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In this relative frequency activity, students first read the information about how to calculate probability using a formula. Students solve 24 problems. This page is intended for online use but may be completed on paper. 10 Views 13 Downloads Describing a Distribution Displayed in a Histogram The shape of the histogram is also relative. Learners calculate relative frequencies from frequency tables and create relative frequency histograms. The scholars compare the histograms made from frequencies to those made from relative... 6th Math CCSS: Designed The Difference Between Theoretical Probabilities and Estimated Probabilities Flip a coin to determine whether the probability of heads is one-half. Pupils use simulated data to find the experimental probability of flipping a coin. Participants compare the long run relative frequency with the known theoretical... 7th Math CCSS: Designed Predict the Frequency of an Event Using Results from Experiments Taking surveys is a fun way to gather data from a group and predict results for the whole population. First, review fractions and percents and how to multiply them together. This will be useful later in the video. The video introduces a... 4 mins 6th - 8th Math CCSS: Designed Get on your Mark, Get Set, Go! Collect, Interpret, and Represent Data Using a Bar Graph and a Circle Graph Start an engaging data analysis study with a review of charts and graphs using the linked interactive presentation, which is both hilarious and comprehensive. There are 27 statistics-related vocabulary terms you can use in a word sort.... 4th - 7th Math CCSS: Designed

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Students will learn about the historical background and context of Samba music, they will try a selection of instruments typical to a Samba band set-up and will then specialise on one instrument learning and performing a piece as a whole class, following the necessary signals and breaks characteristic of Samba music. This unit also introduces musical terminology such as: batacuda, mestre, various instrument names, groove, break, polyrhythm, unison, syncopation By the end of this unit it is expected that all students will: be able to perform a simple rhythm within the batucada. Students will also have an understanding of good rehearsal practice and basic manners for social music making, specifically respecting equipment. Most students will: be able to perform a more complex rhythm in the batucada, following all signals given. Students will perform confidently and with accuracy. Some learners will have progressed further and will: be able to perform a more complex rhythm in the batucada, take a leading role in the group. Students will perform with confidence and accuracy. How to help your child Encourage students to join extra-curricular groups and encourage students to listen to other forms of music, especially world music, via the internet, radio, etc. Practice at home if students have access to a suitable instrument.

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Students practice vocabulary by playing a game of tag. they partner up for the tag game. When one partner is tagged he or she must write a definition of a vocabulary word from a list of ten then use it in an appropriate sentence. 3 Views 0 Downloads Wishes, Dreams and Goals: Lesson 7 Sixth graders explore language arts by completing a worksheet. In this parts of speech lesson, 6th graders read chapters from The Wish Giver and identify pronouns used within the story. Students complete a word detective worksheet based... 6th English Language Arts

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A visual and auditory demonstration of shifted frequencies What the activity is for Here you can listen to the Doppler effect as the relative velocity between you and a moving object is varied. For this you need a simple piece of apparatus, and a Doppler ball is recommended. There are two ways in which the Doppler effect is important: - The source can be moving towards or away from you. - The source can be spinning, so effectively moving. What to prepare - a Doppler ball - sound processing software To make the Doppler ball take an old tennis ball and cut it in half. Now make a small square hole, to take a slide switch, in one of the halves (a slide switch is recommended because it is more robust). In the middle of one half make a small circular hole, perhaps with a cork borer. Mount a buzzer up against this hole. Now wire up a 9 volt battery to the buzzer and to the slide switch. Pack the ball with foam and stick the two halves together again. Check that operating the slide switch turns the buzzer on and off. We'd recommend that you consider two variations to improve this basic set up. One is to use a larger diameter ball, for the spinning experiment. Mount the buzzer on the equator. Larger is not necessarily better – choose one that you can spin relatively rapidly. A second is to use a throw toy (shaped much like a rugby football, with fins to prevent tumbling when thrown) to prevent the ball rotating, when thrown. Mount the buzzer on the nose, but do remember to allow for its impact to be cushioned. The tennis ball is relatively soft, but obviously should not be thrown directly at students. What happens during this activity You need to practice. You should aim to throw the ball without it spinning. And you should be able to spin the ball on the table so that the buzzer spins round and round the axis of rotation (so along an equator). Start by exploring expectations as the ball moves towards or away from the students – just along a line. Draw on their everyday experience in order to generate predictions. The change in pitch at quite reasonable speeds will be noticeable, but do make sure that the ball does not spin as you throw it. This demonstration will provide a clear experience of the Doppler effect. More subtly, you can link measurements of Doppler spreading to a tabletop experiment. Here the ball is spun. So sometimes the source is travelling towards the students and sometimes it is travelling away from them. Therefore sometimes the pitch will be higher than if the ball was not spinning and sometimes it will be lower. So the emitted frequency is spread into a small range of frequencies as a result of the rotation. That is Doppler spreading. The faster the ball spins, the wider the range of frequencies. It is this that is used to measure the rate of rotation of distant astronomical objects. You might like to use a microphone and sound processing software, showing frequencies, as the ball spins. It's much harder to make such measurements with the ball moving in a straight line, unless you're very skilful.

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When, where, and how life first appeared are among science's biggest questions. A new model attributes life's formation to bombardment by meteorites. It also suggests there was only a short period during which life could have begun. Natural selection provides a powerful force for life to grow and develop, but getting started required the bringing together of nucleobases to form what became RNA. The most popular suggestions for the location of this event are hydrothermal vents at the bottom of the ocean and what Darwin called a warm little pond (WLP). A nuclear reactor has recently been proposed as well, but it is yet to be properly reviewed. According to McMaster University graduate student Ben Pearce, WLPs have several advantages: “Their wet and dry cycles have been shown to promote the polymerization of nucleotides into chains possibly greater than 300 links,” Pearce writes in Proceedings of the National Academy of Sciences. “Furthermore, clay minerals in the walls and bases of WLPs promote the linking of chains up to 55 nucleotides long.” Attempts to replicate the conditions around hydrothermal vents have produced RNA chains too short to be likely starter kits for life. However, WLPs still need nucleobases to join together in the first place, and the atmosphere back then is not thought to have been something well-suited to their formation. Moreover, three sorts of nucleobases have been found in meteorites. How likely then was it that nucleobases could reach Earth aboard a meteorite, survive passage through the atmosphere, and splashdown in a suitable pond where wet-dry cycles could cause them to join together to become life's first RNA? We know the early Earth was peppered by meteorites, although the record of the exact rate has been lost to erosion and geologic forces. Pearce and his co-authors use the rate of cratering on the Moon to calculate the number of impacts the Earth experienced in its first few hundred million years and factored in that only carbonaceous meteorites are likely to be suitable carriers. In addition, only a few of those traveled slowly enough to not burn up in the atmosphere. These estimates were compared with likely numbers of lakes and ponds on the Earth's very limited continental crust at the time. The authors conclude that prior to 4.17 billion years ago, there were sufficient cases of suitable meteorites touching down in WLPs to make seeding credible. RNA formation needed to occur before the nucleobases seeped out of the pond, which required temperatures of 50-80ºC (122-176ºF), but that is considered likely at the time. The paper concludes that life could have begun within just a few cycles of rainfall and drought after a meteorite strike, particularly if sedimentation protected the nucleobases from UV radiation.

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- Practice using fractions in a variety of ways. - Practice understanding of fractions by using math manipulatives. - Practice basic words or phrases by giving students a problem and a list of relevant terms, e.g., "numerator," "denominator," - Practice fractions by having students observe their surroundings, e.g., what fraction of classmates have black hair, have brown eyes. - Practice pointing out the importance of fractions in the world around them and in successful careers. - Practice fraction problems by having students write their own fractions based on their own experiences. - Practice fraction problems by having students work in small groups to create their own surveys around fractions based on classmates' preferences

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Although the origins of life remains elusive, researchers are beginning to stumble across evidence to suggest that organic material, created in space, may have been transported to Earth through the impact of comets and meteors. With the need to examine these meteorites in finer detail, scientists at NASA now believe they have developed technology capable of analyzing the individual components of the most infinitesimal of sample sizes, from collected space dust. On previous occasion, researchers have identified constituents of genetic material, alongside individual amino acids, hidden away inside carbonaceous chondrites (a.k.a. carbon-rich meteorites). Amino acids are the subunits required to make larger protein macromolecules – including those used to make hair and nails – and cellular structures that can regulate and catalyze chemical reactions. Meanwhile, DNA is required for carrying instructions on the development and function of living organisms. Aside from amino acids and constituents of DNA, other biologically critical “building blocks” have been discovered inside meteorite samples, including sugar-related compounds and nitrogen heterocycles. Carbonaceous chondrites are, nonetheless, relatively infrequent and only make up a twentieth of all retrieved meteorites. The afore-mentioned building blocks are also found at extremely low concentrations – in the parts-per-million or -billion range. However, with Earth receiving a consistent supply of dust particulate from comets and asteroids, the planet is subject to a steady supply of extraterrestrial organic material. This is something that Michael Callahan, based at NASA’s Goddard Space Flight Center, reflected upon in a recent press release. Callahan explains that, regardless of their tiny size, interplanetary space dust can actually deliver relatively high quantities of organic material, but, thus far, few studies have been performed into their organic composition; Callahan indicates that researchers have been unable to effectively analyze collected specimens of space particulate for “biologically relevant molecules,” due to an absence of technology capable of analyzing the miniscule samples. In light of this, Callahan and his research group at Goddard’s Astrobiology Analytical Laboratory have devised an advanced technique to inspect a sample, weighing just 360 micrograms, from the Murchison meteorite. The Murchison meteorite was witnessed falling from the skies as a bright fireball, close to the town of Murchison in Victoria, Australia. The carbonaceous chondrite split up into several fragments, which were scattered over the region; all in all, a total sample size of 100 kilograms was acquired. When the meteorite was initially inspected, researchers established that it housed around 15 amino acids, including a mixture of left- and right-handed subunits (i.e. a racemic mixture), leading scientists to believe that the amino acids were not terrestrial in nature. Callahan recently explained that their advanced analytical techniques were able to explore sample sizes that were 1,000 times smaller than conventionally required. To put the sample size the group used into perspective, 360 micrograms equates to the weight of a few eyebrow hairs. Incredibly, using a technique called nanoflow liquid chromatography, the team were able to use small sample sizes to reproduce the same results that other research groups had obtained in the past, when using much larger samples. Nanoflow liquid chromatography was used to separate the sample molecules, which were then given an electric charge through nanoelectrospray ionization. The charged molecules were then transported to a high-resolution mass spectrometer, which identified the molecules based upon their mass. Explaining the potential applications for the highly sensitive instrument, Callahan indicates that it could prove critical to analyzing micrometeorites, cometary particles and interplanetary dust particulate. Coauthor of the latest research paper Daniel Glavin also discussed the implications of their advanced analytical tool: “This technology will also be extremely useful to search for amino acids and other potential chemical biosignatures in samples returned from Mars and eventually plume materials from the outer planet icy moons Enceladus and Europa.” Ultimately, the team believe that their space dust analysis techniques could be applied to future sample-return missions, based on the limited sample sizes that are collected. Callahan considers that their work could pave the way for routinely “… targeting biologically relevant samples,” where traditional methods usually looked at inorganic or elemental composition. By James Fenner Top Image Credit: Michael Callahan

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Week 2: February 12 – 14 th Resonance and Electron Pushing What is it? Resonance is a theory proposed by Linus Pauling to accurately depict molecules that could not be drawn with a single Lewis structure. For example, consider the following acetate ion (chemical formula C H 2 3: 2- Which one is correct? Chemical testing shows these bonds are shorter than single bonds but long than double bonds; also, both oxygens have a slight negative charge. So, how does one know which oxygen be drawn with negative charge and which should have the lone pair? The answer, of course, lies in resonance structures. Resonance structures are a combination of different Lewis Structures that contribute to make a real hybrid molecule. In other words, two or more ‘fake’ Lewis Structures combine to make the ‘real’ picture. Don’t be fooled by the method of drawing resonance structures and multiple different figures: resonance structures DO NOT actually exist! My chemistry teacher in high school described resonance as such: You want to show someone a unicorn. But you can’t find a unicorn. So instead you show them a horse and a rhinoceros and tell them a unicorn is a mixture of both. Other people like the 2 colors of paint mixing to make a new color metaphor; I’m personally fond of the unicorn. How to draw Resonance Structures The following list of rules describes a good checklist you can go through for each resonance structure to make sure it is correct. With practice these rules will become 1. Connectivity of the atoms does not change. Resonance is the sharing of electrons in π orbitals (double bonds) and p orbitals (lone pairs). Never break sigma (single) bonds! 2. All contributing structures have the same number of valence electrons. 3. Obey the rules of covalent bonding. No Texas Carbons! Priority Rules

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The Fifteenth Amendment Back in the day on March 30th, 1870 the 15th amendment was added to the constitution of the United States. Coming in the post-Civil War era, the last of the “reconstruction amendments” attempted to federalize enfranchisement for black males. Three versions of the 15th amendment were debated in Congress before final ratification. The agreed upon version was moderate as it simply prohibited states from denying the vote on the basis of race, color or having been enslaved previously. Radical Republicans in Congress had foreseen the coming of Jim Crow in advocating for a version that went further in terms of prohibiting states from imposing property, literacy or birth restrictions on the vote. Of course, since that version was not accepted, the South was able to effectively thwart the 15th amendment by turning to infamous mechanisms such as violence, poll taxes, literacy tests and grandfather clauses. It would be nearly a century later, when an emergent Civil Rights Movement demanded that the Voting Rights Act be legislated so that the 15th Amendment could be fully and effectively be implemented.

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This Study Jams! + & - Without Regrouping lesson plan also includes: - Answer Key - Join to access all included materials Addition and subtraction are essential skills for all young mathematicians. Explain the step-by-step process with respect to place value using these real-world examples. Focus is on numbers in the tens, hundreds, and thousands, making this appropriate for second and third grade classes. Included assessment challenges learners with word problems involving a variety of contexts for addition and subtraction. - Provides very clear and explicit instructions for adding and subtracting multi-digit numbers - Assessment includes the addition of three and four numbers - Presentation allows for printing of step-by-step instructions and example problems

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This resource is a Year 6 Mathematics lesson plan on Geometry: Properties of Shapes. Included in this resource is: A detailed lesson plan including lesson objectives, outcomes, starter, main activity and timings (based on a 1 hour lesson). There is also two types of worksheets differentiated based on ability. The Green Sheet (as detailed in the lesson plan) is for the lower-ability children, and the Blue Sheet is for the higher-ability children, with the opportunity for you to decide on the activity most appropriate for those children in the middle. The activity itself is for the majority the same, as is the final outcome, and the basic knowledge of the topic. The worksheets come as two sets of Green and Blue, one set is a Task List of the activities, the second is a Worksheet with space for answers/drawings removing the need for books during the lesson. For those children who are significantly struggling there is also a Net Guidance Sheet. The learning objectives (DfE, 2014) for this lesson are: 1. To recognise, describe and build 3-D shapes 2. To make nets for 3-D shapes 3. To draw 2-D shapes using given dimensions and angles A free download of one of the worksheet sets is available for you to take a look at before you buy, however the lesson plan helps considerably as does having the differentiated worksheet. If you do choose to download this resource or the free one I would really appreciate it if you could leave a review.

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ESL Quiz Subjects and Verbs 1 In this language arts worksheet, students read 5 sentences and choose the correct missing subject or verb. This is designed as an online ESL quiz but can be done on paper. 3 Views 0 Downloads - Activities & Projects - Graphics & Images - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Writing Prompts - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Subject Object Pronoun Practice Practice substituting subjects and objects in a sentence with the correct pronouns. A grammar worksheet prompts young learners to fill in the blanks for ten missing subjects, and then ten missing objects in different sentences. 2nd - 4th English Language Arts CCSS: Adaptable Conversation Pieces: A Verb Tense Activity Teach your English language learners about conversations by inviting them to participate in a conversation about an interesting object. Through this conversation, learners will naturally use various verb tenses and practice asking and... 3rd - 8th English Language Arts CCSS: Adaptable Conjugating Verbs: Verb Tense and Aspect | Parts of Speech App Take a look at an in depth video to learn all there is to know about conjugating verbs. Find out what conjugating verbs are, why we conjugate verbs, and all the rules to properly form grammatically correct sentences. After gaining much... 13 mins 3rd - 6th English Language Arts CCSS: Adaptable

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- Edexcel - C1, Sequences and Series - AQA - C2, Sequences and Series - OCR - C2, Sequenes and Series A sequence is a list of numbers, in it's basic definition. This list can be of a finite / infinite length.e.g. 2,4,6,8.. is a sequence of all positive even numbers. There are many types of sequences, we shall be looking at the Arithmetic Series / Progression. A series is the sum of the terms in a sequence. Again these can be finite and infinite, depending on the sequence itself. An Arithmetic Sequence is a sequence of numbers, such that difference between the terms is a constant. e.g. 5,9,13,17,21 .. this difference here is + 4. This difference is called the common difference. Each number in the sequence, is called a term. We call the first term (u1), second term (u2), third term (u3)... and so on. This is just notation. In the previous sequence example, 5 would be the first term, 9 the second, 13 the third.. and so on. The first term of a sequence is a. While the common difference is d. Nth term, is a rule for finding any term in the sequence. Say if i wanted to find the 28th term of the previous sequence, it would be very long to add 4 each time, to get till the 28th term. Instead we can form a rule to find any term in that sequence. The formula for finding the nth term of a sequence is : U(n) = a + (n-1)d a = first term d= common difference n = the term you're finding *This formula will work for any Arithmetic Sequence. How we got this formula ? As you know the first term is a. If each term goes up by a common difference, the second term must be a + d. The third term must be a + d + d = a + 2d, The fourth term must be a + d + d + d = a +3d.... and so on... if we look for the nth term it must be a + (n-1)d. a) Say we have an arithmetic sequence with the first term being 9. The common difference is -4. Find the 80th term ? Here a is 9, d = -4 , and n=80 Use the formula U(80) = 9 + (80-1)*-4 =9 + (79*-4) We also need to be able to find the Sum of an Arithmetic Sequence. There is a formula, we also need to be able to prove that formula (abit confusing, i'll include it in my image notes). n = the number of terms a1 = first term (a) d = common difference a) Find the sum of the first ten terms b) Find the sum of the terms starting from the 11th term and ending with the 28th term. Identify a and d. a = 2, d = +3 a) Use the Formula : S(10) = 10/2 [ 2(2) + (10-1)3] = 5 [4 + 9(3)] = 5 [4 + 27] = 5 *31 b) Use the Formula, note a is different. They want to start from the 11th term, so the 11th term will be a. Use the nth term formula to find the 11th term : (Here we use a as 2) =2 + (11-1)*3 = 2 + (10)*3 = 2 + 30 11th term is 32, which is the a Count how many terms are from 11 to 28. (18 terms), Now use the formula : S(18) = 18/2 [ 2(32) + (18-1)*3] = 9 [64 + 17*3] = 9 [64 + 51] = 9 x115 The sigma sign Σ, is another notation you need to be able to interpret. It is simply the summation of an arithmetic sequence. I will use an example to make you understand it: |Proof for the Sum of Arithmetic Series|

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1 shades of meaning activity worksheet for units 1-6 (weeks 1-4). Each worksheet uses a word from the reading vocabulary list of the week. 1 blank template to use your own words This activity can be used to introduce the shades of meaning concept. They can also be used for weekly practice, assessment, or for stations/centers. Students use the dictionary to look up and copy the definition of each of the three words. Students use the definitions to determine an order of strength and write the words in the correct boxes. Put students in groups of 3-4. When all groups are finished, they share their results and the class can see if everyone agreed. To save time, provide students with the definitions to copy, rather than looking them up. Use digital dictionaries. There are times when two words have such a similar meaning, that one is not clearly stronger than the other. In this case, it is appropriate for more than one answer to be correct. When having students copy definitions from the dictionary, watch for multiple meanings. It’s a great opportunity for students to have to choose the meaning that matches the other two words.

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How Much Truth is in Probability Sixth graders conduct experiments with on-line spinners and hand-held spinners to determine the experimental probabilities of spinning each color. They compare the experimental and theoretical probabilities of both types of spinners. 3 Views 0 Downloads - Activities & Projects - Graphics & Images - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Writing Prompts - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Study Jams! Probability as a Fraction Pick a card, any card... and then follow along with this step-by-step presentation as Sam from the Study Jams! crew determines what chance he has of drawing a jack from a deck of cards. This context serves to clearly model how fractions... 4th - 7th Math CCSS: Adaptable Understand the Law of Large Numbers by Comparing Experimental Results to the Theoretical Probability If we flip four tails in a row, does that mean all coin flips will be tails? With the law of large numbers, your mathematicians will learn that with more trials their experimental probability will get closer to the theoretical... 5 mins 6th - 8th Math CCSS: Designed Predict the Frequency of an Event Using the Theoretical Probability Once your mathematicians are familiar with probability, show them how to predict an outcome with theoretical probability. This final video in a series about probability demonstrates how to set up a probability and use it to predict a... 3 mins 6th - 8th Math CCSS: Designed

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This Develop Events in a Narrative Using Description and Dialogue video also includes: Dialogue really brings a story to life and can reveal a lot about its characters, plot, and setting. Explore how this literary technique is used to engage an audience as young writers begin drafting their narrative response to The Story of Dr. Dolittle. To encourage original student work, consider pausing the video and allowing children to begin their writing before viewing the examples provided by the instructor. - If you aren't logged in to Learnzillion, you will be prompted to create a free account to access all materials for this resource - Models how to hook readers using actions and dialogue to begin a piece of narrative writing - Allows learners to monitor their progress through the writing process - Adaptable to Common Core writing standards across the upper-elementary grade levels - Assumes prior knowledge about how to include dialogue in narrative writing - A rubric is required to to provide clear expectations for student writing

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Students examine a feeling word and represent it in a dramatic presentation. Through this, students present and observe the different situations that different feelings can exist in. 3 Views 0 Downloads - Activities & Projects - Graphics & Images - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Writing Prompts - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: New Review Pyotr Ilyich Tchaikovsky—1812 Overture Projects Imagine being commissioned to compose a work for a huge celebration that should be exciting and patriotic. A work that would commemorate a dramatic battle victory. What instruments would you use? What melodies to tell the tale and echo... 7th - 12th Visual & Performing Arts A Look at Exclusion Through Improvisation Building a realistic understanding of the trials Jews suffered during WWII isn't always easy. This plan employs student constructed dramatic freeze frame scenes to help build a deeper understanding of Jewish Ghettos, concentration camps,... 7th - 9th Visual & Performing Arts Spanish Drama: Latin America Young scholars explore Hispanic countries. For this Hispanic culture and language lesson, students choose an Hispanic country to research. Young scholars explore given websites and prepare a dramatization incorporating the facts they... 8th - 12th Visual & Performing Arts The American Dream: Gatsby on the Stage "So we beat on, boats against the current, borne back ceaselessly into the past..." Use this Great Gatsby novel study instructional activity to reinforce literary analysis in your class. Working in groups, young readers write a script... 8th - 11th English Language Arts

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Lesson 16 Student Outcomes Students solve two inequalities joined by “and” or “or,” then graph the solution set on the number line. "And" and "Or" Statements Recall that for a statement separated by “and” to be true BOTH statements must be true. If it is separated by “or,” at least one statement must be true. 1. Solve each compound inequality for x and graph the solution on a number line. a. 9 + 2x < 17 and 7 - 4x < -9 b. 6 ≤ x/2 ≤ 11 a. Give an example of a compound inequality separated by “or” that has a solution of all real number. b. Take the example from (a) and change the “or” to an “and.” Explain why the solution set is no longer all real numbers. Use a graph on a number line as part of your explanation. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

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To create a custom lesson, click on the check boxes of the files you’d like to add to your lesson and then click on the Build-A-Lesson button at the top. Click on the resource title to View, Edit, or Assign it. 11-12.C.1. Nature of Science: Students exercise the basic tenets of scientific investigation, make accurate observations, exercise critical thinking skills, apply proper scientific instruments of investigation and measurement tools, and communicate results in problem solving. Students evaluate the validity of information by utilizing the tools of scientific thinking and investigation. Students summarize their findings by creating lab reports using technical writing including graphs, charts, and diagrams to communicate the results of investigations. 11-12.C.1.1. Understand Systems, Order, and Organization 11-12.C.1.1.1 Use the periodic table to predict physical and chemical properties. 11-12.C.1.2. Understand Concepts and Processes of Evidence, Models, and Explanation 11-12.C.1.2.1 Describe the historical development of the periodic table. 11-12.C.1.2.3 Explain and interpret the key concepts of the kinetic molecular theory. 11-12.C.1.2.4 Distinguish the common theories defining acids and bases. 11-12.C.1.3. Understand Constancy, Change, and Measurement 11-12.C.1.3.1 Identify, compare and contrast physical and chemical properties and changes and appropriate computations. 11-12.C.1.3.6 Express concentrations of solutions in various ways including molarity. Quiz, Flash Cards, Worksheet, Game The Mole 11-12.C.1.3.7 Interpret how the presence of solute particles affect the properties of a solution and be able to do calculations involving colligative properties. 11-12.C.1.6. Understand Scientific Inquiry and Develop Critical Thinking Skills 11-12.C.1.6.1 Demonstrate an understanding of the scientific method. 11-12.C.1.7. Understand That Interpersonal Relationships Are Important in Scientific Endeavors 11-12.C.1.7.1 Explain how a series of historically related and documented experiments led to the current model and structure of the atom. 11-12.C.1.8. Understand Technical Communication 11-12.C.1.8.1 Correctly write symbols, formulas and names for common elements, ions and compounds. 11-12.C.2. Physical Science: Students explain the structure and properties of atoms, including isotopes. Students explain how chemical reactions, while requiring or releasing energy, can neither destroy nor create energy or matter. Students explain the differences between fission and fusion. Students explain the interactions of force and mass in describing motion using Newton's Laws. Students explain how energy can be transformed from one form to another while the total amount of energy remains constant. Students classify energy as potential and/or kinetic, and as energy contained in a field. 11-12.C.2.1. Understand the Structure and Function of Matter and Molecules and Their Interactions 11-12.C.2.1.1 Explain and understand how electrons are involved in the formation of chemical bonds using the octet rule and Lewis dot diagrams. 11-12.C.2.1.3 Predict physical properties of compounds based upon the attractive forces between atoms and molecules. 11-12.C.2.1.4 Distinguish and classify all matter into appropriate categories. 11-12.C.2.1.5 Explain the relationship and reactions of acids, bases, and salts. 11-12.C.2.1.6 Explain the role of dissociation and ionization in producing strong, weak, and nonelectrolytes. 11-12.C.2.2. Understand Concepts of Motion and Forces 11-12.C.2.2.1 Describe the Kinetic Molecular Theory as it applies to phases of matter. 11-12.C.2.3. Understand the Total Energy in the Universe is Constant 11-12.C.2.3.1 Explain and calculate the changes in heat energy that occur during chemical reactions and phase changes. Quiz, Flash Cards, Worksheet, Game Heat 11-12.C.2.3.2 Demonstrate the conservation of matter by balancing chemical equations. 11-12.C.2.3.3 Differentiate between exothermic and endothermic chemical reactions during chemical or physical changes. 11-12.C.2.4. Understand the Structure of Atoms 11-12.C.2.4.1 Interpret the classic historical experiments that were used to identify the components of an atom and its structure. 11-12.C.2.4.2 Deduce the number of protons, neutrons and electrons for an atom or ion. 11-12.C.2.4.4 Determine and illustrate electron arrangements of elements using electron configurations and orbital energy diagrams. 11-12.C.2.5. Understand Chemical Reactions 11-12.C.2.5.2 Classify, write and balance chemical equations for common types of chemical reactions and predict the products. 11-12.C.2.5.3 Describe the factors that influence the rates of chemical reactions. 11-12.C.5. Personal and Social Perspectives; Technology: Students understand that science and technology interact and impact both society and the environment. 11-12.C.5.1. Understand Common Environmental Quality Issues, Both Natural and Human Induced 11-12.C.5.1.1 Demonstrate the ability to work safely and effectively in a chemistry laboratory. ID.CC.RST.11-12.Reading Standards for Literacy in Science and Technical Subjects Reading Standards for Literacy in Science and Technical Subjects Integration of Knowledge and Ideas RST.11-12.8. Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. RST.11-12.9. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. Craft and Structure RST.11-12.4. Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topics. ID.CC.WHST.11-12.Writing Standards for Literacy in Science and Technical Subjects Writing Standards for Literacy in Science and Technical Subjects Research to Build and Present Knowledge WHST.11-12.7. Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. Production and Distribution of Writing WHST.11-12.4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. Text Types and Purposes WHST.11-12.2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. WHST.11-12.2(a) Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. WHST.11-12.2(b) Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience's knowledge of the topic. WHST.11-12.2(c) Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. WHST.11-12.2(d) Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers. WHST.11-12.2(e) Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the significance of the topic).

