.840 --> 00:01:52.050 which you might've heard can be a safety hazard 00:01:52.050 --> 00:01:53.370 found in our food. 00:01:53.370 --> 00:01:55.630 So cells are fascinating to look at, 00:01:55.630 --> 00:01:58.620 but we generally can't see them with our eyes alone. 00:01:58.620 --> 00:01:59.960 Most cells are so small 00:01:59.960 --> 00:02:02.340 that we need a microscope to see them. 00:02:02.340 --> 00:02:04.620 In fact, all of these pictures of cells here 00:02:04.620 --> 00:02:07.750 were taken with the aid of microscopes. 00:02:07.750 --> 00:02:09.810 And something else that I find really cool 00:02:09.810 --> 00:02:13.500 is that some organisms are made up of only a single cell, 00:02:13.500 --> 00:02:16.400 while others are made up of many cells. 00:02:16.400 --> 00:02:18.720 So organisms that are made up of one cell 00:02:18.720 --> 00:02:20.440 are called unicellular, 00:02:20.440 --> 00:02:23.230 and organisms that are made up of many cells 00:02:23.230 --> 00:02:25.130 are called multicellular. 00:02:25.130 --> 00:02:27.540 Uni telling us that there is only one cell, 00:02:27.540 --> 00:02:30.890 and multi telling us that there are many cells. 00:02:30.890 --> 00:02:33.410 So an example of a unicellular organism 00:02:33.410 --> 00:02:37.000 would be the e-coli bacteria that I mentioned a minute ago. 00:02:37.000 --> 00:02:39.330 Each bacterium is a single cell 00:02:39.330 --> 00:02:42.847 that's responsible for taking in nutrients, reproducing, 00:02:42.847 --> 00:02:45.890 and doing all the things that it needs to stay alive. 00:02:45.890 --> 00:02:48.310 So an example of a multicellular organism 00:02:48.310 --> 00:02:51.910 would be you, me, or most any other organism 00:02:51.910 --> 00:02:54.150 that you can see with the naked eye. 00:02:54.150 --> 00:02:56.220 And the cells of multicellular organisms 00:02:56.220 --> 00:03:00.000 are often specialized to carry out specific functions. 00:03:00.000 --> 00:03:01.090 So for example, 00:03:01.090 --> 00:03:04.080 some cells help the organism absorb nutrients, 00:03:04.080 --> 00:03:06.270 while others transmit information, 00:03:06.270 --> 00:03:10.050 or defend against bacteria and viruses. 00:03:10.050 --> 00:03:11.510 So going back to our comparison 00:03:11.510 --> 00:03:13.490 between building blocks and cells, 00:03:13.490 --> 00:03:15.990 specialized cells are like different building blocks 00:03:15.990 --> 00:03:19.630 of different sizes, shapes, and colors. 00:03:19.630 --> 00:03:20.780 And these different blocks 00:03:20.780 --> 00:03:22.710 can come together to build something larger, 00:03:22.710 --> 00:03:24.400 like this airplane here. 00:03:24.400 --> 00:03:26.730 Similarly, cells with different structures 00:03:26.730 --> 00:03:29.740 and functions come together to make something larger, 00:03:29.740 --> 00:03:33.063 an organism like this adorable kitten right here. 00:03:34.150 --> 00:03:35.970 So to sum up cells and organisms, 00:03:35.970 --> 00:03:39.530 today, we learned that cells are the smallest unit of life. 00:03:39.530 --> 00:03:42.770 We talked about how all organisms are made up of cells, 00:03:42.770 --> 00:03:46.580 and that organisms can be unicellular or multicellular. 00:03:46.580 --> 00:03:48.750 So I hope that now you have a good understanding 00:03:48.750 --> 00:03:50.160 of cells and organisms, 00:03:50.160 --> 00:03:52.900 as well as a new perspective about building blocks, 00:03:52.900 --> 00:03:56.323 not the toys, but the cells that make up life itself.

Subtracting with place value blocks (regrouping)

https://www.youtube.com/watch?v=F63kWrYg6fY

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https://www.youtube.com/api/timedtext?v=F63kWrYg6fY&ei=xFWUZfyCFaeEmLAP_rGFgAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=6DC3F9CFE80F6724C9107591F82DA2B9BC9A306C.8729311BEA9CE60BD4524934A34258B0BB433C96&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.500 --> 00:00:01.860 - [Instructor] What we want to do in this video 00:00:01.860 --> 00:00:06.760 is figure out what 438 minus 272 is 00:00:06.760 --> 00:00:08.930 and to help us think about that 00:00:08.930 --> 00:00:13.550 we have these place value blocks right over here. 00:00:13.550 --> 00:00:15.630 So you can see 438. 00:00:15.630 --> 00:00:20.170 We have four hundreds, 100, 200, 300, 400. 00:00:20.170 --> 00:00:23.950 We have three tens, one, two, three 00:00:23.950 --> 00:00:25.750 and then we have eight ones. 00:00:25.750 --> 00:00:28.370 You can count those eight ones right over there. 00:00:28.370 --> 00:00:30.710 From that, we're going to take away two hundreds, 00:00:30.710 --> 00:00:32.810 so that's 200 right over there, 00:00:32.810 --> 00:00:37.310 seven tens or 70 right over here, and two ones. 00:00:37.310 --> 00:00:38.290 So pause this video 00:00:38.290 --> 00:00:41.040 and see if you can figure out what this is going to be. 00:00:41.950 --> 00:00:42.783 All right. 00:00:42.783 --> 00:00:45.400 Now let's work through this together. 00:00:45.400 --> 00:00:48.730 So first of all, we could start in the ones place 00:00:48.730 --> 00:00:51.430 and we can see we have eight ones 00:00:51.430 --> 00:00:53.070 and then we're gonna take away two ones. 00:00:53.070 --> 00:00:55.250 So that's pretty straight forward. 00:00:55.250 --> 00:00:59.863 We're just going to be left with six ones right over here. 00:01:00.740 --> 00:01:02.860 Now let's go to the tens place. 00:01:02.860 --> 00:01:04.770 Now the tens place is interesting. 00:01:04.770 --> 00:01:06.270 We have three tens here 00:01:06.270 --> 00:01:08.040 and we're trying to take away from that 00:01:08.040 --> 00:01:12.140 one, two, three, four, five, six, seven tens. 00:01:12.140 --> 00:01:15.760 So how do you take seven tens from three tens? 00:01:15.760 --> 00:01:20.760 Well, luckily we can regroup from the hundreds place. 00:01:20.890 --> 00:01:25.890 What if we were to take this piece right over here 00:01:26.280 --> 00:01:28.490 from the hundreds to the tens place 00:01:28.490 --> 00:01:31.750 and now this is going to be the equivalent of 10 tens. 00:01:31.750 --> 00:01:34.250 So let me represent it that way. 00:01:34.250 --> 00:01:36.470 Once again, I took a hundreds. 00:01:36.470 --> 00:01:38.210 That's the same thing as one, two, three 00:01:38.210 --> 00:01:42.380 four, five, six, seven, eight, nine, 10 tens. 00:01:42.380 --> 00:01:43.340 Well, this is useful now, 00:01:43.340 --> 00:01:45.960 because now I have 10 plus three tens, 00:01:45.960 --> 00:01:47.820 or you could say I have 13 tens 00:01:47.820 --> 00:01:50.520 and now I can take away seven tens from that. 00:01:50.520 --> 00:01:51.920 So let's do that. 00:01:51.920 --> 00:01:56.920 Let's take away one, two, three, four, five, six, seven 00:02:00.120 --> 00:02:05.060 and what we are left with is six tens right over here. 00:02:05.060 --> 00:02:08.990 So now I have six tens left, six ones left 00:02:08.990 --> 00:02:11.100 and in the hundreds, I have three hundreds. 00:02:11.100 --> 00:02:12.270 I'm gonna take away two of them. 00:02:12.270 --> 00:02:15.330 So I'm gonna take away 100 and 200. 00:02:15.330 --> 00:02:17.550 So I'm left with just 100 there. 00:02:17.550 --> 00:02:21.710 So I'm left with one hundred, six tens and six ones. 00:02:21.710 --> 00:02:26.297 So this is one hundred, six tens and six ones, or 166.

Using probability to make fair decisions

https://www.youtube.com/watch?v=Z_5f3kys52o

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https://www.youtube.com/api/timedtext?v=Z_5f3kys52o&ei=xFWUZdj4E6-4vdIPhp6OqAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=B5D12EFF527779934E01DA94C7D8AE4AF8ECEA2D.A0A132CA7EF2C7A1DABE1C66329A53F25627987E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.260 --> 00:00:01.970 - [Instructor] We're told that Roberto and Jocelyn 00:00:01.970 --> 00:00:05.420 decide to roll a pair of fair six-sided dice 00:00:05.420 --> 00:00:08.107 to determine who has to dust their apartment. 00:00:08.107 --> 00:00:11.730 If the sum is seven, then Roberto will dust. 00:00:11.730 --> 00:00:15.840 If the sum is 10 or 11, then Jocelyn will dust. 00:00:15.840 --> 00:00:19.860 If the sum is anything else, they'll roll again. 00:00:19.860 --> 00:00:22.589 Is this a fair way to decide who dusts? 00:00:22.589 --> 00:00:24.730 Why or why not? 00:00:24.730 --> 00:00:25.950 So pause this video and see 00:00:25.950 --> 00:00:28.989 if you can figure this out before we do it together. 00:00:28.989 --> 00:00:31.130 All right, now let's do this together. 00:00:31.130 --> 00:00:33.050 So what I wanna do is make a table that shows 00:00:33.050 --> 00:00:35.600 all of the different scenarios for rolling 00:00:37.559 --> 00:00:40.610 two fair six-sided dice. 00:00:40.610 --> 00:00:44.800 So let me make columns for roll one. 00:00:44.800 --> 00:00:48.140 So that is when you get a one. 00:00:48.140 --> 00:00:49.520 This is when you get a two. 00:00:49.520 --> 00:00:51.287 This is when you get a three. 00:00:51.287 --> 00:00:53.680 This is when you get a four. 00:00:53.680 --> 00:00:55.520 This is when you get a five. 00:00:55.520 --> 00:00:58.880 And then, this is when you get a six. 00:00:58.880 --> 00:01:02.290 And then here, let's do the other die. 00:01:02.290 --> 00:01:04.350 So this is when you get a one. 00:01:04.350 --> 00:01:06.820 This is when you get a two. 00:01:06.820 --> 00:01:08.790 This is when you get a three. 00:01:08.790 --> 00:01:10.766 This is when you get a four. 00:01:10.766 --> 00:01:13.150 This is when you get a five. 00:01:13.150 --> 00:01:15.680 And then, this is when you get a six. 00:01:15.680 --> 00:01:16.830 So one way to think about it 00:01:16.830 --> 00:01:21.370 is this is roll one 00:01:21.370 --> 00:01:22.790 or let me write it this way, 00:01:22.790 --> 00:01:25.400 d1 and d2. 00:01:25.400 --> 00:01:28.753 This could be a one, a two, a three, a five or a six. 00:01:29.812 --> 00:01:33.700 And this could be a one, a two, a three, a four, 00:01:33.700 --> 00:01:36.070 a five or a six. 00:01:36.070 --> 00:01:40.210 Now what we could do is fill in these 36 squares 00:01:40.210 --> 00:01:41.530 to figure out what the sum is. 00:01:41.530 --> 00:01:42.380 Actually, let me just do that 00:01:42.380 --> 00:01:43.600 and I'll try to do it really fast, 00:01:43.600 --> 00:01:44.670 one + one is two. 00:01:44.670 --> 00:01:49.150 So it's three, four, five, six, seven. 00:01:49.150 --> 00:01:53.070 This is three, four, five, six, seven, eight. 00:01:53.070 --> 00:01:57.430 This is four, five, six, seven, eight, nine. 00:01:57.430 --> 00:02:02.030 This is five, six, seven, eight, nine, 10. 00:02:02.030 --> 00:02:06.970 This is six, seven, eight, nine, 10, 11. 00:02:06.970 --> 00:02:07.890 Last but not least, 00:02:07.890 --> 00:02:11.950 seven, eight, nine, 10, 11 and 12, 00:02:11.950 --> 00:02:13.721 took a little less time than I suspected. 00:02:13.721 --> 00:02:15.610 All right, let's think about this scenario. 00:02:15.610 --> 00:02:18.740 If the sum is seven, then Roberto will dust. 00:02:18.740 --> 00:02:20.750 So where is the sum seven? 00:02:20.750 --> 00:02:24.680 So we have that ones, twice, three times, 00:02:24.680 --> 00:02:27.250 four, five, six. 00:02:27.250 --> 00:02:30.990 So six out of, so six of these outcomes 00:02:30.990 --> 00:02:32.560 result in a sum of seven. 00:02:32.560 --> 00:02:36.290 And how many possible equally likely outcomes are there? 00:02:36.290 --> 00:02:38.470 Well, there are six times six 00:02:38.470 --> 00:02:41.630 equally possible outcomes or 36. 00:02:41.630 --> 00:02:43.108 So six out of the 36 00:02:43.108 --> 00:02:44.730 or this is another way of saying 00:02:44.730 --> 00:02:48.920 there's a 1/6 probability that Roberto will dust. 00:02:48.920 --> 00:02:51.590 And then, let's think about the 10s or 11s. 00:02:51.590 --> 00:02:53.480 If the sum is 10 or 11, 00:02:53.480 --> 00:02:56.023 then Jocelyn will dust. 00:02:56.860 --> 00:02:58.530 So 10 or 11, 00:02:58.530 --> 00:03:01.180 so we have one, two, 00:03:01.180 --> 00:03:05.100 three, four, five. 00:03:05.100 --> 00:03:10.100 So this is only happening five out of the 36 times. 00:03:10.120 --> 00:03:11.610 So in any given roll, 00:03:11.610 --> 00:03:14.230 it's a higher probability that Roberto 00:03:14.230 --> 00:03:16.810 will dust than Jocelyn will dust. 00:03:16.810 --> 00:03:18.470 And of course, if neither of these happen, 00:03:18.470 --> 00:03:19.740 they are going to roll again. 00:03:19.740 --> 00:03:20.920 But on that second roll, 00:03:20.920 --> 00:03:23.630 there's a higher probability that Roberto will dust 00:03:23.630 --> 00:03:24.860 than Jocelyn will dust. 00:03:24.860 --> 00:03:27.280 So in general, this is not fair. 00:03:27.280 --> 00:03:30.720 There's a higher probability that Roberto dusts. 00:03:30.720 --> 00:03:32.933 So this is our choice.

3 Minute Breather for Teachers

https://www.youtube.com/watch?v=X4bl_VTyMa0

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https://www.youtube.com/api/timedtext?v=X4bl_VTyMa0&ei=xFWUZYK_K5vVxN8PxJG_8AM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=0426BB9B7444D10B3AD66530865378CDDAB2A452.DA26C72A0603282807092E6AD9096354F7607518&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.330 --> 00:00:04.553 - Welcome, teachers, for this short guided meditation. 00:00:06.170 --> 00:00:07.880 Remind yourself that meditation, 00:00:07.880 --> 00:00:10.240 there's no right way to do it. 00:00:10.240 --> 00:00:14.900 It's just an opportunity to still your mind, 00:00:14.900 --> 00:00:19.430 take a break from all the thoughts that you normally have, 00:00:19.430 --> 00:00:22.580 the planning, the to-do's of the future, 00:00:22.580 --> 00:00:23.793 thoughts of the past, 00:00:25.090 --> 00:00:28.803 and just be in the moment, and be still. 00:00:30.720 --> 00:00:33.930 So let's start by taking a few deep 00:00:33.930 --> 00:00:37.323 and controlled breaths together in through our nose. 00:00:40.110 --> 00:00:40.943 Hold. 00:00:46.650 --> 00:00:48.473 And out through our mouths. 00:00:56.190 --> 00:00:57.493 In through our nose. 00:01:00.240 --> 00:01:01.073 Hold. 00:01:09.380 --> 00:01:10.980 And then out through your mouth. 00:01:16.590 --> 00:01:19.690 Now I encourage you to continue to breathe 00:01:19.690 --> 00:01:23.473 in a deep and controlled way, 00:01:24.460 --> 00:01:28.233 but as you do so, try to put a smile on your face. 00:01:29.440 --> 00:01:31.373 It might feel a little artificial, 00:01:32.830 --> 00:01:35.090 but I promise it'll actually feel good. 00:01:35.090 --> 00:01:38.470 Even if your mood might not have made you want to smile, 00:01:38.470 --> 00:01:41.370 just put a big cheesy smile on your face 00:01:41.370 --> 00:01:42.963 as you continue to breathe in. 00:01:48.240 --> 00:01:49.073 And out. 00:01:58.150 --> 00:02:00.250 So as you go through the rest of your day, 00:02:01.310 --> 00:02:03.833 encourage you to take breaks like this, 00:02:05.370 --> 00:02:08.373 moment of pause, moment of stillness, 00:02:09.760 --> 00:02:12.233 approached with a sense of acceptance, 00:02:13.520 --> 00:02:18.253 a sense of curiosity, even a sense of humor. 00:02:21.470 --> 00:02:23.643 And remind yourself that as a teacher, 00:02:24.900 --> 00:02:27.313 you give so much of yourself to others, 00:02:28.940 --> 00:02:30.940 but you need to have a source of energy. 00:02:32.560 --> 00:02:34.600 And so for their sake, 00:02:34.600 --> 00:02:36.900 it's important that you take care of yourself. 00:02:39.470 --> 00:02:42.143 It's important that you give your mind a break, 00:02:43.917 --> 00:02:45.490 and be in the moment, 00:02:45.490 --> 00:02:48.953 in a moment of stillness and acceptance. 00:02:51.610 --> 00:02:52.770 And maybe in a little way, 00:02:52.770 --> 00:02:56.870 resolve and refresh everything that's going on 00:02:56.870 --> 00:03:01.523 to tackle the day, the weeks, the months ahead. 00:03:05.148 --> 00:03:06.065 Thank you.