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Determine the sign of the function represented by the figure below in real When we’re determining the sign of a function, we have three choices: positive, zero, or negative. When a function falls into the shaded areas in green, we call it positive. That is to say, when the output or the 𝑦-value of a function is positive, the sign of the function is positive. Likewise, the sign of a function is negative, if it falls in the areas shaded red. If the 𝑦-value or the output of your function is negative, the sign of the function is negative. We also have a third option, when the sign of the function is zero. That is the case when the output or the 𝑦-value of your function is zero, and when your function lands on the 𝑥-axis on Let’s look back at the original problem we were asked about. Where would this function be positive? Where are the 𝑦-values positive? Okay. We have this space from negative one to three where the 𝑦-values are all positive. For zero, we have two places where this function crosses the 𝑥-axis, at negative one and at three. Our function falls in the negatives everywhere to the left of negative one. It’s also negative everywhere that’s to the right of positive three. Now, how should we write this? How should we represent this? We’ll start with the positive case. When 𝑥 falls between negative one and three, it’s positive. This is how we would write it. We use these brackets facing outward to represent 𝑥 that does not include negative one and three. It’s not equal to negative one and three, only between those two places. Another way to represent that looks like this. You might be more familiar with the parentheses that means does not include negative one and three. But, both these parentheses and the outward facing brackets mean the same thing. And where is our function equal to zero? When 𝑥 equals negative one and three, the sign of our function is zero. And where is our 𝑥-value negative? What we wanna say here, is that it’s negative everywhere. It’s not positive or zero. We want to say, it’s negative everywhere else. 𝑥 is negative when it is any number, or all real numbers with the exception of, subtracted from, the portion from negative one to three. In other words, any time it’s not positive or zero, our function is negative. All reals minus the piece from negative one to three.

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This activity provides instructions for encouraging your young child to participate in drama. - Pencil or pen - Encourage your child to write an original play. He may want to base his play on something that has happened to him, such as winning a special award or the birth of a new sibling. If he doesn't know where to begin, use a familiar nursery rhyme, song, or story as a starting point. - Explain to your child that a play includes more than just the words spoken by the actors. A play also includes set information, which tells about the scenery where the play takes place, and stage directions, which tell the actors what they should be doing as they say their lines. To distinguish stage directions from the actor's lines, have your child enclose stage directions in parentheses and underline them (like this). - Your child's play can be as simple or elaborate as he wishes to make it. - The finished play can be read aloud or acted out complete with cast, costumes, and a set. - This activity will probably require a lot of parental involvement, so be prepared to help your child as much as needed.

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Concentric circles : In this section, we are going to learn about Concentric circles. Already we are familiar with Circles. When a small stone was dropped in still water, you might have seen circular ripples were formed. Which is the center of these circles ? Is it not the place where the stone was dropped ? The circles with different measures of radii and with the same center are called concentric-circles. The center is known as common center. Circles drawn in a plane with a common center and different radii are called concentric-circles. See the figure given below. Look at the following two figures : The above figure represents two concentric-circles. In the above figure, the area between the two concentric -circles are shaded with red color. The red colored area is known as circular ring. In the figure given above, C₁ and C₂ are two circles having the same center O with different radii r₁ and r₂ respectively. Circles C₁ and C₂ are called concentric-circles. The area bounded between the two circles is known as circular ring. Width of the circular ring = OB – OA = r₂ - r₁ ( r₂ > r₁) Draw concentric-circles with radii 3 cm and 5 cm and shade the circular ring. Find its width. Given: The radii are 3 cm and 5 cm. Steps for construction : Step 1 : Draw a rough diagram and mark the given measurements. Step 2 : Take any point O and mark it as the center. Step 3 : With O as center and draw a circle of radius OA = 3 cm Step 4 : With O as center and draw a circle of radius OB = 5 cm. Thus the concentric-circles C₁ and C₂ are drawn. Width of the circular ring = OB – OA Width of the circular ring = 5 – 3 Width of the circular ring = 2 cm. After having gone through the stuff given above, we hope that the students would have understood "Concentric-circles". Apart from the stuff given above, if you want to know more about "Concentric-circles", please click here Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here. APTITUDE TESTS ONLINE ACT MATH ONLINE TEST TRANSFORMATIONS OF FUNCTIONS ORDER OF OPERATIONS MATH FOR KIDS HCF and LCM word problems Word problems on quadratic equations Word problems on comparing rates Converting repeating decimals in to fractions

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Differentiated instruction (sometimes referred to as differentiated learning) involves providing students with different avenues to acquiring content; to processing, constructing, or making sense of ideas; and to developing teaching materials so that all students within a classroom can learn effectively, regardless of differences in ability. Differentiated instruction, according to Carol Ann Tomlinson (as cited by Ellis, Gable, Greg, & Rock, 2008, p. 32), is the process of “ensuring that what a student learns, how he/she learns it, and how the student demonstrates what he/she has learned is a match for that student’s readiness level, interests, and preferred mode of learning”. Differentiation stems from beliefs about differences among learners, how they learn, learning preferences and individual interests (Anderson, 2007). "Research indicates that many of the emotional or social difficulties gifted students experience disappear when their educational climates are adapted to their level and pace of learning.Differentiation in education can also include how a student shows that they have mastery of a concept. This could be through a research paper, role play, podcast, diagram, poster, etc. The key is finding how your students learn and displays their learning that meets their specific needs. Source: Wiki Pedia

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This Interpreting Expressions lesson plan also includes: Here is one lesson on interpreting algebraic expressions. Pupils evaluate expressions given an input, play a game in cooperative groups, match algebraic expressions to their quantity in context, and participate in a group discussion. The plan concretely connects the abstract expressions of Algebra to real-life situations. Your class will be hooked with the mention of chocolate. - Well-organized lesson plan - Learners connect algebra expressions to real-world applications and scenarios - Learners use logical reasoning to explain their matches and possible misconceptions associated with the expressions - Achievement of a deep understanding of interpreting algebra expressions - Mistake in Lesson Tasks, section four (should be a y instead of an x for the second truck's capacity) - Multiplication and division symbols missing in some expressions in Matching Activity. However, this can become a challenge to students to find some common misconceptions and correct them

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The changes in chemical reactions can be modelled using equations. In general, you write: The reactants are shown on the left of the arrow, and the products are shown on the right of the arrow. Do not write an equals sign instead of an arrow. If there is more than one reactant or product, they are separated by a plus sign. A word equation shows the names of each substance involved in a reaction, and must not include any chemical symbols or formulae. For example: copper + oxygen → copper oxide In this reaction, copper and oxygen are the reactants, and copper oxide is the product. A balanced equation gives more information about a chemical reaction because it includes the symbols and formulae of the substances involved. There are two steps in writing a balanced equation: In the example above (the reaction between copper and oxygen to make copper oxide), we get this in the first step: Cu + O2 → CuO This is unbalanced because there is one copper atom on each side of the arrow, but two oxygen atoms on the left and only one on the right. To balance the equation, you need to adjust the number of units of some of the substances until we get equal numbers of each type of atom on both sides. You should never change the formula of a substance to do this. Here is the balanced symbol equation: 2Cu + O2 → 2CuO You can see that we now have two copper atoms and two oxygen atoms on each side. This matches what happens in the reaction: Here are some other examples of balanced equations. Check that you understand why they are balanced:

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Activity 1: Units of Measurement Suitable for: Year 2 to Year 6 Learning Focus: To recognise and learn the units of measurement for time You’d be surprised how many pupils believe that time, like other measurement follows the metric system and that there are 100 minutes in an hour. This activity gives them an aide memoire for time measures and also provides some calculator practice. Use the attached worksheet with the class filling in the gaps by referring to a clock. If you have access to them it’s useful to let the pupils have a card click each or between two so they can see the measures close up. Ask them to count how many small marks (seconds and minutes) there are on the clock face. Some will be clever and count in fives, others will do it one at a time, and fill the space on the sheet with information. Continue with minutes and hours. Now ask them to use calculators to answer questions such as . . . “How many seconds are there in 5 minutes?” “How many hours are there in a week?” “How many weeks in 5 years?” Activity 2: Strategies for telling the time Suitable for: Year 1 to Year 6 Learning Focus: To be able to use strategies for helping to tell the time Learning to tell the time is very difficult at first as countless pupils will testify. There are some mini strategies that they can use to help make it easier for them. Share these with them and hopefully those little problems will start to disappear. Which hand is which? Some pupils confuse which hand is the minute hand and which is the hour hand meaning that twenty to six becomes half past eight. An easy way to remember is that the word “minute” is longer than the word “hour” so the minute hand is the longer one. Past or to? Another common problem but again easily resolved. Show the pupils the minute hand on the twelve and the hour hand on the four and they’ll know it’s four o’clock. Show them now the minute hand moving from 1 to 30 minutes and they’ll see it’s gone PAST the 12 that shows the “o’clock” time. From 31 to 60 they’ll see that it’s moving up TO the 12 so it’s minutes TO the next hour. How many days in a month? This is a really tricky one for some pupils but memorising the rhyme on the worksheet, it will get a lot easier. Another way is to realise that with the exception of August, alternate months have 31 days i.e. January, March, May, July, (August), October, December. Activity 3: 24 hour clock Suitable for: Year 3 to Year 6 Learning Focus: To understand how 24 hour clock time is formulated Using the 24 hour clock can seem daunting for pupils but when they see it’s just an extension of digital time but without the “am” or “pm” and you remind them that it’s only a case of keeping on counting from 12 instead of starting again at 1, they’ll see it’s quite easy. Equally, changing back from 24 hour time to 12 hour only means that if the hour is greater than 12, subtract 12 and you’ll have the time in the afternoon or evening. Give them some practice with the attached question sheet. Activity 4: Calculating duration Suitable for: Year 4 to Year 6 Learning Focus: To be able to calculate the duration between two times One of the biggest mistakes made here by pupils is thinking that they can simply do a subtraction. This works fine with say, calculating the time between 8.15 and 11.38 but when faced with finding the time between 11.29 am and 3.15 pm, all kinds of problems appear. For that type of question, pupils often try a vertical subtraction which will work as long as you remember that there are 60 minutes in an hour. Instead, number lines are the best way of calculating duration. They enable pupils to calculate duration even when days are included. To calculate the duration from 09.33 am to 3.12 pm, write the times at each end of a line. Then count the minutes to the next hour, the hours up to the time you’re ending with then add on the final minutes. For some practice, use the questions on the accompanying sheet.

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ASCII stands for American Standard Code for Information Interchange. It is a numeric value given to different characters and symbols, for computers to store and manipulate. For example: ASCII value of the letter 'A' is 65. Check out the complete list of ASCII values. # Program to find the ASCII value of the given character # Take character from user c = input("Enter a character: ") print("The ASCII value of '" + c + "' is",ord(c)) Enter a character: p The ASCII value of 'p' is 112 Here we have used ord() function to convert a character to an integer (ASCII value). This function actually returns the Unicode code point of that character. Unicode is also an encoding technique that provides a unique number to a character. While ASCII only encodes 128 characters, current Unicode has more than 100,000 characters from hundreds of scripts. We can use chr() function to inverse this process, meaning, return a character for the input integer. >>> chr(ord('S') + 1) chr() are built-in functions.

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Basic Math and Pre-Algebra PART 1. The World of Numbers CHAPTER 7. Ratios, Proportions, and Percentages We have two basic ways of comparing numbers: an addition/ subtraction method and a multiplication/division method. The addition/subtraction method makes statements like 15 is 7 more than 8, or 49 is 1 less than 50. The multiplication/ division method compares numbers by saying things like 63 is 3 times as large as 21, or 12 is half of 24. In this chapter, you’ll focus on that comparison by multiplication and division. You’ll learn to use ratios and extended ratios to help you figure out unknown numbers, and you’ll solve proportions by cross-multiplying. Once you understand percentages, you’ll be able to explore how they’re using in different kinds of problem solving. Twice the size, half as many, three times as much. In your daily language, you frequently use the idea of multiplying or dividing as a way to compare numbers. Usually, in conversation, you’ll make the comparison using a simple whole number compared to 1: twice the size or three times as much. Or you might use division in the form of a simple fraction, like half as many. But you could make other comparisons, not always comparing to 1. If you had two lamps, one 2 feet tall and one 3 feet tall, you could say one is 1.5 times taller than the other, but more often, you’ll stay with the whole numbers and say the taller lamp is to the shorter one as 3 is to 2. Or you could say the shorter lamp is to the taller one as 2 is to 3. Understanding Ratios and Extended Ratios A ratio is a comparison of two numbers by division. If one number is three times the size of another, you say the ratio of the larger to the smaller is “3 to 1.” This can be written as 3:1 or as 3 the fraction 3/1. You could also compare the smaller to the larger by saying the ratio is 1 to 3. A ratio is a comparison of two numbers by division. When you are told that the ratio of one number to another is 5:2, you are not being told that the numbers are 5 and 2, but that when you divide the first by the second, you get a number equal to 5/2. This happens when the first number is 5 times some number and the second is 2 times that number. If that’s all you know about the numbers, you have a sense of their relative size, but that’s about all. If you have some other information, you might be able to figure out what the numbers actually are. Suppose two numbers are in ratio 7:3 and their sum is 50. You know that the first of the numbers you’re looking for is 7 times some number and the other is 3 times that same number, so that they divide to 7/3. With the extra piece of information that they add to 50, you can try to find the numbers by guess and test. If the numbers were actually 7 and 3, they would add to 10. Multiply each one by 2 and you have 14 and 6, which add to 20. A little more experimentation will tell you that 7 x 5, or 35, and 3 x 5, or 15, will add to 50. That guess and test method can run into some problems. For example, most people won’t guess anything but whole numbers, and the answer won’t always be a whole number, or it might be a very large whole number. Try using a letter, maybe n, called a variable, for the number you don’t know. If the numbers are in ratio 6:5, one is 6n and the other is 5n. If they add to 88, you can say 6n + 5n = 88. That means that 11n = 88, and n must be 8. The numbers are 6 x 8 = 48 and 5 x 8 = 40. A variable is a letter or other symbol that takes the place of an unknown number. An extended ratio compares more than two numbers. Extended ratios are usually written with colons, because you don’t want to put more than two numbers into a fraction. Extended ratios are actually a condensed version of several ratios. If the apples, oranges, and pears in a fruit bowl are in ratio 8:3:2, it means that that the number of apples is 8 times some number, the number of oranges is 3 times that number, and the number of pears is 2 times that number. It also means that the ratio of apples to oranges is 8:3, the ratio of oranges to pears is 3:2 and the ratio of apples to pears is 8:2. An extended ratio combines several related ratios into one statement. It is a way to express the ratios a:b, b:c, and a:c in one statement: a:b:c. Suppose that a smoothie contains pomegranate juice, orange juice, and yogurt, in a ratio of 2:5:3. If you want to make 5 cups of the smoothie to sip throughout the day, how much of each ingredient will you need? If the numbers actually were 2 and 5 and 3, they would add to 10 cups. You need 5 cups, so let’s say 2n cups of pomegranate juice, 5n cups of orange juice, and 3n cups of yogurt, to make a total of 5 cups. 2n + 5n + 3n = 5 10n = 5 n = 1/2 The multiplier is ½, so you need cup of pomegranate juice, cups of orange juice, and cups of yogurt. When you're working with ratios that involve measurements, make sure the units match. If you try to say the ratio of the length to the width of a room is 15 feet to 120 inches, when you go on to use that relationship, you'll be confused about whether your numbers are feet or inches, and you'll likely get the wrong numbers. Make it 15 feet by 10 feet or 180 inches by 120 inches, and your work will be easier and more accurate. 1. If the ratio of girls to boys in Math Club is 5:3, and there are 32 members of the club, how many boys are members? 2. The local car dealer sold 40 cars last month. The ratio of gas-powered vehicles to hybrids was 7:1. How many hybrids were sold? 3. The desired ratio of the red roses to white roses in a bouquet is 2:3. If the florist wants the bouquet to have a total of 20 roses, how many white roses and how many red roses will she need? 4. If the ratio of lions to tigers to bears at the zoo is 4:7:4, and there are 45 of these animals all together, how many tigers are there? 5. The ratio of red balloons to white balloons to blue balloons in the auditorium is 21:20:9. If there are 900 balloons in the auditorium, how many are blue? A proportion is a statement that two ratios are equal. The equation 1/3 = 2/6 is an example of a proportion. It says the ratio of 1 to 3 is the same as the ratio of 2 to 6, or, in other words, that the fractions are equal. When you look at the statement that two ratios are equal as a proportion, you can talk about the four numbers that make up the proportion as the means and the extremes. It’s a little easier to understand which numbers are means and which are extremes and why if you write the ratios with colons, so let’s write 1/3 = 2/6 as 1:3 = 2:6. The extremes are the numbers on the ends, the 1 and the 6. They’re far out. The word mean talks about the middle, so the numbers in the middle, the 3 and the 2, are the means. When you do write it as a pair of equal fractions, it looks like this. A proportion is two equal ratios. The means of a proportion are the two middle numbers. The extremes are the first and last numbers. Proportions can be used to compare things. When you create a proportion, it’s important to be consistent about the order. If you want to say that the ratio of the shortest side of the big triangle to the shortest side of the small triangle is equal to the ratio of their longest sides, be sure that your second ratio is big triangle to small triangle just like the first ratio. If you change the order, the proportion won’t be true. In any proportion, the product of the means—the two middle terms—is equal to the product of the extremes—the first and last terms. For example, in the proportion 5/8 = 15/24, 8 x 15 = 5 x 24. This multiplying of means and extremes is called cross-multiplying. Whenever you have two equal ratios you can cross-multiply, and the two product will be equal. Knowing that will often let you find a number that’s missing from the proportion. You could use a question mark or other symbol to stand for the missing number, but let’s use an x for now. When you multiply with a variable, especially when you use the variable x, it’s easy to confuse the variable with the times sign x, so you may want to use other ways to write multiplication, like a dot or parentheses. Instead of writing 5 x x, you can write 5∙x or 5(x). Keep in mind that cross-multiplying can only be done in a proportion. You can cross-multiply when you have two equal ratios, but not in any multiplication with fractions. Finding the product of the means and the product of the extremes of a proportion, and saying that those products are equal, is called cross-multiplying. Suppose you’re told that two numbers are in ratio 7:4, and the smaller number is 14. But what’s the larger number? You can use the means-extremes properties of proportions to help you find out. If I give you the proportion x/14 = 7/4, you can use cross-multiplying to help you find the value of the number I called x. If you multiply the means you get 4 times the unknown number or 4x. The product of the extremes, 7 x 14, is 98. The product of the means is equal to the product of the extremes, so 4x must equal 98, or 4x = 98. Dividing 98 by 4 tells you that x = 98/4 = 24.5. When you're cross-multiplying, don't be in a rush to do the arithmetic, especially if your numbers are large. Your work may be easier if you write out the multiplication but don't actually do it. Then when you divide to find the value of the variable, you may see a shortcut. Why do the work of multiplying 42 x 35 if, a moment later, you're going to divide by 21? Leave the multiplication in factored form, and the division may be easier. Solve the proportion to find the value of the variable. Percent as a Standard Ratio The word percent means “out of 100.” If you shoot 100 free throws at basketball practice and you sink 60 of them, you made 60 out of 100 shots, or 60 percent. But what if you shot 75 and made 40? What percentage is that? Is that better or worse than 60 percent? You can use proportions to convert any ratio to a percentage. A percentage is a ratio that compares numbers to 100. 42 percent means 42 out of 100, or 42:100. Percentages are sometimes written using the percent symbol, %. Ratios can be hard to compare if they are “out of” different numbers. Which is larger: 4 out of 9 or 5 out of 12? If you compare them as fractions, 4/9 and 5/12, it might help to change to a common denominator. You could use 36 as the common denominator so 4/9 = 16/36 and 5/12 = 15/36, and you can see that 4/9 is larger. Changing ratios to percentages is like changing fractions to a common denominator. Percentages make it easier to compare different ratios, because they express everything as a part of 100. When you need to change a ratio to a percentage, take your ratio, like 15/20, and set it equal to the ratio P/100. You’re saying 15 is to 20 as P is to 100, or 15 out of 20 is the same as P out of 100. That’s a percentage. Use cross-multiplying to find P. So 15 out of 20 is 75 percent. The rule you want to remember is “part is to whole as percent is to 100” or This proportion can be used to solve almost all percent problems. Percentage problems come in three basic types. One type asks a question like “what is 45 percent of 250?” The second type asks “15 is 30 percent of what number?” and the third is “29 is what percentage of 58?” The first type asks you to find the part, the second asks you to find the whole, and the last asks for the percentage. Suppose your town requires that a candidate receive at least 51% of the vote to be elected mayor. If the population of the town is 1,288, what is the minimum number of votes a candidate must receive to be elected? You know the percentage and the whole, and you’re looking for the part of the population that is required for election. Start with Cross-multiply, and you’ll find that the product of the means is 1,288 x 51 = 65,688 and the product of the extremes is 100p. The product of the means is equal to the product of the extremes, so 100p = 65688, and dividing by 100 tells you p = 656.88. (Since no one can cast a fraction of a vote, round this to 657 votes.) When you use the rule, the important part is getting the numbers in the right positions. Certain words in the problem can signal this for you. The word “of” usually precedes the whole amount, and the word “is” can generally be found near the part. Some people remember the rule as Let’s walk through some examples of the different types of problems. First, finding a percentage. What percentage of 58 is 22? Look for “of.” 58 is the whole. Look for “is.” 22 is the part. 22 is about 37.9 percent of 58. You might round an answer like that to 38 percent if you don’t want to deal with the decimal. It will depend on the work you’re doing. If you were going to compare two percentages that were both close to 38 percent, you’d want the decimals so you could see which was bigger. If you want to know how much your savings increased, 38 percent is probably just as informative as 37.9 percent. Let’s look at another example. In this one, you’ll find the whole. 46 is 27% of what number? Look for “of.” The whole is “what number,” which means it is unknown. Look for “is.” 46 is the part. Both 46 and 27 are near the “is” but 27 has the % sign, so you know it is the percentage. 46 is 27% of 170.4, approximately. Again, how much you round will depend on the situation. One last example before we move on. This one asks you to find the part. What is 83% of 112? Look for “of.” 112 is the whole. Look for “is.” “What” is the part, that is, the part is unknown. The percent sign tells you that 83 is the percentage. 83% of 112 is 92.96. Because that decimal terminates after only two places, you can give the exact answer and not bother with rounding. If you feel like those examples all seemed very much the same, you’re right. The process is exactly the same: cross-multiply and divide. The difference is the piece that’s unknown, and, of course, the numbers themselves. Percentages can be greater than 100 percent, and that often happens when you turn a question around. You can say that 2 is 50 percent of 4, or you can reverse the comparison and say 4 is 200 percent of 2. 100 percent is the whole thing, so 200 percent is the whole thing and the whole thing again, or twice as much. The good news is you do the three types of problems exactly the same way even if the percentages are greater than 100 percent. 11. 45 is 20 percent of what number? 12. 16 is what percentage of 64? 13. What is 15% of 80? 14. 63 is what percentage of 21? 15. What is 120 percent of 55?

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Your student will decide which is a metaphor and which is a simile in this worksheet. This multiple choice worksheet asks your student to identify the type of figurative language used in the sentence or phrase. In this worksheet your student will match up the figures of speech with the phrase or sentence. In this worksheet about the famous Christmas poem a visit from. Nicholas, your student will find the similes and metaphors. A hazlitt metaphor is a word or phrase that describes a person or object by referring to something that has similar characteristics, such. The assignment was a breeze. Students underline the metaphor and circle the people or objects that the metaphor is being used to compare. Metaphors are great, until they get mixed up! Students read each sentence and re-write it using a metaphor. The job internet was a breeze. Casey is a night owl. These are examples of metaphors. Print out this free worksheet and have your students identify the metaphors as well as come up with their own. A metaphor worksheet that prompts students read each sentence and explain what the metaphor compares. They seem very down about it all. Extract from: Language Awareness: Metaphor by Dr Rosamund moon. In this worksheet your student will write metaphors and similes about himself. Students underline all the metaphors in this brief story called, The haircut. Students read each sentence and tell what each metaphor is comparing. This worksheet features a variety of metaphors and similes from Shakespeare for your student to anaylze. Your student is asked to explain the meanings of these metaphors and similes in this worksheet. The pennsylvania board of Law Examiners Metaphors about up and down This is an area of zoo high unemployment. They had raised their prices to unreasonable levels. The temperature had been falling steadily all day. There was a collapse in the price of oil. It is the true story of a millionaires meteoric rise from report poverty. They were downtrodden and oppressed. She had never wanted to climb the greasy pole of politics. They look down on everyone who isnt as rich as they are. They regarded tradesmen as their inferiors. I felt as high as a kite. She didnt notice the time slipping. Metaphors about journeys and travelling The baby arrived just after midnight. They remembered the departed in their prayers. His life took an unexpected direction. Whats the best way of doing it? Ive tried being reasonable, and I dont want to go down that road again. I havent yet reached my goal. Id like to return to what david was saying earlier. He always says things in a roundabout way. The conversation drifted towards the subject of money. This term, we will be exploring the psychology of sport. It is an excellent guide to English vocabulary. For more information, visit our website. Definition and meaning - businessDictionary This is a potential minefield for beginners. What do you mean? I really think youre barking up the wrong tree. I found out Id been taken for a ride. They met on a rainy day in January. He lay awake all through the night. This weeks gone so fast. One hippie day, in the distant future, i might go and live abroad. The weeks crawled by until we could meet again. I see what you mean. They recognized the admission fact that they needed to improve. We want to get a range of different views. He kept us in the dark about his plans. Metaphors about place and position we are in a situation where there are no real winners. They found themselves in a very difficult position. Ive been caught between a rock and a hard place. thought crossed her mind that he was lying. I dont want to put any ideas into your head. I had already planted the idea in her mind. It was a carefully constructed theory. Let me know if you dig up anything about him. It was a very stormy relationship. Metaphors about emotion, the news has hit him hard. It had a huge impact on them. He has a fiery temper. The book was received warmly. I felt a chill of fear. She treated us with cool indifference. The future looks very bright. Full hd wallpapers » High Definition quality desktop Metaphors about responsibility, i have to bear the responsibility for this. The responsibility was weighing on my mind. I dont hippie want to be a burden to you. Metaphors that are idioms, spill the beans. Give someone a hand. I was very attached to him. She has split up with her boyfriend. They greeted us warmly.

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String can be called correct if it consists of characters "0" and "1" and there are no redundant leading zeroes. Here are some examples: "0", "10", "1001". You are given a correct string s. You can perform two different operations on this string: Let val(s) be such a number that s is its binary representation. Correct string a is less than some other correct string b iff val(a) < val(b). Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all). The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s. The second line contains the string s consisting of characters "0" and "1". It is guaranteed that the string s is correct. Print one string — the minimum correct string that you can obtain from the given one. In the first example you can obtain the answer by the following sequence of operations: "1001" "1010" "1100" "100". In the second example you can't obtain smaller answer no matter what operations you use.

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Download This Full Lesson: Lets Grow Carrots Lesson Description: Students will work in small groups to research the life cycle of a carrot and learn about the growing process from a local farmer. Groups will make a poster with the steps for planting carrots in containers; then students will plant carrots and care for them until ready to harvest. After harvesting, students will make a carrot snack for the class to enjoy. Note to Teachers: Carrot seeds are very small and will be challenging for younger students to handle. Many seed companies offer pelletized seeds to make planting more manageable. Fingerling carrots are small in size and mature faster than other varieties, which makes them a good choice for growing in the classroom. Keep in mind that the small varieties of carrots need 55-60 days to reach maturity. Many schools have outdoor gardens; if planting carrots outside, refer to online catalogs for more information about suitable varieties. See a list of seed sources at the end of this lesson. - Explore a possible partnership with a local farm/farmer. Find one which will be willing to visit your classroom and talk about planting and harvesting carrots on a farm. - Gather research materials about carrots. - Gather supplies for growing carrots in the classroom. - Gather several carrot recipes for simple carrot snacks. - Seeds (pelletized for ease of handling) - Growing medium (potting soil) - One plastic shoe box for each group with drainage holes drilled in the bottom. If seeds for longer carrots are to be planted, use deeper containers (such as buckets with drainage holes in the bottom). The student will: - Use at least two resources to research carrots. Be sure to note - Soil & climate requirements - Growing cycle - Plant requirements - Participate in planting, watering, monitoring and harvesting carrots. - Take weekly measurements of growth of carrot tops and show on either a bar graph or line graph. - Write a paragraph about the carrot growing experience. - Students will work in small groups to research carrots. They will find information about - Soil requirements - Climate requirements - Carrot production in their region - Life cycle (or growth cycle) - Uses of carrots - Record their findings on chart paper - Draw a poster showing the life cycle of their crop - Following teacher directions, prepare container and plant carrot seeds. Be sure containers are labeled. - After seeds have germinated, measure the tops (the part above ground) once a week, on the same day each week. - Plot measurement information on a line graph. - Have local farmer come to the classroom to talk about growing carrots and why carrots are an important crop. - Participate in the harvest of the crop. - Students should be able to explain how their harvesting techniques may be different from the farmers. - Demonstrate food safety techniques (washing and refridgerating the carrots) - Prepare carrot snack recipe and enjoy! - Write a well-developed paragraph about the carrot growing experience. - Johnny’s Selected Seeds at johnnyseeds.com Carrot variety: Adelaide, 55 days to maturity, length: 2 incnes, seeds available pelletized. - Burpee Seeds at burpee.com Carrot variety: Caracas Hybrid, 57 days to maturity, length: 2-3 inches. - Parks Seeds at parkseed.com Carrot variety: Little Finger Carrots, 60 days to maturity, length: 4 inches. |Common Core ELA: W.3.7 Conduct short research projects that build knowledge about a topic. W.4.7 Conduct short research projects that build knowledge through investigation of different aspects of a topic. W.5.7 Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. |Common Core Math:||3MD.B.4 Generate measurement data by measuring lengths using rules marked with halves and fourths of an inch. Show the data by making a line plot which is marked of in appropriate units – whole numbers, halves, or quarters.|

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On a bright sunny day, you go for shopping. You select a nice pair of jeans and decide to pay using your credit card. But you suddenly realize that you are not able to recollect your pin. What a tragedy!! Now all you can think of is to list all the possible combinations to figure out your pin. How many possible combinations can you make? The answer to this question is difficult if we keep listing each possible combination and counting. In situations like these, the fundamental principle of counting or the multiplication principle comes to our rescue. Let us see what the fundamental principle of counting is all about. Fundamental Principle of Counting Suppose you have 2 pairs of shoes and 3 pairs of socks. In how many ways can you wear them? Now, the possible ways of choosing a pair of shoes are 2, since 2 pairs of shoes are available. With any pair of shoes, any of the 3 pairs of socks can be worn at a time. Therefore, for each pair of shoes, there are 3 choices of socks. Similarly, with 2 pairs of shoes, there are 6 choices of socks available since 2 × 3 = 6. This can be understood more clearly with the help of the following figure. Let A1 and A2 represent the 2pairs of shoes and B1, B2, B3 represent the 3pairs of socks. In the problem stated above, we use the fundamental principle of counting to get the result. The multiplication principle states that if an event A can occur in x different ways and another event B can occur in y different ways then there are x × y ways of occurrence of both the events simultaneously. This principle can be used to predict the number of ways of occurrence of any number of finite events. For example, if there are 4 events which can occur in p, q, r and s ways, then there are p × q × r × s ways in which these events can occur simultaneously. Well, the answer to the initial problem statement must be quite clear to you by now. The credit card pin would involve a sequence of 4 digits and each digit can vary between 0 – 9. Thus, the number of ways of occurrence of each digit is 10. Since it’s a 4 digit pin, the number of possible combinations is 10 × 10 × 10 × 10 = 10000. There are 10000 combinations possible out of which 1 is correct. Well, good luck trying to figure that out. This explains us the fundamental principle of counting which lays the foundation for permutations and combinations. Dependent or Independent? The fundamental principle of counting only works when the choice that is to be made are independent of each other. If one possibility depends on another then a simple multiplication does not work. To learn more about the fundamental principle of counting, permutation, and combination, download BYJU’s- The Learning App.