Inequalities word problems

https://www.youtube.com/watch?v=VEIf5TfceAw

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https://www.youtube.com/api/timedtext?v=VEIf5TfceAw&ei=xFWUZZ2WFYmFp-oP1pCvyAw&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=207CA3D52852C6BAA42C69346CE3FE4806187633.3F049E8D4CB06EE999DD12A44191B904992C89D9&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:03.340 --> 00:00:04.310 - [Instructor] We're told that Eric 00:00:04.310 --> 00:00:05.800 is shorter than Priti. 00:00:05.800 --> 00:00:09.470 Priti is 158 centimeters tall. 00:00:09.470 --> 00:00:12.160 Write an inequality that compares Eric's height 00:00:12.160 --> 00:00:15.640 in centimeters, E, to Priti's height. 00:00:15.640 --> 00:00:18.340 Pause this video and see if you can do that. 00:00:18.340 --> 00:00:20.620 Alright, so we have Eric's height, 00:00:20.620 --> 00:00:23.780 which we are using the variable capital E for, 00:00:23.780 --> 00:00:24.860 And how does it compare? 00:00:24.860 --> 00:00:27.710 It says Eric is shorter than Priti. 00:00:27.710 --> 00:00:31.640 So Eric's height is going to be less than 00:00:31.640 --> 00:00:36.640 whatever Priti's height is, which is 158 centimeters. 00:00:37.570 --> 00:00:39.320 You could think about it on a number line too. 00:00:39.320 --> 00:00:41.680 If I were to draw a number line like this, 00:00:41.680 --> 00:00:46.680 and this is 158 centimeters, Priti's height, 00:00:46.780 --> 00:00:51.350 Eric's is gonna be less than that 'cause he is shorter. 00:00:51.350 --> 00:00:55.200 So it would be all of the values that are to the left of, 00:00:55.200 --> 00:00:56.860 let me do this in another color, 00:00:56.860 --> 00:00:59.330 that are less than that. 00:00:59.330 --> 00:01:00.790 Just like that. 00:01:00.790 --> 00:01:02.763 Let's do another example. 00:01:05.310 --> 00:01:09.030 Here we are told that Sydney wears skirts 00:01:09.030 --> 00:01:14.030 when the temperature is warmer than 25 degrees Celsius. 00:01:14.740 --> 00:01:17.800 Write an inequality that describes T, 00:01:17.800 --> 00:01:21.890 the temperatures at which Sydney wears skirts. 00:01:21.890 --> 00:01:23.180 So again, pause this video and see 00:01:23.180 --> 00:01:24.943 if you can have a go at that. 00:01:26.440 --> 00:01:29.810 Alright. So when does Sydney wear skirts? 00:01:29.810 --> 00:01:34.100 When the temperature is warmer than 25 degrees Celsius. 00:01:34.100 --> 00:01:36.680 Now, warmer means that the temperature is higher 00:01:36.680 --> 00:01:38.550 than 25 degrees Celsius, 00:01:38.550 --> 00:01:43.350 or that the temperature is greater than 25 degrees Celsius. 00:01:43.350 --> 00:01:46.630 And we're using capital T to denote temperature. 00:01:46.630 --> 00:01:51.260 So we would say capital T, this needs to be higher 00:01:51.260 --> 00:01:56.260 than 25 degrees, or greater than 25 degrees Celsius. 00:01:56.890 --> 00:02:00.460 So T is greater than 25. 00:02:00.460 --> 00:02:03.580 Let's do one last example here. 00:02:03.580 --> 00:02:08.580 So here we are told that Lola and Hayley are running a race. 00:02:10.350 --> 00:02:13.610 Lola finishes the race in 53 seconds. 00:02:13.610 --> 00:02:16.950 Hayley finishes after Lola. 00:02:16.950 --> 00:02:19.500 Write an inequality that represents H, 00:02:19.500 --> 00:02:21.970 Hayley's finish time in seconds. 00:02:21.970 --> 00:02:25.360 Pause the video and see if you can think about this. 00:02:25.360 --> 00:02:28.110 Alright, so how does Hayley compare to Lola? 00:02:28.110 --> 00:02:30.800 Hayley finishes after Lola. 00:02:30.800 --> 00:02:33.070 So what does that mean about Hayley's time? 00:02:33.070 --> 00:02:36.470 Well, that means that Hayley is going to take more time 00:02:36.470 --> 00:02:38.370 than Lola to finish the race. 00:02:38.370 --> 00:02:41.530 So whatever Lola's time is, Hayley's time 00:02:41.530 --> 00:02:46.170 is going to be longer, or more, or greater than. 00:02:46.170 --> 00:02:50.620 So Hayley's time is going to be greater than Lola's time, 00:02:50.620 --> 00:02:52.300 which is 53 seconds, 00:02:52.300 --> 00:02:55.253 because Hayley finishes after.

Finding mistakes in one-step equations

https://www.youtube.com/watch?v=CUB5j3Frev0

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https://www.youtube.com/api/timedtext?v=CUB5j3Frev0&ei=xFWUZZymE720xN8PrseoyAs&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=21016C7B09E52EAB74E31E1E2FD9704D03C3E436.A4DE5EAA189E54DCCD784C8889D2A2E0158602E9&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.400 --> 00:00:01.240 - [Instructor] We're told that Lisa 00:00:01.240 --> 00:00:03.290 tried to solve an equation. 00:00:03.290 --> 00:00:07.070 See, 42 is equal to 6a, or six times a. 00:00:07.070 --> 00:00:09.360 And then we can see her steps here. 00:00:09.360 --> 00:00:12.520 And they say, where did Lisa make her first mistake? 00:00:12.520 --> 00:00:14.850 So pause this video, and see if you can figure that out. 00:00:14.850 --> 00:00:17.150 And it might be possible she made no mistakes. 00:00:18.640 --> 00:00:19.910 All right. 00:00:19.910 --> 00:00:22.360 Well, we know she ends up with seven equals six, 00:00:22.360 --> 00:00:26.200 which is sketchy, so let's see what happened here. 00:00:26.200 --> 00:00:29.320 So right over here, it looks like, 00:00:29.320 --> 00:00:31.100 well, she did something a little bit strange. 00:00:31.100 --> 00:00:33.510 She divided the left-hand side by six, 00:00:33.510 --> 00:00:35.990 and the right hand side by a. 00:00:35.990 --> 00:00:38.300 You don't want to divide two sides of an equation 00:00:38.300 --> 00:00:40.090 by two different things. 00:00:40.090 --> 00:00:42.150 Then it's no longer going to be an equation. 00:00:42.150 --> 00:00:43.767 The equality won't hold. 00:00:43.767 --> 00:00:46.710 An algebraically legitimate thing 00:00:46.710 --> 00:00:49.100 is to do the same thing to both sides, 00:00:49.100 --> 00:00:50.510 but she didn't do it here. 00:00:50.510 --> 00:00:54.320 So this is where she made her first mistake. 00:00:54.320 --> 00:00:56.940 Let's give another example here. 00:00:56.940 --> 00:01:00.010 So here it says that Jin tried to solve an equation. 00:01:00.010 --> 00:01:03.780 All right, x plus 4.7 is equal to 11.2. 00:01:03.780 --> 00:01:05.980 Where did Jin make his first mistake? 00:01:05.980 --> 00:01:08.730 Pause this video, and try to figure it out. 00:01:08.730 --> 00:01:09.563 All right, 00:01:09.563 --> 00:01:11.510 so it looks like in order to isolate the x 00:01:11.510 --> 00:01:16.510 on the left-hand side, Jin is subtracting 4.7 from the left, 00:01:16.550 --> 00:01:21.080 and then also subtracting 4.7 from the right. 00:01:21.080 --> 00:01:24.540 So that is looking good, doing the same thing to both sides, 00:01:24.540 --> 00:01:26.920 subtracting 4.7 from both sides. 00:01:26.920 --> 00:01:29.675 And then over here on the left-hand side, 00:01:29.675 --> 00:01:31.368 these two would cancel. 00:01:31.368 --> 00:01:33.760 So you'd be left with just an x, 00:01:33.760 --> 00:01:37.123 and let's see, 11.2 minus 4.7. 00:01:38.325 --> 00:01:42.577 11.2 minus four would be 7.2, 00:01:44.650 --> 00:01:47.250 and then minus the 0.7 would be 6.5. 00:01:47.250 --> 00:01:50.870 So this is where Jin made his mistake, 00:01:50.870 --> 00:01:53.550 on the calculating part. 00:01:53.550 --> 00:01:55.900 Let's do another example, this is a lot of fun. 00:01:56.960 --> 00:02:00.304 So here we are told that Marina tried to solve an equation, 00:02:00.304 --> 00:02:01.580 and we need to figure out 00:02:01.580 --> 00:02:04.770 where Marina made her first mistake. 00:02:04.770 --> 00:02:09.360 All right, one-sixth is equal to two-thirds, why? 00:02:09.360 --> 00:02:11.260 So the first step, 00:02:11.260 --> 00:02:14.680 or the first thing that Marina did right over here 00:02:14.680 --> 00:02:18.630 is to multiply both sides of this equation 00:02:18.630 --> 00:02:21.640 by the reciprocal of two-thirds, which is three halves. 00:02:21.640 --> 00:02:23.990 Multiplied the left-hand side by three halves, 00:02:23.990 --> 00:02:26.520 multiplied the right-hand side by three halves, 00:02:26.520 --> 00:02:29.660 which is a very reasonable thing to do. 00:02:29.660 --> 00:02:30.997 We're doing the same thing to both sides, 00:02:30.997 --> 00:02:33.130 multiplying by three halves. 00:02:33.130 --> 00:02:36.130 And then when we go over here, let's see, 00:02:36.130 --> 00:02:38.920 three halves times one-sixth. 00:02:38.920 --> 00:02:42.370 We could divide the numerator and the denominator by three. 00:02:42.370 --> 00:02:44.960 So it's gonna be one over two. 00:02:44.960 --> 00:02:47.240 So that indeed is going to be one half times one half, 00:02:47.240 --> 00:02:49.540 which is one-fourth, so that checks out. 00:02:49.540 --> 00:02:50.530 And on this side, 00:02:50.530 --> 00:02:52.290 if you multiply three halves times two-thirds, 00:02:52.290 --> 00:02:54.660 that's going to be one, so this checks out. 00:02:54.660 --> 00:02:57.950 So it actually looks like Marina did everything correctly. 00:02:57.950 --> 00:03:02.950 So no mistake, no mistake for Marina. 00:03:03.300 --> 00:03:05.853 Let's do one last example. 00:03:07.380 --> 00:03:10.570 So here, Taylor is trying to solve an equation. 00:03:10.570 --> 00:03:14.210 And so where did Taylor first get tripped up? 00:03:14.210 --> 00:03:16.293 N minus 2.7 is equal to 6.7. 00:03:17.450 --> 00:03:20.220 In order to isolate this N over here, 00:03:20.220 --> 00:03:24.030 I would add 2.7 to both sides, 00:03:24.030 --> 00:03:26.960 but that's not what Taylor did. 00:03:26.960 --> 00:03:31.750 Taylor subtracted 2.7 from both sides. 00:03:31.750 --> 00:03:34.460 So the first place that Taylor starts to trip up, 00:03:34.460 --> 00:03:39.000 or move in the wrong direction is right over here. 00:03:39.000 --> 00:03:43.750 Now, what Taylor did is not algebraically incorrect. 00:03:43.750 --> 00:03:48.750 You would end up with n minus 5.4 is equal to four, 00:03:49.870 --> 00:03:52.290 but it's not going to help you solve this equation. 00:03:52.290 --> 00:03:53.980 You just replaced this equation 00:03:53.980 --> 00:03:55.830 with another equivalent equation 00:03:55.830 --> 00:03:59.440 that is no simpler than the one before. 00:03:59.440 --> 00:04:00.273 And then of course, 00:04:00.273 --> 00:04:02.810 instead of getting n minus 5.4 equals four, 00:04:02.810 --> 00:04:06.030 Taylor calculated incorrectly as well. 00:04:06.030 --> 00:04:07.890 But where they first started to get tripped up, 00:04:07.890 --> 00:04:09.670 or at least not move in the right direction 00:04:09.670 --> 00:04:11.113 would be right over here.