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Like the Romans, the British and the Anglo-Saxons had lots of slaves. A slave was a person who was the property of another person. They were thought of as objects rather than people and could be bought and sold. A slave was called a 'caeth' in Brythonic and a 'theow' or 'thrall' in Old English. They could be men, women Most of the people in a village could be slaves. They probably lived in small houses or grub huts, several slaves to one room. to do what their masters (owners) said. Most of them would have worked very hard. worked in the fields looking after crops and animals. They didn't get any wages although more skilled slaves, like weren't allowed to leave or get a job somewhere else. If they ran away and were caught, they would be executed. owners could do what they liked with their slaves. They were allowed to beat them or even kill them if they wanted to (King Alfred later put a stop to this). But in British areas, slaves could claim compensation (money) if they were treated badly. and the Saxons both had different grades of slave; and they were allowed their own possessions, but not weapons. in the Saxon kingdoms were British and most slaves in the British kingdoms were Saxon. They were usually the families of soldiers killed in battle or peasants from raided villages, like St. Patrick. The English word for the British was 'wealh' (Welsh). This can mean both foreigner and slave. in Saxon areas could be Saxon and, in British areas, they could be British, because the kingdoms were always fighting each other. Criminals or people in debt could also be made could be freed in an owner's will or in a temple or church. This is called 'manumission'. The British wrote manumission documents in gospel books, like the Lichfield trade was big in Britain. Bristol (Wessex) and Corbridge (Northumbria) became important slavery centres. Many slaves were sold abroad, particularly in Rouen (France).

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Parts of Speech. Knowing the different parts of speech and being able to recognize them in the sentences you read as well as the ones you write will help you speak more eloquently, write more clearly, and feel more confident when communicating with others. Capitalization. Knowing which words to capitalize is often common sense (e.g. First words of sentences, names of people, cities, etc.), but even the best of us have trouble keeping track of all the situations where we need capital letters. This brief but handy guide lists most of the situations you will encounter where you will need to capitalize words. Prepositions indicate time, place, or context, letting the reader know when and where things are happening in a sentence. Articles signal and introduce nouns. There are two types of articles: definite and indefinite. Colons serve a few purposes, both grammatical and non-grammatical. Like semicolons, they help to link related clauses without using conjunctions. However, unlike semicolons, the use of a colon does not require both clauses to be independent. Semicolons are used between independent clauses that are closely related (i.e. the second clause further discusses the first) and are not joined by the conjunctions and, but, or, so, nor, yet. Brackets are sometimes used interchangeably with the more common parentheses. However, the two serve different purposes in writing.

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Knowing the words for different areas of math isn’t on the SAT, so don’t worry if the word “permutation” sounds to you like something a mad scientist experiments with. Both of the types of questions we’re looking at here have in something in common: you’ll be asked to find the number of possible situation that can be formed by arranging the pieces of some set. The questions below do that, but in different ways. If a password made of 3 digits only uses the numbers from 1 to 5, inclusive, how many distinct passwords are possible if no digit is used more than once? If Andy’s breakfast is 3 pieces of fruit taken from a bowl that contains 1 apple, 1 orange, 1 banana, 1 peach, and 1 plum, how many different combinations can his meal consist of? Although they ask for the same basic thing, we’d go about these questions differently, because order matters in the first question but doesn’t in the second. That is, 234 is not the same password as 432; but an apple, an orange and a banana are the same set of fruit no matter what order they’re eaten in. Dealing with permutations on the SAT Permutations are what the first example shows. To answer a question like this, there are two ways to go about it. The first one involves a formula. k is the number of desired places, which is 3 in the problem, while n refers to the number of different options you are drawing from, which is 5. While that formula works just fine, it’s not really necessary to memorize it, thankfully. It’s actually easier to use some logic. Draw boxes for each place in line you have—in this case, there are three numbers in the combination, so we’ll draw 3 boxes. Each one represents a number in the lock password. There are five possible numbers we could use for the first digit of the password (1-5), so we’ll put a five in the first box. Because we’ve used one digit, there are only four possible digits that can go in the next box—remember that the question said that no digit is used more than once. And following the same logic through one more step, we get this. Now, if you multiply those together you’ll get the answer. That process is probably easier to remember than the formula, so try it out a few times in with different scenarios before you take your SAT. How SAT combinations are different Look back at the question about Andy’s breakfast, and consider whether it’s logical and clear that the solution uses the formula below. No? Good, I’m not alone there. By the way, the r in that formula is the number of members of the group, similar to k in the permutations formula. And again, rote memorization of the formula will get you there, but there’s a more natural, comfortable way. Let’s just start writing down all of the possible combinations. Each piece of fruit will be assigned a letter: A for apple, B for banana, C for…ummm…orange, D for peach, and E for plum. Alright, so it would have been nicer looking if the question had told us there was a carrot, a dragonfruit, and an entawak (yes, that’s a real thing), but who cares. Using the alphabet is the easiest way to keep from having to write out whole words. So we start making groups. First write out all the combinations that use A, keeping in mind not to repeat any one letter because he can’t eat the same fruit twice. ABC, ABD, ABE Then keep going with B, no longer using A. Then with C. And there’s nothing else to use. So we count them all up and see that there are 10 different combinations of fruit Andy might have. A question like this on the SAT generally won’t make you write out more than fifteen different combinations, so it’s actually time-efficient to just do that rather than worrying about the formula. Just remember to ask yourself, “Does order matter?” If it doesn’t, then start writing out the possibilities. If it does, then draw a box for each place in line.

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Statistics Definitions > Continuity Correction Factor Watch the video showing an example or read the article below: What is the Continuity Correction Factor? A continuity correction factor is used when you use a continuous probability distribution to approximate a discrete probability distribution. For example, when you want to use the normal to approximate a binomial. According to the Central Limit Theorem, the sample mean of a distribution becomes approximately normal if the sample size is “large enough.” for example, the binomial distribution can be approximated with a normal distribution as long as n*p and n*q are both at least 5. Here, - n = how many items are in your sample, - p = probability of an event (e.g. 60%), - q = probability the event doesn’t happen (100% – p). The continuity correction factor accounts for the fact that a normal distribution is continuous, and a binomial is not. When you use a normal distribution to approximate a binomial distribution, you’re going to have to use a continuity correction factor. It’s as simple as adding or subtracting .5 to the discrete x-value: use the following table to decide whether to add or subtract. Continuity Correction Factor Table If P(X=n) use P(n – 0.5 < X < n + 0.5) If P(X > n) use P(X > n + 0.5) If P(X ≤ n) use P(X < n + 0.5) If P (X < n) use P(X < n – 0.5) If P(X ≥ n) use P(X > n – 0.5) Let’s make the table a bit more concrete by using x = 6 as an example. The column on the left shows what you’re looking for (e.g. the probability that x = 6), while the right-hand column shows what happens to 6 after the continuity correction factor has been applied. Continuity Correction Factor Example The following example shows a worked problem where you’ll actually use the continuity correction factor to solve a probability problem using the z-table. Sample problem: If n = 20 and p = .25, what is the probability that X ≥ 8? Step 1: Figure out if your sample size is “large enough”. Start by working out n*p and n*q: np = 20 * .25 = 5 (note: this is also the mean x̄) nq = 20 * .75 = 15 These are both over 5, so we can use the continuity correction factor. Step 2: Find the variance of the binomial distribution: n*p*q = 20 * .25 * .75 = 3.75 Set this number aside for a moment. You’ll use this value in Step 4 to find a z-score. Step 3: Use the continuity correction factor on the X value. For this example, we have a greater than or equals sign (≥), so the table tells us: P(X ≥ n) use P(X > n – 0.5) X ≥ 8 becomes X ≥ 7.5. Step 4: Find the z-score. You’ll need all three values from above: - The mean (x̄) from Step 1, - The variance (s) from Step 2, - The Xi value from Step 3. Step 5: Look up Step 4 in the z-table. 1.29 = .4015. Why is the continuity correction factor used? While the normal distribution is continuous (it includes all real numbers), the binomial distribution can only take integers. The small correction is an allowance for the fact that you’re using a continuous distribution. Check out our Youtube channel, where you’ll find tons of videos to help with stats.------------------------------------------------------------------------------ Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free! Comments? Need to post a correction? Please post a comment on our Facebook page.

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Economists use real gross domestic product (GDP) when they want to monitor the growth of output in an economy. Nominal GDP, typically referred to as just GDP, uses the quantities and prices in a given time period to track the total value produced in an economy over a certain time. Conversely, real GDP tracks the total value produced using constant prices, isolating the effect of price changes. As a result, real GDP is an accurate gauge of changes in the output level of an economy. The Bureau of Economic Analysis (BEA) calculates real GDP by removing the effects of inflation from GDP using a GDP price deflator. The deflator is the difference in prices between the current year and base year chosen by the BEA for comparison. For example, if prices rose by 5% since the base year, the deflator would be 1.05. Nominal GDP is divided by this deflator, yielding real GDP. Output growth is a key estimate for policymakers. For example, the Federal Reserve factors GDP into its decisions on influencing the money supply, and these decisions affect the entire economy. If GDP growth is low or negative, the fed funds rate is decreased, making it more difficult for banks to acquire capital. As a result, banks can make fewer loans to individuals and businesses, which slows down economic growth. This is an appropriate policy response when the economy is in a downturn, but nominal GDP cannot convey that information. Negative growth of nominal GDP may be due to a decrease in prices or a decrease in output, but negative growth of real GDP can only be due to a decrease in output. (For more, see: Nominal vs. Real GDP.)

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The definition of due process according to Wilson (2009) is protection against arbitrary deprivation of life, liberty, or property as guaranteed in the 5th and 14th amendments. Throughout the history of the United States, its constitutions, statues and case law have provided standards for fair treatment of citizens by federal, state and local governments. “Due process is one of the most controversial. ” Doctrines currently applied by the Supreme Court. Due process of law is administered through courts of justice in accordance with established and sanctioned legal principles and procedures, and the safeguards for the protection of individual rights. In the United States, due process first appears in the Fifth Amendment of the Constitution. The Constitution was ratified in the year 1791 on December 15th. This amendment wasn’t for the states, but was at the federal level of government. Due process also appeared in the 14th amendment that was ratified in the year 1868 on July 9th. With this new ratification, it was established at both federal and state levels that no person “shall be deprived of life, liberty, or property without due process of law. ” As determined by custom and law, due process has become a guarantee of civil as well as criminal rights. Now today in the United States through interpretation of the law, due process has grown to include, among other things, provision for ensuring an accused person a fair and public trial before a competent tribunal, the right to be present at the trial, and the right to be heard in his/her own defense. This process was founded upon the basic principle that every man shall have his day in court, and the benefit of the general law of due process. Explain how due process protects the accused against abuses by the federal government. The right to due process is the right to be treated fairly by your government. This amendment protects your right to be treated fairly by the federal government. Most people don’t know that before the Fourteenth Amendment was passed, the Bill of Rights only protected you from unfair treatment by the federal government. The Fourteenth Amendment has been used to protect you from unfair treatment by state and local governments. Due process means that members of your government must use fair methods or procedures when doing their jobs. With the amendments made there are now fair decisions and procedures set in place to make sure citizens are being treated fairly. If someone has committed a crime according to The Bill of Rights, you have the right to have a lawyer. A lawyer is a person to help defend you. If the government doesn’t allow you a lawyer it would have violated your right to due process which is guaranteed by the Constitution. This doesn’t mean the government will pay for a lawyer but it will help you if you cannot afford to pay for one yourself. With the changes in the amendment the accused has the right to present evidence, including the right to call witnesses. Also they accused has the right to know the opposing evidence that will be used against them during the trail. Due process is a constitutional right of all citizens and gives us the power to be treated fairly. This right should always be held in the highest regard and never taken for granted. Now with these changes people who are in authority to preform search and seizures, they are not able to perform and unreasonable search. Now evidence will not be permitted into the court rooms. This is now a more far practice and it’s the same across the board for all people.

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The material is also available in a PDF format: Decision-making: Suggestions for school staff [317KB] Effective decision-making skills are important for children’s learning in many areas When children are supported to make responsible decisions at school it helps them manage their own behaviour and relate more effectively to others. Many situations provide opportunities to teach and reinforce children’s developing decision-making skills at school. These arise in formal learning, social activities, play, and in choosing appropriate behaviour in the school grounds. School staff can assist children to manage their behaviour at school by teaching skills for decision-making and encouraging children to use them in a range of situations. Teach skills for decision-making and goal-setting For younger students: Provide opportunities to make simple decisions. Asking students to explain the reasons for their choices helps them develop skills of evaluation. Comment on decisions made by characters in stories (eg “Do you think Charlie made a good decision? Do you think he should have done something different?”) Model the steps for decision-making by talking through decisions you need to make. For older students: Explicitly teach the steps of decision-making and provide practice in using them. Build goal-setting and decision-making steps into assigned learning tasks by making them an explicit component of task instructions. This builds their capacity for self-regulated learning, which has been shown to enhance academic performance. Step 1: What’s my goal? Step 2: What strategies/options can help? Step 3: What are the pros and cons of each option? Step 4: Choose the best one to try. Step 5: Evaluate how my choice worked. What do I need to change? Involve students in decision-making Even younger students can be involved (with guidance) in deciding on classroom and school rules. Children accept that adults will make the fi nal decision, but appreciate being consulted and having the opportunity to contribute to the rules. In addition to building children’s decision-making skills, this helps them to own and accept rules as necessary and fair. Providing students with some choice over what and how they learn can enhance motivation as well as responsibility Encourage children’s decision-making to promote responsible behaviour Asking, “Was that a good decision?” helps children to evaluate their actions. Asking, “What’s a better way to handle it?” prompts them to choose a better option. Asking, “What can we do about this?” invites them to discuss a problem and to get your help in thinking of a strategy for managing it better. Support growing independence by fostering decision-making Primary school children often expect school staff to make decisions for them. This sometimes occurs even for relatively minor decisions that children could make for themselves. Teaching and reinforcing the steps of decision-making helps to support children to develop independence and confidence in their own judgment. For example, a child who is given a specific suggestion in response to the question, “What should we play?” learns that adults are good at determining what he or she should do. When the response is, “Let’s see, what ideas do you have?” he or she is encouraged to take responsibility for generating options. Further ‘scaffolding’ can help the child to evaluate the options and make a choice, at the same time increasing confidence for deciding independently in the future.

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Phonetic Words And Stories, Book1 In this book, the vowels are color-coded. Each vowel sound is printed in a particular color. This helps students notice the vowels in words. The color-coding also helps students become aware that different vowel patterns can represent the same sound, and in some cases, one vowel pattern can represent more than one sound. Book 1 teaches basic vowel sounds, consonant blends, consonant digraphs. and a few other common patterns. Students play the "robot game" as they study pages with new phonetic words and pictures. The game helps students analyze the sounds in each word so that it will be easier to read it. After learning several new sets of words, students read a short practice story to apply their new knowledge.

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A simple definition of empathy is the ability to share another person's feelings and emotions as if they were your own. So, how can we teach children empathy, if they don't have the cognitive skills to truly understand the concept. In order to teach this concept, we need to begin by praising kind behavior and encouraging children to talk about their feelings. Therefore, young children need to recognize their feelings and it is essential for adults to connect feelings to behaviors. For example, "It was very nice how you helped the new boy at school, he may have been feeling nervous." It is important for adults to recognize a child’s behavior, as they will know you value your efforts. Allow children to talk about their feelings. It is important for children to know that you care about how they feel. Listen attentively when they tell you about an incident that took place at school or at home. Also, allow children to express their opinion related to an incident. For example, if a child says “Billy was teasing Sally today on the playground. I thought that was mean and it made me angry.” Respond by saying, “So you were not happy with the way Billy acted?” Responding will encourage the child to elaborate. Also, it is important to express your feelings to children. They will learn that adults have feelings and emotions too. Feelings and emotions are a normal part of life, and learning to cope with them is an important part of growing up. Empathy needs to be nurtured throughout a child’s life. Learning empathy requires practice and guidance. Regularly considering other people’s viewpoints and situations helps make empathy a natural impulse and helps children get better at understanding the feelings and perspectives of others. In the Carrie Flower Curriculum, we developed an activity that allows children to identify and express feelings. The activity uses emotion cards that portray a specific emotion on each card. Small groups of students introduce their emotion card to the class. Each group is responsible for figuring out how to be responsive to their card's feelings. For example, if one card has a sad face, what can they do to help? If another card shows a happy face, how can they use that positive feeling to benefit others? Discussions included with this activity include: a. How can we identify our own feelings? b. Provide mirrors for children to look at their own faces. Have them act out various emotions and describe what happens to their faces when they feel certain emotions. c. How can we express our feelings in positive, healthy ways? d. How can we help those around us with their feelings? Write each idea on the chart paper. The charts can be displayed in the hallway or classroom after the lesson. It will serve as a reminder to students to identify and express feelings in a helpful manner. In fact, you can encourage students to add other ideas as they think of them. I hope you find these discussions and activities helpful in your classrooms or at home with your own children. I would love to hear your opinions or any ideas you may wish to share when teaching children social and emotional skills. Please feel free to comment below. Thank you. Until next time, Dr. G.

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- Have a list division word problems for your students to figure out using manipulatives. Example problem: Kimmy is inviting two friends over after school. Her mom helped her bake 15 cookies. How many will each of them get? - Provide bowls, cups, or some other kind of container as well as counters for this center. - Students read the problems and figure out the answers using the manipulatives. For example, for the problem above students would count out 15 counters and divide them amongst 3 containers to find the answer. - Students should draw a representation of how they figured out the problem. They should also write the math function the represents the problem -- for the above problem. 15 / 3 = 5

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The following terms and definitions are often associated with and provide a common, working language for ADL’s educational anti-bias programs and resources. The definitions are written for older youth to adult reading levels, unless otherwise specified, and some include age-appropriate versions for younger ages. Ability: Having the mental and/or physical condition to engage in one or more major life activities (e.g., seeing, hearing, speaking, walking, breathing, performing manual tasks, learning or caring for oneself). Ableism: Prejudice and/or discrimination against people with mental and/or physical disabilities. Activist: Someone who gets involved in activities that are meant to achieve political or social change; this also includes being a member of an organization which is working on change. - Elementary school version: A person who uses or supports actions such as protests to help make changes in politics or society. Ageism: Prejudice and/or discrimination against people because of their real or perceived age. Although ageism is often assumed to be bias against older people, members of other groups, such as teens, are also targets of prejudice and/or discrimination based on their age. Aggressor: Someone who says or does something harmful or malicious to another person intentionally and unprovoked. - Elementary school version: Someone who says or does hurtful things on purpose and over and over. Ally: Someone who speaks out on behalf of or takes actions that are supportive of someone who is targeted by bias or bullying, either themselves or someone else. - Elementary school version: Someone who helps or stands up for someone who is being bullied or the target of bias. Anti-bias: An active commitment to challenging prejudice, stereotyping and all forms of discrimination. Anti-Semitism: Prejudice or discrimination that is directed towards Jews. Anti-Semitism is based on stereotypes and myths that target Jews as a people, their religious practices and beliefs, and the Jewish State of Israel. Bias: An inclination or preference either for or against an individual or group that interferes with impartial judgment. - Elementary school version: A preference either for or against an individual or group that affects fair judgment. Bigotry: An unreasonable or irrational attachment to negative stereotypes and prejudices. - Elementary school version: Prejudice and/or discrimination against a person or group based on stereotypes. Bisexual: A person who is emotionally, physically and/or romantically attracted to some people of more than one gender. Bullying: Repeated actions or threats of action directed toward a person by one or more people who have (or are perceived to have) more power or status than their target in order to cause fear, distress or harm. Bullying can be physical, verbal, psychological or any combination of these three. Bullying behaviors can include name-calling, obscene gesturing, malicious teasing, rumors, slander, social exclusion, damaging a person’s belongings, threats and physical violence. - Elementary school version: When a person or a group behaves in ways—on purpose and over and over—that make someone feel hurt, afraid or embarrassed. Bystander: Someone who sees bias or bullying happening and does not say or do anything. All forms of bias can be both explicit (aware, voluntary and intentional) and implicit (unaware, involuntary and unintentional). All manifestations of bias and discrimination can be both personal (an individual act of bias, meanness or exclusion) or institutional (supported and sanctioned by power and authority that confers privilege on members of a dominant group while disadvantaging members of other groups).

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When an object obeys simple harmonic motion, it oscillates between two extreme positions. The period of motion measures the length of time it takes an object to complete oscillation and return to its original position. Physicists most frequently use a pendulum to illustrate simple harmonic motion, as it swings from one extreme to another. The longer the pendulum's string, the longer the period of motion. Divide the string's length, measured in meters, by the factor measuring acceleration due to gravity, 9.81 meters per second per second. If the string measures 0.6 meters, then the equation is 0.6 / 9.81 = 0.06116. Find the square root of this answer. In the example, the square root of 0.06116 is 0.2473. Multiply this result by twice the constant pi, 6.2832. In the example, you would multiply 0.2473 by 6.2832 to get 1.55 seconds. This is the period of motion.

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In 7th grade Spanish, students have been learning how to describe where things are by using estar + a preposition. They played games with each other like “Where is the pencil? Where are the pencils?”. Students also looked at maps of different cities such as Madrid, Mexico City, Guatemala City, and Quito and then described to each other where different monuments or attractions were in relation to other things so that visitors could find their way around. Recently, students started unpacking the difference between the verbs ser and estar, which both mean “to be”. Students started by brainstorming different sentences they have heard each of these verbs in and wrote them on a piece of paper. Each table group presented their brainstorm to the class in Spanish. After the presentations, we discussed some specific purposes served by each verb. Estar for example, is a verb we use to talk about the location of an object (the ball is on the table). Ser is a verb that can be used to talk about where we are from and to describe others. We will continue our exploration of using these verbs with other speaking, reading, listening, and writing activities! 8th grade students have been working hard to master their reflexive verbs! They created how-to guides that explained how to conjugate these different kinds of verbs, which helped them better understand the ways of using and conjugating them. Students flexed their creativity muscles by completing mini-stories using reflexive verbs as well. There were many stories written about the daily routines of children and their families, but also about non-human characters, like trees and ducks as well. The creativity they demonstrated in these stories was fantastic, and made their work enjoyable for them and their classmates. Don Quixote and Sancho Panza We have also been learning about how to understand a text written in Spanish, even if we do not understand every word. Students interacted in pairs, only in Spanish, to read a text about a mysterious text message, to answer questions about what happened in the text, and also worked individually to describe what happened in the story. Using strategies like looking for context clues, cognates, and words that they already know, students were able to work through this challenging story and learned more about the famous literary characters Don Quixote and Sancho Panza. In 6th grade Spanish, students have been learning how to describe different animals with adjectives and verbs. Unlike English, in Spanish, adjectives need to agree with their nouns in number and gender. That means if students wanted to write about a dog, they would need to change their adjective to match the noun. Dog in Spanish is perro. It is masculine and in this case, it is singular. An adjective describing this dog would also have to be masculine and singular. If we wanted to say that the dog was nice, we would say el perro simpático. To add a little more difficulty and action to their sentences, students also incorporated the -ar verbs they have been learning about. Recently, students completed comics about a character walking through an enchanted forest and narrating the different animals s/he encountered.Descriptions in these comics included happy worms singing, sad gorillas painting, and egotistical foxes dancing. Students put in great work and effort to this project and came up with some very creative descriptions to describe their own enchanted forests. Students also added to their repertoire of verbs by learning how to conjugate -er and -ir verbs as well. After learning the steps of how to conjugate these verbs, we enjoyed watching this great video to help us practice all of the conjugations! I’m excited to see how students use their new verbs and skills to continue to build on their knowledge of Spanish in fun ways. Before winter break, students were able to delve into a world of stories in Spanish. They were given many options of books written in Spanish that they were able to choose and practice reading aloud independently for the first half of a class. After this time, students joined together in small groups and read their stories aloud to each other. Using gestures, tone, and body language, they encouraged their group mates to understand what their story was about. After this, students watched and read several versions of a story called “El Principe Ceniciento” which is a play on the story of Cinderella, but with a fairy godmother who was a little confused and not very experienced at her job. Students discussed with each other how they could understand a story all in Spanish if they did not understand each word. They learned that by using their senses, knowledge of basic Spanish, and cognates to follow the story. After break, students have been working on learning a new kind of verb to be able to talk about their daily routines. These are reflexive verbs, which is a verb where someone does something to themselves, for example “I brush my hair” or “I bathe myself.” Students will continue to practice these verbs by interviewing each other about their daily routines, reading about daily routines of others, and will write about their own. Over the last few weeks, students in 6th grade have been working with a dialogue and adding to it as we learn new sentence structures. They began by learning about how to greet someone in Spanish and how to say goodbye; paying attention to whether these interactions were formal and informal. They are now turning these dialogues into their final term projects and adding an exchange of how are you’s and conjugated verbs. In these conversations that students are writing, they have two characters, one formal and one informal. They will use their evolving dialogue structure to demonstrate their ability to address people formally and informally and show their progression of conjugating regular, -ar verbs. Students will also show their knowledge of using different adjectives to describe how they are. After completing these projects, students will have a firm grasp how to have a simple conversation with new people in Spanish and be able to express how they are feeling and talking about what they and other people in their lives do. I can’t wait to see what they come up with! Point People: Phelana, Wendy, Lydia Culmination of Pay It Forward projects – display of research, art, poetry, actions, website Students will be stationed with a display board, art project, website. They can talk about their issue – the root causes, impacts, solutions…, perform their spoken word poem, show their lobbying … Continue reading Point Person: Colleen firstname.lastname@example.org Having a social atmosphere for families to get to know each other and have a meeting for adults in CMR and activity for students in the downstairs lab.

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After a long day at work or school, you finally get into a coffee shop and order a cup of coffee and some cinnamon rolls. You notice the aroma of the coffee and the sweet scent of the cinnamon rolls, and feel relaxed in an instant. This is how your sense of smell works – the airborne chemicals of the food stimulate your sensory receptors that correspond to the sense of smell. The smell sensory receptors are classified under a bigger group of sensory receptors known as chemoreceptors. These chemoreceptors carry out a process called transduction, wherein chemical signals from the stimulus are transformed into action potentials. Action potentials are short-lasting events that lead to the recognition of the chemical signals, and thus, the stimulus. The smell sensory receptors are found in a tissue in the nasal cavity called the olfactory epithelium. This patch of tissue is comprised of three types of cells: Basal cells - cells that undergo regular process of division in order to produce new sensory neurons as replacement for dying neurons Supporting cells - cells located in between basal cells and sensory neurons Sensory neurons - cells paired with primary cilia and contain the olfactory receptors that receive chemical signals from the stimulus Cilia are hair-like protuberances that are necessary for processing molecules that we smell, also known as "odorant molecules". The cilia of sensory neurons are covered with mucus where the odorant molecules are dissolved. Once dissolved, the molecules undergo a binding process which activate the G protein in the sensory receptor. When G protein is activated, the enzyme on the cilia begins to work by catalyzing the conversion of ATP (cell energy). This leads to the sodium (Na+) electrolytes to enter the cell. Once there's an influx of sodium, the plasma membrane's potential is continuously reduced, a process called depolarization. When the depolarization of the plasma membrane reaches its limit or threshold, an action potential is generated. The action potential is then transferred by the olfactory nerve to the brain. The brain processes the action potential as a sensory information, and once the brain is done evaluating it, a normal person would be able to recognize and perceive the particular odor. Photo by Zachary Veach There are thousands of odors around us, yet our sense of smell only includes one kind of cell. How can we differentiate one odor from another then? Many scientists agree that each olfactory receptor is able to bind to different kinds of odorants according the odorant chemicals' intensity. For example: Odorant Coffee binds to the olfactory receptors on neurons #7, #11, and #345. Odorant Cinnamon binds to the olfactory receptors on neurons #7, #23, and #543. The brain will interpret these as two different odors, and would normally correspond to one being the coffee, and the other being the cinnamon. This means you're free to copy, share and adapt any parts (or all) of the text in the article, as long as you give appropriate credit and provide a link/reference to this page. That is it. You don't need our permission to copy the article; just include a link/reference back to this page. You can use it freely (with some kind of link), and we're also okay with people reprinting in publications like books, blogs, newsletters, course-material, papers, wikipedia and presentations (with clear attribution).