One-step multiplication equations: fractional coefficients

https://www.youtube.com/watch?v=vksy7e3hY8Q

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https://www.youtube.com/api/timedtext?v=vksy7e3hY8Q&ei=xFWUZZG6ErCKvdIPxLSi6A0&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=9854565E579450B94ED6A3C73A0C53774EE69AE4.0D3AD3CF781A75982A2B2E358FB56773F36E6AC9&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.770 --> 00:00:02.440 - Let's say that we have the equation, 00:00:02.440 --> 00:00:06.730 two-fifths X is equal to 10. 00:00:06.730 --> 00:00:08.703 How would you go about solving that? 00:00:09.640 --> 00:00:11.230 Well, you might be thinking to yourself, 00:00:11.230 --> 00:00:12.980 it would be nice if we just had an X 00:00:12.980 --> 00:00:15.620 on the left-hand side instead of a two-fifths X, 00:00:15.620 --> 00:00:17.820 or if the coefficient on the X were one 00:00:17.820 --> 00:00:19.120 instead of a two-fifths. 00:00:19.120 --> 00:00:21.400 And the way that we might do that, 00:00:21.400 --> 00:00:22.730 is if we were to multiply 00:00:22.730 --> 00:00:27.440 both sides of this equation by five halves. 00:00:27.440 --> 00:00:29.490 Why five halves? 00:00:29.490 --> 00:00:30.670 Well, five halves, 00:00:30.670 --> 00:00:31.503 if you notice, 00:00:31.503 --> 00:00:33.880 when I multiply five halves times two-fifths, 00:00:33.880 --> 00:00:35.540 it's going to get us to one. 00:00:35.540 --> 00:00:37.417 Five times two is 10, 00:00:37.417 --> 00:00:39.140 two times five is 10. 00:00:39.140 --> 00:00:41.460 So it's going to be 10 over 10 or one, 00:00:41.460 --> 00:00:44.800 or you could think about five divided by five is one, 00:00:44.800 --> 00:00:47.220 two divided by two is one. 00:00:47.220 --> 00:00:48.670 And you might say, "Is that magical? 00:00:48.670 --> 00:00:51.100 How did you think of five halves?" 00:00:51.100 --> 00:00:53.670 Well, five halves is just the reciprocal of two-fifths. 00:00:53.670 --> 00:00:56.420 I just swapped the numerator and the denominator 00:00:56.420 --> 00:00:57.600 to get five halves. 00:00:57.600 --> 00:00:59.960 And then why did I multiply it times the right-hand side? 00:00:59.960 --> 00:01:01.247 Well, anything I do to the left hand, 00:01:01.247 --> 00:01:03.640 I also want to do to the right hand. 00:01:03.640 --> 00:01:07.460 So the left-hand side simplifies to this is all one. 00:01:07.460 --> 00:01:10.792 So it's just going to be X is equal to, 00:01:10.792 --> 00:01:14.470 or we could say one X is equal to 10 times five halves. 00:01:14.470 --> 00:01:17.020 That's the same thing as 50 halves. 00:01:17.020 --> 00:01:19.410 I could write it this way, 50 over two, 00:01:19.410 --> 00:01:22.910 which is the same thing as 25. 00:01:22.910 --> 00:01:24.160 Let's do another example. 00:01:25.010 --> 00:01:26.410 Let's say we have the equation, 00:01:26.410 --> 00:01:28.010 14 is equal 00:01:28.010 --> 00:01:30.660 to seven-thirds B. 00:01:30.660 --> 00:01:32.533 See if you can solve this. 00:01:33.460 --> 00:01:34.600 Well, once again, 00:01:34.600 --> 00:01:36.080 it'd be nice if the coefficient 00:01:36.080 --> 00:01:38.030 on the B weren't seven-thirds, 00:01:38.030 --> 00:01:39.410 but instead were just a one. 00:01:39.410 --> 00:01:42.160 If it's just B is equal to something. 00:01:42.160 --> 00:01:43.580 Well, we know how to do that. 00:01:43.580 --> 00:01:46.330 We can multiply both sides of this equation 00:01:46.330 --> 00:01:50.040 times the reciprocal of the coefficient on B 00:01:50.040 --> 00:01:52.050 times the reciprocal of seven-thirds. 00:01:52.050 --> 00:01:54.210 What's the reciprocal of seven-thirds? 00:01:54.210 --> 00:01:56.060 Well, the denominator will become the numerator. 00:01:56.060 --> 00:01:57.960 The numerator becomes a denominator. 00:01:57.960 --> 00:02:00.700 It's going to be three-sevenths. 00:02:00.700 --> 00:02:01.533 Now, of course, 00:02:01.533 --> 00:02:03.020 I can't just do it on one side. 00:02:03.020 --> 00:02:05.540 I have to do it on both sides. 00:02:05.540 --> 00:02:08.920 So on the right-hand side of this equation, 00:02:08.920 --> 00:02:10.460 three divided by three is one, 00:02:10.460 --> 00:02:11.870 seven divided by seven is one. 00:02:11.870 --> 00:02:13.390 Those all cancel out to one. 00:02:13.390 --> 00:02:15.030 So you're just left with one B 00:02:15.030 --> 00:02:17.510 or just to B and 30, 00:02:17.510 --> 00:02:20.206 or three-sevenths times 14, 00:02:20.206 --> 00:02:23.690 you might see this as 14 over one. 00:02:23.690 --> 00:02:24.790 And you could say okay, 00:02:24.790 --> 00:02:28.801 this is going to be three times 14 over seven times one, 00:02:28.801 --> 00:02:29.730 or you could say, 00:02:29.730 --> 00:02:33.770 hey, let's divide both a numerator and denominator by seven. 00:02:33.770 --> 00:02:36.280 So this could be two. And this could be one. 00:02:36.280 --> 00:02:39.893 So your left with three times two over one times one 00:02:39.893 --> 00:02:43.200 which is just going to be equal to six. 00:02:43.200 --> 00:02:45.550 Let's do another example. 00:02:45.550 --> 00:02:47.020 Let's say 00:02:47.020 --> 00:02:48.620 that we had 00:02:48.620 --> 00:02:51.530 one sixth A 00:02:51.530 --> 00:02:54.710 is equal to two-thirds. 00:02:54.710 --> 00:02:57.363 How could we think about solving for A. 00:02:58.380 --> 00:02:59.680 Well, once again, it would be nice, 00:02:59.680 --> 00:03:03.410 if this one-sixth were to become a one 00:03:03.410 --> 00:03:05.980 and we could do that by multiplying by 6. 00:03:05.980 --> 00:03:09.150 Six-sixths is the same thing as one. 00:03:09.150 --> 00:03:11.300 And to make it clear that this is the reciprocal, 00:03:11.300 --> 00:03:15.120 we could just write six wholes as six ones 00:03:15.120 --> 00:03:18.350 or six wholes when you multiply these, 00:03:18.350 --> 00:03:20.080 this is all going to be equal to one. 00:03:20.080 --> 00:03:23.610 So you're left with one A on the left-hand side, 00:03:23.610 --> 00:03:25.470 but of course, you can't just do it on the left-hand side. 00:03:25.470 --> 00:03:28.840 You have to also do it on the right-hand side. 00:03:28.840 --> 00:03:31.540 So A is going to be equal to, 00:03:31.540 --> 00:03:35.760 over here we could say two times six over three times one. 00:03:35.760 --> 00:03:38.560 So that would be twelve-thirds 00:03:38.560 --> 00:03:39.620 or we could say, 00:03:39.620 --> 00:03:42.060 look, six and three are both divisible by three. 00:03:42.060 --> 00:03:43.582 So six divided by three is two, 00:03:43.582 --> 00:03:45.585 three divided by three is one, 00:03:45.585 --> 00:03:48.940 two times two is four over one times one. 00:03:48.940 --> 00:03:53.053 So it's going to be four wholes or just four and we're done.

Analyzing relationships between variables using tables and equations

https://www.youtube.com/watch?v=Pf-s9zNDSCk

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https://www.youtube.com/api/timedtext?v=Pf-s9zNDSCk&ei=xFWUZZKxKde2mLAPm8edoA4&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=24BEA02EEB024BDC96F7A1BD63700C57D36C1EC3.9BD03D3857D05115272F205504D50C247A107496&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.610 --> 00:00:03.850 - [Narrator] We're told Rava is researching an electric car. 00:00:03.850 --> 00:00:07.710 She finds this graph, which shows how much range, 00:00:07.710 --> 00:00:09.430 measured in kilometers, 00:00:09.430 --> 00:00:13.500 the car gains based on charging time. 00:00:13.500 --> 00:00:15.330 All right, and they say, first, 00:00:15.330 --> 00:00:18.410 fill in the missing values in the table below. 00:00:18.410 --> 00:00:21.070 And if you are so inspired, pause this video, 00:00:21.070 --> 00:00:24.070 and see if you can have a go at that as well. 00:00:24.070 --> 00:00:25.540 All right, well they give us a few points, 00:00:25.540 --> 00:00:27.600 and I'm assuming these are points on a line. 00:00:27.600 --> 00:00:31.790 And we can see when the charging time is 15 minutes, 00:00:31.790 --> 00:00:33.540 the range is 180. 00:00:33.540 --> 00:00:36.430 So we could see when the charging time is 15 minutes, 00:00:36.430 --> 00:00:38.920 the range is 180. 00:00:38.920 --> 00:00:43.030 We can see when the charging time is 30 minutes, 00:00:43.030 --> 00:00:48.030 the range is 360 kilometers, so I could write that there. 00:00:48.570 --> 00:00:53.570 And then we see when the charging time is 45 minutes, 00:00:54.400 --> 00:00:59.270 the range is 540 kilometers. 00:00:59.270 --> 00:01:01.380 So that's all nice. 00:01:01.380 --> 00:01:03.390 But then they give us a few other points here. 00:01:03.390 --> 00:01:07.200 They say what happens when we are at T equals 10, 00:01:07.200 --> 00:01:10.940 or T equals one, which aren't easy to pick out here? 00:01:10.940 --> 00:01:12.490 But this is where it might be useful, 00:01:12.490 --> 00:01:13.970 if we assume that this is a line, 00:01:13.970 --> 00:01:17.020 what is the relationship between these? 00:01:17.020 --> 00:01:19.910 So let's see, to go from 15 to 180, 00:01:19.910 --> 00:01:22.110 it looks like you're multiplying by 12. 00:01:22.110 --> 00:01:26.080 To go from 30 to 360, it looks like we're multiplying by 12. 00:01:26.080 --> 00:01:28.420 To go from 45 to 540, 00:01:28.420 --> 00:01:31.260 it looks like we are multiplying by 12. 00:01:31.260 --> 00:01:34.130 So assuming K is just going to be 12 times T, 00:01:34.130 --> 00:01:37.500 we know that when T equals one, K is 12, 00:01:37.500 --> 00:01:42.063 and when T equals 10, 10 times 12 is 120. 00:01:43.100 --> 00:01:45.530 All right, now the second part, they say write an equation 00:01:45.530 --> 00:01:49.000 Rava can use to find out how much charging time, T, 00:01:49.000 --> 00:01:54.000 it takes to gain any number of kilometers in range, K. 00:01:54.460 --> 00:01:56.660 All right, well we already established a relationship. 00:01:56.660 --> 00:02:01.660 We said that K is equal to 12 times whatever T is. 00:02:02.640 --> 00:02:05.540 That's what we just established in this table up here, 00:02:05.540 --> 00:02:06.870 but that's not what they want. 00:02:06.870 --> 00:02:09.500 They wanna find out how much charging time, T, 00:02:09.500 --> 00:02:13.660 it takes to gain any number of kilometers in range, K. 00:02:13.660 --> 00:02:17.050 So what we need to do here is solve for T. 00:02:17.050 --> 00:02:19.380 So let's divide both sides by 12 00:02:20.430 --> 00:02:23.820 to just have a T by itself on the right-hand side. 00:02:23.820 --> 00:02:28.500 And we are going to be left with T is equal to K over 12. 00:02:28.500 --> 00:02:31.010 T is equal to K over 12 and notice, 00:02:31.010 --> 00:02:34.070 you could put any number of kilometers of range in here 00:02:34.070 --> 00:02:36.110 and you're essentially just going to divide it by 12, 00:02:36.110 --> 00:02:38.110 and that will give you how much charging time. 00:02:38.110 --> 00:02:41.130 And I guess this would assume an infinitely large battery, 00:02:41.130 --> 00:02:42.900 which we know doesn't exist. 00:02:42.900 --> 00:02:45.380 But for the sake of this problem, here we have it. 00:02:45.380 --> 00:02:47.883 Here is the equation Rava can use.

Writing equations for relationships between quantities

https://www.youtube.com/watch?v=5T9gSp2W3Oc

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https://www.youtube.com/api/timedtext?v=5T9gSp2W3Oc&ei=xFWUZf7VEorNhcIPzsijyAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245300&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=66594A05F00AA377B5BE3C0C2AE9687DABEBC384.313AEC44DF688FC38EB40DC542A60650F1B3F650&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.250 --> 00:00:02.270 - [Narrator] We're told Amad is going to walk 00:00:02.270 --> 00:00:06.030 20 kilometers for a charity fundraiser. 00:00:06.030 --> 00:00:07.290 In the first part of this question, they say, 00:00:07.290 --> 00:00:10.980 write an equation that represents how many hours, t, 00:00:10.980 --> 00:00:15.140 the walk will take if Amad walks at a constant rate 00:00:15.140 --> 00:00:17.760 of r kilometers per hour. 00:00:17.760 --> 00:00:20.720 Pause this video and see if you could have a go at that. 00:00:20.720 --> 00:00:23.120 All right, now let's work through this together. 00:00:23.120 --> 00:00:25.050 So you might be familiar with the notion 00:00:25.050 --> 00:00:29.270 that distance is equal to rate times time. 00:00:29.270 --> 00:00:31.558 For example, if you were to walk at a rate 00:00:31.558 --> 00:00:35.100 of five kilometers per hour 00:00:35.100 --> 00:00:36.900 for two hours, 00:00:36.900 --> 00:00:40.180 you would say five times two, five kilometers per hour, 00:00:40.180 --> 00:00:43.890 times two hours, would give you 10 kilometers. 00:00:43.890 --> 00:00:45.210 Now in this situation, 00:00:45.210 --> 00:00:48.880 they've given us the number of kilometers 00:00:48.880 --> 00:00:50.610 or the distance in this situation, 00:00:50.610 --> 00:00:53.090 so in this situation d is equal to 20. 00:00:53.090 --> 00:00:55.840 So 20 is going to be equal to our rate, 00:00:55.840 --> 00:00:58.740 which we are told is going to be r kilometers per hour, 00:00:58.740 --> 00:01:02.600 times our time, which is t hours. 00:01:02.600 --> 00:01:04.890 Now they're asking us for an equation 00:01:04.890 --> 00:01:08.330 that represents how many hours the walk will take 00:01:08.330 --> 00:01:11.340 if Amad walks at a constant rate of r. 00:01:11.340 --> 00:01:12.750 So the way that it's phrased, 00:01:12.750 --> 00:01:15.960 it sounds like they want us to solve for t, 00:01:15.960 --> 00:01:19.510 where t is going to be equal to some expression here 00:01:19.510 --> 00:01:23.500 that deals with r and probably some other things, 00:01:23.500 --> 00:01:27.690 so if we put in any r here, then we can get the time. 00:01:27.690 --> 00:01:29.450 So if we know what the rate is, 00:01:29.450 --> 00:01:30.760 if you put that in here, 00:01:30.760 --> 00:01:32.460 because it's already solved for t, 00:01:32.460 --> 00:01:34.540 we'll be able to solve for that time. 00:01:34.540 --> 00:01:37.340 You could think of r as the independent variable 00:01:37.340 --> 00:01:39.260 that you could try different values out for, 00:01:39.260 --> 00:01:41.050 and that t is the dependent variable. 00:01:41.050 --> 00:01:44.100 It's the thing that we have solved for. 00:01:44.100 --> 00:01:45.080 So let's do that. 00:01:45.080 --> 00:01:49.870 Let's rewrite this expression here by solving for t 00:01:49.870 --> 00:01:52.040 and I could do it right over here. 00:01:52.040 --> 00:01:55.080 If I have 20 is equal to rt, 00:01:55.080 --> 00:01:58.270 if I wanna solve for t, what can I do? 00:01:58.270 --> 00:02:01.033 Well, I could divide both sides by r. 00:02:01.970 --> 00:02:03.970 If I do that on the right-hand side, 00:02:03.970 --> 00:02:05.360 then I'm just left with a t here, 00:02:05.360 --> 00:02:07.620 because an r divided by r is just one. 00:02:07.620 --> 00:02:09.410 And on the left, I have 20 over r, 00:02:09.410 --> 00:02:13.900 so I have t is equal to 20 over r 00:02:13.900 --> 00:02:14.733 and we're done. 00:02:14.733 --> 00:02:17.675 This will tell us how many hours Amad 00:02:17.675 --> 00:02:20.590 will take to walk based on the rate. 00:02:20.590 --> 00:02:21.423 You give me a rate. 00:02:21.423 --> 00:02:22.620 I'm just gonna divide 20 by that 00:02:22.620 --> 00:02:24.210 and I'm going to give you t. 00:02:24.210 --> 00:02:25.720 You might say, why is this useful? 00:02:25.720 --> 00:02:28.150 Well, this is useful because now that we have it written 00:02:28.150 --> 00:02:30.940 this way, any time someone gives an r to you, 00:02:30.940 --> 00:02:33.103 you just take 20 divided by that and it essentially 00:02:33.103 --> 00:02:36.320 is already gonna solve for what your time is, 00:02:36.320 --> 00:02:40.010 how long Amad's gonna have to walk. 00:02:40.010 --> 00:02:42.610 Question two, how many hours will the walk take 00:02:42.610 --> 00:02:44.500 if Amad walks at a constant rate 00:02:44.500 --> 00:02:46.640 of 6 kilometers per hour? 00:02:46.640 --> 00:02:48.020 Well, here is an example of that, 00:02:48.020 --> 00:02:50.030 where they are giving us the actual rate 00:02:50.030 --> 00:02:51.320 and they want the time. 00:02:51.320 --> 00:02:54.620 So we just take the 6 and replace it in for r, 00:02:54.620 --> 00:02:58.280 so we get t is equal to 20 over 6, 00:02:58.280 --> 00:03:01.710 which is 3 and 1/3 hours, 00:03:01.710 --> 00:03:04.500 which would be the same thing as 3 hours and 20 minutes, 00:03:04.500 --> 00:03:06.360 depending on how you wanna view it. 00:03:06.360 --> 00:03:08.163 Let's do another example here. 00:03:09.550 --> 00:03:12.100 So here we're told at the end of each day, 00:03:12.100 --> 00:03:14.390 a restaurant makes soup with whatever amount 00:03:14.390 --> 00:03:16.610 of vegetable stock is unused that day. 00:03:16.610 --> 00:03:18.630 Let me re-center this a little bit. 00:03:18.630 --> 00:03:22.950 The soup recipe calls for 400 milliliters of water 00:03:22.950 --> 00:03:27.330 for every 500 milliliters of vegetable stock. 00:03:27.330 --> 00:03:30.810 Write an equation that represents how much water 00:03:30.810 --> 00:03:34.400 the restaurant should use, and we'll use the variable w, 00:03:34.400 --> 00:03:38.070 with any amount of vegetable stock, v. 00:03:38.070 --> 00:03:40.660 All right, and then we'll do part two right after that, 00:03:40.660 --> 00:03:43.040 so let's look at this, 400 milliliters of water 00:03:43.040 --> 00:03:45.400 for every 500 milliliters of vegetable stock. 00:03:45.400 --> 00:03:47.350 And so to get my head around this, 00:03:47.350 --> 00:03:48.970 I like just to think about, 00:03:48.970 --> 00:03:50.480 let's put a little table here, 00:03:50.480 --> 00:03:52.880 and so you could say amount of water, 00:03:52.880 --> 00:03:54.250 let me write it this way, 00:03:54.250 --> 00:03:58.720 water and vegetable stock, 00:03:58.720 --> 00:04:01.093 vegetable stock. 00:04:02.100 --> 00:04:05.120 So for every 500 milliliters of vegetable stock, 00:04:05.120 --> 00:04:07.680 so if you had 500 milliliters of vegetable stock, 00:04:07.680 --> 00:04:09.180 and I won't write the milliliters, 00:04:09.180 --> 00:04:11.870 then you're going to have 400 milliliters of water. 00:04:11.870 --> 00:04:15.580 If you had 1,000 here, which is two times that, 00:04:15.580 --> 00:04:17.120 well, you're gonna have twice as much water, 00:04:17.120 --> 00:04:19.140 which is going to be 800. 00:04:19.140 --> 00:04:22.080 And so you can see this relationship that's forming. 00:04:22.080 --> 00:04:24.580 No matter what the vegetable stock is, 00:04:24.580 --> 00:04:28.360 if you essentially take 4/5 of that, 00:04:28.360 --> 00:04:29.910 that is the amount of water. 00:04:29.910 --> 00:04:32.350 You take 4/5, that is the amount of water. 00:04:32.350 --> 00:04:35.360 So if you had only 5 milliliters of vegetable stock, 00:04:35.360 --> 00:04:39.150 you take 4/5, you get the amount of water. 00:04:39.150 --> 00:04:42.610 So another way to think about it is the water 00:04:42.610 --> 00:04:44.560 that you need to use is going to be 4/5 00:04:45.680 --> 00:04:48.570 of the amount of vegetable stock 00:04:48.570 --> 00:04:50.690 that you are going to be using, 00:04:50.690 --> 00:04:53.870 and so actually we just did part one. 00:04:53.870 --> 00:04:56.090 We wrote an equation that represents how much water 00:04:56.090 --> 00:04:59.280 the restaurant should use with any amount of vegetable stock 00:04:59.280 --> 00:05:00.650 and the way that they phrased it, 00:05:00.650 --> 00:05:05.310 we're solving for w given some v that you might have. 00:05:05.310 --> 00:05:07.330 And since we're solving for w here, 00:05:07.330 --> 00:05:09.450 we would consider w the dependent variable 00:05:09.450 --> 00:05:10.680 and v as the independent variable. 00:05:10.680 --> 00:05:12.880 You can give me different vs 00:05:12.880 --> 00:05:15.730 and then I can put that into this little equation here, 00:05:15.730 --> 00:05:17.850 and I can solve for the w, 00:05:17.850 --> 00:05:19.890 so we've done the first part. 00:05:19.890 --> 00:05:23.230 If there are 800 milliliters of unused vegetable stock, 00:05:23.230 --> 00:05:27.160 how much water should the restaurant use to make soup? 00:05:27.160 --> 00:05:29.720 Well, we can just take this 800 00:05:29.720 --> 00:05:32.740 and substitute it in for v to figure that out. 00:05:32.740 --> 00:05:34.770 In this situation, the amount of water to use 00:05:34.770 --> 00:05:39.770 is 4/5 times 800, 00:05:40.020 --> 00:05:44.280 and that's going to be, let's see, 800 divided by 5, 00:05:44.280 --> 00:05:49.280 100 divided by 5 is 20 and so, 00:05:49.290 --> 00:05:50.330 and then you're gonna have 8 of those, 00:05:50.330 --> 00:05:54.550 so it's 160, so this was 160 times 4 00:05:54.550 --> 00:05:58.560 is equal to 640 milliliters, 00:05:58.560 --> 00:06:00.203 and we are done.