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Getting to grips with the 4 basic arithmetic operations (Add / Subtract / Multiply / Divide ) when using fractions can easily be achieved once you know some basics rules: With adding and subtracting, the rule is to make sure the denominators are the same before you can add or subtract fractions. if not, then multiply one (Case II) (or both fractions (Case III) ) by a number so as to end up with fractions having the same number as the denominator. - Case I: Fractions have the same denominator. We simply add or subtract the numerator. - Case II: Fractions have different denomintors. However, multiplying on of the fractions by a number (in this example by 2) we end up with both fractions having the same denominator. - Case III: This is the most complex example. In this case, we have to multiply both fractions by a number so as to obtain the same denominator in both fractions. The first fration is multiplied by 4 an d the second fraction by 7. The full video lesson on adding and subtracting fractions is found here.

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The lesson discusses the science and chemistry of the human body. Most students are aware of the basic “ingredients” of the human body, but may not realize the numerous elements that are part of it. The lesson also discusses their usefulness to the body, and what might happen to the body without some of the chemicals. Students should have some prior knowledge about chemistry before this lesson is used. Several interactive websites and age appropriate videos are included with the lesson. The lesson can be used in conjunction with lessons related to the human body or other chemistry lessons. Sample Classroom Procedure / Teacher Instruction: - Ask students: How much do you think your body is worth in dollars? - Allow for responses and discussion. Additionally, ask why they believe it is worth that amount. - Allow for responses and discussion. Ask students if they believe it is possible to “build” a human body by purchasing and using the available chemicals. Why or why not? - Allow for responses and discussion. Introduce Chemistry of the Body. - Distribute Chemistry of the Body content pages. Read and review the information with the students. Save the final question for the lesson closing. Use the additional resources to enhance understanding. - Distribute Activity page. Read and review the instructions. Review the use of scale and proportion with students. (It is recommended teachers create larger outline images of the body, distribute construction paper, or use other large sheets of paper. The larger the paper, the easier it will be for students to label the elements.) Tell students they do not necessarily need to shade using layers of colors. However, they must label each color, or may use a key to show which color represents each chemical. Distribute colored pencils. Allow sufficient time for completion. - Once completed, students share the colored images of the body. Allow some students to recite the amounts of each chemical. You may also ask students to tell what each chemical does for the body. - Distribute Practice page. Check and review the students’ responses. - Distribute the Homework page. Read aloud a sample recipe. Encourage students to use their imagination. The next day, ask students to correct false statements and share “recipes”. - In closing, ask students: The top 4 elements of the human body are oxygen, carbon, hydrogen, and nitrogen. Create a method of remembering the four elements in order from must to least. Common Core State Standards: CSS.ELA-Literacy.RI.4.2, CCSS.ELA-Literacy.RI.4.3, CCSS.ELA-Literacy.RI.4.4, CCSS.ELA-Literacy.RI.5.2, CCSS.ELA-Literacy.RI.5.3, CCSS.ELA-Literacy.RI.5.4, CCSS.ELA-Literacy.RST.6.2, CCSS.ELA-Literacy.RST.6.4, CCSS.ELA-Literacy.RST.6.7 Class Sessions (45 minutes): At least 2 class sessions Want more science resources? Check out our other Science Lesson Plans!

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How does a rocket engine work? A rocket engine works by ejecting stored material. It pushes on this material to make the material accelerate and the material pushes back on the engine. If the force that the ejected material exerts on the engine is upward and greater than the rocket’s weight, the rocket will accelerate upward. Most rocket engines are chemical engines. They combine stored chemical fuels to produce hot, high-pressure gas. This gas is allowed to expand out of a narrow orifice—the throat of the engine’s exhaust nozzle. Gases always accelerate toward lower pressure, so the high-pressure gas moves faster and faster as it rushes out of the nozzle. It reaches sonic velocity (the speed of sound) in the nozzle’s throat and continues to move faster and faster as it flows out of the nozzle’s widening bell. By the time the gas leave the engine completely, it’s traveling several thousand meters per second. A liquid fuel rocket has an exhaust velocity of about 4,500 meters per second or about 3 miles per second. Accelerating the gas to this enormous speed takes a huge force—the engine pushes down hard on the gas. The gas pushes back and propels the rocket upward.

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About This Chapter Circles - Chapter Summary Continue your study of plane geometry with this chapter on circles. Our experienced instructors can help you study the properties of circles and provide you with tips for proving their similarity. You can also examine the radii, tangents and chords that intersect them. Lessons showing you how to find the lengths of chords and the inscribed angles of tangents are included as well. You can also explore the relationship between arcs and radians and practice calculating the area of a sector. Additional lessons help you apply these skills when working with inscribed and circumscribed triangles and quadrilaterals. Instructors go on to break down the formula for a circle and show you how to write it when presented with a circle's center and radius. You can also learn how to find the center and radius when given a circle's equation by completing the square. Topics of discussion found in this chapter include: - Inscribed angles - Radii and chords - Arc length Take advantage of the illustrations included in this chapter's video lessons to get the hang of working with circles. This same material is also presented in the form of transcripts that feature links to supplementary text lessons. Use them to discover definitions of key terms and improve your understanding of the lesson topics. There are also multiple-choice quizzes you can take at any point during your studies in order to assess your grasp of the material. 1. Properties of Shapes: Circles Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate. 2. Inscribed Angle: Definition, Theorem & Formula Circles are all around us in our world. Inscribed angles are angles that sit inside a circle with the vertex on the circumference of the circle. Inscribed angles have a special relationship with the intercepted arc. 3. How to Find the Radius of a Circle: Definition & Formula In this lesson, you will discover the definition of a radius. You will also learn how to find the radius of a circle using three different formulas based on diameter, circumference, and area. 4. What is a Chord in Math? In this lesson, you will learn what a chord of a circle is in math. You will also learn other basic parts of a circle, including the diameter and radius. Finally, you will see which of these parts is a chord and which is not. 5. How to Construct a Tangent of a Circle It's pretty amazing what you can draw with just a straight edge and a compass! In this lesson, you'll learn how you can draw tangents of a circle, whether you are given a point on the circle or outside of the circle and if you have two circles. 6. Arc Length of a Sector: Definition and Area In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course - About the TExES Math 7-12 Exam - Real Numbers - Mathematical Models - Complex Numbers & the Complex Plane - Number Theory - Number Patterns - Functions and Graphs - Linear Functions - Quadratic Functions & Polynomials - Evaluating Piecewise & Composite Functions - Rational and Radical Functions - Inequalities and Absolute Values - Exponentials & Logs - The Unit Circle - Trigonometric Functions - Using a Scientific Calculator for Calculus - Understanding Limits in Math - Understanding Rate of Change - Calculating Derivatives of Functions - Derivatives and Graphs - Optimization in Calculus - Definite Integrals and Sums - Integration Applications in Calculus - Working with Measurement - Finding Volume, Area & Perimeter - Introduction to Proofs and Constructions - Congruence and Similarity - Real World Shapes - Coordinate Geometry - Understanding Transformations in Math - Conic Sections - Understanding Vectors - Measuring & Displaying Data - Data Distribution Overview - Sampling in Statistics - Distribution & Inference in Statistics - Inference About a Mean - Regression and Correlation - Finding Probability - Probability Distributions and Statistical Inference - Experiments and Surveys - Mathematical Process & Perspectives - Teaching Strategies & Activities for the Math Classroom - Differentiated Instructional Strategies for the Math Classroom - Using Student Assessments in the Math Classroom - TExES Mathematics 7-12 Flashcards

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Key Facts & Summary - The enthalpy of a chemical system refers to the "heat content" of the system. - Enthalpy is given the symbol H - Enthalpy change refers to the amount of heat released or absorbed when a chemical reaction and it is given the symbol ΔH - A reaction is exothermic when it releases energy, and ΔH = negative. - A reaction is defined endothermic when it absorbs energy, therefore the ΔH = positive. The amount of heat evolved or absorbed in a reaction carried out at constant pressure is called enthalpy changes. It is given the symbol ΔH, read as "delta H". It is important to remember that The term "enthalpy change" only applies to reactions done at constant pressure. The standard enthalpy changes apply when the reaction is run at standard conditions, which are : - 298 K (25°C) - a pressure of 1 bar (100 kPa). - where solutions are involved, a concentration of 1 mol dm-3 Also, the compounds need to be present in their standard state. That is the physical and chemical state that you would expect to find it in under standard conditions. That means that the standard state for water, for example, is liquid water, - not steam or water vapour or ice. Oxygen's standard state is the gas, - not liquid oxygen or oxygen atoms. Enthalpy changes are calculated using Hess's law: If a process can be written as the sum of several steps, the enthalpy change of the process equals the sum of the enthalpy changes of the individual steps. If we know the enthalpy changes of a series of reactions that add up to give an overall reaction, we add these enthalpy changes to determine the enthalpy change of the overall reaction. If we know the standard enthalpies of formation, ΔH, of the reactants and products of a reaction we can calculate the enthalpy change of the reaction using the following shorthand version of Hess's law: Where Σ ΔH indicate the sum of the change of enthalpies. Hess's Law is says that if you convert reactants A into products B, the overall enthalpy change will be exactly the same whether you do it in one step or two steps or however many steps. A reaction is exothermic when it releases energy, and ΔH = negative. On the other hand, a reaction is defined endothermic when it absorb energy, therefore the ΔH = positive. Scheme 1. Graphic representation of changes of enthalpy in the reactions. In an exothermic reaction - Heat is a product of the reaction. - Temperature of reaction mixture increases. - Hproducts < Hreactants - ΔH = Hproducts - Hreactants = a negative number In an endothermic reaction - Heat is a reactant in the reaction. - Temperature of reaction mixture decreases. - Hproducts > Hreactants - ΔH = Hproducts - Hreactants = a positive number Let's have a look now to the following picture: This shows a chemical reaction between the same reagents, producing the same products, but going through two different ways. In one case, there is a direct conversion; in the other, there is a two-step process involving some intermediates. As you can see, in either case, the overall enthalpy change is the same, because it is governed by the relative positions of the reactants and products on the enthalpy diagram. If you go via the intermediates, you do have to put in some extra heat energy to start with, but you get it back again in the second stage of the reaction sequence. This is true for any reaction. Let's use an example and explore better this topic: H2O2(l) → H2O(l) + 1/2 O2(g); ΔH = -98.2 kJ The symbol for a standard enthalpy change of reaction is ΔH°r. For enthalpy changes of reaction, the "r" (for reaction) is often missed off - it is just assumed. The "kJ mol-1" (kilojoules per mole) refers to the quantities of all the substances given in the equation. In this case, 98.2 kJ of heat is evolved when 1 moles of hydrogen peroxide liquid reacts to form 1 mole of water liquid and 1 moles of oxygen gas. Whenever a standard enthalpy change is quoted, standard conditions are assumed. If the reaction has to be done under different conditions, a different enthalpy change would be recorded. But this is a problem for another time. Let's use the same reaction in a usual enthalpy problem: Hydrogen peroxide decomposes according to the following thermochemical reaction: H2O2(l) → H2O(l) + 1/2 O2(g); ΔH = -98.2 kJ How do we calculate the change in enthalpy, ΔH, when 1.00 g of hydrogen peroxide decomposes in this reaction? First of all, we need to know the enthalpy change value, which is given here. If it is not given, there are tables indicating them. The thermochemical equation tells us that ΔH for the decomposition of 1 mole of H2O2 is -98.2 kJ. Now, we need to know the number of moles of the relevant compound to calculate the answer. We use the Periodic Table to add up the masses of hydrogen and oxygen atoms in hydrogen peroxide: the molecular mass of H2O2 is 34.0 (2 x 1 for hydrogen + 2 x 16 for oxygen), which means that 1 mol H2O2(l) = 34.0 g H2O2 Using these data we can calculate: ΔH = 1.00 g H2O2 x 1 mol H2O2 / 34.0 g H2O2 x -98.2 kJ / 1 mol H2O2 ΔH = -2.89 kJ Let's use another example and take in consideration the following reaction: CS2(l) + 3 O2(g) → CO2(g) + 2 SO2(g) C(s) + O2(g) → CO2(g); ΔH = -393.5 kJ/mol S(s) + O2(g) → SO2(g); ΔH = -296.8 kJ/mol C(s) + 2 S(s) → CS2(l); ΔH = 87.9 kJ/mol To solve this type of problem, we can follow a few rules: -The reaction can be reversed. This will change the sign of ΔH. -The reaction can be multiplied by a constant. -The value of ΔH must be multiplied by the same constant. Any combination of the first two rules may be used. Let's start finding one of the reactants or products where there is only one mole in the reaction. In our case, one CO2 and the first reaction has one CO2 on the product side. C(s) + O2(g) →CO2(g), ΔH= -393.5 kJ/mol This gives us the CO2 we need on the product side and one of the O2 moles we need on the reactant side. To get two more O2 moles, use the second equation and multiply it by two. Remember to multiply the ΔH by two as well. 2 S(s) + 2 O2(g) → 2 SO2(g), ΔH = 2(-326.8 kJ/mol) Now we have two extra S and one extra C molecule on the reactant side. The third reaction also has two S and one C on the reactant side. Reverse this reaction to bring the molecules to the product side. Remember to change the sign on ΔHf. CS2(l) → C(s) + 2 S(s), ΔHf = -87.9 kJ/mol When all three reactions are added, the extra two sulfur and one extra carbon atoms are canceled out, leaving the target reaction. All that remains is adding up the values of ΔH ΔH = -393.5 kJ/mol + 2(-296.8 kJ/mol) + (-87.9 kJ/mol) ΔH = -393.5 kJ/mol - 593.6 kJ/mol - 87.9 kJ/mol ΔH = -1075.0 kJ/mol Therefore, the answer to our initial question, the change in enthalpy for the above reaction is -1075.0 kJ/mol. Clayden Jonathan Clayden, Nick Geeves, Stuart Warren ISBN: 978-0199270293

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Or download our app "Guided Lessons by Education.com" on your device's app store. Adventures with Action Verbs Students will be able to use action verbs when writing. - Ask students what a verb is. - Tell students that VerbsAre words that describe ActionsOr states of being. - Explain that verbs like CookAre action verbs because they describe actions someone is taking. Verbs like IsDescribe states of being. Explicit Instruction/Teacher modeling(10 minutes) - Show students the stack of index cards. Explain that on each of the cards is an action verb. - When you flip over a card, you will act out the action verb. - Model how to do this a couple of times. Guided practise(10 minutes) - Ask for volunteers to act out the words on the cards. - Call a student to the front of the class and pick a card for them to act out. - If you run out of cards, have students share examples of action verbs that other students can act out. Independent working time(15 minutes) - Tell students that using action verbs helps to bring writing to life. Explain they will be using action verbs to write an exciting movie scene. - Hand out the Lights, Camera, Action (Verbs)! worksheets to each student. Have them work independently to complete their writing. Support:Brainstorm a list of action words that students can use in their movie scenes. Keep the list posted on the board or on a piece of paper next to the students who need it. Enrichment:If students finish early, they can complete the Action Words #2 worksheet. - Assess how students are using action words in their writing. Review and closing(10 minutes) - Ask for volunteers to share their writing. - After each person shares, ask students to identify action verbs that they heard.

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What Is Math Workshop? Math workshop is known by various names: math workshop, leveled math groups, guided math, differentiated groups, etc. Whatever you call it, math workshop is a valuable way to teach math concepts. Math workshop is an instructional method where teachers 1) hold brief math warm-up sessions (number talks, calendar time, fluency practice, etc.); 2) present a math topic to the whole group; 3) hold small-group leveled sessions to fine-tune and/or differentiate; 4) give students multiple and varied opportunities to practice; and finally, 5) close with time to reflect or share. What Math Workshop looks like Expect to see engaged students in a math workshop session. It begins with a short warm-up to get students thinking with their math brains, which is then followed by a 10- to 15-minute whole-group mini-lesson where a new skill is introduced. Later, four to eight students sit with their teacher. The rest are engaged in practice activities. One group may be playing a game. Some may sit alone or in pairs. Students who require intervention may work on targeted review. Finally, everyone comes together to close the session. Some useful suggestions are: - During small-group, use math talk and math tools to reinforce and expand on concepts taught in the mini-lesson. This is also a good time for one-on-on conferencing or observation. - Other students typically rotate, according to a schedule, through each of three to five stations for 10–20 minutes each. They practice previously learned or new skills. They may work alone, with partners, or in small groups. Independent activities may include: - task cards - simple games - fluency practice sheets - math journals - interactive notebook pages - Close math workshop with a short recap. Answer any remaining questions. Encourage students to share “a-ha” moments or to work in their journals. Additionally, you could provide exit tickets to allow students to show what they learned (and provide a quick formative assessment). Organization and planning are key Organization is key to making a success of your math workshop program. Start slowly because it can be overwhelming. Here are some tips: - Make a rough plan for the year. Figure out what you need to teach and how long it will take to cover it. - Be flexible. Due to the nature of math workshop, things may take longer or shorter than you expect. - Choose a few key independent practice activities to use all year long. This way, students will always know the rules. Choose activities that can easily be adapted to multiple concepts. Some simple examples are Read the Room, path games, task cards, etc. - Fill a tote with things that students will need during small groups, such as dry-erase markers, crayons, or pencils. - Place manipulatives where students can get to them on their own. You can start math workshop at any time. Don’t wait until the “right time”. It requires planning and organizating, so you can’t start today. But, maybe you can start tomorrow! If you’re putting together a full-year plan, ask: What do I need to teach and how long do I have to cover it? Write it down. Remember, these are rough estimates. Begin with a mini-lesson. Teach one quick concept, model it, and show students examples. Next, pre-teach one of the rotation activities. Add it to the mini-lesson. Repeat this until each rotation has been practiced and learned. This is less frustrating for the students and for you. Make a visual schedule to share with the class so that everyone knows what they’re doing and where they’re supposed to be. You need very little to get started, such as: - A special space to meet with students - A designated space for all your math manipulatives - A storage solution to hold games and game pieces - A visual schedule - Patience, hope, and determination! Setting up math workshop can be challenging. But once there’s a schedule and once students know what to do next... it’s a most efficient and effective way to teach math to all students.

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Scientists also use direct evidence from observations of the rock layers themselves to find the relative age of rock layers.The principle of inclusions states that inclusions found in other rocks (or formations) must be older than the rock that contain them. Geologists call it relative dating — we know which one is older but do not know how old they are.This is actually pure logic and it can be applied not only in geology, but it is especially useful for geologists. Inclusions of foreign rocks that are found in igneous rocks are named xenoliths.For liquids and solids the standard is usually water at 4°C or some other specified temperature.For gases the standard is often air or hydrogen at the same temperature and pressure as the substance.If this is the case, we can not say that the inclusion is older than the rock that surrounds it. (Units) the ratio of the density of a substance to the density of a standard substance under specified conditions.The same principle is also used in relative dating of sedimentary rocks. Scientists have good evidence that Earth is very old, approximately four and one-half billion years old.Scientific measurements such as radiometric dating use the natural radioactivity of certain elements found in rocks to help determine their age.Note that there are one larger and several smaller pieces of granite within kersantite. So we can also say that kersantite contains xenoliths of granite. It was already solid rock when it was intruded by mafic lamprophyric magma that scraped some pieces off of granitic rock and embedded them within the solidifying magma.True xenoliths are definitely older than their host rocks but sometimes igneous rocks contain cognate inclusions or restite material. S-type granites for example (granite with a sedimentary protolith) may contain such inclusions which are genetically related to its host rock.

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Printable Charts 99 Chart – The number chart can be used for teaching number patterns and number relationships,operations, problem solving, number sense, counting skills, and skip counting. 100 Chart – The number chart can be used for teaching number patterns and number relationships,operations, problem solving, number sense, counting skills, and skip counting. Fill in Blank … Category: Counting and Cardinality Worksheets Common Core Counting & Cardinality Worksheets - CCSS. Math.Content. K.CC.A.1 Count to 100 by ones & by tens. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.B.4 5 a b c Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one & only one number name & each number name with one and only one object. Last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Each successive number name refers to a quantity that is one larger. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. K.CC.C.6 7 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group by using matching and counting strategies. Compare two numbers between 1 and 10 presented as written numerals. Permanent link to this article: http://theteacherscafe.com/printable-100-and-99-charts/

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Most of the time in the English language, when we want to say that there is more than one of something, we just add an –s to the end of the word. Easy enough. However, there are quite a few words that change entirely when they are made plural. These words are quite tricky for children with language delays to learn because they don’t always follow any logical rules. When children say irregular plural nouns incorrectly, they can sound much younger than they really are. Here are some steps to help your child learn those crazy ones. Irregular Plural Nouns Step One: Make a Word List First you will need to compile your list of irregular plural nouns word pairs and create materials to help your child practice. Come up with a list of word pairs that have irregular plural nouns. For example, “foot” and “feet” would be one pair. You can choose word pairs that you know your child has trouble with or select from a list of commonly used pairs. Write down all of your words and decide how you will present them to your child. If your child can read, you can just use written words on flashcards or index cards. However, if your child is not reading yet, you can make a collection of pictures of each word that you can use as flashcards. You can use the ones on the following page or you can make your own using images you find online or in clipart. Come up with a list of about 20 words that you want to target. Unfortunately, you simply can’t teach your child every irregular plural noun out there, but you can teach the most common ones now and then teach him others as he comes across them in life. Here are examples of word pairs you may want to use: When you have a list of about 20 word pairs, you are ready to move on to the next step. Irregular Plural Nouns Step Two: Drill Word Pairs Now it’s time to teach each of these word pairs to your child. You can explain any rules that you see, such as changing an “f” at the end of the word to a “v” but since there are very few such rules about these words, you will need to teach most pairs directly. Show your child the list of words or the picture flashcards that you have created. Explain to him that most of the time when we want to say that there is more than one of something, we add an –s to the word. Then explain to him that these words are different and that they must change when there is more than one. Go over the list with him to show him what you mean. You can say “when there is one of these, we call it a foot. But when you talk about two of them, we say ‘feet’”. Then, tell your child it’s his turn to practice. Try some of these activities to see what works best for your child: - Straight drill and practice: Say a singular word to your child and ask him what the plural pair is. For example, you say “foot” and your child should say “feet”. Just do this over and over again. - For a little more fun, you can play memory. Turn over all of the picture flashcards and have your child turn over two cards. Have your child tell you what’s on each card. Make sure he uses the correct irregular plural nouns on those that need it. If the two words match (are from the same pair), then he gets to keep them. See which of you can get the most matches. - Get a fun app for your tablet such as Plurality for I-Pad. This app will allow you to play memory games with irregular plural nouns. This is a great way to drill and practice because kids will typically play on the I-Pad for very long periods of time. Irregular Plural Nouns Step Three: Make Sentences With Word Pairs Now that your child knows the irregular plural nouns, it’s time for him to start using them in sentences. Show your child a pair of words from the last step. Tell your child that you will need to create a sentence using both of those words. You can get him started with a sentence like “I see one foot and two feet.” Have him repeat the sentence back to you with the correct irregular plural noun. Then, show him another pair and have him say the same sentence but now with this pair of words. Once he gets the hang of it, see if he can come up with some more creative sentences, like “I fed the monster one cactus and he spit out two cacti”. Irregular Plural Nouns Step Four: Correcting in Conversation The only thing left is for your child to start using the correct irregular plural nouns in conversation. Start paying attention to how your child is saying these words in conversational speech. Chances are, he’s still using the incorrect word when he’s not focusing on it like when you practice with the flash cards and that’s ok! Start by correcting those irregular plural nouns about 10% of the time when you hear them in conversation. This means you’re not correcting him all the time (that would drive him nuts) but you’re slowly beginning to bring his awareness to the fact that he needs to be saying those correctly in conversation. Gradually, increase the percentage of his irregular plural noun errors that you hear. As your percentage increases, his accuracy should also increase. Ease into this so that by the time you’re correcting him 90-100% of the time, he’s already doing it most of the time anyway so there aren’t many errors for you to correct. Make sure you correct him in a gentle manner so that he doesn’t feel like you’re picking on him. Where to Find More Info: This guide, along with 38 others, is included in Ms. Carrie’s E-Book: Speech and Language Therapy Guide: Step-By-Step Speech Therapy Activities to Teach Speech and Language Skills At Home or In Therapy. This guide includes detailed information on teaching various speech and language skills, including this one, along with worksheets, handouts, sample IEP goals, data collection, and video demonstrations. For more information, click the button below: More Resources for Speech-Language Pathologists: Looking for more therapy ideas and resources to help you provide the BEST services to your clients? Join us in The SLP Solution, our membership program for speech-language professionals! Inside the membership, you’ll find: - Step-By-Step Guides for teaching a variety of speech/language/communication skills - Pre-Made Worksheets and Therapy Activities for hundreds of different topics - Training Videos for dealing with difficult disorders or problems - Answers to Your Questions in our exclusive SLP community - Tools and Resources to help you with your paperwork and admin tasks - Continuing Education through our monthly webinars and webinar recordings To join us in the full SLP Solution, or to snag a free membership, click on the button below!

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1.An element ‘X’ forms an oxide with formula X2O3. State the valency of ‘X’ and write the formula of its chloride 2. Define mole. How many grams of sodium will have the same number of atoms as 6 grams of magnesium ? (Given Na5 23u, Mg5 24 u) 3. You are given an elements . Find out (a) Number of protons, electrons and neutrons in ‘X’ (b) Valency of ‘X’ (c) Write the chemical formula of the compound formed when ‘X’ react with (i) hydrogen, (ii) carbon 168X 4. An elements has mass number 35 and atomic number 17 find (i) the number of neutron in the element, and (ii) the number of electrons in the outermost shell. 5. Name the anion and cation which constitute the molecule of magnesium oxide 6. Percentage of three elements calcium, carbon and oxygen in a sample of calcium carbonate is given as : Calcium =40% ; Carbon =12.0% ; Oxygen = 48% If the law of constant proportion is true, what weights of these elements will be present in 1.5 g of another sample of calcium. Carbonate ? (Atomic mass of Ca = 40 u, C = 12 u, O = 16 u) 7. The description of atomic particles of two elements X and Y is given below : X Y Protons 8 8 Neutrons 8 9 Electrons 8 8 (i) What is the atomic number of Y? (ii) What is the mass number of X? (iii) What is the relation between X and Y? (iv) Which element/elements do they represent? (v) Write the electronic configuration of X? (vi) Write the cation/anion formed by the element 8. Which of the following are isotopes and which are isobars? Argon, Protium, Calcium, Deuterium. Explain why the isotopes have similar chemical properties but they differ in physical properties? 9.What is the number of molecules in 0.25 moles of oxygen ? Avogadro’s no. 6.02×10 23 . 10. Write down the formulae of (a) sodium carbonate (b) Ammonium chloride (c) Zinc oxide (d) Aluminium hydroxide11.What do the following symbols formulae stand for : (a) 2O (b) O2 (c) O3 (d) H2O (ii) Give the chemical formulae of the following compounds : (a) Potassium Carbonate (b) Calcium chloride (iii) Calculate the formulae unit mass of Al2 (SO4)3 (Given atomic mass of Al – 27u, S – 32u, O – 16u) 12. Write the chemical formula of ammonium sulphate. 13. The composition of nuclei of two atomic species X and Y are given below X Y Protons 17 17 Neutrons 18 20 Find the mass number of X and Y. State the relationship between X and Y 14. Find the mass of the following : (i) 0.5 mole of oxygen gas (ii) 3.011×10 23 atoms of oxygen (iii) 6.022×10 24 molecules of oxygen (Given atomic mass of 0=16u; No. of molecule=6.022×10 23 per mole 15. S -2 has completely filled K,L and M shells. Find its atomic number. 16. Find the number of particles in each of the following : (i) 0.1 mole of C atoms (ii) 46 g of Na atoms (Given that Na = 23u ; No. of molecule=6.022×10 23 per mole 17. Calculate the number of moles present in (i) 60g of calcium (ii) 3.011×10 23 number of oxygen atoms (Given that Ca = 40u ; Avogadro number= 6.022×10 23 ) 18. State one use each of an isotope of (i) uranium , (ii) iodine. 19. The chemical formula of oxide of an element X is X2O5. Write the chemical formula of its chloride. 20. Calculate the number of particles in each of the following : (i) 7 g of Nitrogen molecules (ii) 0.5 mole of carbon atoms (Given N=14 u ; C=12 u ; Avogadro number= 6.022×10 23 ) 21. Which of the following compounds have polyatomic ions ? NaOH, NaCl, Na2O, NaNO3 22. Sulphur dioxide (SO2) is a colourless pungent smelling gas and is a major air pollutant. (a) Write the electronic configuration of its constituent elements „sulphur and Oxygen. (Given, ). (b) Write valency of Sulphur and Oxygen. (c) Are sulphur and oxygen isotopes of same element. Explain your answer. (Given 32 S16 , 16O8) 23. What is the mass of 0.5 mole of NH3 ? Given Atomic mass of N = 14u, Atomic mass of H = 1u. (c) Calculate the number of particles in 31 g of P4molecules. Atomic mass of P=31u. ( Avogadro number= 6.022×10 23 ) (d) Find the number of moles in 87g of K2SO4 (Atomic mass of K=39u, S=32u 24. A light and a heavy object have the same momentum. What is the ratio of their kinetic energies ? Which one has a larger kinetic energy ? (ii) A ball is dropped from a height of 10m. If the energy of the ball reduces by 40% after striking the ground, how much high can the ball bounce back ? (g=10 ms -2 ) 25. Write the names of compounds represented by the following formulae : (i) KNO3 (ii) Al2(SO4)3 (iii) CCl4 (iv) H2S 26. Two boys Ram and Shyam have mass equal to 40 kg each. They start climbing a rope separately and both reach a height of 6 m. Ram takes 20 seconds and Shyam takes 25 seconds to complete the task. Who has more power? Explain your answer. (Take g =10 m/s 2 ) 27. (a) What would be the formula of chloride of ‘X’ if it is a metal and its oxide has the formula XO ? (b) Write a difference between an atom and an ion. (c) Give an example of each : (i) Triatomic molecule. (ii) Polyatomic ion. (iii) molecule of a compound (iv) cation (v) an element with valency – 3 28. In an office, a tube light of 40W, a fan of 75 W and a cooler of 150 W are installed. If the appliances are used for 8 hours per day, find the energy consumed per day in commercial unit. 29. a)Calculate the mass of 0.72 g molecule of CO2. (At mass of C=12 u, O=16 u) (b) Calculate the number of moles of iron in iron sheet containing 10 22 atoms of iron. 30. Calculate the molar mass of Nitric acid (HNO3). (Atomic Mass of H=1u, N=14u, O=16u) (b) Calculate the no. of moles in 270 g of Aluminium. (Atomic mass of Al=27 u) (c) Calculate the mass of 0.5 moles of Helium gas (Atomic mass He=4u.) Due to paucity of time it would not be possible for us to provide the answers to all your queries. We are providing solutions to some your good queries. Try solving rest of the questions yourself and if you face any difficulty then do get back to us. A-1) Element X = Al ( aluminum) Oxide of Al - Al2O3 Chloride of Al - AlCl3 A-9) Number of molecules in 0.25 moles of oxygen = 0.25 * 6.023*1023 = 1.505*1023 particles. A-21) Out of NaOH, NaCl, Na2O, NaNO3, compound having polyatomic ion is NaNO3.