Dependent & independent variables

https://www.youtube.com/watch?v=SGC_d7O7_Eg

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en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:03.280 - [Teacher] Let's say that you love to eat apples, 00:00:03.280 --> 00:00:06.360 and you are going to buy a apples, 00:00:06.360 --> 00:00:08.250 so a is the number of apples, 00:00:08.250 --> 00:00:11.100 number of apples, 00:00:11.100 --> 00:00:12.410 but you also have a budget, 00:00:12.410 --> 00:00:13.880 so you have to care about costs, 00:00:13.880 --> 00:00:17.990 so let's say C is equal to the total cost, 00:00:17.990 --> 00:00:21.530 and let's say that the price of an apple is $2, 00:00:21.530 --> 00:00:24.483 so $2 per apple. 00:00:25.530 --> 00:00:28.950 There's several ways that we can express the relationship 00:00:28.950 --> 00:00:31.840 between the total cost and the number of apples. 00:00:31.840 --> 00:00:34.930 One way is if we solve for the total cost, 00:00:34.930 --> 00:00:38.400 and we say, okay, the total cost is gonna be $2 per apple 00:00:38.400 --> 00:00:40.250 times the number of apples, 00:00:40.250 --> 00:00:41.403 so it's going to be 2a. 00:00:43.210 --> 00:00:46.270 Another way that we could rewrite this 00:00:46.270 --> 00:00:49.440 if we were to divide both sides of this by two, 00:00:49.440 --> 00:00:52.730 we would get that the number of apples 00:00:52.730 --> 00:00:57.730 is equal to cost over two. 00:00:57.900 --> 00:01:00.700 These are equivalent expressions I should say 00:01:00.700 --> 00:01:02.470 these are equivalent equations, 00:01:02.470 --> 00:01:04.310 but the way they've been written, 00:01:04.310 --> 00:01:06.770 make it useful for different scenarios. 00:01:06.770 --> 00:01:09.360 For example, on the left-hand side here, 00:01:09.360 --> 00:01:11.760 it's really easy to try out different As 00:01:11.760 --> 00:01:14.680 and then think about how that will affect the cost, 00:01:14.680 --> 00:01:16.790 and so when it's written like this, 00:01:16.790 --> 00:01:18.030 we would call the variable 00:01:18.030 --> 00:01:19.930 that it's easy to try out different values, 00:01:19.930 --> 00:01:22.880 we would call that the independent variable, 00:01:22.880 --> 00:01:25.580 independent variable, 00:01:25.580 --> 00:01:28.870 and then the one that we are essentially solving for 00:01:28.870 --> 00:01:30.420 that we then spit out a value 00:01:30.420 --> 00:01:32.780 after we compute using the independent variable, 00:01:32.780 --> 00:01:34.860 you call that the dependent variable. 00:01:34.860 --> 00:01:36.280 You could view it as, 00:01:36.280 --> 00:01:37.960 look in this situation, 00:01:37.960 --> 00:01:40.970 the cost is dependent on the number of apples 00:01:40.970 --> 00:01:42.580 you choose to eat. 00:01:42.580 --> 00:01:44.180 Now, when we wrote it over here, 00:01:44.180 --> 00:01:45.380 this looks a little bit different. 00:01:45.380 --> 00:01:48.900 Now the number of apples is solved for, 00:01:48.900 --> 00:01:52.890 and we compute how many apples based on the cost, 00:01:52.890 --> 00:01:55.660 so this would be a scenario where you have a budget 00:01:55.660 --> 00:01:57.310 and you tell me what the budget is 00:01:57.310 --> 00:01:59.350 and I could tell you the number of apples. 00:01:59.350 --> 00:02:00.640 So in this situation, 00:02:00.640 --> 00:02:02.660 C is the independent variable, 00:02:02.660 --> 00:02:04.740 and since we have solved for a, 00:02:04.740 --> 00:02:07.170 a is the dependent variable. 00:02:07.170 --> 00:02:09.700 This is useful if I give you a number of apples 00:02:09.700 --> 00:02:11.200 and you want to know the total cost, 00:02:11.200 --> 00:02:14.000 and this is useful if you have a certain cost 00:02:14.000 --> 00:02:17.993 and then you want to find out the number of apples.

Writing expressions with parentheses

https://www.youtube.com/watch?v=cFNbX-2R78M

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https://www.youtube.com/api/timedtext?v=cFNbX-2R78M&ei=ylWUZcmrKcmQvdIP9bO7oAQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=A6653D22144B5D4FF48E41C282CA125334F37AC2.3C32FD133099017EC1D842A225C2A183486DF49E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.150 --> 00:00:01.470 - [Narrator] We have two different statements 00:00:01.470 --> 00:00:02.303 written in English 00:00:02.303 --> 00:00:04.800 that I would like you to pause this video 00:00:04.800 --> 00:00:07.373 and try to write as an algebraic expression. 00:00:08.230 --> 00:00:10.650 All right, now let's work on this first one. 00:00:10.650 --> 00:00:12.374 So you might be tempted to say, all right, I have five. 00:00:12.374 --> 00:00:14.300 So let me just write a five, 00:00:14.300 --> 00:00:15.960 times and I'll write a dot 00:00:15.960 --> 00:00:17.420 because when we're dealing with algebra, 00:00:17.420 --> 00:00:19.970 if you write a traditional multiplication sign, 00:00:19.970 --> 00:00:21.630 it can get confused with an X. 00:00:21.630 --> 00:00:23.120 So five times 00:00:23.120 --> 00:00:24.730 the difference of X and two. 00:00:24.730 --> 00:00:25.980 The difference of X and two, 00:00:25.980 --> 00:00:30.050 we could write as X minus two, 00:00:30.050 --> 00:00:32.460 but this expression has a problem 00:00:32.460 --> 00:00:33.990 because whoever's interpreting it, 00:00:33.990 --> 00:00:35.730 if they're following order of operations, 00:00:35.730 --> 00:00:36.920 which they should, 00:00:36.920 --> 00:00:38.510 that would mean that they would multiply 00:00:38.510 --> 00:00:39.970 the five and the X first 00:00:39.970 --> 00:00:41.600 and then subtract two. 00:00:41.600 --> 00:00:43.390 But that's not what's going on in the sentence. 00:00:43.390 --> 00:00:45.030 It's five times, 00:00:45.030 --> 00:00:47.290 not X, but the difference of X and two. 00:00:47.290 --> 00:00:48.950 So what you need to do is 00:00:48.950 --> 00:00:50.590 put parentheses here 00:00:50.590 --> 00:00:52.240 to make sure that you take the difference 00:00:52.240 --> 00:00:53.730 of X and two first, 00:00:53.730 --> 00:00:56.480 and then multiply that by five. 00:00:56.480 --> 00:00:58.100 Now, with that in mind, 00:00:58.100 --> 00:01:00.440 let's tackle this example right over here, 00:01:00.440 --> 00:01:02.603 10 times the sum of Y and three. 00:01:03.460 --> 00:01:04.293 Well, once again, 00:01:04.293 --> 00:01:07.000 if you just wrote 10 times 00:01:07.000 --> 00:01:08.030 the sum 00:01:08.030 --> 00:01:09.690 of Y and three, 00:01:09.690 --> 00:01:11.520 you'll run into the same problem. 00:01:11.520 --> 00:01:13.070 someone would interpret this as, 00:01:13.070 --> 00:01:14.879 hey, maybe I should multiply 10 and Y first, 00:01:14.879 --> 00:01:17.800 because that's what order of operations would tell me to do, 00:01:17.800 --> 00:01:18.750 but that's not what we want. 00:01:18.750 --> 00:01:20.780 We want 10 times, not just Y, 00:01:20.780 --> 00:01:23.050 but the sum of Y and three. 00:01:23.050 --> 00:01:24.590 So that's where the parentheses 00:01:24.590 --> 00:01:26.260 are really important to make sure 00:01:26.260 --> 00:01:28.930 that we take the sum of Y and three first 00:01:28.930 --> 00:01:31.263 and then multiply that by 10.

Writing algebraic subtraction expressions

https://www.youtube.com/watch?v=eFXcsXnKkjw

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https://www.youtube.com/api/timedtext?v=eFXcsXnKkjw&ei=ylWUZfvGMquMp-oPkYWjwAE&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=2BDD80AEF7630880E5445DDCB8C5B2A29413BCE7.B62100A6468F0895F92FD2B47962EC176AB0869E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:01.550 - [Instructor] We have different statements here 00:00:01.550 --> 00:00:05.240 that can each be expressed as an algebraic expression, 00:00:05.240 --> 00:00:07.110 and as you might have guessed, 00:00:07.110 --> 00:00:09.750 I would love you to pause this video 00:00:09.750 --> 00:00:12.480 and try to write each of these statements 00:00:12.480 --> 00:00:15.273 as an algebraic expression before we do it together. 00:00:16.700 --> 00:00:19.360 All right, now let's work on it together. 00:00:19.360 --> 00:00:24.360 So this first statement, we have two less than x. 00:00:24.410 --> 00:00:27.390 So my brain thinks, all right, let me start with x, 00:00:27.390 --> 00:00:29.340 and how am I going to get two less than that? 00:00:29.340 --> 00:00:31.920 Well, I'm going to subtract two. 00:00:31.920 --> 00:00:33.630 And this is an interesting example 00:00:33.630 --> 00:00:35.580 because you see the order that we see it 00:00:35.580 --> 00:00:37.840 in the sentence is not the order 00:00:37.840 --> 00:00:39.450 that we would necessarily write it 00:00:39.450 --> 00:00:41.300 in the expression right over here. 00:00:41.300 --> 00:00:44.380 Very important to think about, what is going on here? 00:00:44.380 --> 00:00:47.290 What is being described? 00:00:47.290 --> 00:00:51.340 Now, this next statement, y fewer than three. 00:00:51.340 --> 00:00:54.760 Well, in my mind, I'm going to start with three 00:00:54.760 --> 00:00:57.060 and I'm going to be y fewer than that. 00:00:57.060 --> 00:00:58.760 So I'm gonna start with three 00:00:58.760 --> 00:01:02.480 and then I'm going to be y fewer than that. 00:01:02.480 --> 00:01:04.420 Now, these first two statements are similar 00:01:04.420 --> 00:01:06.760 in that you have something less than something else 00:01:06.760 --> 00:01:08.930 or something fewer than something else. 00:01:08.930 --> 00:01:11.963 They just swapped the number and the variable. 00:01:12.850 --> 00:01:17.850 Now, this third statement, x decreased by five. 00:01:18.580 --> 00:01:20.710 So my mind is thinking, what am I starting with? 00:01:20.710 --> 00:01:24.810 I'm starting with an x and I'm decreasing it by five. 00:01:24.810 --> 00:01:26.670 So I can do that as minus five, 00:01:26.670 --> 00:01:28.793 or I'm gonna take five away from it.