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Throughout the Earth’s vast history, the planet has undergone many glacial phases. These phases affect the extent of snow cover at all latitudes. Over the last 500 million years, multiple “icehouse” climates and interglacial warm periods have occurred (Figure 1). These periods of change alter the planet’s snow cover from extending close to the equator, to no snow at all. More recently, during the last glacial maximum period 18,000 years before present, perennial snow coverage extending into southern United States. This glacial age was part of the Quaternary period, a time with episodic glacial cycles lasting two million years in the Northern Hemisphere (Figure 2). The glacial cycles occurred as glacial advances and interglacial retreats, occurring on approximate 100,000-year time intervals. For the past 10,000 years, the Earth has been in a state of interglacial retreat. The 100,000-year time intervals correlate with solar radiation variation, due to Earth’s orbit and axial properties called Milankovitch Cycles. These Milankovitch Cycles cause slow variations in the seasonal distribution of radiation across the planet, as well as climate system feedbacks involving snow/ice albedo, atmospheric water vapour, and carbon dioxide (CO2). During times of higher solar radiation, the Earth transforms into a warm, humid interglacial and during times of lower solar radiation, a cold, dry glacial state prevails. Generally, the alteration from a global state of glacial to interglacial occurs at a faster rate than interglacial to glacial state. This transpires because as glacial ice warms and melts, a positive feedback commences, melting ice at a faster rate. Additionally, as this glacial ice melts, carbon dioxide trapped within air bubbles are released – contributing to a warmer atmospheric temperature (NOAA, 2008). The last glacial period in Canada peaked about 21,000 years ago, at which time almost all of Canada was covered by ice. Ice retreated slowly at first, with the ice sheets still present in the northern United States 14,500 years ago. They began to thin and retreat dramatically over the next several thousand years, until ice finally cleared out of Hudson Bay about 8,000 years ago. North America's Laurentide Ice Sheet was the largest of the ice sheets, exceeding even present-day Antarctica in ice volume, so it drove the timing and pace of the global-scale deglaciation. Summer sunshine in the far north was quite strong during the last deglaciation (the early Holocene), which appears to have driven an "overshoot" of ice retreat coming out of the last glaciation. Most mid-latitude glaciers in the northern hemisphere melted back or disappeared during in the early to mid-Holocene, around 6,000 years ago, including the Columbia Icefields in the Canadian Rockies. Ice cores in Greenland and the Canadian high Arctic indicate that there was substantial summer melt at this time, exceeding the average summer melt totals of the 20th century. Despite this, fragments of the North American ice sheet actually survived until present day in the Canadian Arctic, including the Penny and Barnes Ice Caps on Baffin Island and several of the larger icefields on Devon and Ellesmere Islands. Very old Pleistocene ice is found in the lower section of these ice caps. Mountain glaciers and polar icefields re-advanced as summer sunshine weakened in northern latitudes over the last several thousand years. The moraine (glacial rock deposits) record indicates several sequences of glacier advance and retreat, culminating in the Little Ice Age advance between the years 1600 and 1900. Many northern hemisphere glaciers reached their maximum recent extent during this period (e.g. Solomina et al., 2008; Ivy-Ochs et al., 2009) before a relatively dramatic, worldwide retreat of glaciers began in the late 1800s. In many places, such as western Canada, Alaska, and Patagonia in southern South America, lake sediments and tree fragments that have emerged from glacier retreat indicate that some mountain glaciers have retreated past anything seen in more than 3,000 years. Arctic ice caps are also responding to recent climate warming, although sometimes more subtly because the available solar energy for melting in the high Arctic is limited. Material on this page was provided by Professor Shawn Marshall (Canada Research Chair in Climate Change, Department of Geography, University of Calgary, Alberta) and Maren Pauly (Department of Geography, University of Waterloo).

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What is Standard Form? Note that it is sometimes not clear on a graphing calculator that the top half and bottom half of the ellipse are connected because of the way the calculator draws the top and bottom halves separately. If you do it to the left-hand side, you can do to the right-hand side-- or you have to do to the right-hand side-- and we are in standard form. Let's look again at our basic parabola after such a transformation. We have seen that we can transform slope-intercept form equations into standard form equations. Horizontal translations affect the domain on the function we are graphing. If we translate by some positive real number a, then our parabolas equation is changed "in the parentheses". And now to get it in slope intercept form, we just have to add the 6 to both sides so we get rid of it on the left-hand side, so let's add 6 to both sides of this equation. After this lesson, you will be able to: It could be adjusted for more advanced students by requiring the equations to be inequalities or using more elaborate equations. By solving a system of three equations with three unknowns, you can obtain values for a, b, and c of the general form. Example 1 You are given the point 4,3 and a slope of 2. A parabola intersects its axis of symmetry at a point called the vertex of the parabola. When you are given the vertex and at least one point of the parabola, you generally use the vertex form. We can see more clearly here by one, or both, of the following means: So let's put it in point slope form. Your point is -1,5. First, standard form allows us to write the equations for vertical lines, which is not possible in slope-intercept form. And that is standard form. The usual approach to this problem is to find the slope of the given line and then to use that slope along with the given point in the point-slope form for a linear equation. And then 4 times 3 is The Y, you're able to figure out the y-intercept from this. Now the last thing we need to do is get it into the standard form. Consider our basic parabola without the scaling: We know how to use the point-slope form, so the final answer is: So we have slope intercept. What of the transformations I alluded to earlier not already covered? How do we know which is correct. At point-slope form, neither the x nor the y-intercept kind of jump out at you. However, the vertical reflection of our graph in the absence of an additional vertical translation results in the following equation and graph. And we're left with 16Y is equal to So what can we do here to simplify this? See the section on solving equations algebraically to review completing the square. It could be a negative 3 and 6. Note that the major axis is vertical with one focus is at and other at Part V - Graphing ellipses in standard form with a graphing calculator To graph an ellipse in standard form, you must fist solve the equation for y. We are then asked to make a change to our equation which will move the vertex to the second quadrant. And it's a form that you might have already seen.Standard Form) P1. Write an equation of the line whose slope m is 3/4 and whose y-intercept b is (SIF and Standard Form) E2. Write an equation of the line that passes through the point (6, -3) and has a slope of (SIF and Standard Form) P2. Write an equation of the line that passes through the point (-3, 0) and has a slope of 1/3. The point slope form of a linear equation is written as. In this equation, m is the slope and (x 1, y 1) are the coordinates of a point. Let’s look at where this point-slope formula comes from. Determine a Quadratic Equation Given Its Roots • MHR 53 Method 2: Use a Graphing Calculator. Use the information given to identify three points and draw a sketch. The quadratic function f(x) = a(x - h) 2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. If a is positive, the graph opens upward, and if a is negative, then it opens downward. Notice how the graph moved to the right by 2 units. These are the rules we will follow: We will always write our equations in the form "x-something" and resulting horizontal translation is in the direction of the sign of the something and a number of units equal to its absolute value. Meanwhile, the equation 2x = 4 is equivalent to the equation x = 2, which is also in standard form (with a = 1). If either a or b is zero, we know how to graph the equation and how to read off an equation from a graph.Download

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How do we hear? Sound consists of vibrations of air in the form of waves which it is picked up by the ear; the ear consists of three parts: the outer ear, the middle ear and the inner ear. The outer ear has a shape that assists in collecting sound waves from the air which are then funnelled down the ear canal. At the end of the ear canal passage the sound waves impinge on the eardrum or tympanic membrane. The eardrum separates the outer ear from the middle ear. The middle ear is a small cavity which is ventilated from the back of the nose through the Eustachian tube. The Eustachian tube allows for equalization of pressure on both sides of the eardrum enabling it to vibrate efficiently. The muffled sound with a head cold is often associated with Eustachian tube blockage. The middle ear cavity is normally air filled. It contains three ossicles or bones which are the smallest bones in the human body. They are generally termed the hammer (malleus), anvil (incus) and the stirrup (stapes). The three middle ear bones are connected to one another and act as a lever system to transmit and amplify movements of the tympanic membrane produced by sound waves. These sound waves are then transmitted to the oval window of the inner ear. The oval window is a membrane which separates the middle ear from the inner ear. The organ of hearing in the inner ear is the cochlea which is a fluid-filled system. The fluid called endolymph and perilymph are in contact with the inner side of the oval window. Vibrations of the middle ear bones are passed through the oval window and are transmitted through the cochlear fluid to nerve receptors in the cochlea. The nerve receptors in the cochlea respond to the frequency of the sound vibrations. The human ear has nerve receptors sometimes called hair cells. There are two types of hair cells, outer hair cells and inner hair cells. Each human ear has about 13,000 outer hair cells and 3,500 inner hair cells. Nerves from these receptors carry impulses to the brain, which interprets them as a sound of a certain pitch or loudness. The complex wave patterns of speech sound produce a pattern of nerve impulses. The brain learns by experience to attach some particular significance to the impulse pattern. The brain stores this pattern in memory and when it is received again, it is recognized. If any part of the hearing system fails to develop adequately or is damaged which will interrupt the normal process of the sound transmission and will cause a hearing loss.

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Infix : An expression is called the Infix expression if the operator appears in between the operands in the expression. Simply of the form (operand1 operator operand2). Example : (A+B) * (C-D) Prefix : An expression is called the prefix expression if the operator appears in the expression before the operands. Simply of the form (operator operand1 operand2). Example : *+AB-CD (Infix : (A+B) * (C-D) ) Given a Prefix expression, convert it into a Infix expression. Computers usually does the computation in either prefix or postfix (usually postfix). But for humans, its easier to understand an Infix expression rather than a prefix. Hence conversion is need for human understanding. Input : Prefix : *+AB-CD Output : Infix : ((A+B)*(C-D)) Input : Prefix : *-A/BC-/AKL Output : Infix : ((A-(B/C))*((A/K)-L)) Algorithm for Prefix to Infix: - Read the Prefix expression in reverse order (from right to left) - If the symbol is an operand, then push it onto the Stack - If the symbol is an operator, then pop two operands from the Stack Create a string by concatenating the two operands and the operator between them. string = (operand1 + operator + operand2) And push the resultant string back to Stack - Repeat the above steps until end of Prefix expression. Infix : ((A-(B/C))*((A/K)-L)) - Infix to Prefix conversion using two stacks - Convert Infix To Prefix Notation - Postfix to Prefix Conversion - Prefix to Postfix Conversion - Postfix to Infix - Stack | Set 2 (Infix to Postfix) - Infix to Postfix using different Precedence Values for In-Stack and Out-Stack - Decimal to octal conversion with minimum use of arithmetic operators - Evaluation of Prefix Expressions - Longest prefix which is also suffix - Strings from an array which are not prefix of any other string - Maximum occurrence of prefix in the Array - Longest Common Prefix using Sorting - String from prefix and suffix of given two strings - Longest Common Prefix using Trie If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

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Students learn “if-then” moves using the properties of equality to solve equations. Students also explore moves that may result in an equation having more solutions than the original equation. Lesson 13 Summary Assuming that there is a solution to an equation, applying the distribution, commutative, and associative properties and the properties of equality to equations will not change the solution set. Feel free to try doing other operations to both sides of an equation, but be aware that the new solution set you get contains possible CANDIDATES for solutions. You have to plug each one into the original equation to see if they really are solutions to your original equation. 1. Solve the equation for x. For each step, describe the operation and/or properties used to convert the equation. 5(2x - 4) - 11 = 4 + 3x 2. Consider the equation x + 4 = 3x + 2 a. Show that adding x + 2 to both sides of the equation does not change the solution set. b. Show that multiplying both sides of the equation by x + 2 adds a second solution of x = -2 to the solution set. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

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OBJECTIVES COVERED (pupils will learn ..) SUGGESTED MAIN ACTIVITIES: DOWNLOADABLE VERSION, RESOURCES and LINKS: How and why Homo Sapiens (the species that you belong to) evolved The differences and similarities between Homo Sapiens and other living things Watch the lesson powerpoint which introduces the subject to pupils. 1. ENGLISH: draw a labelled diagram of the human body, listing reasons why the different features have evolved (can be easily turned into an ART activity if you make a jointed cardboard skeleton. 2. PE: design a fitness circuit with one or more stations that test each part of the human body to see how it works, such as a jumping section (to show springy foot arches) or a throwing section (to show opposable thumbs). NOTE: this is very similar to a task in the full day version of our Evolution and Inheritance science workshop, where pupils complete a PE circuit activity whilst looking at model body joints. Then present your station(s) to the class. 3. HOMEWORK/ICT: research more information about the differences in the human body to present to the class in a mini project (NOTE TO TEACHERS: remember to emphasise to pupils that EVERY feature of the human body has evolved for a reason, no matter how unlikely it seems). Feedback work/presentations/pe station to class and complete the questions at the end of the presentation. LESSON NO and TITLE: 6 of 6: HUMAN EVOLUTION: from apes to you!

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You may remember the rules of directed numbers (which is just a fancy way of saying positive and negative numbers), but find them trickier to apply. This is very common and many students feel this way. Because the rules differ for addition and subtraction, compared with multiplication and division. Two positive symbols make a positive overall. A positive and a negative symbol make a negative overall. A negative and a positive symbol make a negative overall. Two negative symbols make a positive overall. The Exception > subtracting negative numbers: The complication comes when adding negative numbers. They only affect each other if the signs are positioned next to each other. So in the sum 3 - - 5, the signs would impact each other because they're together. However, in the sum -3 - 6, the signs would not impact each other as they are not together. Let's put these rules into context with some examples now. e.g. Work out the value of: 6 - + 2 In this question we have a + and a - together, so they will affect each other. They will become a negative overall. So we can rewrite the sum as: 6 - 2 If we picture a mental number line, to take 2 from 6, we move 2 spaces to the left on the number line to arrive at: 4 e.g. Work out the value of: - 3 - - 5 In this question we have a - and a - together, so they will affect each other and become a positive overall. However, the - at the start of the sum is on its own so does not need to be changed at all. This means we can rewrite the sum as: - 3 + 5 Start at -3 on your mental number line and move 5 spaces to the right (as this is an addition sum) to reach: 2 In this activity, you will apply the rules related to positive and negative numbers to work out answers to subtraction sums.

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INDIAN REMOVAL ACT The Indian Removal act was a major piece of legislation passed by President Andrew Jackson on May 28, 1830. The act made it so that the President could grant Indian tribes unsettled prairieland in the west, specifically what is now Oklahoma. This may seem like this was the President doing right by the Native Americans, but it was actually quite the opposite. Although they were given territory west of the Mississippi, these people were essentially being evicted from their native lands, where their ancestors had been long before the arrival of the white man from Europe. The reason for the removal was because the natural land in the southeast was very fertile land for agriculture, and was an opportunity for the plantation owners to grow more cotton (which they would force another group of people to reside on and maintain for them). With the movement south from the original states to as far west as the Mississippi, it became clear that the white man would not tolerate the presence of the Indians there, no matter how peaceful they were. Jackson “negotiated” treaties with the native tribes which granted them the land in Oklahoma, if they decided to stay, their rights as a tribe would be taken away and the Native Americans would simply become citizens of the state that their lands resided in. Many of the treaties were accepted simply because the tribes wanted to maintain some land rights while avoiding hostility with Jackson and the United States military. As a result, the United States gained almost 3/4ths of Alabama and Florida, as well as smaller portions of Georgia, Tennessee, Mississippi, Kentucky, and North Carolina. All of which were previously controlled by various tribes. Although many of the tribes felt as though it was a lost cause to try and maintain their original land, other tribes decided to stay and fight. The Creeks and the Seminoles decided to wage war against the United States, with neither instance leading to anything other than the deaths of thousands of people, the loss of 40 to 60 million dollars and further blemishes on our history books. Many saw Jackson for his paternalistic and patronizing attitudes towards the Native Americans, which often times led to brutal and inhumane courses of action. The United States never intended to move west of the Mississippi River, but sure enough, after they had run out of space for agriculture in the east, many decided to move west, meaning that the new land that the Native Americans had received from the Indian Removal Act, after sacrificing so much, was to be taken away from them once again. This is a common theme throughout American history. The Native Americans were constantly shifted from one area to the next, each getting smaller in turn. It all plays apart in the horrible history of their people after the emergence of the Europeans on American soil.

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Teachers often require students to build a 3-D model of an atom for a science class project. This helps students to grasp the role that protons, neutrons and electrons play in the inner workings of the atom. While building the model, students gain a hands-on understanding of the balance that is essential in atoms of any element. How large the model atom is depends on the periodic element modeled. Building multiple atoms, including isotopes, of a single element can also make an excellent last-minute science fair project. Calculate the number of protons, electrons and neutrons needed for the model element you are constructing. The number of protons and electrons is equal to the element's atomic number. The number of electrons is equal to the atomic mass minus the atomic number. An isotope of an element has either more or less neutrons than a standard atom. Paint the Styrofoam balls. The protons, neutrons and electrons should each be painted a different color so you can distinguish between the model's essential parts. Stick a toothpick into each ball to use as a handle while painting to keep your fingers clean. Glue the balls which represent the protons and neutrons together to form a mass. The two colors should look well-mixed. This will form the nucleus of the atom. Stick the kabob skewers into the nucleus. They should be all the way around the nucleus at random locations. Press an electron onto the exposed tip of each of the skewers. Put a dot of glue on the end of the skewer before pressing the Styrofoam ball onto it. This will keep the electron from coming loose from the atom later. Create a key on a sheet of typing paper or on a larger poster board. Replicate the element's information from the periodic table on the key. Also include a key that decodes the colors used to paint the protons, electrons and neutrons. - atom image by Brett Bouwer from Fotolia.com

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To undertake this activity there is an expectation that students have an understanding of binary numbers and how to count in binary. Refer to the introduction to binary lesson. Revise what students know about counting in binary, if possible use binary cards or write a decimal number on the board eg ‘21’ to model how to represent that number in binary, which is 10101. Use the following table with headings to show the progression of the binary numeral system much like 1s, 10, 100, 1000 for decimal system. Binary is a doubling pattern of 1, 2, 4, 8, 16 etc. Use the table to ensure all students can count in binary and represent decimal numbers in binary. Note remember to start from the left when using the table to make a decimal number. For example to make the number 31 do I need a 16, YES. Do I need and 8, NO. Do I need a 4, YES. Do I need a 2, NO. Do I need a 1, YES. So the binary number is 10101. Repeat this process for other numbers. Try making numbers 1-31. Ask what the largest number than can be made in this table. Numbers larger than 31. If we add another column how can we make the number 43? How can we make the number 251? Discuss the pattern of doubling to get 64 and 128 and add these two new columns. Differentiate the task depending on your student’s familiarity and skills using a spreadsheet. Scaffold the learning by providing a spread sheeting file which has the set up partly completed. The files provided are MS Excel. Some students who are well skilled in using a spreadsheet can design their own converter and may not need a file to scaffold their learning. Provide this file for students that have a basic understanding of how to use a spreadsheet. As a starting point ask students to test the sheet to see how it operates. Can they work out how the ASCII decimal number is calculated? Ask students if they can make their converter work up to the decimal number of 255. Encourage students to test and check to see if auto sum is correct and outputs in the cell as the correct ASCII Decimal Number. For students who want to add a conditional if statement to automatically represent o or 1 as on or off, use this file. In this example the conditional statement reads if cell (above) = 1 then show On, else if cell = 0 show Off. A completed version might look similar to this, see the file here. For students that are interested in creating an interface refer to this example. Refer to this version of the completed spreadsheet with tips that explain how the sheet is set up. Computers today use the binary system to represent information. It is called binary because only two different digits are used. It is also known as base two (normally we use base 10). Each zero or one is called a bit (binary digit). A bit is usually represented in a computer’s main memory by a transistor that is switched on or off, or a capacitor that is charged or discharged. One bit on its own can’t represent much, so they are usually grouped together in groups of eight, which can represent numbers from 0 to 255. A group of eight bits is called a byte.

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Hi, I'm Charlie Kasov, and this is a tutorial on how to do the order of operations. So, the order of operations, the most important thing is memory. memorize the order of operations based on PEMDAS, please excuse my dear aunt sally. And, that's parentheses, exponent, multiplication, division, addition, subtraction. So, when we do PEMDAS, we're saying that parentheses are more important than exponents, exponents are more important than multiplication and division, and multiplication and division are more important than addition or subtraction. Now, these two, and these two are just lumped together, in terms of their importance over the ones to the right. If you had division first, then multiplication, you can do that first. Let's look at an example, two X squared, plus two X squared. So, for two X squared, because both of these are in parentheses, we have to raise both to the second power. So, two squared is four, and X squared remains X squared, plus two X squared. We're not going to raise this two to the second power because it's not inside the parentheses. There is no parentheses. So, now we have four X squared, plus two X squared. We can finally do the addition, which is going to be six X squared. And, that is the basics on how to do order of operations.

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By the end of this section, you will be able to: - Define and distinguish between instantaneous acceleration and average acceleration. - Calculate acceleration given initial time, initial velocity, final time, and final velocity. The information presented in this section supports the following AP® learning objectives and science practices: - 3.A.1.1 The student is able to express the motion of an object using narrative, mathematical, and graphical representations. (S.P. 1.5, 2.1, 2.2) - 3.A.1.3 The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. (S.P. 5.1) In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration, the greater the change in velocity over a given time. The formal definition of acceleration is consistent with these notions, but more inclusive. Average Acceleration is the rate at which velocity changes, where is average acceleration, is velocity, and is time. (The bar over the means average acceleration.) Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are , meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second. Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both. Acceleration as a Vector Acceleration is a vector in the same direction as the change in velocity, . Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both. Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion. When an object's acceleration is in the same direction of its motion, the object will speed up. However, when an object's acceleration is opposite to the direction of its motion, the object will slow down. Speeding up and slowing down should not be confused with a positive and negative acceleration. The next two examples should help to make this distinction clear. Making Connections: Car Motion Consider the acceleration and velocity of each car in terms of its direction of travel. Because the positive direction is considered to the right of the paper, Car A is moving with a positive velocity. Because it is speeding up while moving with a positive velocity, its acceleration is also considered positive. Because the positive direction is considered to the right of the paper, Car B is also moving with a positive velocity. However, because it is slowing down while moving with a positive velocity, its acceleration is considered negative. (This can be viewed in a mathematical manner as well. If the car was originally moving with a velocity of +25 m/s, it is finishing with a speed less than that, like +5 m/s. Because the change in velocity is negative, the acceleration will be as well.) Because the positive direction is considered to the right of the paper, Car C is moving with a positive velocity. Because all arrows are of the same length, this car is not changing its speed. As a result, its change in velocity is zero, and its acceleration must be zero as well. Because the car is moving opposite to the positive direction, Car D is moving with a negative velocity. Because it is speeding up while moving in a negative direction, its acceleration is negative as well. Because it is moving opposite to the positive direction, Car E is moving with a negative velocity as well. However, because it is slowing down while moving in a negative direction, its acceleration is actually positive. As in example B, this may be more easily understood in a mathematical sense. The car is originally moving with a large negative velocity (−25 m/s) but slows to a final velocity that is less negative (−5 m/s). This change in velocity, from −25 m/s to −5 m/s, is actually a positive change ( of 20 m/s. Because the change in velocity is positive, the acceleration must also be positive. Making Connection - Illustrative Example The three graphs below are labeled A, B, and C. Each one represents the position of a moving object plotted against time. As we did in the previous example, let's consider the acceleration and velocity of each object in terms of its direction of travel. Object A is continually increasing its position in the positive direction. As a result, its velocity is considered positive. During the first portion of time (shaded grey) the position of the object does not change much, resulting in a small positive velocity. During a later portion of time (shaded green) the position of the object changes more, resulting in a larger positive velocity. Because this positive velocity is increasing over time, the acceleration of the object is considered positive. As in case A, Object B is continually increasing its position in the positive direction. As a result, its velocity is considered positive. During the first portion of time (shaded grey) the position of the object changes a large amount, resulting in a large positive velocity. During a later portion of time (shaded green) the position of the object does not change as much, resulting in a smaller positive velocity. Because this positive velocity is decreasing over time, the acceleration of the object is considered negative. Object C is continually decreasing its position in the positive direction. As a result, its velocity is considered negative. During the first portion of time (shaded grey) the position of the object does not change a large amount, resulting in a small negative velocity. During a later portion of time (shaded green) the position of the object changes a much larger amount, resulting in a larger negative velocity. Because the velocity of the object is becoming more negative during the time period, the change in velocity is negative. As a result, the object experiences a negative acceleration. Example 2.1 Calculating Acceleration: A Racehorse Leaves the Gate A racehorse coming out of the gate accelerates from rest to a velocity of 15.0 m/s due west in 1.80 s. What is its average acceleration? First we draw a sketch and assign a coordinate system to the problem. This is a simple problem, but it always helps to visualize it. Notice that we assign east as positive and west as negative. Thus, in this case, we have negative velocity. We can solve this problem by identifying and from the given information and then calculating the average acceleration directly from the equation . 1. Identify the knowns. , (the minus sign indicates direction toward the west), . 2. Find the change in velocity. Since the horse is going from zero to , its change in velocity equals its final velocity: . 3. Plug in the known values ( and ) and solve for the unknown . The minus sign for acceleration indicates that acceleration is toward the west. An acceleration of due west means that the horse increases its velocity by 8.33 m/s due west each second, that is, 8.33 meters per second per second, which we write as . This is truly an average acceleration, because the ride is not smooth. We shall see later that an acceleration of this magnitude would require the rider to hang on with a force nearly equal to his weight. Instantaneous acceleration , or the acceleration at a specific instant in time, is obtained by the same process as discussed for instantaneous velocity in Time, Velocity, and Speed—that is, by considering an infinitesimally small interval of time. How do we find instantaneous acceleration using only algebra? The answer is that we choose an average acceleration that is representative of the motion. Figure 2.29 shows graphs of instantaneous acceleration versus time for two very different motions. In Figure 2.29(a), the acceleration varies slightly and the average over the entire interval is nearly the same as the instantaneous acceleration at any time. In this case, we should treat this motion as if it had a constant acceleration equal to the average (in this case about ). In Figure 2.29(b), the acceleration varies drastically over time. In such situations it is best to consider smaller time intervals and choose an average acceleration for each. For example, we could consider motion over the time intervals from 0 to 1.0 s and from 1.0 to 3.0 s as separate motions with accelerations of and , respectively. The next several examples consider the motion of the subway train shown in Figure 2.30. In (a) the shuttle moves to the right, and in (b) it moves to the left. The examples are designed to further illustrate aspects of motion and to illustrate some of the reasoning that goes into solving problems. Example 2.2 Calculating Displacement: A Subway Train What are the magnitude and sign of displacements for the motions of the subway train shown in parts (a) and (b) of Figure 2.30? A drawing with a coordinate system is already provided, so we don't need to make a sketch, but we should analyze it to make sure we understand what it is showing. Pay particular attention to the coordinate system. To find displacement, we use the equation . This is straightforward since the initial and final positions are given. 1. Identify the knowns. In the figure we see that and for part (a), and and for part (b). 2. Solve for displacement in part (a). 3. Solve for displacement in part (b). The direction of the motion in (a) is to the right and therefore its displacement has a positive sign, whereas motion in (b) is to the left and thus has a minus sign. Example 2.3 Comparing Distance Traveled with Displacement: A Subway Train What are the distances traveled for the motions shown in parts (a) and (b) of the subway train in Figure 2.30? To answer this question, think about the definitions of distance and distance traveled, and how they are related to displacement. Distance between two positions is defined to be the magnitude of displacement, which was found in Example 2.2. Distance traveled is the total length of the path traveled between the two positions. (See Displacement.) In the case of the subway train shown in Figure 2.30, the distance traveled is the same as the distance between the initial and final positions of the train. 1. The displacement for part (a) was +2.00 km. Therefore, the distance between the initial and final positions was 2.00 km, and the distance traveled was 2.00 km. 2. The displacement for part (b) was Therefore, the distance between the initial and final positions was 1.50 km, and the distance traveled was 1.50 km. Distance is a scalar. It has magnitude but no sign to indicate direction. Example 2.4 Calculating Acceleration: A Subway Train Speeding Up Suppose the train in Figure 2.30(a) accelerates from rest to 30.0 km/h in the first 20.0 s of its motion. What is its average acceleration during that time interval? It is worth it at this point to make a simple sketch: This problem involves three steps. First we must determine the change in velocity, then we must determine the change in time, and finally we use these values to calculate the acceleration. 1. Identify the knowns. (the trains starts at rest), , and . 2. Calculate . Since the train starts from rest, its change in velocity is , where the plus sign means velocity to the right. 3. Plug in known values and solve for the unknown, . 4. Since the units are mixed (we have both hours and seconds for time), we need to convert everything into SI units of meters and seconds. (See Physical Quantities and Units for more guidance.) The plus sign means that acceleration is to the right. This is reasonable because the train starts from rest and ends up with a velocity to the right (also positive). So acceleration is in the same direction as the change in velocity, as is always the case. Example 2.5 Calculate Acceleration: A Subway Train Slowing Down Now suppose that at the end of its trip, the train in Figure 2.30(a) slows to a stop from a speed of 30.0 km/h in 8.00 s. What is its average acceleration while stopping? In this case, the train is decelerating and its acceleration is negative because it is toward the left. As in the previous example, we must find the change in velocity and the change in time and then solve for acceleration. 1. Identify the knowns. , (the train is stopped, so its velocity is 0), and . 2. Solve for the change in velocity, . 3. Plug in the knowns, and , and solve for . 4. Convert the units to meters and seconds. The minus sign indicates that acceleration is to the left. This sign is reasonable because the train initially has a positive velocity in this problem, and a negative acceleration would oppose the motion. Again, acceleration is in the same direction as the change in velocity, which is negative here. This acceleration can be called a deceleration because it has a direction opposite to the velocity. The graphs of position, velocity, and acceleration vs. time for the trains in Example 2.4 and Example 2.5 are displayed in Figure 2.33. (We have taken the velocity to remain constant from 20 to 40 s, after which the train decelerates.) Example 2.6 Calculating Average Velocity: The Subway Train What is the average velocity of the train in part b of Example 2.2, and shown again below, if it takes 5.00 min to make its trip? Average velocity is displacement divided by time. It will be negative here, since the train moves to the left and has a negative displacement. 1. Identify the knowns. , , . 2. Determine displacement, . We found to be in Example 2.2. 3. Solve for average velocity. 4. Convert units. The negative velocity indicates motion to the left. Example 2.7 Calculating Deceleration: The Subway Train Finally, suppose the train in Figure 2.34 slows to a stop from a velocity of 20.0 km/h in 10.0 s. What is its average acceleration? Once again, let's draw a sketch: As before, we must find the change in velocity and the change in time to calculate average acceleration. 1. Identify the knowns. , , . 2. Calculate . The change in velocity here is actually positive, since 3. Solve for . 4. Convert units. The plus sign means that acceleration is to the right. This is reasonable because the train initially has a negative velocity (to the left) in this problem and a positive acceleration opposes the motion (and so it is to the right). Again, acceleration is in the same direction as the change in velocity, which is positive here. As in Example 2.5, this acceleration can be called a deceleration since it is in the direction opposite to the velocity. Sign and Direction Perhaps the most important thing to note about these examples is the signs of the answers. In our chosen coordinate system, plus means the quantity is to the right and minus means it is to the left. This is easy to imagine for displacement and velocity. But it is a little less obvious for acceleration. Most people interpret negative acceleration as the slowing of an object. This was not the case in Example 2.7, where a positive acceleration slowed a negative velocity. The crucial distinction was that the acceleration was in the opposite direction from the velocity. In fact, a negative acceleration will increase a negative velocity. For example, the train moving to the left in Figure 2.34 is sped up by an acceleration to the left. In that case, both and are negative. The plus and minus signs give the directions of the accelerations. If acceleration has the same sign as the velocity, the object is speeding up. If acceleration has the opposite sign as the velocity, the object is slowing down. Check Your Understanding An airplane lands on a runway traveling east. Describe its acceleration. If we take east to be positive, then the airplane has negative acceleration, as it is accelerating toward the west. It is also decelerating: its acceleration is opposite in direction to its velocity. PhET Explorations: Moving Man Simulation Learn about position, velocity, and acceleration graphs. Move the little man back and forth with the mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you.

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- By Rob Miles Working with text In the previous chapter, we saw that we can write expressions that work with text. It turns out that we can also create variables that can hold text. customer_name = 'Fred' This statement looks exactly like the statement we used to create the total variable except that the value being assigned is a string of text. The variable customer_name is different from the total variable in that it holds text rather than a number. We can use this variable anywhere we would use a string. message = 'the name is '+customer_name In the expression being assigned, the text in the variable customer_name is added onto the end of the string "the name is ". As customer_name currently holds the string "Fred" (we set this in the previous statement), the above assignment would create another string variable called message which contains "the name is Fred". Marking the start and end of strings When I first saw how strings worked in Python, I wondered how to enter text containing a single quote. For example, let’s say you want to print the message, “It’s a trap.” We know Python uses the single quote character to define the limits (or delimit) of a string of text. However, the single quote in the word “it’s” would confuse Python, making it think the string had ended early. One way to solve this problem is to enclose the string with double quotation marks rather than single quotation marks. print("It's a trap") Python lets you use either kind of quotation mark (single or double) to delimit a string of text in a program. This works, but of course the next thing I want to ask is, “How do you enter text that contains both single and double quotes?” The designer of Python thought of that, too, and allows us to use “triple quotes” to delimit a string. A triple quote is three single- or double-quote characters in a row: print('''...and then Luke said "It's a trap"''') This statement prints this message: ...and then Luke said "It's a trap" Triple quoted strings look a bit cumbersome, but they have another advantage over “ordinary” strings. Any new lines in a triple-quoted string are made part of the string. To see how this might be useful, consider the instructions for the “Nerves of Steel” party game that we looked at in Chapter 3. print('Welcome to Nerves of Steel') print() print('Everybody stand up') print('Stay standing as long as you dare.') print('Sit down just before you think the time will end.') To produce these instructions, I had to write several print statements. By using a triple-quoted string, I can make this a lot easier. print('''Welcome to Nerves of Steel Everybody stand up Stay standing as long as you dare. Sit down just before you think the time will end. ''') The print statement now spans several lines. When the program runs, the new lines are printed so that the text looks as it did before, although it now spans several lines. Note that the blank line below the heading is also preserved when the print is performed. One thing to remember is that you must use matching delimiters to start and end a string. If you start the string with triple quotes, you must end it that way, too. Escape characters in text Another way to include quote characters in a string of text is to use an escape sequence. Normally, each character in a string represents that character. In other words, an A in a string means ‘A’. However, when Python sees the escape character—the backslash (\) character—it looks at the text following the escape character to decide what character is being described. This is called an escape sequence. There are many different escape sequences you can use in a Python string. The most useful escape sequences are shown in the following table. |ESCAPE SEQUENCE||WHAT IT MEANS||WHAT IT DOES| |\\||Backslash character (\)||Enter a backslash into the string| |\’||Single quote (‘)||Enter a single quote into the string| |\”||Double quote (“)||Enter a double quote into the string| |\n||ASCII Line Feed/New Line||End this line and take a new one| |\t||ASCII Tab||Move to the right to the next tab stop| |\r||ASCII Carriage return||Return the printing position to the start of the line| |\a||ASCII Bell||Sound the bell on the terminal| Python includes other escape sequences, but these will suffice for now. If you’re wondering what ASCII (American Standard Code for Information Interchange) means, it is a mapping of numbers to printed characters. It was developed in the early 1960s for use by computers and persists to this day. (In Chapter 2, we learned that ASCII is the standard that maps the letter W to the decimal value 84). ASCII is a perfectly fine standard if you don’t want to print more than 100 or so different characters. However, because many modern languages use more than 100 characters, UNICODE has become the new standard. UNICODE allows for many more characters, emojis, and emoticons. Some Python escape sequences produce UNICODE characters from our programs. UNICODE characters are frequently used in Graphical User Interfaces (GUIs).. Not all the escape sequences above work on all computers. Also, their functions are not always consistent from one computer to another. For example, the \a escape sequence, which means ASCII Bell, was intended to sound the bell on a mechanical computer terminal. However, if you print this sequence, there is no guarantee that the computer you’re using will make a sound. The paragraph return character, \r, which is supposed to send the print head of a computer terminal back to the start of the line, is not very useful and may not do anything on some computers. The most useful escape sequences are those that you can use to print quotes and the backspace character. You can also use the new line character (\n) to make new lines in strings you print. Within Python programs, the end of a line of text is always marked by a single new line character. The underlying operating system might work differently, for example the Windows operating system uses the sequence “\r\n” (a return followed by a new line feed) to mark the end of each line of text in a file. The Python system performs automatic translation of line endings to match the computer system being used, so our programs can always use a single new line character to mark the end of a line. Read in text using the input function Up until now, all our programs have worked with values stored in the Python code itself. These are called literal values because they are literally “just there” in the code. We use the input function to make a “complete” program that takes in data, does something with it, and then produces a result. name = input() This statement would pause the program and wait for the user to type in a string and press the Enter key. The string of text is stored in the variable called name. We can make the program display a prompt for the user by adding a string to the call for the input function. name=input('Enter your name please: ') The name variable will contain whatever string the user types in. If the user just presses the Enter key without typing anything, the name variable will contain an empty string. You can also use the input statement to pause your program so that the user can read the results. input('Press Enter to continue') In the statement above, the result of the call to the input function is ignored.

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Basic Concepts of Force Feedback A particular instance of force feedback is called an effect, and the push or resistance is called the force. Most effects fall into one of the following categories: Constant force. A steady force in a single direction. Ramp force. A force that steadily increases or decreases in magnitude. Periodic effect. A force that pulsates according to a defined wave pattern. Condition. A reaction to motion or position along an axis. Two examples are a friction effect that generates resistance to movement of the joystick, and a spring effect that pushes the stick back toward a certain position after it has been moved from that position. The strength of the force is called its magnitude. Magnitude is measured in units ranging from 0 (no force) through 10,000 (maximum force for the device, defined for C/C++ and Microsoft Visual Basic as DI_FFNOMINALMAX). A negative value indicates force in the opposite direction. Magnitudes are linear: a force of 10,000 is twice as great as one of 5,000. Ramp forces have a beginning and ending magnitude. For a periodic effect, the basic magnitude is the force at the peak of the wave. The direction of a force is the direction from which it comes. A positive force on a given axis pushes from the positive toward the negative. Effects also have duration, measured in microseconds. Periodic effects have a period, or the duration of one cycle, also measured in microseconds. The phase of a periodic effect is the point along the wave at which playback begins. The following illustration represents a sawtooth periodic effect with a magnitude of 5,000, or half the maximum force for the device. The horizontal axis represents the duration of the effect, and the vertical axis represents the magnitude. Points above the center line represent positive force in the direction defined for the effect, and points below the center line represent negative force, or force in the opposite direction. A force may be further shaped by an envelope. An envelope defines an attack value and a fade value, which modify the beginning and ending magnitude of the effect. Attack and fade also have duration, which determines how long the magnitude takes to reach or fall away from the sustain value, the magnitude in the middle portion of the effect. The following diagram shows an envelope. The attack level is set to 8,000 and the fade level to 1,000. The sustain level is defined by the basic magnitude of the force to which the envelope is being applied; in the example, it is 5,000. In this case, the attack is greater than the sustain, giving the effect an initial strong kick. Both the attack and the fade level can be either greater or less than the sustain level. The next diagram shows the result of the envelope being applied to the periodic effect in the first diagram. The envelope is mirrored on the negative side of the magnitude. An attack value of 8,000 means that the initial magnitude of the force in either direction is 80 percent of the maximum possible. Periodic effects and conditions can also be modified by the addition of an offset, which defines the amount by which the waveform is shifted up or down from the base level. The practical effect of applying a positive offset to the sawtooth example would be to strengthen the positive force and weaken the negative one - in other words, the force would peak more strongly in one direction than in the other. Finally, the overall magnitude of an effect can be scaled by gain, which is analogous to a volume control in audio. A single gain value can be applied to all effects for a device. You might want to do this to compensate for stronger or weaker forces on different hardware or to accommodate the user's preferences.

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About This Chapter Standard: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. (CCSS.ELA-LITERACY.L.7.2) About This Chapter Here your students will get a boost in their knowledge of basic grammatical principles, learning to use punctuation and capitalization properly in our short videos taught by experienced English teachers. They will also explore sentence structure and improper word usage. Specifically, these videos describe: - Colons, semicolons, periods, apostrophes, and quotation marks - Subject-verb agreement and parallelism - Sentence structure - Capitalization rules - Commonly confused words - Question and exclamation marks - Hyphens, brackets, parentheses, dashes, and ellipses Student aptitude in these skills will be demonstrated as they create copy generally free of common errors and effectively proofread their own work as well as that of their peers. They will be able to explain why a given correction is necessary and identify words which have been used incorrectly. How to Use These Lessons in Your Classroom Use these simple activities to help introduce these video lessons in class. After watching the video on complex subject-verb agreement, ask students to build their own complex sentences. Have them begin with a simple sentence with a single subject and predicate. Next guide them to take that same sentence and first invert the word order, then make the single subject a compound subject, and, finally, write a sentence with an interrupting phrase. They should have four sentences for each iteration of the exercise. Alternatively, you might take sample sentences from a text you are reading as a class and have the students modify the sentences by simplifying or complicating them. First watch the video on parallelism with your students. Then split the class into small groups and provide each group with a printout of several sentences lacking balance due to one of the error categories mentioned in the video. Instruct each small group to come up with a balanced sentence, discussing amongst themselves which parts disagree and how to make them more balanced. Have each group explain one of their corrections and discuss the results as a class. Assigning these videos as homework is easy. You can either have all of your students watch the videos and complete their corresponding quizzes at home, or you can use your teacher interface to assign specific lessons to students who need extra practice in that area. Proctor the chapter test in class to see how well-prepared students are for upcoming tests. 1. Punctuation: Using Colons, Semicolons & Periods Periods, colons, and semicolons all have the ability to stop a sentence in its tracks, but for very different purposes. In this lesson, learn how and why we use them in our writing. 2. Complex Subject-Verb Agreement: Inverted Order, Compound Subjects & Interrupting Phrases Learn how subject-verb agreement is essential to written language. Three common problems with subject-verb agreement are discussed with tips for avoiding the most common errors. 3. Parallelism: How to Write and Identify Parallel Sentences Sentences that aren't parallel sound funny, even if they look perfectly correct at first glance. Learn what makes a sentence parallel, how to revise a sentence to make it parallel, and how to write beautiful, balanced sentences of your own. 4. Sentence Structure: Identify and Avoid 'Mixed Structure' Sentences A mixed structure sentence is a common error that occurs when a writer starts a sentence with one structure but switches to a different structure in the middle of the sentence. This video will teach you how to spot and avoid this type of error. 5. Capitalization Rules in Writing Capitalization is a very important concept in standard grammar in the written form of the English language. Watch this video lesson to learn what capitalization is and when to use it. 6. Commonly Confused Words in English Is it 'accept' or 'except?' 'Affect' or 'effect?' How do you know when to use 'there,' 'their,' or 'they're?' Watch this video lesson to learn about some confusing words in English and how to properly use each one. 7. Question Mark: Definition & Use A question mark (?) is a form of punctuation placed at the end of a sentence. Its main purpose is to specify a query or question. In this lesson, we will take a look at when you should and should not use a question mark in your writing. 8. Exclamation Mark: Use & Meaning The exclamation mark (!), also called the exclamation point, is a form of punctuation that is sometimes used at the end of a single word, phrase or complete sentence. Its goal is to express an extremely strong and intense statement. 9. Apostrophe: Use & Examples In this lesson, we will learn about the apostrophe and how it's useful to us. See a few examples of common apostrophe mistakes and learn how to correct them. 10. Parentheses and Dashes: Correct Usage Parentheses and dashes are two different (but often confused) ways of setting off a chunk of information within a sentence - do you know how to use them correctly? 11. Using Hyphens, Brackets, Ellipses & Quotation Marks Writing not only consists of letters and words but many forms of punctuation. Watch this video lesson to learn about four types of punctuation: hyphens, brackets, ellipses, and quotation marks. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the Common Core ELA Grade 7 - Language: Standards course - English Language Conventions: CCSS.ELA-Literacy.L.7.1 - Phrases and Clauses: CCSS.ELA-Literacy.L.7.1A - Types of Sentences: CCSS.ELA-Literacy.L.7.1B - Modifiers: CCSS.ELA-Literacy.L.7.1C - Comma Rules: CCSS.ELA-Literacy.L.7.2A - Spelling: CCSS.ELA-Literacy.L.7.2B - English Language Knowledge: CCSS.ELA-Literacy.L.7.3A - Determining Meaning with Context: CCSS.ELA-Literacy.L.7.4A-D - Figurative Language: CCSS.ELA-Literacy.L.7.5A-C - English Vocabulary: CCSS.ELA-Literacy.L.7.6

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8-7 It's in the System - Concepts and Explanation Solving Linear Equations Students have used tables or graphs to find solutions. They can solve simple linear equations, y = mx + b or mx + b = nx + c, and simple equations with parentheses, y = a(x + b). In this Unit, students solve equations for different variables symbolically, writing equivalent forms of the equation. 1. Subtract 12x from each side of the equation. 12x + 3y = 9 3y = -12x + 9 2. Divide each side of the equation by 3. y = -4x + 3 1. Divide each side of the equation by 3. 12x + 3y = 9 Subtract 4x from each side of the equation 4x + y = 3 y = 3 -4x 3. Rearrange the order of terms y = -4x + 3 Solving Linear Inequalities Solving an inequality is very similar to solving a linear equation. The rules for operations with inequalities are identical to those for equations, with one exception. When multiplying (or dividing) an inequality by a negative number, you must reverse the direction of the inequality sign. 5x + 7 ≤ 42 5x ≤ 35 x ≤ 7 Solving this inequality is similar to solving 5x + 7 = 42. The operations (+, -, x, ÷) are applied to each side of the inequality. You usually show this solution on a number line. -5x + 7 ≤ 42 -5x ≤ 35 x ≥ -7 Reverse the direction of the inequality sign. Solving Systems of Linear Equations There are three standard methods for solving a system of linear equations. The graphing method involves producing straight-line graphs for each equation and then reading coordinates of intersection points as the solution(s). The linear combination method relies on two basic principles; (1) If one of the equations is replaced by a new equation formed by adding the two original equations, the solution is unchanged. (2) The solutions of any linear equation Ax + By = C are the same as the solutions of KAx + KBy = KC, where K is a nonzero number. The equivalent form method is the process of rewriting the equations in y = ax + b form and then setting the two expressions for y equal to each other. The intersection point has coordinates (30, 20), so the solution of the system is x = 30 and y = 20. Adding the two equations gives -9y = -9. The solution is y = 1 and x = 1. Since y = y, -2x + 5 = 3x - 5. The solution is x = 2 and y = 1. Solving Systems of Linear Inequalities Systems of inequalities tend to have infinite solution sets. The solution of a system of distinct, nondisjoint linear inequalities is the intersection of two half-planes, which contain infinitely many points In general, there are four regions suggested by a system of linear inequalities such as the following: Region 1 contains the solutions to the system. Points in Regions 2 and 3 satisfy one, but not both, of the inequalities. The fourth region satisfies neither inequality.

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How We Hear The human ear can be divided functionally into 3 sections: the outer, middle and inner ear. All three parts work together to conduct sounds from our listening environment to the brain for processing. The Outer Ear The external ear has two parts: the PINNA which is the outside portion of the ear that is visible on the side of the head, and the EAR CANAL which extends from the pinna to the TYMPANIC MEMBRANE (eardrum). The pinna is mostly skin and cartilage and a few muscular attachments. The pinna collects and directs sounds down the ear canal. The twists and folds of the pinna enhance high pitched sounds and also enable us to determine the location of the sound source, providing better ability to hear from the front and sides compared to sounds behind us. Cupping the hand behind the pinna can provide slight amplification to sounds coming from the front because it effectively enlarges the sound collection surface area. The ear canal is a small, tunnel-like tube that connects the pinna to the eardrum. The outer two thirds of the canal is cartilaginous and contains glands that produce CERUMEN (earwax), while the inner one third is surrounded by bone. The Middle Ear The middle ear consists of an air-filled space between the eardrum and inner ear that contains a chain of three OSSICLES (tiny bones) linked together via tiny ligaments and muscles that support and adjust tension as required to conduct sounds. The eardrum is a concave shaped layer of membrane at the end of the ear canal. Sounds travel down the ear canal and strike the eardrum, causing it to vibrate. These vibrations are then transferred through the ossicles to the snailed-shaped organ known as the COCHLEA (inner ear). The bones are known as the MALLEUS, INCUS and STAPES (also known as the hammer, anvil and stirrup). Sound sets this whole structure into vibration and the stapes vibrates into an opening in the cochlea, transferring sound energy into the fluids and tissues of the cochlea. There is a small tube that connects the middle ear space to the back of the throat known as the EUSTACHIAN TUBE. This tube is normally closed but opens momentarily upon yawning or swallowing. This periodic opening maintains equalization of the air pressure between the middle ear and outside air pressure. This pressure must be equalized for most effective transfer of sounds through the middle ear. If it becomes unequal as with rapid altitude change (i.e. on an airplane) or with a cold, the sudden opening of the Eustachian tube produces a ‘pop’ along with improved hearing because the pressure balance has been restored. Children have smaller, less efficiently positioned Eustachian tubes compared to adults, and this contributes to a higher incidence of blocked ears and subsequent ear infections. The Inner Ear The inner ear is comprised of two functionally separate sections: the VESTIBULAR (balance) portion and the COCHLEA (hearing portion). These two are interconnected and each serves it’s own vital function. The vestibular portion enables us to sense motion and head position in relation to gravity. This area makes it possible to maintain sharp visual focus with the many small and rapid motions of the head that occur as we engage in walking or other activities. The cochlea is a coiled canal within the dense bone tissue of the skull. Resembling a snail’s shell, it houses three fluid-filled membraneous canals extending it’s full length. The central canal houses the ORGAN OF CORTI, which is comprised of specialized cells and their supporting tissues. Vibratory energy propagated through the fluid produces deformation of the organ of Corti, in turn resulting in shearing forces on the tiny hair-like projections it contains. This shearing action triggers an electro-chemical signal that travels through the auditory nervous pathway which then projects to the brainstem and upward to the auditory processing centres of the brain where we ultimately ‘make sense’ of what we have heard. This is a simplified description of a complex activity that ultimately results in what we know as ‘hearing’. Note: the original post can be found here. About the Author: Tina Stafferton is the primary audiologist at Sound Hearing Care. Tina has been providing hearing healthcare to all ages in the Windsor and Essex county area since 1999. Tina has worked extensively in both hospital and private settings. She maintains close relationships with all her patients and prides herself on flexible, individualized care with an emphasis on proven technology. Tina is a member in good standing with the College of Audiologists and Speech-Language Pathologists of Ontario (CASLPO) and is a registered provider with the Assistive Devices Program (ADP). Tina regularly attends conferences and workshops to keep abreast of the rapidly changing technology and research in the areas of hearing and amplification. M.S. Audiology, Wayne State University (1999) Doctor of Audiology (Au.D) Wayne State University (2006) She owns a clinic in Tecumseh and Belle River. To learn more, please visit her website www.soundhearingcare.ca

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1.1: The whole number system describes place value relationships and forms the foundation for efficient algorithms 1.1.a: Students can: Use place value and properties of operations to perform multi-digit arithmetic. 1.1.a.ii: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 1.2: Parts of a whole can be modeled and represented in different ways 1.2.a: Students can: Develop understanding of fractions as numbers. 1.2.a.i: Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; describe a fraction a/b as the quantity formed by a parts of size 1/b. 1.2.a.ii: Describe a fraction as a number on the number line; represent fractions on a number line diagram. 1.2.a.iii: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 1.2.a.iii.1: Identify two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 1.2.a.iii.2: Identify and generate simple equivalent fractions. Explain why the fractions are equivalent. 1.2.a.iii.4: Compare two fractions with the same numerator or the same denominator by reasoning about their size. 1.3: Multiplication and division are inverse operations and can be modeled in a variety of ways 1.3.a: Students can: Represent and solve problems involving multiplication and division. 1.3.a.i: Interpret products of whole numbers. 1.3.a.ii: Interpret whole-number quotients of whole numbers. 1.3.a.iii: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 1.3.a.iv: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. 1.3.a.v: Model strategies to achieve a personal financial goal using arithmetic operations. 1.3.b: Students can: Apply properties of multiplication and the relationship between multiplication and division. 1.3.b.i: Apply properties of operations as strategies to multiply and divide. 1.3.b.ii: Interpret division as an unknown-factor problem. 1.3.c: Students can: Multiply and divide within 100. 1.3.c.i: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. 1.3.c.ii: Recall from memory all products of two one-digit numbers. 1.3.d: Students can: Solve problems involving the four operations, and identify and explain patterns in arithmetic. 1.3.d.i: Solve two-step word problems using the four operations. 1.3.d.iv: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. 3.1: Visual displays are used to describe data 3.1.a: Students can: Represent and interpret data. 3.1.a.i: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. 3.1.a.ii: Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs. 3.1.a.iii: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. 4.2: Linear and area measurement are fundamentally different and require different units of measure 4.2.a: Students can: Use concepts of area and relate area to multiplication and to addition. 4.2.a.ii: Find area of rectangles with whole number side lengths using a variety of methods. 4.2.a.iii: Relate area to the operations of multiplication and addition and recognize area as additive. 4.2.b: Students can: Describe perimeter as an attribute of plane figures and distinguish between linear and area measures. 4.2.c: Students can: Solve real world and mathematical problems involving perimeters of polygons. 4.2.c.i: Find the perimeter given the side lengths. 4.2.c.ii: Find an unknown side length given the perimeter. Correlation last revised: 9/24/2019

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A verb is a word (or group of words) which says what a person or a thing is, has or does, or what happens or is done, to a person or a thing. Example: Nina wrote a letter to her friend. We have two different kinds of verbs in a sentence: the main verb and the helping verb. The main verb has a meaning of its own (write, push etc.) whereas the helping verb does not have any meaning of its own, it only helps the main verb (is, had etc.). Main verbs have three basic forms -Base Form, Past Form and Past Participle Form. Example: accompany-accompanied-accompanied The main verbs that take an object are called transitive verbs. These verbs transit or pass over the action from the subject to the object. Example: My father gave me a book on my birthday. On the other hand, the verbs which do not transit or pass over the action from the subject to the object are called intransitive verbs. Example: The child is sleeping. Verbs are divided into strong and weak verbs, according to the way in which they form their past tense and past participle. Strong verbs are those in which vowels inside the verb is changed to indicate different tenses. Example: go-went-gone. Verbs which form their past and past participle tenses by adding‘t’, ‘d’, ‘ed’ to its present form are called weak verbs. Example: love-loved-loved

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RES/342 Week Two TWO OR MORE SAMPLE HYPOTHESIS TESTING Last week, we reviewed the 5-step procedure for performing a simple hypothesis test of a single mean. In this week, we examine hypothesis testing under several other conditions including large and small samples, comparing two independent samples, two dependent samples, Analysis of Variance (ANOVA), and proportions. This Week in Relation to the Course "Hypothesis testing refers to a general class of procedures for weighing the strength of statistical evidence-more specifically, for determining whether the evidence supporting one hypothesis over the other is sufficiently strong" (Glasserman, 2001, ¶1). While the 5-step procedure for performing various types of hypothesis tests is the same, the selection of the test statistic (step 3) depends on the nature of the hypothesis and the test data. Here we study how various test conditions alter the determination of the test statistic. Hypothesis Testing Conditions Two large, independent samples It is common to sample from two different populations to determine if the populations have the same mean. In this condition, when the sample size is sufficiently large (30 or more), and the samples are independent. The test statistic is the z statistic, calculated as: Because the sample size is large enough, this formula works effectively with the standard deviation of the sample. This is fortunate because we usually do not know the standard deviation of the population from which the sample was drawn The formula uses the difference between the two sample means divided by the square root of the variance of the distribution of differences in sample means. Note that if the means are indeed equal, then the difference between the two sample means will be zero. When the sample size is less than 30, and we are relying on the sample standard deviation, the test statistic is the t statistic and is calculated as follows: The assumptions that accompany this scenario are a) the populations are normally distributed, b) the populations are independent and, c) the standard deviations of the sampled populations are equal. Given that we are using a sample to draw conclusions about a population, it is entirely likely that there is little knowledge of the nature of the population. For that reason, to assure equal standard deviations, s2p, a pooled value, is used. The pooled value comes from a formula that in effect provides an "average" value for the variance of each population: Two sample test of proportions Another commonly used test uses sample proportions to determine if the populations from which they are drawn are different. The formula is: This test also requires a "pooled" proportion, pc. The pooling is accomplished with: When the populations from which we are sampling are dependent, a paired sample is used to generate the value of the test statistic, t: The numerator is the average of the difference of the paired samples; the denominator the standard deviation of the differences of the paired samples divided by the square root of the number of pairs. An example of the paired t test would be to compare the cost of a renting a car from Hertz compared with Avis in the same 10 cities. The cost would depend on which company you rented from. Analysis of Variance (ANOVA) is used to test the equality of the means of three or more groups based on sample data. ANOVA is really a test of means even though it sounds like a test of variance. Building on the hypothesis testing techniques discussed on the first two weeks, ANOVA uses an F test (rather than a Z or t test) to compare multiple means. A hypothesis test using an F statistic can determine whether three or more sample means are statistically significantly different from each other, otherwise one may conclude that they are from the same population. The concepts of variance and sums of squared differences used in ANOVA can be used to evaluate the output of linear regression, the topic of Week Four. Practical Application and Questions for Thought The most critical aspect of hypothesis testing is choosing the correct measure of the test statistic. In all other respects, the 5-step hypothesis testing protocol is exactly the same. Given a business scenario, the following questions need to be asked and answered: Are the data independent or dependent? Dependent data suggests the paired t test is appropriate. Is the problem a test of means or proportions? Is the sample small (<30) or large? Consider the following example. A baseball team wants to test the effect of using an iridescent baseball instead of a plain white one. Would batting averages be higher if the league changed to an iridescent baseball? The starting lineup goes into a batting cage (one at a time) to face a pitching machine set to release a straight fastball at 88 mph. Each batter gets 10 swings at a standard baseball. The process is repeated with the iridescent ball. Since the starting line up is nine players, the sample size is considered small. Since the outcomes depend on which ball is being hit, the samples are dependent. Therefore, the appropriate test in this case is a paired t test. By analyzing the data in any scenario, the appropriate test statistic should reveal itself. When comparing the salaries of a sample of male executives and a sample of female executives, are the data independent or dependent? How Readings Solidify Concepts This week's readings show many variations of hypothesis testing. Most are built on an understanding of descriptive statistics studied in previous weeks. Most of the examples are accompanied by a small diagram depicting a normal distribution and markings for the critical value and observed value. Drawing a diagram is a great aid to visualizing what the research question really asks. The simulation provides an example of how different types of data require different test statistics, yet the hypothesis testing procedure is the same. Performing tests of hypotheses, determining critical values, calculating the test statistic, these things are not overly difficult and better still, can be solved with Excel® or statistical software packages. However, the researcher must first know what kind of test is required, and this is determined by the data being studied and the question being asked. Glasserman, P. (2001). Hypothesis testing. Retrieved October 9, 2004, from http://www-1.gsb.columbia.edu/faculty/pglasserman/B6014/HypothesisTesting.pdf The expert examines hypothesis testing for ANOVA. Neat, step-by-step explanation is provided.