Evaluating expressions like 5x² & ⅓(6)ˣ

https://www.youtube.com/watch?v=ccyZpjKvJV8

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https://www.youtube.com/api/timedtext?v=ccyZpjKvJV8&ei=ylWUZfD0JI6qp-oP0f-XOA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=8C4EC054F57193484226C36E1721F325C67B849A.67CEFF7982E44E36ACDF5193EEE22AB3574E9569&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.120 --> 00:00:02.050 - [Instructor] What I want you to do is evaluate 00:00:02.050 --> 00:00:04.340 the expression 5x squared 00:00:04.340 --> 00:00:07.150 when x is equal to three. 00:00:07.150 --> 00:00:09.100 Pause this video and have a go at that. 00:00:10.530 --> 00:00:12.220 All right, well, we just have to think 00:00:12.220 --> 00:00:14.050 about every place we see an x, 00:00:14.050 --> 00:00:16.000 we'll now replace it with a three. 00:00:16.000 --> 00:00:18.500 So this is going to be equivalent to five times, 00:00:18.500 --> 00:00:19.780 instead of x squared, 00:00:19.780 --> 00:00:23.800 it's going to be five times three squared. 00:00:23.800 --> 00:00:25.500 And we know from order of operations, 00:00:25.500 --> 00:00:26.980 we do the exponents first. 00:00:26.980 --> 00:00:28.520 That's why I actually put a parentheses 00:00:28.520 --> 00:00:31.060 around the three squared to just make that clear. 00:00:31.060 --> 00:00:33.940 And three squared is, of course, equal to nine 00:00:33.940 --> 00:00:38.750 and five times nine is equal to 45. 00:00:38.750 --> 00:00:41.810 Let's do another example that's a little bit different. 00:00:41.810 --> 00:00:44.610 Let's say I have the expression 1/3 00:00:44.610 --> 00:00:49.000 times six to the x power, 00:00:49.000 --> 00:00:53.800 and I want to evaluate it when x is equal to two. 00:00:53.800 --> 00:00:56.443 Pause the video again and see if you can work that out. 00:00:57.300 --> 00:00:59.590 Well, once again, everywhere where we see an x, 00:00:59.590 --> 00:01:00.980 we'll replace that with a two. 00:01:00.980 --> 00:01:02.320 So this is going to be the same thing 00:01:02.320 --> 00:01:06.880 as 1/3 times six squared. 00:01:06.880 --> 00:01:10.360 Where we saw the x, we now replace that with a two. 00:01:10.360 --> 00:01:12.780 And so this is going to be equal to, 00:01:12.780 --> 00:01:15.560 we do the exponent first, order of operations, 00:01:15.560 --> 00:01:17.190 so it's going to be 1/3 00:01:17.190 --> 00:01:20.790 times six squared is 36, 00:01:20.790 --> 00:01:24.603 and 1/3 of 36 is equal to 12. 00:01:24.603 --> 00:01:25.771 And we're done!

Order of operations with fractions and exponents

https://www.youtube.com/watch?v=jAVbApE7lJ8

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https://www.youtube.com/api/timedtext?v=jAVbApE7lJ8&ei=ylWUZZ6BDvuKmLAPybmZeA&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=999A72AF0188C16F68A9C72B9B97FCDBCEE11941.3E0F741AED4352B5DB3969DC2A929E9E8E1515D0&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.360 --> 00:00:01.210 - [Instructor] Pause this video 00:00:01.210 --> 00:00:03.230 and see if you can evaluate this expression 00:00:03.230 --> 00:00:05.460 before we do it together. 00:00:05.460 --> 00:00:07.850 All right, now let's work on this together. 00:00:07.850 --> 00:00:10.720 And we see that we have a lot of different operations here. 00:00:10.720 --> 00:00:12.720 We have exponents. We have multiplication. 00:00:12.720 --> 00:00:14.500 We have addition. We have division. 00:00:14.500 --> 00:00:16.280 We have parentheses. 00:00:16.280 --> 00:00:19.020 And so to interpret this properly, 00:00:19.020 --> 00:00:23.430 we just have to remind ourselves of the order of operations. 00:00:23.430 --> 00:00:26.700 So you start with parentheses, then go to exponents, 00:00:26.700 --> 00:00:28.050 then multiplication and division, 00:00:28.050 --> 00:00:30.470 then addition and subtraction. 00:00:30.470 --> 00:00:33.780 So we see that we're going to, whatever is over here, 00:00:33.780 --> 00:00:35.510 we're eventually going to square it. 00:00:35.510 --> 00:00:38.510 That's the only place that we have the parentheses. 00:00:38.510 --> 00:00:39.930 But how are we going to evaluate 00:00:39.930 --> 00:00:42.890 what's inside of these parentheses? 00:00:42.890 --> 00:00:45.660 So let's, then, think about, all right, 00:00:45.660 --> 00:00:49.810 we have an exponent here that we can evaluate. 00:00:49.810 --> 00:00:53.490 We know that 2 squared is the same thing as 2 times 2, 00:00:53.490 --> 00:00:55.730 which is the same thing as 4. 00:00:55.730 --> 00:00:57.790 No more exponents to evaluate. 00:00:57.790 --> 00:01:00.470 So then we go to multiplication and division. 00:01:00.470 --> 00:01:04.820 So we know by how this fraction sign is written 00:01:04.820 --> 00:01:06.640 that we need to evaluate the numerator 00:01:06.640 --> 00:01:09.380 and then divide it by the entire denominator 00:01:09.380 --> 00:01:10.830 right over here. 00:01:10.830 --> 00:01:13.320 Now in this numerator, we have to remind ourselves 00:01:13.320 --> 00:01:16.350 that we do this multiplication before we do this addition. 00:01:16.350 --> 00:01:18.650 We don't just go left to right. 00:01:18.650 --> 00:01:20.780 So we know that it's 1 plus, 00:01:20.780 --> 00:01:23.560 and I could put parentheses here to really emphasize 00:01:23.560 --> 00:01:25.510 that we do the multiplication first. 00:01:25.510 --> 00:01:26.880 So before this gets too messy, 00:01:26.880 --> 00:01:28.590 let me just rewrite everything. 00:01:28.590 --> 00:01:30.950 I'm going to do this multiplication up here first, 00:01:30.950 --> 00:01:32.090 and actually in the denominator 00:01:32.090 --> 00:01:34.960 I'm going to do this multiplication first as well. 00:01:34.960 --> 00:01:39.080 So this is all going to simplify to 1 over 14 00:01:39.080 --> 00:01:41.770 or 1/14 times, 00:01:41.770 --> 00:01:43.450 Now this numerator here is going to be 00:01:43.450 --> 00:01:47.170 1 plus 4 times 3. 00:01:47.170 --> 00:01:49.303 4 times 3 is 12. 00:01:50.620 --> 00:01:53.640 All of that is going to be over 00:01:53.640 --> 00:01:57.220 7 plus 2 times 3, 00:01:57.220 --> 00:02:00.240 which is of course equal to 6. 00:02:00.240 --> 00:02:04.650 And then I am going to have our plus 1 here, 00:02:04.650 --> 00:02:06.463 and then I square everything. 00:02:07.370 --> 00:02:11.270 Well now we can evaluate this numerator 00:02:11.270 --> 00:02:13.900 and this denominator. 00:02:13.900 --> 00:02:15.623 Find another color to do it in. 00:02:16.490 --> 00:02:18.710 This numerator, 1 plus 12, 00:02:18.710 --> 00:02:21.770 is going to be equal to 13. 00:02:21.770 --> 00:02:26.410 And 7 plus 6, interestingly, is also equal to 13. 00:02:26.410 --> 00:02:28.740 So we 1/14 or 1 divided by 14 00:02:28.740 --> 00:02:30.930 times this whole thing squared, 00:02:30.930 --> 00:02:34.980 and inside you have 13 divided by 13 plus 1. 00:02:34.980 --> 00:02:38.090 Well, we know we need to do division before we do addition. 00:02:38.090 --> 00:02:41.600 So we will want to evaluate this part 00:02:41.600 --> 00:02:43.940 before we do the addition. 00:02:43.940 --> 00:02:46.540 What is 13 divided by 13? 00:02:46.540 --> 00:02:48.610 Well that's just going to be equal to 1. 00:02:48.610 --> 00:02:52.840 So I can rewrite this as 1 over 14 00:02:52.840 --> 00:02:57.383 times 1 plus 1, 00:02:58.400 --> 00:02:59.880 all of that squared. 00:02:59.880 --> 00:03:03.640 And now we'll want to do this parentheses. So let's do that. 00:03:03.640 --> 00:03:08.423 1 plus 1 is going to be equal, of course, to 2. 00:03:09.400 --> 00:03:11.580 And then we're going to do the exponents. 00:03:11.580 --> 00:03:16.100 2 squared is, of course, equal to 4. 00:03:16.100 --> 00:03:19.870 And then we're going to multiply 1 over 14 times 4. 00:03:19.870 --> 00:03:21.900 Now you could interpret this, and they're equivalent. 00:03:21.900 --> 00:03:23.200 You could say, hey, this is the same thing 00:03:23.200 --> 00:03:26.040 as multiplying 1/14 times 4. 00:03:26.040 --> 00:03:27.680 Or you could say this is the same thing 00:03:27.680 --> 00:03:31.460 as multiplying 1 times 4 divided by 14. 00:03:31.460 --> 00:03:35.490 1 times 4 divided by 14. 00:03:35.490 --> 00:03:36.590 Either way you look at it, 00:03:36.590 --> 00:03:40.880 you're going to get 4 over 14, and we're done. 00:03:40.880 --> 00:03:42.440 If you want, you could rewrite this 00:03:42.440 --> 00:03:46.090 by dividing both the numerator and the denominator by 2, 00:03:46.090 --> 00:03:48.730 and you could get 2 over 7. 00:03:48.730 --> 00:03:51.260 But that's how we can evaluate 00:03:51.260 --> 00:03:53.110 this pretty complex expression 00:03:53.110 --> 00:03:56.853 just step-by-step looking at what we can simplify first.

Order of operations introduction

https://www.youtube.com/watch?v=eoYThjIAhOc

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https://www.youtube.com/api/timedtext?v=eoYThjIAhOc&ei=ylWUZZ_bMv6ImLAP5uapgAM&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=12797E5387EAED05F7BD62A9E7FD80B571488289.852E48D9A15E5DF8161F021C2C1BDD970829CE0F&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.160 --> 00:00:01.200 - Every few months, 00:00:01.200 --> 00:00:04.760 you'll see an expression like this go viral on social media 00:00:04.760 --> 00:00:06.610 because it looks simple 00:00:06.610 --> 00:00:09.490 but depending on how people interpret this expression, 00:00:09.490 --> 00:00:11.800 they often get different answers. 00:00:11.800 --> 00:00:14.240 So first, why don't you pause this video 00:00:14.240 --> 00:00:18.550 and think about what you think three plus two times five 00:00:18.550 --> 00:00:19.913 is equal to. 00:00:21.880 --> 00:00:24.260 All right, now let's work through this together. 00:00:24.260 --> 00:00:26.560 Now some of you might have interpreted this 00:00:26.560 --> 00:00:29.140 as we should just go from left to right. 00:00:29.140 --> 00:00:30.230 So you might've said, all right, 00:00:30.230 --> 00:00:32.280 let me first add three plus two. 00:00:32.280 --> 00:00:33.660 So I can do that part first, 00:00:33.660 --> 00:00:35.680 which is of course equal to five. 00:00:35.680 --> 00:00:39.850 And then I could multiply that times five. 00:00:39.850 --> 00:00:44.630 And that is going to get me to 25. 00:00:44.630 --> 00:00:47.170 Now others of you would have said no, 00:00:47.170 --> 00:00:49.410 that makes no sense at all. 00:00:49.410 --> 00:00:53.400 We know that we should do some operations before others. 00:00:53.400 --> 00:00:57.130 For example, multiplication should come before addition. 00:00:57.130 --> 00:00:58.990 And so if you follow that, 00:00:58.990 --> 00:01:03.490 you would do the two times five first to get 10. 00:01:03.490 --> 00:01:06.830 And so this would become three plus 10, 00:01:06.830 --> 00:01:11.210 which is of course, going to be equal to 13. 00:01:11.210 --> 00:01:13.073 Who do you think would be right? 00:01:14.020 --> 00:01:16.130 Well, it turns out that the second way of doing it 00:01:16.130 --> 00:01:17.340 is the correct way 00:01:17.340 --> 00:01:19.100 and that's because we have something known 00:01:19.100 --> 00:01:21.920 as order of operations. 00:01:21.920 --> 00:01:25.290 And the order of operations is the convention 00:01:25.290 --> 00:01:27.750 that mathematicians have decided to use 00:01:27.750 --> 00:01:31.127 in order for us to have one way to interpret an expression 00:01:31.127 --> 00:01:33.810 like this and the order of operations 00:01:33.810 --> 00:01:35.760 are to do parentheses first. 00:01:35.760 --> 00:01:36.700 So, for example, 00:01:36.700 --> 00:01:40.700 if you really wanted to add the three and the two first, 00:01:40.700 --> 00:01:43.180 you should put parentheses around it 00:01:43.180 --> 00:01:46.500 to say, hey, that's what you've got to do first. 00:01:46.500 --> 00:01:49.360 But then after parentheses, do exponents, 00:01:49.360 --> 00:01:52.500 which is really, you could view as repeated multiplication, 00:01:52.500 --> 00:01:54.900 then do multiplication and division. 00:01:54.900 --> 00:01:58.050 Then do addition and subtraction. 00:01:58.050 --> 00:02:01.910 Now, some people might just memorize this as PEMDAS, 00:02:01.910 --> 00:02:05.340 or PEDMAS or something like that. 00:02:05.340 --> 00:02:06.290 And you can do that, 00:02:06.290 --> 00:02:08.220 but there's a rationale to this. 00:02:08.220 --> 00:02:09.600 Parentheses are just, 00:02:09.600 --> 00:02:11.520 the person who writing the expression saying 00:02:11.520 --> 00:02:13.740 do this for sure first. 00:02:13.740 --> 00:02:14.710 But then if you think about it, 00:02:14.710 --> 00:02:17.490 exponents are repeated multiplication 00:02:17.490 --> 00:02:19.950 and multiplication is repeated addition. 00:02:19.950 --> 00:02:23.200 So you're doing the most repeated things first, 00:02:23.200 --> 00:02:25.620 then next repeated things like multiplication. 00:02:25.620 --> 00:02:27.910 And then you go straight to the addition. 00:02:27.910 --> 00:02:29.930 The reason why multiplication and division 00:02:29.930 --> 00:02:31.030 are on the same line 00:02:31.030 --> 00:02:33.480 and addition and subtraction on the same line 00:02:33.480 --> 00:02:36.690 is the convention there is just go left to right. 00:02:36.690 --> 00:02:40.420 So now that we are armed with our order of operations, 00:02:40.420 --> 00:02:44.280 let's tackle another slightly hairier expression. 00:02:44.280 --> 00:02:47.270 And I use the term hairy for a little bit more complex. 00:02:47.270 --> 00:02:51.560 So two times 10, minus eight, 00:02:51.560 --> 00:02:56.170 divided by four, plus one. 00:02:56.170 --> 00:02:58.610 Pause the video and see how you could evaluate this 00:02:58.610 --> 00:03:01.023 now that you know about order of operations. 00:03:02.560 --> 00:03:04.470 All right, now let's do this together. 00:03:04.470 --> 00:03:06.480 We don't see any parentheses here. 00:03:06.480 --> 00:03:08.220 We don't see any exponents here 00:03:08.220 --> 00:03:12.170 but we do see some multiplication and division here. 00:03:12.170 --> 00:03:14.360 So we could see it over here. 00:03:14.360 --> 00:03:16.070 This two times 10. 00:03:16.070 --> 00:03:19.470 And we also have this eight divided by four. 00:03:19.470 --> 00:03:21.600 So that's what we're going to want to do first. 00:03:21.600 --> 00:03:25.530 So that two times 10, that is going to be equal to 20. 00:03:25.530 --> 00:03:29.010 The eight divided by four, is of course, equal to two. 00:03:29.010 --> 00:03:34.010 And then we have 20 minus two plus one. 00:03:35.050 --> 00:03:38.420 And this is now going to get us, if we go left to right, 00:03:38.420 --> 00:03:41.580 which we should do when we're just adding and subtracting, 00:03:41.580 --> 00:03:46.580 is we get 20 minus two is 18, plus one, 00:03:46.630 --> 00:03:49.860 which is going to be equal to 19. 00:03:49.860 --> 00:03:51.270 And we're done. 00:03:51.270 --> 00:03:52.103 Now, you might say, well, 00:03:52.103 --> 00:03:54.980 what if we wanted someone to add the four and the one first? 00:03:54.980 --> 00:03:56.170 Well, one way to do that 00:03:56.170 --> 00:03:59.300 is you could have added a parentheses there to force it 00:03:59.300 --> 00:04:02.130 or you could have even written your division differently. 00:04:02.130 --> 00:04:05.170 For example, you could use a fraction sign 00:04:05.170 --> 00:04:06.210 to make things clearer. 00:04:06.210 --> 00:04:08.620 If we wanted to add the four plus one first, 00:04:08.620 --> 00:04:12.890 instead of writing eight divided by four plus one like that, 00:04:12.890 --> 00:04:17.890 you could write eight over four plus one. 00:04:17.960 --> 00:04:21.240 Now of course, this is fundamentally different 00:04:21.240 --> 00:04:22.560 than this right over here. 00:04:22.560 --> 00:04:25.190 'Cause here we would do the eight divided by four first, 00:04:25.190 --> 00:04:26.600 then add the plus one, 00:04:26.600 --> 00:04:29.220 while here, you would add the four plus one 00:04:29.220 --> 00:04:31.303 and then divide eight by that.