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The Sea Floor is blanketed with sediments composed primarily of the remains of plants and animals that live in the oceans which cover three-quarters of the Earth's surface. Sea-floor sediments also include particles of soil, dust, volcanic ash, and fragments of vegetation that are washed off the land by rivers and floods, blown in by winds, or left by melting icebergs. In the deep oceans throughout the world, sea-floor sediments have piled up continuously over thousands to millions of year, silently recording the history of changes in climate and ocean conditions as far back as the time of the dinosaurs 60-80 million years ago. Over the past 50 years, modern engineering and scientific techniques in paleoceanography have accessed these deep-water sea-floor archives and have read their messages about natural climate changes that occurred before the recent global warming started about 150 years ago. The importance of the sea-floor archives is that they allow an examination of past natural cycles of climate change and how the marine and land biological communities responded to fluctuations that include conditions hotter than the increase of 2-6 degrees C forecast for the present global warming. Before about 1947, knowledge about climate change was mainly based on written historical records and the study of fossil plants and animals scattered over the continents in short sections that escaped destruction by glaciers during the Ice Age. In 1947, the new technology of piston coring and an international Deep Sea Drilling Program (DSDP) that enabled sampling of long sections of sea floor sediments revolutionized the science of climate change. Working from ships dedicated to scientific research, these new methods enabled the retrieval of unbroken sediment cores up to 2,625 ft. (800 m.) long, covering time spans of up to 10 million years. The archival data in the sea floor records consists mainly of tiny fossil marine phytoplankton and zooplankton called microfossils, mixed in with fine sand or mud swept off the land, and dust particles, including pollen grains from forests and grasslands on the continents. The oceanic microfossils, pollen, and sediment particles provide proxy (indirect) records of oceano-graphic or atmospheric conditions in ancient times. The main oceanic plant microfossils are diatoms, dinoflagellate cysts, and coccoliths; the main animal microfossils are foraminifera and radiolarians, all of which are less than a few millimeters in length. The shells of even the tiniest (pinhead-size) marine microfossils carry an imprint of the ocean's temperature, salinity, and carbon production at the time they were alive. When extracted in the thousands from the sea, floor sediments by sieving just a handful of ocean mud, the microfossils can be analyzed by chemical methods (stable isotope measurements), or by statistical analysis of their population composition, to reveal the oceanographic conditions at their time of death. The kinds of pollen found in the sediment samples tell us how much forest or grassland there was on the continents surrounding the ocean, while the amount of inorganic sediment provides a proxy-signal of river flooding or sea ice. The results of the chemical and biological studies of the sea-floor sediment cores from all the world's oceans show a zigzag pattern of alternating warm and cold climates extending back at least 5 million years. To understand the cause of this saw-tooth climate record, methods were developed for calculating the age of the warm-cold cycles. Radiocarbon dating of the youngest sediments showed that the temperature peaks corresponded to warm periods lasting about 6,000 to 10,000 years, while the dips represented longer periods of glacial conditions lasting 20,000-30,000 years. Paleomagnetic records of periodic reversals in the Earth's magnetic field, together with dating from the decay of radioactivity in rock fragments containing uranium or potassium and argon, allowed a time- scale to be placed against the sea floor proxy-climate records. Cambridge University scientist Sir Nicholas Shackleton then showed that the oxygen in the marine microfossil shells came in two forms, one lighter, one heavier, called isotopes, and he showed that when ice sheets develop on the continents, the lighter oxygen-16 isotope diminishes in the oceans because it is locked up in the frozen water on land. When the ice sheets melt, however, the light oxygen returns to the oceans and again appears in the microfossil shells. Using this proxy-climatic data from the sea floor records, in 1976, Nick Shackleton, Jim Hays, and John Imbrie were able to decipher the encoded climate messages in the sea-floor sediments and confirmed that the ice-volume cycles correspond to seasonal and geographical changes in the amount of the sun's energy received at the Earth's surface, because of shifts in the position of the Earth's movement around the Sun, as predicted in the early 20th century by Russian scientist Milutin Milankovitch. The sea floor records of climate change revealed a history of 40-50 ice age cycles in the Northern Hemisphere, completely revising the old idea that there were just four glacial intervals during the Pleistocene Ice Age. The proxy-climate records from fossil phytoplank-ton (dinoflagellates) in sea-floor sediments in the Canadian Arctic region west of Greenland also confirm climate model estimations of summer ice-free conditions and sea-surface temperature increases of 4-6 degrees C that followed the end of the last glacial cycle. These arctic sea floor records show that the natural warming cycles took place over one to two centuries, long enough for marine and land plants and animals to adjust to the climate change. Less is known about the older pre-Ice Age sea floor records, but oxygen isotope data from 40 DSDP and ODP sites now extend back over the past 124 million years. These show that several times 50-120 million years ago, temperatures as much as 12 degrees C warmer than today. These proxy-temperature data come from measurements of the ratio of magnesium to calcium (Mg/Ca) in fossil foraminifera. The boron isotopes in these microfossils also suggest that very high levels of carbon dioxide accompanied this hothouse ocean. The sea floor records also reveal several times, just before and after the extinction of the dinosaurs, when vast quantities of organic carbon were buried in some of the ocean basins during periods called Oceanic Anoxic Events (OAEs). The OEAs seem to be related to times of extreme warmth and great variability of surface water in the subtropical to tropical latitudes of the Atlantic Ocean. The OEAs lasted about .5-1 million years and were accompanied by maj or extinctions of marine biota and wholesale changes in the composition and structure of marine animal populations. Overall, the sea-floor climate data show that very warm temperatures and hothouse conditions prevailed until about 55 million years ago, after which there was a slow drift toward the Pleistocene Ice Age and the oscillations between greenhouse and icehouse conditions. SEE ALSO: Climatic Data, Oceanic Observations; Greenland Cores; Ice Ages; Ocean Component of Models; Oceanic Changes; Oceanography; Paleoclimates; Vostok Core. BIBLIOGRApHY. John Imbrie and K.P. Imbrie, Ice Ages: Solving the Mystery (Enslow, 1979); Dick Kroon, "Exceptional Global Warmth and Climatic Transients Recorded in Oceanic Sediments," JOIDES Journal (v.28/1, 2002); Peta Mudie, Andre Rochon, and Elizabeth Levac, "Decadal-Scale Sea Ice Changes in the Canadian Arctic and the Impact on Humans during the Past 4,000 Years," Environmental Archaeology (v.10, 2005); W.F. Ruddiman, Plows, Plagues and Petroleum (Princeton University Press, 2005). Geological Survey of Canada Atlantic Was this article helpful? Your Alternative Fuel Solution for Saving Money, Reducing Oil Dependency, and Helping the Planet. Ethanol is an alternative to gasoline. The use of ethanol has been demonstrated to reduce greenhouse emissions slightly as compared to gasoline. Through this ebook, you are going to learn what you will need to know why choosing an alternative fuel may benefit you and your future.

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Studying the Earth’s interior poses a significant challenge due to the lack of direct access. Many processes observed at the Earth’s surface are driven by the heat generated within the Earth, however, making an understanding of the interior essential. Volcanism, earthquakes, and many of the Earth’s surface features are a result of processes happening within the Earth. Much of what we know regarding the Earth’s interior is through indirect means, such as using seismic data to determine Earth’s internal structure. Scientists discovered in the early 1900s that seismic waves generated by earthquakes could be used to help distinguish the properties of the Earth’s internal layers. The velocity of these waves (called primary and secondary waves, or P and S waves) changes based on the density of the materials they travel through. As a result, seismic waves do not travel through the Earth in straight lines, but rather get reflected and refracted, which indicates that the Earth is not homogeneous throughout. The Earth’s interior consists of an inner and outer core, the mantle, and the crust. Located in the center of the Earth is the inner core, which is very dense and under incredible pressure, and is thought to be composed of an iron and nickel alloy. It is solid, and surrounded by a region of liquid iron and nickel called the outer core. The outer core is thought to be responsible for the generation of the Earth’s magnetic field. A very large portion of the Earth’s volume is in the mantle, which surrounds the core. This layer is less dense than the core and consists of a solid that can behave in a plastic (deformable) manner. The thin outer layer of the Earth is the crust. The two types, continental and oceanic crust, vary from each other in thickness, composition, and density. - Inner Core - Magnetic Field - Outer Core - Polar Wandering Curves - Seismic Tomography - Seismic Waves

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This lesson begins by looking at a definition of mindfulness and finding out what students already know. They then read a text about mindfulness, before focusing on vocabulary and grammar from the text. Finally, they carry out a mindfulness activity themselves and discuss the experience. The text used in the student worksheet for this lesson is available with interactive exercises for learners on our LearnEnglish website - Provide reading and speaking practice around the topic of mindfulness - Teach or review a set of mind-related activities, e.g. judging, paying attention. Expand students’ ability to make comparisons with more advanced comparative and superlative structures. Age and level: Secondary students and adults at CEF level B1+ or B2 Approximately 50 minutes The lesson plan and student worksheets can be downloaded in PDF format below.

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This quiz addresses the requirements of the National Curriculum KS1 Maths and Numeracy for children aged 6 and 7 in year 2. Specifically this quiz is aimed at the section dealing with choosing and using appropriate standard units to estimate and measure mass (using kg/g). Weighing accurately and choosing the correct unit to measure weight is an important skill and may take some practise. Children in Year 2 are taught to understand that the standard units grams are used for smaller items with less mass (or weight), whilst kilograms are used for heavier objects. This quiz will help your child to choose the appropriate standard unit to measure mass or weight.

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Educators and parents can guide children to learn through play. By asking thought provoking questions and making our thinking visible to make sense of the world, we “show, not tell” children how to think and learn. Through play, children can develop social and cognitive skills, mature emotionally, and gain the self-confidence required to engage in new experiences and environments. Key ways that young children learn include playing, being with other people, being active, exploring new experiences, talking to themselves, communication with others, meeting physical and mental challenges, being shown how to do new things, practicing and repeating skills, and having fun.The relationship between play and learning is natural. Let your children drive the experience as you play with them. Engage your children in conversation. Be creative and thoughtful in talking to them. Have fun learning together.

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Solar cells generate electricity by "shoving" electrons from the incident sunlight out of their normal orbit into the so-called conduction band. To overcome this band gap, the photons must transmit a fixed amount of energy to the electrons. However, some light particles carry at least twice as much energy as is actually necessary for this electron jump. If this energy is previously lost in the form of heat, an upstream photon splitter can transfer this energy to two light particles. Both photons could then excite electrons and produce electricity over them. To turn their idea into a prototype, scientists propose an additional layer of aluminum arsenide or gallium phosphide. Applied to the solar cell, this material captures the high-energy photons. In this case, electrons are put into an excited state for a short time. If they fall back to their original energy level over two levels, two photons are to be created. Both then carry enough energy to generate electricity in the silicon crystal. The best yield is theoretically possible if this photon splitter is located on the backside of the solar cell. A disadvantage here is that most semiconductor cells, such high-energy light particles can not fly through unhindered. Certain "dye-sensitized cells" offer themselves here as a solution. But even if the photon splitter is located on the front, the current efficiency could be increased to a maximum of 38.6 percent. displayJan Oliver Löfken

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About This Chapter Spelling & Capitalization for Kids - Chapter Summary Students can gain full comprehension of the basics of spelling and capitalization by reviewing the short and engaging lessons in this chapter. Developed by top instructors, the lessons serve as a fantastic learning tool to help students understand vowels, root words, homophones, suffixes and more. After finishing this chapter, students will be prepared to do the following: - Describe the basics of vowels and consonants - Define dipthongs, syllables, prefixes and suffixes - Demonstrate an understanding of the rules of spelling - Identify and spell words that are difficult to spell - Exhibit knowledge of root words - Differentiate between and describe homophones and homonyms - Showcase an understanding of the rules of capitalization All lessons in this chapter are available via any computer, smartphone or tablet with an Internet connection. This enables students to study spelling and capitalization before, during or after school. With each lesson is a short quiz designed to assess students' knowledge of the concepts it covers. A chapter exam is also available to gauge comprehension of the lessons. 1. Vowels & Consonants: Lesson for Kids Explore how the alphabet is broken down into two categories and how to identify which letters are consonants and which are vowels. Learn a fun strategy for remembering the two. 2. Diphthong Lesson for Kids: Definition & Examples There are many rules that contribute to the English language, and some are followed effortlessly by those who speak it. One such rule is that of diphthongs, and in this lesson you will find out what diphthongs are, learn how to recognize them, and practice finding them in sentences on your own. 3. Syllables Lesson for Kids: Definition & Rules Did you know that words are often like puzzles, made of smaller pieces or parts? These pieces of words are called syllables and this lesson will teach you how to find and use them. Read on to learn more about syllables! 4. Spelling Rules: Lesson for Kids In this lesson, we're going to take a look at some rules that you can follow to be an excellent speller. You will see examples of how to spell common words you use often when you speak, write, and read. Let's dive in and get started! 5. Difficult Words to Spell: Lesson for Kids Think of a time when you've been tricked. That's just what the English language does to you sometimes with spelling. In this lesson, you'll learn how to tackle words that might seem difficult to spell. 6. Root Words: Lesson for Kids This lesson is about root words, prefixes, and suffixes. You will learn how to identify root words and how to use root words to help discover the meaning of an unfamiliar word. 7. Prefixes Lesson for Kids: Definition & Examples Have you ever unbuttoned your coat, retied your shoes, or told your friend how impossible the math test was? If so, then you've used words with prefixes. In this lesson, you'll learn what prefixes are and what they can do to a word. 8. Suffixes Lesson for Kids: Definition & Examples In this lesson, we are going to learn about word parts that can change the meaning of a word. These word parts are added to the end of a word. They are called suffixes. 9. Homonyms: Lesson for Kids Wave, tire, and well all have something in common. They are all homonyms. In today's lesson we will learn what is special about these words and how to find them. 10. Homophones: Lesson for Kids Homophones are words that sound the same but have different meanings. Read the following lesson to learn how to tell homophones apart, how to tell the difference between 'problem pairs' of homophones and how to choose the right homophone in your own writing. 11. Capitalization Lesson for Kids: Rules & Definition Capitalizing words allows them to be set apart from the other words in a sentence. A capital letter is like a highlight; it draws the reader's attention to it. Read the following lesson to learn the rules of capitalization. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the NAPLAN Year 3: Test Prep & Practice course - Understanding the NAPLAN Tests - Overview of Grammar for Kids - Punctuation Rules for Kids - Reading Comprehension for Kids - The Writing Process for Kids - Counting, Number Patterns & Estimation for Kids - Decimals & Fractions for Kids - Addition, Subtraction, Multiplication & Division for Kids - Math Word Problems for Kids - Understanding Geometry for Kids - Time, Money & Measurement for Kids - Reading Basic Graphs, Charts & Figures for Kids - NAPLAN Year 3 Flashcards

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What are the functions of viruses? A complete virus particle is called a virion. The main function of the virion is to deliver its DNA or RNA genome into the host cell so that the genome can be expressed (transcribed and translated) by the host cell. The viral genome, often with associated basic proteins, is packaged inside a symmetric protein capsid. A virion (virus particle) has three main parts: - Nucleic acid – this is the core of the virus with the DNA or RNA (deoxyribonucleic acid and ribonucleic acid respectively). - Protein Coat (capsid) – This is covering over the nucleic acid that protects it. - The flu is a viral infection caused by the influenza virus, a respiratory virus. The common cold is also a viral infection caused by the adenovirus or coronavirus and there are many, many subsets with a lot of variability. That's why it's said there's no cure for the common cold [and] there's no real vaccine. - Apply Recognised Hygiene Measures - Always keep your hands clean. - Follow tips for Coughing and Sneezing Without Contaminating. - Avoid touching your nose, eyes and mouth. - Avoid contact with people that are sick as they may be contagious. - Clean your surroundings regularly, as well as the sanitary appliances you use. - They don't have a metabolism, they lack the chemical process needed to "live". The virus can reproduce on there own by injecting DNA or RNA asexually, so yes they can reproduce. The virus does in fact pass some traits onto its offspring such as resentfulness to a type of medicine. A virus does not belong to any of the five kingdoms of life. Even more odd, a virus is not made up of cells. Viruses do not eat, they do not produce waste, nor do they do many of the functions that other living things do. In fact, the only thing they can do is reproduce. - 16% of Cancers Are Caused by Viruses or Bacteria. Strictly speaking, cancer is not contagious. But a fair number of cancers are clearly caused by viral or bacterial infections: lymphomas can be triggered by the Epstein-Barr virus, which also causes mononucleosis. - the virus attaches itself to a specific host cell (the cell in which it will reproduce) the virus injects its genetic material into the host cell. the host cell uses the genetic material to make new viruses. the host cell splits open, releasing the viruses. - Viral and bacterial infections are both spread in basically the same ways. A person with a cold can spread the infection by coughing and/or sneezing. Bacteria or viruses can be passed on by touching or shaking hands with another person. Viruses are only able to replicate themselves by commandeering the reproductive apparatus of cells and making them reproduce the virus's genetic structure instead. Thus, a virus cannot function or reproduce outside a cell, thereby being totally dependent on a host cell in order to survive. - Viruses are only able to replicate themselves by commandeering the reproductive apparatus of cells and making them reproduce the virus's genetic structure instead. Thus, a virus cannot function or reproduce outside a cell, thereby being totally dependent on a host cell in order to survive. - Viruses cause familiar infectious diseases such as the common cold, flu and warts. For most viral infections, treatments can only help with symptoms while you wait for your immune system to fight off the virus. Antibiotics do not work for viral infections. There are antiviral medicines to treat some viral infections. - Viruses are often considered non-living as they exist in an inert state outside of a host cell. They consist of a strand of nucleic acid, either DNA or RNA, surrounded by a protective protein coat (the capsid). Sometimes they have a further membrane of lipid, referred to as an envelope, surrounding the protein. Updated: 12th November 2019

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Soil erosion can have a devastating impact across the globe and a serious threat for modern agriculture. The increased demand for agriculture has led to forests and natural grasslands being converted to farm fields and pastures. However, many of the plants grown, such as coffee, cotton and palm oil, can significantly increase soil erosion beyond the soil’s ability to maintain and renovate. It can also lead to increased pollution and sedimentation in streams and rivers or, because these areas are often less able to hold onto water, can worsen flooding. This problem is particularly urgent considering the ever-expanding human population and climate change. Researchers from the Universities of Bristol and Exeter have revealed the crucial function the microscopic roots hairs play in binding and reinforcing soil. While the larger-scale root properties such as diameter, length and surface area have been extensively studied to understand their role in preventing soil erosion, the effect that micro-scale properties, such as root hairs, has is less well documented. The research team looked at how wild plants Arabidopsis thaliana, which produced root hairs, compared with an almost identical Arabidopsis with the same root hair structure in reducing soil erosion. They found that, when planted in sufficient density, plants with root hairs reduced soil loss almost completely - while otherwise identical plants without hairs could not stem the flow of erosion. Three methods were used to explore the soil retention benefits of root hairs. First, the samples were placed in a sterile gel, in a petri dish, and then subjected to increasing centrifugal force. The study found that the hairless seedlings were easier to remove from the gel compared to seedlings abundant with root hairs. Second, the study found that root hairs were also shown to stabilise the plant in the soil, as they increased the force needed to uproot the plant. Third, in the experimental landscapes laboratory at Exeter, root hairs reduced water erosion to almost zero. Professor Claire Grierson, one of the study’s lead authors from Bristol’s School of Biological Sciences explained: “These findings could be the key in helping to tackle soil erosion. There are three possible ways root hairs could enhance soil, either the soil might bind directly to root hair surfaces, root hairs might release material that reinforces soil, or root hairs might release material that is processed by microbes into something that can reinforce soil. “We hope our knowledge about the properties of plants that minimise soil erosion will allow the creation and selection of best-suited agricultural plants.” Professor Quine, an expert in Earth System Science at the University of Exeter, added: “This exciting, truly interdisciplinary project across biology, maths, engineering and environmental science has given us invaluable new insights into the influence of microscopic root structures on the macroscopic behavior of soils. “I was amazed at the difference that root density made in reducing soil erosion to almost zero, when root density was high, whereas soil loss was still significant when roots at the same density had no hairs. “We are excited to explore how the hairs exert this extraordinary influence.” The team are now working to distinguish between these hypotheses and identify the molecules involved. This research was an interdisciplinary collaboration led by Professor Claire Grierson at Bristol, environmental scientist Professor Tim Quine at the University of Exeter, and Professor Tannie Liverpool and Dr Isaac Chenchiah of the School of Mathematics at Bristol. Micro-scale interactions between Arabidopsis root hairs and soil particles influence soil erosion by C Grierson et al in Communications Biology.

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Exploring fronted adverbials Home learning focus To understand what fronted adverbials are and how to punctuate them correctly. This lesson includes: one video to help you understand fronted adverbials Watch this short clip to learn about fronted adverbials. What’s an adverbial? An adverbial is a word or phrase that adds more information to a verb. Adverbials are used to explain how, where or when something happened. For example: Ian ate a banana earlier today. 'Earlier today' is an adverbial as it adds detail about when Ian ate the banana. What’s a fronted adverbial? A fronted adverbial is when the adverbial phrase is at the front (or start) of the sentence, before the verb. For example: Earlier today, Ian ate a banana. Here, 'earlier today' is a fronted adverbial as it adds detail about when Ian ate the banana at the front of the sentence, before the verb ‘ate’. You may need paper and a pen or pencil for some of these activities. Complete this short activity by highlighting the fronted adverbials. Remember: Fronted adverbials are used at the start of a sentence. Rewrite these sentences by moving the adverbial phrase to the front of the sentence. Remember: You must use a comma after your fronted adverbial. The lion leaped from the tall grass as quick as a flash. The howler monkeys wake up the whole jungle with their loud calls in the morning. The badgers' home was built under the woodland ground. This time, add your own fronted adverbials to the sentences. The fox stared at the mouse. The giraffe reached for the leaf on top of the tree. The owl soared through the sky. Fronted adverbials explain how, where or when something happened. Watch the following video and focus on all the things that happen in spring. Now write six sentences about what happens in spring using a fronted adverbial in every sentence. Choose something you saw in the video and then think of an adverbial to describe the action you saw. For example: The plants grew + Quickly = Quickly, the plants grew. You also could use this Fronted Adverbials word mat to help you write some impressive sentences.

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In this social skills lesson plan, students will get to practice identifying how to be a friend. Friendship is an important social skill for kindergarten students to master as they begin to form a new community of peers at school. Social skills are an essential part of children’s emotional health and well-being. They also play an important role in creating a safe and inviting classroom community. Use this collection of lesson plans to teach children important social skills, such as how to be a good friend, how to recognize how others are feeling, strategies for regulating emotions, the importance of empathy, and more.

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About This Chapter Geometry - Chapter Summary Watch the videos in this chapter to prepare for the geometry-related questions on the TASC Math test. The lessons provide an overview of the different types of shapes as well as their properties and mathematical formulas; some of the topics include: - Points, lines and angles - Properties of shapes - Perimeters and area - The Pythagorean Theorem - Vertical and complementary angles - Three-dimensional shapes - Surface area of cubes, rectangle prism, cylinder and pyramid This chapter is broken down into multiple lessons that focus on different topics within geometry. Each lesson includes a short video, transcript with key vocabulary terms and a multiple-choice quiz. There is also a chapter test that you can use to test your knowledge and figure out if you are ready to move on to the next chapter. TASC Math Objectives Similar to the GED and HiSET, the TASC is a high school equivalency exam that tests your knowledge in math, science, reading, writing and social studies. The math subtest is 105-115 minutes long and includes 55 questions; questions types include multiple-choice, gridded-response, constructed-response and technology-enhanced formats. The math exam is divided into two parts, and you can use a calculator on the first part. Geometry questions make up about 23% of the test. You can use this chapter to prepare for questions that relate to recognizing the properties of shapes and the use geometric formulas. 1. Points, Lines & Angles in Geometry After watching this video lesson, you should understand the basic terms that form the foundation of geometry. Learn what a point is, what a line is, what an angle is, and learn about a special type of angle called a right angle. 2. Types of Angles: Vertical, Corresponding, Alternate Interior & Others In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements. 3. Vertical Angles & Complementary Angles: Definition & Examples Special angles make your life easier. Learn how you can use the properties of special angles to help you find the measurements of missing angles in this video lesson. 4. Geometric Constructions Using Lines and Angles Watch this video lesson to learn about geometric construction and how you can copy line segments and angles without using any numbers. All you need is a straight edge and a compass. 5. Circular Arcs and Circles: Definitions and Examples What is a circle? In this lesson, find out all about the circle and its many parts, including circular arcs and semicircles. Also, discover how a locus works in creating a circle, parallel lines and more. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the TASC Mathematics: Prep and Practice course - TASC Math: Real Numbers - TASC Math: Complex and Imaginary Numbers Review - Intro to Algebraic Expressions - Intro to Algebraic Equations - TASC Math: Exponents and Exponential Expressions - Overview of Square Roots - TASC Math: Radical Expressions - TASC Math: Functions - TASC Math: Graphing and Functions - Overview of Sequences - TASC Math: Inequalities - TASC Math: Algebraic Distribution - TASC Math: Linear Equations - TASC Math: Factoring - TASC Math: Quadratic Equations - TASC Math: Graphing and Factoring Quadratic Equations - TASC Math: Properties of Polynomial Functions - TASC Math: Rational Expressions - TASC Math: Measurement - Shapes in Geometry - Volume & Surface Area - TASC Math: Calculations, Ratios, Percent & Proportions - TASC Math: Data, Statistics, and Probability - Making Inferences & Justifying Conclusions in Math - TASC Mathematics Flashcards

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A worksheet that focuses on converting units of capacity in the metric system. Use this worksheet to determine student understanding when converting between the metric units of milliliters, liters, kiloliters, and megaliters. Students connect the decimal representations to the metric system when finding the equivalent number of larger units. The final section of the worksheet asks students to identify the rule when converting between these metric capacity units. An answer sheet is included. Common Core Curriculum alignment Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement ... Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. We create premium quality, downloadable teaching resources for primary/elementary school teachers that make classrooms buzz! Request a change You must be logged in to request a change. Sign up now! Report an Error You must be logged in to report an error. Sign up now!

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Repeat, Repeat, Repeat Spaced repetition – once introduced, keep using the vocab so learners become familiar with it – review new vocabulary at the end of each lesson and the beginning of the next. Encourage the use of flashcards and/or apps like Quizlet and Brainscape for repetition between lessons. Typically, a word needs to be used 14 times before it is considered ‘learned’. Teach in Context Learners need to have somewhere to ‘put’ new vocabulary., if it is taught in context, studies have shown that they are more likely to retain it than words in isolation. Context also helps with comprehension of new vocabulary. So, if it is not relevant to the lesson – don’t introduce it yet!. Learners need to understand 95% (Laufer) of a text to make it enjoyable and comprehensible. Reading is an excellent way to be introduced to new vocabulary in context. Try graded readers, newspapers, magazines, internet articles – anything that interests the learner (sport, music, film reviews or even whole novels). Teach Word Formations Introduce learners to the different affixes that, using the same word stem, give a different meaning. With a knowledge of these prefixes & suffixes, learners can rapidly increase their working vocabulary. A little basic morphology and learners can create word families of verbs, nouns, adjectives and adverbs all from one word. Chunks and Collocations Words are rarely used in isolation – teach your learners which words are commonly used together. Verbs and nouns together aid fluency. Knowing the function of a word (in action) makes it easier to understand and remember. Use Corpus based dictionaries and sites for practical examples like BNC/BYU and Just-the-Word. Encourage learners to create lexical sets when learning new vocabulary. Include synonyms and antonyms and anything relevant. Writing words as a ‘web’ can make the words more memorable and connections and relationships between words easier to see than in a standard list. For an excellent example see vocabulary maps.