Quantitative electrolysis

https://www.youtube.com/watch?v=v5qQusbk-j0

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https://www.youtube.com/api/timedtext?v=v5qQusbk-j0&ei=ylWUZZq_J4_YxN8Plc-K6AQ&caps=asr&opi=112496729&xoaf=5&hl=en&ip=0.0.0.0&ipbits=0&expire=1704245306&sparams=ip%2Cipbits%2Cexpire%2Cv%2Cei%2Ccaps%2Copi%2Cxoaf&signature=29BD327757A2E71D668C3580E20A1E69322D4C86.7106D66D5ED3F5789BCEDA5FA40F5F051CECE16E&key=yt8&lang=en&name=Default&fmt=vtt

en

WEBVTT Kind: captions Language: en 00:00:00.350 --> 00:00:02.600 - [Instructor] We already know that in an electrolytic cell, 00:00:02.600 --> 00:00:04.260 current or movement of electrons 00:00:04.260 --> 00:00:06.990 is used to drive a redox reaction. 00:00:06.990 --> 00:00:10.700 And if we look at a generic reduction half-reaction, 00:00:10.700 --> 00:00:12.880 the stoichiometry of the half reaction 00:00:12.880 --> 00:00:15.580 shows how many electrons are needed 00:00:15.580 --> 00:00:18.610 to reduce a generic metal ion. 00:00:18.610 --> 00:00:22.780 For example, if we say that our generic metal ion is M2+, 00:00:22.780 --> 00:00:27.560 it takes two electrons to turn M2+ into the solid metal. 00:00:27.560 --> 00:00:32.560 So one mole of M2+ ions requires two moles of electrons 00:00:33.110 --> 00:00:35.800 to form one mole of the metal. 00:00:35.800 --> 00:00:39.240 So we could use this mole ratio of one mole of metal 00:00:39.240 --> 00:00:42.350 to two moles of electrons to figure out, 00:00:42.350 --> 00:00:44.840 say, how much of a metal is produced 00:00:44.840 --> 00:00:47.130 in an electrolytic reaction. 00:00:47.130 --> 00:00:48.480 So this is an example 00:00:48.480 --> 00:00:51.840 of a quantitative electrolysis problem. 00:00:51.840 --> 00:00:55.630 Moles of electrons are related to the amount of charge 00:00:55.630 --> 00:00:58.540 that passes through the electrolytic cell 00:00:58.540 --> 00:01:02.687 because one mole of electrons carries 96,485 coulombs. 00:01:04.890 --> 00:01:06.660 So we could set this up as a constant 00:01:06.660 --> 00:01:08.190 called Faraday's constant. 00:01:08.190 --> 00:01:10.390 So Faraday's constant is symbolized by F, 00:01:10.390 --> 00:01:15.390 and it's equal to 96,485 coulombs per mole of electrons. 00:01:16.460 --> 00:01:20.550 And charge is related to current and time by this equation. 00:01:20.550 --> 00:01:23.440 So I is equal to Q over t; 00:01:23.440 --> 00:01:27.720 where I is the current; Q, capital Q is the charge; 00:01:27.720 --> 00:01:29.240 and t is the time. 00:01:29.240 --> 00:01:33.200 Sometimes, you see a lower case Q for charge. 00:01:33.200 --> 00:01:35.740 Charge is measured in coulombs, 00:01:35.740 --> 00:01:38.580 and time is in seconds. 00:01:38.580 --> 00:01:42.380 And one coulomb per second is equal to one ampere, 00:01:42.380 --> 00:01:45.870 so current is measured in amperes. 00:01:45.870 --> 00:01:48.090 Next, let's look at a conversion chart that shows 00:01:48.090 --> 00:01:51.500 how to approach quantitative electrolysis problems. 00:01:51.500 --> 00:01:54.570 And let's start over here with this box on the far left, 00:01:54.570 --> 00:01:57.900 which says that charge is equal to current times time. 00:01:57.900 --> 00:01:59.970 This comes from our equation for current, 00:01:59.970 --> 00:02:02.000 I is equal to Q over t. 00:02:02.000 --> 00:02:04.550 So solving for charge, solving for Q, 00:02:04.550 --> 00:02:06.920 Q is equal to I times t 00:02:06.920 --> 00:02:10.190 or charge is equal to current times time. 00:02:10.190 --> 00:02:13.440 Charge is related to moles of electrons 00:02:13.440 --> 00:02:15.770 by Faraday's constant. 00:02:15.770 --> 00:02:19.000 So we can convert back and forth between the two 00:02:19.000 --> 00:02:21.260 using Faraday's constant. 00:02:21.260 --> 00:02:24.690 And moles of electrons are related to the moles 00:02:24.690 --> 00:02:27.320 of the substance that we're interested in the problem 00:02:27.320 --> 00:02:29.500 by the balanced half-reaction. 00:02:29.500 --> 00:02:31.330 So the balanced half-reaction allows us 00:02:31.330 --> 00:02:34.310 to convert back and forth between moles of electrons 00:02:34.310 --> 00:02:36.130 and moles of substance. 00:02:36.130 --> 00:02:37.380 And from stoichiometry, 00:02:37.380 --> 00:02:39.370 we know that the moles of a substance 00:02:39.370 --> 00:02:42.840 is related to the grams of the substance by the molar mass. 00:02:42.840 --> 00:02:45.710 So the molar mass allows us to convert back and forth 00:02:45.710 --> 00:02:47.580 between these quantities. 00:02:47.580 --> 00:02:49.640 So it helps to look at a conversion chart 00:02:49.640 --> 00:02:51.400 when doing these sorts of problems. 00:02:51.400 --> 00:02:53.910 However, if you don't remember the chart, 00:02:53.910 --> 00:02:56.860 you can always use dimensional analysis and units 00:02:56.860 --> 00:02:59.460 to figure out the answer to the question. 00:02:59.460 --> 00:03:01.190 Next, let's use our conversion chart 00:03:01.190 --> 00:03:04.530 to figure out a quantitative electrolysis problem. 00:03:04.530 --> 00:03:07.740 Let's say we have an aqueous solution of silver nitrate 00:03:07.740 --> 00:03:12.740 and a constant current of 2.40 amperes is applied 00:03:12.940 --> 00:03:16.020 for 1,225 seconds. 00:03:16.020 --> 00:03:19.550 And our goal is to figure out the mass of silver 00:03:19.550 --> 00:03:20.870 that has formed. 00:03:20.870 --> 00:03:24.290 As a quick reminder, an aqueous solution of silver nitrate 00:03:24.290 --> 00:03:29.290 contains Ag+ ions and nitrate anions in solution. 00:03:29.340 --> 00:03:34.150 So the applied current is used to reduce the Ag+ ions 00:03:34.150 --> 00:03:36.570 to form solid silver. 00:03:36.570 --> 00:03:38.690 And since our goal is to figure out the mass 00:03:38.690 --> 00:03:40.700 of the solid silver that's formed, 00:03:40.700 --> 00:03:44.130 we're trying to find grams of substance. 00:03:44.130 --> 00:03:49.130 And in the problem we're given the current and the time, 00:03:49.230 --> 00:03:51.870 so we're starting over here in the first box 00:03:51.870 --> 00:03:54.230 with the current and the time. 00:03:54.230 --> 00:03:56.450 So let's think about the steps that we need 00:03:56.450 --> 00:03:58.410 to solve this problem. 00:03:58.410 --> 00:04:01.750 The first step is to find the charge, 00:04:01.750 --> 00:04:04.580 which we can get from the current and the time. 00:04:04.580 --> 00:04:07.550 The second step is to convert charge 00:04:07.550 --> 00:04:10.440 into moles of electrons. 00:04:10.440 --> 00:04:11.900 From moles of electrons, 00:04:11.900 --> 00:04:16.900 we can convert that into the moles of silver in this case. 00:04:17.070 --> 00:04:19.820 And in the fourth step for this problem, 00:04:19.820 --> 00:04:24.600 we can convert moles of silver into grams of silver. 00:04:24.600 --> 00:04:28.240 So step one is to find the charge. 00:04:28.240 --> 00:04:32.440 And Q, the charge, is equal to the current times the time. 00:04:32.440 --> 00:04:35.760 So the current is equal to 2.40 amperes. 00:04:35.760 --> 00:04:36.593 And remember, 00:04:36.593 --> 00:04:39.880 one ampere is equal to one coulomb per second. 00:04:39.880 --> 00:04:44.610 So we plug in 2.40 coulombs per second. 00:04:44.610 --> 00:04:48.180 And the time is 1,225 seconds, 00:04:48.180 --> 00:04:51.260 so we plug that in, seconds cancels out, 00:04:51.260 --> 00:04:56.020 and we get that Q is equal to 2,940 coulombs. 00:04:56.020 --> 00:05:00.440 So that's the charge that's transferred in that time period. 00:05:00.440 --> 00:05:01.700 Now that we have the charge, 00:05:01.700 --> 00:05:02.810 in the second step, 00:05:02.810 --> 00:05:05.120 our goal is to find the moles of electrons. 00:05:05.120 --> 00:05:07.730 And charge is related to moles of electrons 00:05:07.730 --> 00:05:09.800 by Faraday's constant. 00:05:09.800 --> 00:05:13.340 So dividing the charge by Faraday's constant 00:05:13.340 --> 00:05:15.330 causes coulombs to cancel out, 00:05:15.330 --> 00:05:20.330 and we get 0.0305 moles of electrons. 00:05:20.330 --> 00:05:22.280 And now that we have moles of electrons, 00:05:22.280 --> 00:05:26.230 in step three, we can find the moles of silver. 00:05:26.230 --> 00:05:29.340 Looking at the balanced equation for our half reaction 00:05:29.340 --> 00:05:32.540 showing the reduction of silver ions, 00:05:32.540 --> 00:05:37.540 one mole of silver ions requires one mole of electrons 00:05:38.060 --> 00:05:41.240 to form one mole of solid silver. 00:05:41.240 --> 00:05:44.660 So our mole ratio of silver to moles of electrons 00:05:44.660 --> 00:05:46.410 is one-to-one, 00:05:46.410 --> 00:05:48.800 which gives us this conversion factor 00:05:48.800 --> 00:05:52.810 of one mole of silver per one mole of electrons. 00:05:52.810 --> 00:05:55.480 So if we multiply our moles of electrons 00:05:55.480 --> 00:05:59.240 by our conversion factor, moles of electrons cancels out, 00:05:59.240 --> 00:06:03.630 and that gives us 0.0305 moles of silver. 00:06:03.630 --> 00:06:06.340 In this case, our mole ratio was one-to-one, 00:06:06.340 --> 00:06:09.410 but if we were reducing a different metal ion, 00:06:09.410 --> 00:06:11.910 our mole ratio might not be one-to-one. 00:06:11.910 --> 00:06:14.500 So we have to be extra careful on the step 00:06:14.500 --> 00:06:17.270 to make sure we get the right mole ratio. 00:06:17.270 --> 00:06:19.080 And since we have moles of silver, 00:06:19.080 --> 00:06:21.020 in our fourth and final step, 00:06:21.020 --> 00:06:24.980 we can convert moles of silver into grams of silver. 00:06:24.980 --> 00:06:28.350 So multiplying moles of silver by the molar mass of silver, 00:06:28.350 --> 00:06:31.750 which is 107.87 grams per mole, 00:06:31.750 --> 00:06:36.750 moles cancel and this gives us 3.29 grams of silver. 00:06:37.190 --> 00:06:40.940 It's also possible to do all four steps at once 00:06:40.940 --> 00:06:43.700 in a dimensional analysis approach. 00:06:43.700 --> 00:06:45.090 So looking at our units, 00:06:45.090 --> 00:06:50.090 if we multiply 1,225 seconds by 2.40 coulombs per second, 00:06:51.460 --> 00:06:54.500 seconds cancels out and gives us coulombs. 00:06:54.500 --> 00:06:57.300 Multiplying that by one mole of electrons 00:06:57.300 --> 00:07:02.220 per 96,485 coulombs, cancels out coulombs. 00:07:02.220 --> 00:07:05.600 Next, we have our conversion factor of one mole of silver 00:07:05.600 --> 00:07:07.640 per one mole of electrons, 00:07:07.640 --> 00:07:10.040 so moles of electrons cancels out. 00:07:10.040 --> 00:07:12.030 And multiplying that by the molar mass 00:07:12.030 --> 00:07:16.150 of 107.87 grams per one mole, 00:07:16.150 --> 00:07:18.640 moles of silver will cancel out 00:07:18.640 --> 00:07:22.410 and give us a final answer of 3.29 grams. 00:07:22.410 --> 00:07:25.953 So we get the same answer, no matter which approach we take.