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Click on an oval to select your answer. To choose a different answer, click one different oval. Sometime after midnight on February 8, 1969, a large, bright meteor entered Earth's atmosphere and broke into thousands of pieces, plummeted to the ground, and scattered over an area 50 miles long and 10 miles wide in the state of Chihuahua in Mexico. The first meteorite from this fall was found in the village of Pueblito de Allende. Altogether, roughly two tons of meteorite fragments were recovered, all of which bear the name Allende for the location of the first discovery. Individual specimens of Allende are covered with a black, glassy crust that formed when their exteriors melted as they were slowed by Earth's atmosphere. When broken open, Allende stones are revealed to contain an assortment of small, distinctive objects, spherical or irregular in shape and embedded in a dark gray matrix (binding material), which were once constituents of the solar nebula-the interstellar cloud of gas and dust out of which our solar system was formed. The Allende meteorite is classified as a chondrite. Chondrites take their name from the Greek word chondros-meaning "seed" -an allusion to their appearance as rocks containing tiny seeds. These seeds are actually chondrules: millimeter-sized melted droplets of silicate material that were cooled into spheres of glass and crystal. A few chondrules contain grains that survived the melting event, so these enigmatic chondrules must have formed when compact masses of nebular dust were fused at high temperatures-approaching 1,700 degrees Celsius-and then cooled before these surviving grains could melt. Study of the textures of chondrules confirms that they cooled rather quickly, in times measured in minutes or hours, so the heating events that formed them must have been localized. It seems very unlikely that large portions of the nebula were heated to such extreme temperatures, and huge nebula areas could not possibly have lost heat so fast. Chondrules must have been melted in small pockets of the nebula that were able to lose heat rapidly. The origin of these peculiar glassy spheres remains an enigma. Equally perplexing constituents of Allende are the refractory inclusions: irregular white masses that tend to be larger than chondrules. They are composed of minerals uncommon on Earth, all rich in calcium, aluminum, and titanium, the most refractory (resistant to melting) of the major elements in the nebula. The same minerals that occur in refractory inclusions are believed to be the earliest-formed substances to have condensed out of the solar nebula. However, studies of the textures of inclusions reveal that the order in which the minerals appeared in the inclusions varies from inclusion to inclusion, and often does not match the theoretical condensation sequence for those metals. Chondrules and inclusions in Allende are held together by the chondrite matrix, a mixture offine-grained, mostly silicate minerals that also includes grains of iron metal and iron sulfide. At one time it was thought that these matrix grains might be pristine nebular dust, the sort of stuff from which chondrules and inclusions were made. However, detailed studies of the chondrite matrix suggest that much of it, too, has been formed by condensation or melting in the nebula, although minute amounts of surviving interstellar dust are mixed with the processed materials. All these diverse constituents are aggregated together to form chondritic meteorites, like Allende, that have chemical compositions much like that of the Sun. To compare the compositions of a meteorite and the Sun, it is necessary that we use ratios of elements rather than simply the abundances of atoms. After all, the Sun has many more atoms of any element, say iron, than does a meteorite specimen, but the ratios of iron to silicon in the two kinds of matter might be comparable. The compositional similarity is striking. The major difference is that Allende is depleted in the most volatile elements, like hydrogen, carbon, oxygen, nitrogen, and the noble gases, relative to the Sun. These are the elements that tend to form gases even at very low temperatures. We might think of chondrites as samples of distilled Sun, a sort of solar sludge from which only gases have been removed. Since practically all the solar system's mass resides in the Sun, this similarity in chemistry means that chondrites have average solar system composition, except for the most volatile elements; they are truly lumps of nebular matter, probably similar in composition to the matter from which planets were assembled.

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Give kids a fun way to practice using parts of speech with this fill-in-the-blank story template! You and your students will be in a fit of giggles as you listen to each other read their completed zoo-inspired stories aloud! Can your second graders differentiate between singular and plural nouns? Let's find out! Use this sorting activity to let your students distinguish between singular and plural using regular and irregular plural nouns. People, places, and things—these are what nouns are made of. Our common nouns worksheets encourage students to better understand nouns and how they work. Using noun reviews, glossaries, vocabulary cards, and more, your child will get to know nouns in a fun environment. Whether your young learner needs help writing journals or long-form essays, our common nouns worksheets build a great foundation.

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The repeaters take the signal they receive from the network devices and regenerate it to keep it intact during its transmission through the physical environment. Since all components of the physical environment of a network (copper, fiber optic cables and wireless media) have to control the attenuation that limits the possible distance between the different nodes of the network, repeaters are an excellent way to extend the net physically. When an electrical signal travels along a medium it gets attenuated depending upon the medium characteristics. That is why a LAN cannot send signal beyond a certain limit imposed by the different types of LAN technologies. To increase the length of the LAN, repeaters are frequently used. Repeaters in its simplest form relay analog electric signal. It means that they transmit the physical layer signals or data and therefore correspond to the bottom layer of OSI model. Repeater amplifies the signal, which has got attenuated during the course of transmission because of the physical conditions imposed by the transmission media. It also restores the signal to its original shape. The specific characteristic of repeater is that whatever it receives it transmits to the other LAN segment. This does not understand the frame format and also physical addresses. In other words, it is a transparent device. Therefore, multiple LANs connected by repeaters may be considered as a single LAN. Since repeaters are devices that operate in the physical layer, they do not examine the data packets they receive, nor do they know any of the logical or physical addresses related to those packets. It means that the location of a repeater hardly affects the transmission speed of the information flow in the network. The repeater is limited to expanding the data signals received from a particular segment of the network and passing them to another segment of the network, as the data moves to its final destination. The repeaters extend the data signal from one segment of the network and pass it to another segment of the network, thus expanding the size of the network. Repeaters are also often called concentrators. Hubs that have the same functions as repeaters to amplify the signal are known as active hubs or multiport repeaters. All these devices (regardless of the term used to designate them) operate in the physical layer of the OSI model. The term hub or hub describes how the wiring connections of each node of a network are centralized and connected in a single device. It usually applied to Ethernet, Token Ring and FDDI (Fiber Distributed Data Interface) concentrators supporting individual modules that concentrate multiple types of functions in a single device. Typically, hubs include slots to accept several modules and a standard rear panel for routing, filtering, and connection to different transmission media (for example Ethernet and Token Ring). The first or "first-generation" hubs are advanced wiring boxes that offer a central connection point connected to several points. Its main benefits are the conversion of media (for example from coaxial to optical fiber), and some quite primitive management functions such as automatic partitioning when a problem detected in a given segment. The "second generation" intelligent hubs base their potential on the management possibilities offered by the radio topologies (Token Ring and Ethernet). It has the capacity of management, supervision, and remote control, allowing network managers to offer a more extended period of network operation thanks to the acceleration of diagnosis and troubleshooting. However, they have limitations when trying to use as a universal configuration and management tool for complex and heterogeneous architectures. The new "third-generation" hubs offer a process based on RISC (Reduced Instructions Set Computer) architecture along with multiple high-speed boards. These boards consist of several independent Ethernet, Token Ring, FDDI and management buses, which eliminates traffic saturation of current second-generation products. An Ethernet hub is called a "multiport repeater." The device simultaneously repeats the signal to multiple cables connected to each of the hub ports. At the other end of each cable is a network node, for example, a personal computer. An Ethernet hub becomes a smart hub when it can support added intelligence for monitoring and control functions. Smart hubs allow users to divide the network into segments with easy error detection while providing an orderly network growth structure. The remote management capability of smart hubs makes it possible to diagnose a problem remotely and isolates a point with problems from the rest of the network so that other users are not affected. The most popular type of Ethernet hub is the 10BaseT hub. In this system the signal arrives through twisted-pair cables to one of the doors, being electrically regenerated and sent to the other outputs. This element is also responsible for disconnecting the outputs when an error situation occurs. A Token Ring hub is called Multistation Access Unit (MAU). MAUs differ from Ethernet hubs because the first ones repeat the data signal only to the next station in the ring and not to all the nodes connected to it as an Ethernet hub does. Passive MAUs have no intelligence; they are simply relaying. Active MAUs not only repeat the signal, but they also amplify and regenerate it. Smart MAUs detect errors and activate procedures to recover from them. Generally, the maximum size of an Ethernet is considered to be 500 meters. When two Ethernet with maximum size segments are connected together using repeater will make the total length to 1000meters.In the same manner two repeaters connect three segments together and transmit signal from one end to another. That is, signal can travel up to 3000 meters. Is it possible to extend the length of LAN in this manner up to any arbitrary length? The answer is no. Ethernet follows CSMA/CD access mechanism for successful transmissions of signal which is based on low delay. By extending the length of Ethernet beyond certain limit will greatly hamper delay time of CSMA/CD mechanism. It is shown that maximum four repeaters are used to extend Ethernet segments into a single Ethernet network. However, connection between two segments can be extended over a long distance by using fiber modems. This is, known as Fiber Optic Intra Repeater Link (FOIRL). The main disadvantage associated with repeaters is their transparent nature because the signal received at one segment is truly transmitted to the other segment. Repeater does not understand the language of frame and therefore, cannot distinguish between noise and signal. When a collision occurs on one segment, the same along with noise produced by collision is reproduced on the other segment by repeater. Classification of Repeaters Repeaters can be classified into two categories. These are local and remote repeaters. Local repeaters are used to connect LAN segments separated by a very small distance. Remote repeaters are used to connect LAN segments that are far from each other. A transmission line known as a link segment is provided between two remote repeaters. No nodes can be connected to this line.

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Python round() function is used to perform rounding operation on numbers. Table of Contents Python round() function syntax is: The number is rounded to ndigits precision after the decimal point. If ndigit is not provided or is None, then nearest integer is returned. While rounding the input number to an integer, if both round up and round down values are equally close then even number is returned. For example, 10.5 will be rounded to 10 whereas 11.5 will be rounded to 12. Any integer value is valid for ndigits (positive, zero, or negative). Python round() function examples Let’s look at some example of round() function. round() to integer print(round(10, 2)) print(round(10.2)) print(round(10.8)) print(round(11.5)) 10 10 11 12 round() to even side # if both side of rounding is same, even is returned print(round(10.5)) print(round(12.5)) round() with ndigit as None print(round(1.5)) # OR print(round(1.5, None)) round() with negative ndigit print(round(100, 0)) print(round(100.1234, -4)) print(round(100.1234, -5)) 100 100.0 0.0 Python round float When rounding is applied on floating point numbers, the result can be sometimes surprising. It’s because the numbers are stored in binary format and mostly decimal fractions cannot be represented exactly as binary fractions. Python does the approximation and presents us the rounded value, because of this floating point arithmetic can sometimes result in surprising values. >>>.1 + .1 == .2 True >>>.1 + .1 + .1 == .3 False >>>.1 + .1 + .1 + .1 == .4 True Let’s see some examples of round() function with floats. print(round(2.675, 2)) print(round(1.2356, 2)) print(round(-1.2356, 2)) 2.67 1.24 -1.24 Notice that first float rounding seems wrong. Ideally, it should be rounded to 2.68. This is the limitation of arithmetic operations with floats, we shouldn’t rely on conditional logic when dealing with floating point numbers. round() with custom object We can use round() function with a custom object too if they implement __round__() function. Let’s look at an example. class Data: id = 0 def __init__(self, i): self.id = i def __round__(self, n): return round(self.id, n) d = Data(10.5234) print(round(d, 2)) print(round(d, 1)) Reference: Official Documentation

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Viruses mutate. What does that mean for us? In this course, you will learn that viruses can change over time as a result of mutations, and why this matters for public health. Microbes are all around us. Viruses are the smallest and simplest type of microbe. Viruses infect living cells. Some viruses infect cells in our body and make us sick. Our body quickly recognizes and fights off most of the viruses around us, before they make us sick. But sometimes our body meets a virus that is new and unfamiliar. Where do new viruses come from? Viruses can change over time as they develop mutations in their genetic material. Genetic material is hereditary and contains instructions for life. The genetic material of a virus has the genes that determine how the virus looks and behaves. Mutations can change small things about how a virus looks, how it causes sickness, how it spreads, whether our immune system can recognize it, or how difficult it is to treat. For some viruses, mutations can build up as more and more infections occur. More infections mean more chances for mutations. To learn more about virus mutations and how and why they happen, we need to look more closely at the genetic material of viruses. Continue to learn more. A virus has one mission: Make and spread more viruses. But first it has to copy its genetic material. Viruses can use either DNA or RNA as their genetic material. Because of this, there are two basic different types of viruses: “RNA viruses” and “DNA viruses”. A virus has to copy or replicate its DNA or RNA to make more viruses. But it can’t do this on its own - it must get inside a cell in a living thing first. Getting inside a cell starts with the virus using special proteins on its surface to attach to other proteins on the cell. A virus can only attach to and infect certain cells (like lung cells) in certain living things. Some viruses infect only humans. Others can infect both animals and humans. After a virus attaches itself to a cell, it enters the cell and releases its DNA or RNA. Then the virus takes over - it’s the new boss in town. The virus uses the cell’s copying machinery to replicate its own DNA or RNA. The copies get packaged into many new virus particles that leave the cell and spread to other cells. But the replication process isn’t perfect. There can be mistakes, like typos, in the strings of letters in the copied DNA or RNA. These mistakes are called mutations. Mutations happen in all living things, including us! As we reproduce, our children might have slight changes in their genes. But these changes rarely make much of a difference. Viruses reproduce much, much more quickly, and produce many more copies, than we and other living things do. So they can collect more mutations. Mutations over time can slowly change a virus. - Viruses are the smallest microbes that carry genetic material - DNA or RNA. - New viruses can emerge when viruses create copies of their DNA or RNA inside of cells, but the copies have “typos” or mutations. Mutations can be good or bad for a virus. A mutation might help a virus infect new types of cells. Sometimes, mutations allow a virus from animals to start infecting humans. This is called “spillover”. A mutation might also work against a virus, making it less able to make copies. Some antiviral medicines are made to force viruses to gain many more mutations than usual. Most mutations simply change the “looks” of the virus without changing how it behaves. Many critical mutations must occur to create a new “strain” that behaves very differently. But some viruses change more quickly than others, creating new strains more often. Why is this? It has a lot to do with what kind of genetic material each virus uses. DNA viruses like the chickenpox virus use DNA copy machinery in our cells to make more of themselves. This copy machinery works slowly and goes through “proof-reading”. RNA viruses like the Influenza (flu) virus use different copy machinery than DNA viruses do. This RNA copy machinery is faster and sloppier and does not have proofreading. Because of this, most RNA viruses get more mutations and change more quickly than DNA viruses. To learn more, let’s compare two types of RNA viruses: coronaviruses and flu viruses. The flu virus mutates very often. It has 8 RNA segments for its genetic material instead of one! This means more chances for mutations, but also for mixing-and-matching of segments into new viruses. Imagine a person was infected by two strains of flu at once. Inside their infected cells, new virus particles could mix-and-match RNA segments from these two strains. A new type of flu could form. We need a new flu shot every flu season because new flu strains always emerge that can escape our immune system. Their outer shells look different. What about coronaviruses? With only one large piece of RNA, they mutate more slowly than flu viruses do. They also have their own type of proofreading that helps to prevent mutations. The mutation rate of coronaviruses is slow enough for scientists to track it. This is good news. It gives scientists time to study the virus, learn more about it, and work towards a vaccine. Vaccines are important for slowing or stopping the spread of viruses and helping to prevent new strains from emerging. If a virus can no longer infect people, it can’t replicate or mutate. You can help to prevent virus mutations! Avoid spreading viruses: Wear a mask, wash your hands, and stay home if you are sick. Make sure to get your flu shot, and stay up to date on your vaccines! Mutations might sound scary but science is on our side. Scientists make vaccines for new flu strains every year. Scientists are also studying mutations in the novel coronavirus to track it. Keep your immune system strong so that you can fight off viruses before they replicate in your cells. Protect animals and ecosystems. Follow recommendations from CDC, healthcare workers and other experts. What did you think of this course? Dr. Lauring is an associate professor at the University of Michigan, where his lab studies how RNA viruses evolve so quickly. His lab focuses on aspects of mutation rate and mutational tolerance in poliovirus, influenza, and other RNA viruses. Dr. Spindler is a Professor at the University of Michigan. Her lab studies ways that viruses, such as mouse adenovirus, cause encephalitis. Dr. Spindler also co-hosts the weekly science podcast This Week in Virology. Lifeology is funded by LifeOmic. Make sure to try out their FREE wellness apps for iOS and AndroidLearn more

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Notes of chapter: Visualising Solid Shapes are presented below. Indepth notes along with worksheets and NCERT Solutions. (1) Two dimensional figure- The figure which has only two dimensions, i.e., length and breadth is known as two dimensional figure. We can write it as 2-D.These 2-D figures are also called plane figures. Eg: – Rectangle, square, triangle etc. (2)Three dimensional figure- The figure which has three dimensions, i.e., length, breadth and height is known as three dimensional figure. We can write it as 3-D.These 3-D figures are also called solid figures. Eg:- Cuboid, cube, cone etc. (3) Parts of 3-D figure- A point where two or more lines, curves and faces of a solid figure meet is known as vertices. In simple words, corners of any figure are known as vertices. Vertex is singular form of vertices. A cube has 8 corners or vertices. The line segments which join vertices and faces of 3D figures are known as edges. A cube has 12 edges. The flat surfaces of 3-D figures are known as faces. A cube has 6 faces. In above figure- ABCD, DCHE, ADEF, BCHG, EFGH and ABFG are faces of a cube. A 2-D outline of a solid or 3- d figure which can be folded to form a 3- D figure, is known as net. Eg:- Net of a cube is presenting below:- (5)Types of sketches of solids- A sketch which does not have proportional lengths but describes all parts of the solid is knows as oblique sketch. Eg:- Oblique sketch of cube (ii) Isometric sketch – A sketch which have proportional lengths and describes all parts of the solid is knows as an isometric sketch. It is drawn on an isometric dot paper. Eg:- Isometric sketch of cube (6) Different sections of a solid can be viewed in many ways- (i) Cross- section- When a solid is viewed by its slice or cutting is known as cross- section of that solid shape. Types of cross-section (a) Horizontal cut- When a solid is cut parallel to its base is known as horizontally cut of that solid shape. Eg:-Horizontal cut of the vegetables Horizontal cut of the papaya (b)Vertical cut – When a solid is cut perpendicular to its base is known as vertical cut. Eg:- Vertical cut of vegetables Vertical cut of the papaya (ii) Shadow play- When a solid (3-D) is viewed by its 2-D shadow is known as shadow play of that solid shape. Shadow of people (iii)Certain angle play When a solid shape is viewed from the different angles is known as certain angle play. When an observer is standing in front of the object is known as front view. Front view of telephone When an observer is standing in back of the object is known as back view. Back view of telephone When an observer is standing by the side of the object is known as side view. Side view of telephone When an observer is standing at the top of the object is known as top view. Top view of telephone A map is a pictorial presentation of a definite place. Eg:- Map of school, map of market, map of city, map of country etc. A 3D shape with flat polygonal faces, straight edges and sharp corners (vertices), is known as polyhedra. Plural of polyhedra is known as polyhedron. Eg:- Square, cubes, pyramid, prism etc. Prism is a polyhedron whose base and top are congruent polygons and whose lateral faces are parallelogram in shape. A prism is named after its base, as a hexagonal prism has hexagon base. A pyramid is a polyhedron whose base is a polygon of any number of sides and whose lateral faces are triangles with a common vertex. A pyramid is named after its base, as a hexagonal pyramid has hexagon base. (9) Types of polyhedron Convex polyhedron are those polyhedron that have no portions of their diagonals in their exteriors. Concave polyhedron are those polyhedron that have some portion of their diagonal in the exteriors. The polyhedron that have faces made up of regular polygons and the same number of faces meet at each vertex, are called regular polyhedron. The polyhedron that have faces made up of irregular polygons and the same number of faces do not meet at each vertex, are called irregular polyhedron. Euler’s Formula is a relationship among faces (F), vertices (V) and edges (E) of polyhedron. F + V – E = 2

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Science, Tech, Math › Math Worksheets for Elementary Math: Doubles Addition Explaining the Addition of Doubles to Young Mathematicians Share Flipboard Email Print Math Arithmetic Math Tutorials Geometry Pre Algebra & Algebra Statistics Exponential Decay Functions Worksheets By Grade Resources View More By Deb Russell Math Expert Deb Russell is a school principal and teacher with over 25 years of experience teaching mathematics at all levels. our editorial process Deb Russell Updated March 08, 2019 01 of 03 Teaching Kindergarteners Simple Addition Adding doubles is an easy yet essential step to early math education. Jon Boyes/Getty Images When teachers first introduce children to mathematics in kindergarten and first grade, each core concept must be presented thoroughly and with as comprehensive of an explanation as possible. For this reason, it's important to explain the addition of doubles to young mathematicians early in the process of teaching addition in order to ensure they properly understand the fundaments of basic arithmetic. Although there are a variety of teaching tools such as printable doubles addition worksheets and counters, the best way to demonstrate the concept of doubles addition is to walk students through the addition of each number one through 10 to itself through the use of visual aids. By walking students through each addition set through tactile demonstration (say for instance using buttons as counters), teachers are able to practically display the concepts of basic mathematics in a way that young children can comprehend. 02 of 03 The Ideal Curriculum for Early Addition D. Russell There are a variety of hypotheses about the best way to teach kindergarten and first-grade students basic addition, but most of them point to using concrete objects like buttons or coins to demonstrate basic addition facts for numbers from one through 10. Once the child understands the concept of asking questions like "If I have 2 buttons and I get 3 more buttons, how many buttons do I have?" it's time to move the student to pen-and-paper examples of these questions in the form of basic math equations. Students should then practice writing out and solving all equations for numbers one through 10 and study graphs and charts of these number facts that will help them when they begin learning more complicated addition later in their education. By the time students are ready to move on to the concept of doubling a number—which is the first step to understanding multiplication in first and second grades—they should fundamentally grasp regular addition of numbers one through 10. 03 of 03 Worksheet Instructions and Utility in Teaching Allowing students to practice simple addition, especially of doubles, will give them the chance to memorize these simple calculations. However, it's important when first introducing students to these concepts to provide them with tactile or visual aids to help calculate the sums. Tokens, coins, pebbles, or buttons are great tools for demonstrating the practical side of math. For instance, a teacher might ask a student, "If I have two buttons then I buy two more buttons, how many buttons will I have?" The answer, of course, would be four, but the student could walk through the process of adding these two values by counting out two buttons, then another two buttons, then counting all of the buttons together. For the worksheets below, challenge your students to complete the exercises as quickly as possible with and without the use of counters or counting tools. If a student misses any of the questions once he or she hands it in for review, set aside time to work individually with the student to demonstrate how he or she arrived at his or her answer and how to illustrate the addition with visual aides. Worksheets for Practicing Simple Addition Print the addition of doubles worksheet 1 of 10 in PDF format.Print the addition of doubles worksheet 2 of 10 in PDF format.Print the addition of doubles worksheet 3 of 10 in PDF format.Print the addition of doubles worksheet 4 of 10 in PDF format.Print the addition of doubles worksheet 5 of 10 in PDF format.Print the addition of doubles worksheet 6 of 10 in PDF format.Print the addition of doubles worksheet 7 of 10 in PDF format.Print the addition of doubles worksheet 8 of 10 in PDF format.Print the addition of doubles worksheet 9 of 10 in PDF format.Print the addition of doubles worksheet 10 of 10 in PDF format.

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Our Asking for Clarification lesson plan teaches students how to ask for clarification in an effective way. During this lesson, students are asked to practice working in a group to ask and answer clarification questions both from a list and that they come up with themselves. Students are also asked to read passages and then choose the best clarification question for that passage from a list, demonstrating their understanding of clarifying questions and how to best use them. At the end of the lesson, students will be able to ask for clarification and further explanation as needed about the topics and texts under discussion. Common Core State Standards: CCSS.ELA-LITERACY.SL.2.1.C

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Sentence structure - complex sentences Students need to elaborate and extend their ideas to make a detailed, precise and coherent piece of text. The use of a variety of sentence structures including extended simple sentences and complex sentences create texts that are more interesting and paint a more vivid picture in the reader’s head. Students are able to confidently enhance their writing by understanding how sentences are structured for effect. Complex sentences result when other more sophisticated devices are used to join clauses; this means a subordinate (dependent) clause is joined with a main (or independent) clause. There are three main ways to join clauses to make complex sentences. By using: - Relative pronouns – that, which, who, whose - Conjunctions (subordinating) – while, because, although, as, when, until, unless, through, by, since, whenever, if, where, before, etc - Verb structures (non-finite) – (participle) verb forms that end in –ing or –ed or an infinitive verb form such as to go, to become, to see Activities to support the strategy Activity 1: vary sentence beginnings Often when students start with the subject their sentences begin to sound monotonous and the sentences do not flow well. The aim of these activities is to avoid the subject-verb pattern. (For example: I love shopping. My friend and I will go shopping all the time. We love to buy clothes. She likes buying jeans.) The following activities need to be explicitly taught – modelled, guided and then independently applied – as a tool to improve students own writing as well as a way to analyse texts. - Students begin writing with a Participle or Participal Phrase (“ing” or “ed”) or explore authentic texts for examples. Students do not begin each sentence with the same word, but rather the same part of speech. Slithering down the trunk of the tree, I ripped my best pants. Hoping to escape the teacher's attention, Matt crawled into the classroom. Past Participial Phrase (use an “ed” word): Impressed by the ceremony, we left the room in silence. Depressed by the amount of homework, the student collapsed into tears. - Search authentic texts for examples and write passages that begin with a Prepositional Phrase: With a smile on his face, the lion devoured the boy. Across the bay, the light flickered and went out. - Search authentic texts for examples and write passages that begin with a dependent clause (begin with a subordinating conjunction.) These help express relationships such as compare/contrast or cause/effect. Though some critics have complained about his scary dress sense, Tony is still popular. While I was doing the NAPLAN test, my pencil broke. - Use the appositive, (after subject noun or object noun) which is a grammatical construction in which two elements, normally noun phrases, are placed side by side, with one element serving to define or modify the other to create sophisticated writing. For example: A well-respected Mayor, Trifolium knew she could run for prime minister. A struggling street performer, Gary wandered from street to street. - Search authentic texts for examples and write passages that begin with an Infinitive Phrase: (“to + verb”) To cope with the new tax law, taxpayers must comprehend subtle variations in meaning. To reduce expenses, the Department had to trim its staff from twenty–one to twelve. - Search authentic texts for examples and write passages that combine sentences with a relative pronoun: who, whom, whose, which, that Mary spent the money. It belonged to her sister. Mary spent the money that belonged to her sister. The money that belonged to her sister was spent by Mary. For many more examples please go to: bachilleratoiesalhama.wikispaces.com/file/view/Relative+Clauses+Exercises.pdf - Search authentic texts for examples and write passages that have dependent clauses in a pair or in a series (At the beginning or the end of a sentence use: If …, if …, if …, then Subject Verb. When …, when …, when …, Subject Verb. Subject Verb that …, that …, that … If Chris had the money, if he spent the time, if he met a girlfriend, he would take a trip around the world. Whether you use a Mac or whether you own a PC, you can play great games on a computer. You’ll notice in the examples above that this construction must employ dependent clauses, relies on parallelism, and expresses conditions dependent upon the main clause. This is a special pattern that should be used sparingly. It is particularly helpful: - at the end of a single paragraph to summarise the major points, - in structuring a thesis statement having three or more parts (or points), or - in the introductory or concluding paragraph to bring together the main points of a composition in a single sentence. Activity 2: sentence fluency in action Use the following ideas to explicitly teach to, then modify student / teacher selected sentences with small groups, whole class or for independent editing. Original Sentences: Elizabeth walked briskly to the movies. She wanted to see the new Despicable Me. - To use a participle take out the verb (walk or want) and start with it. NB The non-finite clause must be placed directly before the noun doing the action. Revised Sentence: Walking quickly to the movies, Elizabeth was excited to see the new Despicable Me. Revised Sentence: Wanting to see the new Despicable Me, Elizabeth walked briskly to the movies. - To use a dependent clause. Create a cause and effect relationship or compare/contrast Revised Sentence: Because Elizabeth wanted to see the new Despicable Me, she walked quickly to the movies Original Sentence: She saw the lights across the bay. They were twinkling and flickering on the water. - To use a preposition take out the phase and put it at the beginning. Revised Sentence (not complex): Across the bay, she saw the lights twinkling and flickering on the water. Activity 3: sentence mash up Use the proforma ‘independent and dependent clauses’ cut in half. Students write either a dependent or independent clause (as per the sheet) on it and pass it to the next person in the small group. When all the spaces have writing on them students then write up as many humorous sentences with the ones off the sheet. The aim is to pace the clauses in as many as possible places. Students then select the best from theirs to write up onto a large cardboard strip to be displayed in the class. The posters may be useful. Activity 4: sentence dominoes The “S3 Game for grammar and punctuation” cards need to be printed, laminated and cut up. Students in a group of ten (or five and they have 2 each) take one of the cards. The student with the ‘start’ card calls out their card and the person with the answer responds. This continues until everyone has had a turn. Activity 5: sentence types Using the resources Sentence types explicitly teach and then use the resource either as an assessment gathering tool or as an opportunity for students to work as a guided group. ACELA1534: Recognise and understand that subordinate clauses embedded within noun groups/phrases are a common feature of written sentence structures and increase the density of information EN4-3B: Uses and describes language forms and features and structures of texts appropriate to a range of purposes, audiences and contexts.

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