The Nernst equation

https://www.youtube.com/watch?v=PemB4mY4Jfk

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WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:01.153 - [Instructor] We already know 00:00:01.153 --> 00:00:02.810 how to calculate cell potential 00:00:02.810 --> 00:00:04.160 when the reactants and products 00:00:04.160 --> 00:00:06.020 are in their standard states. 00:00:06.020 --> 00:00:08.650 However, what if that's not the case? 00:00:08.650 --> 00:00:11.180 We can find cell potential when reactants and products 00:00:11.180 --> 00:00:12.680 are not in their standard states 00:00:12.680 --> 00:00:15.870 by using the Nernst equation, which is shown here. 00:00:15.870 --> 00:00:17.660 And we're gonna call that cell potential 00:00:17.660 --> 00:00:20.580 the instantaneous cell potential. 00:00:20.580 --> 00:00:23.410 E cell is the instantaneous cell potential, 00:00:23.410 --> 00:00:27.310 the cell potential or voltage at a specific moment in time. 00:00:27.310 --> 00:00:30.920 E naught of the cell is the standard cell potential. 00:00:30.920 --> 00:00:32.330 This is the cell potential 00:00:32.330 --> 00:00:33.900 when the reactants and products 00:00:33.900 --> 00:00:35.960 are in their standard states. 00:00:35.960 --> 00:00:38.520 R is the ideal gas constant. 00:00:38.520 --> 00:00:40.500 T is the temperature. 00:00:40.500 --> 00:00:43.590 N is the number of electrons transferred 00:00:43.590 --> 00:00:45.650 in the redox reaction. 00:00:45.650 --> 00:00:47.790 F is Faraday's constant. 00:00:47.790 --> 00:00:51.200 And Q is the reaction quotient. 00:00:51.200 --> 00:00:54.760 So, this is one way to write the Nernst equation. 00:00:54.760 --> 00:00:57.750 And let's compare this form of the Nernst equation 00:00:57.750 --> 00:01:00.210 to a simplified form. 00:01:00.210 --> 00:01:03.090 In the simplified form of the Nernst equation, 00:01:03.090 --> 00:01:05.730 E of the cell is equal to E naught of the cell, 00:01:05.730 --> 00:01:09.730 minus 0.0592 volts, divided by n, 00:01:09.730 --> 00:01:13.060 times the log of the reaction quotient Q. 00:01:13.060 --> 00:01:15.760 So, going back to the first form of the Nernst equation, 00:01:15.760 --> 00:01:18.580 if we assume the temperature is 25 degrees Celsius, 00:01:18.580 --> 00:01:20.190 or 298 Kelvin, 00:01:20.190 --> 00:01:22.620 we multiply that by the ideal gas constant, 00:01:22.620 --> 00:01:24.520 divide that by Faraday's constant, 00:01:24.520 --> 00:01:27.650 and for changing natural log to log, 00:01:27.650 --> 00:01:31.340 then we end up with this form for the bottom equation, 00:01:31.340 --> 00:01:35.800 0.0592 volts divided by n times the log of Q 00:01:35.800 --> 00:01:39.430 for this second term of the Nernst equation. 00:01:39.430 --> 00:01:42.620 You can use the Nernst equation to quantitatively calculate 00:01:42.620 --> 00:01:46.030 the exact voltage at a specific moment in time. 00:01:46.030 --> 00:01:48.380 However, we're gonna try to think about the Nernst equation 00:01:48.380 --> 00:01:51.000 from a qualitative point of view. 00:01:51.000 --> 00:01:52.870 Let's use the Nernst equation to think 00:01:52.870 --> 00:01:56.160 about the instantaneous cell potential 00:01:56.160 --> 00:01:58.200 for a zinc copper cell. 00:01:58.200 --> 00:02:01.170 And we're gonna look at a few different situations. 00:02:01.170 --> 00:02:02.550 In a zinc copper cell, 00:02:02.550 --> 00:02:05.830 solid zinc is oxidized to zinc two plus ions 00:02:05.830 --> 00:02:10.310 and copper two plus ions are reduced to form solid copper. 00:02:10.310 --> 00:02:13.060 The standard cell potential for the zinc copper cell 00:02:13.060 --> 00:02:18.060 at 25 degrees Celsius is equal to positive 1.10 volts. 00:02:18.090 --> 00:02:21.650 And our goal is to find the cell potential 00:02:21.650 --> 00:02:23.170 at the moment of time 00:02:23.170 --> 00:02:25.740 when the concentration of copper two plus ions 00:02:25.740 --> 00:02:27.820 is equal to 1.0 Mueller 00:02:27.820 --> 00:02:31.410 and the concentration of zinc two plus ions in solution 00:02:31.410 --> 00:02:34.550 is also equal to 1.0 Mueller. 00:02:34.550 --> 00:02:36.620 To find the instantaneous cell potential, 00:02:36.620 --> 00:02:41.010 we're gonna use the simplified form of the Nernst equation. 00:02:41.010 --> 00:02:45.920 E naught of the cell is equal to positive 1.10 volts. 00:02:45.920 --> 00:02:47.220 Next, let's think about n, 00:02:47.220 --> 00:02:50.900 the number of electrons transferred in the redox reaction. 00:02:50.900 --> 00:02:53.060 So, looking at our equation here 00:02:53.060 --> 00:02:55.010 is a solid zinc going to zinc two plus, 00:02:55.010 --> 00:02:56.320 is a loss of two electrons, 00:02:56.320 --> 00:02:58.720 and copper two plus going to solid copper 00:02:58.720 --> 00:03:00.450 is a gain of two electrons. 00:03:00.450 --> 00:03:05.060 So, two electrons were transferred and n is equal to two. 00:03:05.060 --> 00:03:09.310 So, I've gone ahead and made n equal to two in our equation. 00:03:09.310 --> 00:03:12.400 Next, we need to think about the reaction quotient Q. 00:03:12.400 --> 00:03:13.660 Q has the same form 00:03:13.660 --> 00:03:16.290 as the equilibrium constant expression. 00:03:16.290 --> 00:03:19.070 So, if we think about the balanced equation, 00:03:19.070 --> 00:03:21.460 remember, pure solids are left out 00:03:21.460 --> 00:03:24.070 of equilibrium constant expressions. 00:03:24.070 --> 00:03:26.530 So, it would be the concentration of products 00:03:26.530 --> 00:03:29.050 over the concentration of reactants. 00:03:29.050 --> 00:03:31.890 And therefore, Q is equal to the concentration 00:03:31.890 --> 00:03:35.610 of zinc two plus ions, divided by the concentration 00:03:35.610 --> 00:03:37.990 of copper two plus ions. 00:03:37.990 --> 00:03:39.610 Because our goal is to find 00:03:39.610 --> 00:03:41.720 the instantaneous cell potential 00:03:41.720 --> 00:03:44.830 when the concentrations are both equal to one Mueller, 00:03:44.830 --> 00:03:47.560 Q is equal to one divided by one. 00:03:47.560 --> 00:03:49.600 So, Q is equal to one. 00:03:49.600 --> 00:03:53.010 And the log of one is equal to zero. 00:03:53.010 --> 00:03:55.710 Therefore this entire second term 00:03:55.710 --> 00:03:59.080 in the Nernst equation is equal to zero, 00:03:59.080 --> 00:04:01.590 which means the instantaneous cell potential 00:04:01.590 --> 00:04:04.930 is equal to the standard cell potential. 00:04:04.930 --> 00:04:07.230 So, the instantaneous cell potential 00:04:07.230 --> 00:04:12.230 is equal to positive 1.10 volts. 00:04:12.390 --> 00:04:14.170 And this answer makes a lot of sense 00:04:14.170 --> 00:04:18.240 because standard state for solutions 00:04:18.240 --> 00:04:20.670 is a one Mueller concentration. 00:04:20.670 --> 00:04:23.160 Therefore, the instantaneous cell potential 00:04:23.160 --> 00:04:25.840 is equal to the standard cell potential 00:04:25.840 --> 00:04:27.393 at this moment in time. 00:04:28.330 --> 00:04:31.400 Next, let's think about the instantaneous cell potential 00:04:31.400 --> 00:04:34.130 when the concentration of copper two plus ions 00:04:34.130 --> 00:04:36.030 is equal to 10.0 Mueller 00:04:36.030 --> 00:04:38.340 and the concentration of zinc two plus ions 00:04:38.340 --> 00:04:40.890 is equal to 1.0 Mueller. 00:04:40.890 --> 00:04:43.880 The standard cell potential at 25 degrees Celsius 00:04:43.880 --> 00:04:47.540 is still equal to positive 1.10 volts 00:04:47.540 --> 00:04:49.770 and n is still equal to two. 00:04:49.770 --> 00:04:52.370 So, we need to think about the reaction quotient Q 00:04:52.370 --> 00:04:54.250 at this moment in time. 00:04:54.250 --> 00:04:56.280 The concentration of zinc two plus ions 00:04:56.280 --> 00:04:59.100 is equal to 1.0 Mueller so we plug that in 00:04:59.100 --> 00:05:01.230 and the concentration of copper two plus ions 00:05:01.230 --> 00:05:03.610 is equal to 10.0 Mueller. 00:05:03.610 --> 00:05:08.610 So, at this moment in time, Q is less than one. 00:05:09.140 --> 00:05:13.450 The log of a number less than one is negative. 00:05:13.450 --> 00:05:15.807 Therefore, this second term would be negative 00:05:15.807 --> 00:05:19.490 or less than zero. 00:05:19.490 --> 00:05:22.810 And since we are subtracting a negative number, 00:05:22.810 --> 00:05:25.210 we would actually be adding that value 00:05:25.210 --> 00:05:28.140 to the standard cell potential, 00:05:28.140 --> 00:05:30.870 which means that the instantaneous cell potential 00:05:30.870 --> 00:05:34.290 will be greater than the standard cell potential. 00:05:34.290 --> 00:05:36.060 And if you went ahead and calculated 00:05:36.060 --> 00:05:39.070 the instantaneous cell potential with the Nernst equation, 00:05:39.070 --> 00:05:42.730 you would find it's equal to positive 1.13 volts, 00:05:42.730 --> 00:05:47.200 which is greater than positive 1.10 volts. 00:05:47.200 --> 00:05:49.890 Next, let's think about the instantaneous cell potential 00:05:49.890 --> 00:05:52.300 when the concentration of copper two plus ions 00:05:52.300 --> 00:05:55.280 is equal to 1.0 Mueller and the concentration 00:05:55.280 --> 00:05:58.810 of zinc two plus ions is equal to 10.0 Mueller. 00:05:58.810 --> 00:06:00.040 Going to the Nernst equation, 00:06:00.040 --> 00:06:03.840 the standard cell potential is still positive 1.10 volts 00:06:03.840 --> 00:06:06.300 and n is still equal to two. 00:06:06.300 --> 00:06:09.450 So next, we think about the reaction quotient Q. 00:06:09.450 --> 00:06:10.610 At this moment in time, 00:06:10.610 --> 00:06:12.850 the concentration of zinc two plus ions 00:06:12.850 --> 00:06:14.700 is equal to 10.0 Mueller 00:06:14.700 --> 00:06:17.050 and the concentration of copper two plus ions 00:06:17.050 --> 00:06:19.270 is equal to 1.0 Mueller. 00:06:19.270 --> 00:06:24.250 So, at this moment in time, Q is greater than one. 00:06:24.250 --> 00:06:28.260 The log of a number greater than one is positive. 00:06:28.260 --> 00:06:30.680 Therefore the second term in our equation 00:06:30.680 --> 00:06:34.920 will be positive or greater than zero. 00:06:34.920 --> 00:06:38.460 And because we are subtracting a positive number, 00:06:38.460 --> 00:06:40.790 we would be subtracting a value 00:06:40.790 --> 00:06:43.330 from the standard cell potential, 00:06:43.330 --> 00:06:46.080 which means that the instantaneous cell potential 00:06:46.080 --> 00:06:49.580 will be less than the standard cell potential. 00:06:49.580 --> 00:06:51.860 And if you plug the numbers into the Nernst equation, 00:06:51.860 --> 00:06:54.840 you would find that the instantaneous cell potential 00:06:54.840 --> 00:06:58.330 is equal to positive 1.07 volts, 00:06:58.330 --> 00:07:03.330 which is less than the standard cell voltage of 1.10 volts. 00:07:03.480 --> 00:07:05.400 We just saw that at the moment in time 00:07:05.400 --> 00:07:07.500 when the concentration of copper two plus ions 00:07:07.500 --> 00:07:08.930 is equal to 1.0 Mueller 00:07:08.930 --> 00:07:11.000 and the concentration of zinc two plus ions 00:07:11.000 --> 00:07:12.910 is equal to 10.0 Mueller, 00:07:12.910 --> 00:07:14.940 the instantaneous cell potential 00:07:14.940 --> 00:07:18.220 is equal to positive 1.07 volts. 00:07:18.220 --> 00:07:20.850 Let's use this moment in time as a starting point 00:07:20.850 --> 00:07:22.410 and let's think about what happens 00:07:22.410 --> 00:07:24.810 to the instantaneous cell potential 00:07:24.810 --> 00:07:27.340 as the reaction progresses. 00:07:27.340 --> 00:07:31.090 Remember that the instantaneous cell potential is related 00:07:31.090 --> 00:07:32.660 to the instantaneous change 00:07:32.660 --> 00:07:35.760 in free energy, delta G, by this equation. 00:07:35.760 --> 00:07:39.420 Delta G is equal to negative nFE. 00:07:39.420 --> 00:07:41.140 Because we have a positive value 00:07:41.140 --> 00:07:43.110 for the instantaneous cell potential, 00:07:43.110 --> 00:07:45.930 if we plug in a positive value into our equation 00:07:45.930 --> 00:07:48.060 because of the negative sign in the equation, 00:07:48.060 --> 00:07:50.990 we would get a negative sign for delta G. 00:07:50.990 --> 00:07:52.570 And when delta G is negative, 00:07:52.570 --> 00:07:55.040 the reaction is thermodynamically favored, 00:07:55.040 --> 00:07:59.040 which means the reactants will turn into products. 00:07:59.040 --> 00:08:00.890 And as the reactions turn into products, 00:08:00.890 --> 00:08:04.240 the concentration of zinc two plus ions will increase 00:08:04.240 --> 00:08:08.380 and the concentration of copper two plus ions will decrease. 00:08:08.380 --> 00:08:12.040 And think about what that does to the reaction quotient Q. 00:08:12.040 --> 00:08:14.080 There would be an increase in the concentration 00:08:14.080 --> 00:08:17.380 of zinc two plus ions and a decrease in the concentration 00:08:17.380 --> 00:08:19.140 of copper two plus ions. 00:08:19.140 --> 00:08:23.690 So, Q would no longer be equal to 10.0 over 1.0. 00:08:23.690 --> 00:08:26.360 We would see an increase in Q 00:08:26.360 --> 00:08:29.400 as the reactants turn into the products. 00:08:29.400 --> 00:08:33.730 An increased value of Q means that the second term 00:08:33.730 --> 00:08:37.930 in the Nernst equation will be a larger, positive number. 00:08:37.930 --> 00:08:40.800 So, if we subtract a larger positive number 00:08:40.800 --> 00:08:42.650 than we did in the previous example 00:08:42.650 --> 00:08:44.800 from the standard cell potential, 00:08:44.800 --> 00:08:48.340 we would get a lower instantaneous cell potential 00:08:48.340 --> 00:08:51.520 than positive 1.07 volts. 00:08:51.520 --> 00:08:53.500 So, what the Nernst equation tells us 00:08:53.500 --> 00:08:57.460 is as the reaction goes to the right, 00:08:57.460 --> 00:09:01.150 there is an increase in Q and as Q increases, 00:09:01.150 --> 00:09:05.870 there's a decrease in the instantaneous cell potential. 00:09:05.870 --> 00:09:08.390 So, we've just seen as the reaction goes to the right, 00:09:08.390 --> 00:09:10.360 that's an increase in Q. 00:09:10.360 --> 00:09:11.850 And according to the Nernst equation, 00:09:11.850 --> 00:09:15.630 that's a decrease in the instantaneous cell potential. 00:09:15.630 --> 00:09:17.700 And therefore, the instantaneous cell potential 00:09:17.700 --> 00:09:20.530 would decrease from 1.07 volts. 00:09:20.530 --> 00:09:23.040 However, the voltage would still be positive, 00:09:23.040 --> 00:09:26.010 which means that delta G would still be negative, 00:09:26.010 --> 00:09:27.380 which means that the reaction 00:09:27.380 --> 00:09:29.810 is still thermodynamically favored. 00:09:29.810 --> 00:09:31.010 And so, this keeps happening. 00:09:31.010 --> 00:09:33.590 As the reaction goes to the right, Q keeps increasing 00:09:33.590 --> 00:09:37.040 and the instantaneous cell potential keeps decreasing. 00:09:37.040 --> 00:09:39.727 So, we had started out at positive 1.07 volts 00:09:39.727 --> 00:09:41.470 and we saw that that had decreased 00:09:41.470 --> 00:09:44.140 and it keeps on decreasing, keeps on decreasing. 00:09:44.140 --> 00:09:47.510 Eventually the instantaneous cell potential 00:09:47.510 --> 00:09:49.550 will go to zero volts. 00:09:49.550 --> 00:09:51.210 And when the voltage goes to zero, 00:09:51.210 --> 00:09:53.310 if you plug in zero into our equation, 00:09:53.310 --> 00:09:55.820 delta G is equal to zero. 00:09:55.820 --> 00:09:57.700 And when delta G is equal to zero, 00:09:57.700 --> 00:10:00.020 the reaction is at equilibrium. 00:10:00.020 --> 00:10:01.740 And the reaction quotient Q 00:10:01.740 --> 00:10:05.060 is equal to the equilibrium constant K. 00:10:05.060 --> 00:10:08.540 So, if you were to plug in the equilibrium constant K 00:10:08.540 --> 00:10:09.500 in for Q, 00:10:09.500 --> 00:10:12.710 you would find that this entire second term 00:10:12.710 --> 00:10:15.610 would be equal to positive 1.10 volts 00:10:15.610 --> 00:10:18.370 and cancel out the standard cell potential, 00:10:18.370 --> 00:10:22.350 giving an instantaneous potential of zero volts. 00:10:22.350 --> 00:10:25.930 So, if we think about our zinc copper cell as a battery, 00:10:25.930 --> 00:10:28.090 when the reaction reaches equilibrium, 00:10:28.090 --> 00:10:32.750 the voltage is equal to zero and the battery is dead. 00:10:32.750 --> 00:10:34.780 Let's do a quick summary of what we've learned 00:10:34.780 --> 00:10:36.090 from the Nernst equation. 00:10:36.090 --> 00:10:37.780 So, this is the simplified form, 00:10:37.780 --> 00:10:41.430 which is valid at 25 degrees Celsius. 00:10:41.430 --> 00:10:42.910 When Q is equal to one, 00:10:42.910 --> 00:10:45.430 the instantaneous cell potential 00:10:45.430 --> 00:10:48.480 is equal to the standard cell potential. 00:10:48.480 --> 00:10:50.040 When Q is greater than one, 00:10:50.040 --> 00:10:51.940 the instantaneous cell potential 00:10:51.940 --> 00:10:54.760 is less than the standard cell potential. 00:10:54.760 --> 00:10:56.200 When Q is less than one, 00:10:56.200 --> 00:10:57.820 the instantaneous cell potential 00:10:57.820 --> 00:11:00.700 is greater than the standard cell potential. 00:11:00.700 --> 00:11:03.980 And when Q is equal to the equilibrium constant K, 00:11:03.980 --> 00:11:07.990 the instantaneous cell potential is equal to zero volts. 00:11:07.990 --> 00:11:12.290 When Q is equal to K and the potential is equal to zero, 00:11:12.290 --> 00:11:14.680 the reaction is at equilibrium. 00:11:14.680 --> 00:11:16.850 However, for these first three situations, 00:11:16.850 --> 00:11:20.260 Q is not equal to K and the instantaneous cell voltage 00:11:20.260 --> 00:11:21.940 is not equal to zero. 00:11:21.940 --> 00:11:25.683 Therefore, the reaction is not at equilibrium.

Standard potential, free energy, and the equilibrium constant

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WEBVTT Kind: captions Language: en 00:00:00.480 --> 00:00:02.330 - [Instructor] For a generic redox reaction 00:00:02.330 --> 00:00:05.440 where the reactants turn into the products, 00:00:05.440 --> 00:00:09.550 the free energy is related to the potential 00:00:09.550 --> 00:00:11.580 for the redox reaction. 00:00:11.580 --> 00:00:13.520 The equation that relates free energy 00:00:13.520 --> 00:00:16.940 and potential is given by delta G is equal 00:00:16.940 --> 00:00:19.770 to negative nFE. 00:00:19.770 --> 00:00:23.850 Delta G is the instantaneous difference in free energy 00:00:23.850 --> 00:00:26.500 between the reactants and the products 00:00:26.500 --> 00:00:29.290 and refers to the number of electrons 00:00:29.290 --> 00:00:32.490 that are transferred in the redox reaction. 00:00:32.490 --> 00:00:34.860 F is Faraday's constant, 00:00:34.860 --> 00:00:39.500 which tells us the charge carried by one mole of electrons. 00:00:39.500 --> 00:00:44.500 So one mole of electrons carries 96,485 coulombs. 00:00:44.850 --> 00:00:48.570 E refers to the potential of the redox reaction. 00:00:48.570 --> 00:00:52.180 You could also call this the voltage of the redox reaction. 00:00:52.180 --> 00:00:54.190 If the reactants and products are both 00:00:54.190 --> 00:00:55.620 in their standard states, 00:00:55.620 --> 00:00:58.790 we can add the superscript naught to delta G 00:00:58.790 --> 00:01:01.580 and the superscript naught to E. 00:01:01.580 --> 00:01:04.980 So we can use this equation to calculate delta G naught 00:01:04.980 --> 00:01:07.560 from E naught or vice versa. 00:01:07.560 --> 00:01:10.920 We could calculate E naught from delta G naught. 00:01:10.920 --> 00:01:13.490 And remember that delta G naught is connected 00:01:13.490 --> 00:01:17.740 to the equilibrium constant K by this equation. 00:01:17.740 --> 00:01:22.420 Delta G naught is equal to negative RT natural log of K, 00:01:22.420 --> 00:01:26.930 where R is the ideal gas constant and T is the temperature. 00:01:26.930 --> 00:01:28.780 And because delta G naught is a part 00:01:28.780 --> 00:01:30.720 of both of these two equations, 00:01:30.720 --> 00:01:35.440 these two equations connect the standard potential E naught 00:01:35.440 --> 00:01:39.420 to the standard change in free energy delta G naught, 00:01:39.420 --> 00:01:43.280 which is then connected to the equilibrium constant K. 00:01:43.280 --> 00:01:45.940 So let's look at an example of a redox reaction 00:01:45.940 --> 00:01:49.210 where we know the value for the standard potential E naught, 00:01:49.210 --> 00:01:52.430 and first we're gonna calculate delta G naught. 00:01:52.430 --> 00:01:53.900 And then from delta G naught, 00:01:53.900 --> 00:01:57.520 we're gonna calculate the equilibrium constant K. 00:01:57.520 --> 00:01:59.200 So here's our redox reaction, 00:01:59.200 --> 00:02:01.380 and we're gonna calculate delta G naught 00:02:01.380 --> 00:02:05.060 at 25 degrees Celsius from E naught. 00:02:05.060 --> 00:02:07.400 So for this redox reaction, 00:02:07.400 --> 00:02:11.330 E naught is equal to positive 1.54 volts, 00:02:11.330 --> 00:02:14.200 and our goal is to calculate delta G naught 00:02:14.200 --> 00:02:16.560 at 25 degrees Celsius. 00:02:16.560 --> 00:02:18.390 In our redox reaction, 00:02:18.390 --> 00:02:22.520 silver one plus is being reduced to solid silver, 00:02:22.520 --> 00:02:25.280 and solid chromium is being oxidized 00:02:25.280 --> 00:02:27.290 to chromium three plus. 00:02:27.290 --> 00:02:29.650 Now that we've identified what's being oxidized 00:02:29.650 --> 00:02:31.290 and what's being reduced, 00:02:31.290 --> 00:02:35.500 let's write the oxidation and reduction half reactions. 00:02:35.500 --> 00:02:37.980 So for our reduction half reaction, 00:02:37.980 --> 00:02:40.840 we have silver one plus gaining an electron 00:02:40.840 --> 00:02:42.530 to form solid silver. 00:02:42.530 --> 00:02:45.270 And for the oxidation half reaction, 00:02:45.270 --> 00:02:48.530 solid chromium is turning into chromium three plus 00:02:48.530 --> 00:02:50.940 and losing three electrons. 00:02:50.940 --> 00:02:52.070 Next, we need to figure out 00:02:52.070 --> 00:02:54.410 how many electrons are being transferred 00:02:54.410 --> 00:02:56.400 in our redox reaction. 00:02:56.400 --> 00:02:58.090 In the reduction half reaction, 00:02:58.090 --> 00:03:01.180 the silver one plus cation is gaining an electron, 00:03:01.180 --> 00:03:03.730 but in the oxidation half reaction, 00:03:03.730 --> 00:03:06.960 solid chromium is losing three electrons. 00:03:06.960 --> 00:03:09.730 And we need to make the number of electrons equal. 00:03:09.730 --> 00:03:13.130 Therefore, we need to multiply the first half reaction 00:03:13.130 --> 00:03:16.060 through by a factor of three. 00:03:16.060 --> 00:03:19.460 So now when we add together our reactants, 00:03:19.460 --> 00:03:21.230 so all the reactants on one side 00:03:21.230 --> 00:03:24.000 and all the products on the other side, 00:03:24.000 --> 00:03:26.200 the three electrons cancel out 00:03:26.200 --> 00:03:29.440 and give us our overall redox reaction. 00:03:29.440 --> 00:03:31.210 Because three electrons, 00:03:31.210 --> 00:03:33.530 three moles of electrons were being transferred 00:03:33.530 --> 00:03:38.530 in our redox reaction, n is equal to three. 00:03:39.440 --> 00:03:41.360 And since we know that n is equal to three 00:03:41.360 --> 00:03:46.010 and the standard potential is equal to +1.54 volts, 00:03:46.010 --> 00:03:47.790 we're ready to plug into our equation 00:03:47.790 --> 00:03:50.010 to calculate delta G naught. 00:03:50.010 --> 00:03:53.040 So I went ahead and rewrote our redox reaction, 00:03:53.040 --> 00:03:56.280 and our goal is to calculate delta G naught. 00:03:56.280 --> 00:03:57.830 We already know what n is, 00:03:57.830 --> 00:03:59.530 we already know what E naught is, 00:03:59.530 --> 00:04:02.070 and F is Faraday's constant. 00:04:02.070 --> 00:04:05.080 Here's our equation with everything plugged in. 00:04:05.080 --> 00:04:06.470 N is equal to three. 00:04:06.470 --> 00:04:09.320 There were three moles of electrons transferred 00:04:09.320 --> 00:04:12.920 in our redox reaction per mole of reaction. 00:04:12.920 --> 00:04:14.430 F is Faraday's constant, 00:04:14.430 --> 00:04:19.420 which is 96,485 coulombs per mole of electrons. 00:04:19.420 --> 00:04:23.480 And the standard voltage was equal to 1.54 volts. 00:04:23.480 --> 00:04:26.700 One volt is equal to one joule per coulomb, 00:04:26.700 --> 00:04:28.270 so I went ahead and changed the units 00:04:28.270 --> 00:04:31.530 from volts to joules per coulomb. 00:04:31.530 --> 00:04:33.800 Next, we can cancel out some units. 00:04:33.800 --> 00:04:37.140 So moles of electrons will cancel out, 00:04:37.140 --> 00:04:39.610 and coulombs will cancel out, 00:04:39.610 --> 00:04:43.000 and that gives us joules per mole of reaction. 00:04:43.000 --> 00:04:44.030 And after we do the math, 00:04:44.030 --> 00:04:47.170 we find that delta G naught at 25 degrees Celsius 00:04:47.170 --> 00:04:49.210 for this redox reaction is equal 00:04:49.210 --> 00:04:53.360 to -4.46 times 10 to the 5th joules 00:04:53.360 --> 00:04:55.130 per mole of reaction. 00:04:55.130 --> 00:04:56.100 We could also write this 00:04:56.100 --> 00:04:58.770 in terms of kilojoules per mole of reaction. 00:04:58.770 --> 00:05:00.040 So delta G naught is equal 00:05:00.040 --> 00:05:04.800 to -446 kilojoules per mole of reaction. 00:05:04.800 --> 00:05:07.150 Notice that a positive voltage 00:05:07.150 --> 00:05:10.250 and the negative in the equation means 00:05:10.250 --> 00:05:13.750 that we get a negative sign in the final answer. 00:05:13.750 --> 00:05:15.990 And when delta G naught is negative, 00:05:15.990 --> 00:05:19.300 the reaction is thermodynamically favored, 00:05:19.300 --> 00:05:22.070 which means at 25 degrees Celsius, 00:05:22.070 --> 00:05:24.950 silver cations will react with solid chromium 00:05:24.950 --> 00:05:29.210 to form solid silver and chromium three plus ions. 00:05:29.210 --> 00:05:31.330 And what this example shows us is 00:05:31.330 --> 00:05:33.360 whenever the voltage is positive, 00:05:33.360 --> 00:05:36.540 that means a thermodynamically favored reaction 00:05:36.540 --> 00:05:40.300 because delta G naught will be negative. 00:05:40.300 --> 00:05:43.030 Now that we've calculated delta G naught for our reaction, 00:05:43.030 --> 00:05:45.650 let's calculate the equilibrium constant K 00:05:45.650 --> 00:05:47.940 at 25 degrees Celsius. 00:05:47.940 --> 00:05:50.500 So we need to plug in our value for delta G naught, 00:05:50.500 --> 00:05:54.160 the ideal gas constant, the temperature in Kelvin, 00:05:54.160 --> 00:05:57.640 and we'll solve for the equilibrium constant. 00:05:57.640 --> 00:06:00.450 I've gone ahead and plugged everything into our equation. 00:06:00.450 --> 00:06:02.480 So here's the value for delta G naught 00:06:02.480 --> 00:06:04.960 in joules per mole of reaction. 00:06:04.960 --> 00:06:08.560 The ideal gas constant is equal to 8.314 joules 00:06:08.560 --> 00:06:10.700 per Kelvin mole of reaction. 00:06:10.700 --> 00:06:14.390 And 25 degrees Celsius, if we add 273 to that, 00:06:14.390 --> 00:06:17.360 we get 298 Kelvin. 00:06:17.360 --> 00:06:20.500 Looking at the units, Kelvin cancels out 00:06:20.500 --> 00:06:24.630 and so does joules per mole of reaction. 00:06:24.630 --> 00:06:25.970 And solving for K, 00:06:25.970 --> 00:06:29.270 the equilibrium constant is approximately equal 00:06:29.270 --> 00:06:32.060 to 10 to the 78th power. 00:06:32.060 --> 00:06:35.480 And since K is such an extremely large number, 00:06:35.480 --> 00:06:38.780 that tells us the reaction essentially goes to completion, 00:06:38.780 --> 00:06:42.020 and all the reactants turn into products. 00:06:42.020 --> 00:06:43.560 So for a reaction like this, 00:06:43.560 --> 00:06:47.410 it's not necessary to have equilibrium arrows in here. 00:06:47.410 --> 00:06:50.970 We can just draw an arrow going to the right. 00:06:50.970 --> 00:06:54.730 And remember, we started with a positive standard potential 00:06:54.730 --> 00:06:56.710 for this redox reaction. 00:06:56.710 --> 00:06:59.510 So to summarize what we've seen with these calculations, 00:06:59.510 --> 00:07:02.360 a positive value for the standard potential leads 00:07:02.360 --> 00:07:05.000 to a negative value for delta G naught, 00:07:05.000 --> 00:07:08.350 so a thermodynamically favored redox reaction. 00:07:08.350 --> 00:07:10.980 And a negative value for delta G naught leads 00:07:10.980 --> 00:07:15.010 to an equilibrium constant K that is greater than one. 00:07:15.010 --> 00:07:17.680 We've just seen what happens to delta G naught 00:07:17.680 --> 00:07:20.060 and the equilibrium constant K 00:07:20.060 --> 00:07:23.270 when the standard potential is positive 00:07:23.270 --> 00:07:24.950 or greater than zero. 00:07:24.950 --> 00:07:28.030 Now let's think about a generic redox reaction 00:07:28.030 --> 00:07:31.010 where the standard potential is negative, 00:07:31.010 --> 00:07:33.660 so E naught is less than zero. 00:07:33.660 --> 00:07:36.230 So let's think about the sign for delta G naught 00:07:36.230 --> 00:07:40.760 if we plug in a negative value for the standard potential. 00:07:40.760 --> 00:07:42.770 So if we have a negative voltage, 00:07:42.770 --> 00:07:45.890 the two negative signs in the equation 00:07:45.890 --> 00:07:49.330 will give us a positive value for delta G naught. 00:07:49.330 --> 00:07:52.060 A positive value for delta G naught means 00:07:52.060 --> 00:07:54.246 that the forward reaction 00:07:54.246 --> 00:07:56.560 of reactants turning into products 00:07:56.560 --> 00:08:00.620 is a thermodynamically unfavorable reaction. 00:08:00.620 --> 00:08:03.030 And if we were to plug in a positive value 00:08:03.030 --> 00:08:04.600 for delta G naught, 00:08:04.600 --> 00:08:07.300 we would find that the equilibrium constant K 00:08:07.300 --> 00:08:09.580 would be less than one. 00:08:09.580 --> 00:08:11.200 And when K is less than one, 00:08:11.200 --> 00:08:15.000 that tells us whenever the reaction reaches equilibrium, 00:08:15.000 --> 00:08:19.220 there will be a lot more reactants than products. 00:08:19.220 --> 00:08:20.640 Let's look at a quick summary 00:08:20.640 --> 00:08:22.940 of what we've learned from these examples. 00:08:22.940 --> 00:08:24.600 The standard potential E naught 00:08:24.600 --> 00:08:27.440 and the standard change in free energy delta G naught 00:08:27.440 --> 00:08:30.040 are related by the equation on the left. 00:08:30.040 --> 00:08:31.330 And delta G naught 00:08:31.330 --> 00:08:34.160 and the equilibrium constant K are related 00:08:34.160 --> 00:08:36.340 by the equation on the right. 00:08:36.340 --> 00:08:38.000 When E naught is greater than zero, 00:08:38.000 --> 00:08:40.160 delta G naught is less than zero, 00:08:40.160 --> 00:08:43.280 and the reaction is thermodynamically favored, 00:08:43.280 --> 00:08:45.320 which means at equilibrium, 00:08:45.320 --> 00:08:47.270 there'll be more products than reactants, 00:08:47.270 --> 00:08:50.950 and the equilibrium constant K will be greater than one. 00:08:50.950 --> 00:08:53.310 However, when E naught is less than zero, 00:08:53.310 --> 00:08:55.680 delta G naught is greater than zero, 00:08:55.680 --> 00:08:58.970 and the reaction is thermodynamically unfavored, 00:08:58.970 --> 00:09:00.830 which means at equilibrium, 00:09:00.830 --> 00:09:03.140 there'll be more reactants than products, 00:09:03.140 --> 00:09:06.733 and the equilibrium constant K will be less than one.