Datasets:

distilabel-internal-testing

/

fineweb-edu-dedup-filtered

like 0

||Games and Fun Stuff||Feedback||Meeting Forum|| [an error occurred while processing this directive] Return to the Intermediate Level Page. It's all good if you can tell where something is going to move, but what about how it starts moving in the first place? Well, according to Newton's Second Law of Motion, to move an object, you have to apply a force. The larger the object, the larger the force you need to apply. In fact, the relationship is actually really simple: The equation states that force is equal to the mass times the acceleration. In other words, a certain amount of force will accelerate a certain amount of mass. Force is also a vector quantity. For example, if you push a box with a force of 8 N to the right while your friend pushes with a force of 5 N to the left, it would be as if one person was pushing with a force of 3 N to the right. Well, what kind of forces are there? Well, the kinds that you probably will be working with most is weight and friction. WeightThe force that causes an object to fall due to gravity is called the weight of an object. On the surface of the earth, the acceleration of an object due to gravity is about 9.8 m/s2. This is usually refered to as g. So, we can write the equation we stated before in a little different format to specify weight: The subscript W is used to denote that it is the weight force. Also notice that we replaced the a with g. So what about an object sitting on a table? It is not falling because the table is holding it up, right? The object is said to be at equilibrium because it is not being accelerated. The net force on the object is 0. Okay, there is the weight force pulling the object down, so something must push it up to make the net force 0. This force is called the normal force. The normal force (FN) is always exerted perpendicular to the surface that is holding up the object, in this case the table. For a level surface, the magnitude of the normal force is equal to the magnitude of the weight force, except that it acts in the opposite direction. But what about for a slanted surface like a ramp? Well, look at the illustration to the right. The left part of the illustration shows what happens on a level surface. The right part shows what happens on a slanted surface. Notice how the normal force is still perpendicular to the slanted surface. It cancels out the component of the weight force perpendicular to the slanted surface (shown by the dotted line perpendicular to the slanted surface). But it does not cancel out the weight force entirely. So what is left is the component of the weight force parallel to the slanted surface (shown by the dotted line parallel to the slanted surface). This is called the net force (Fnet). As you can see, the net force is directed towards the bottom of the ramp. This is why the block will slide down the ramp. Let's put this in more mathematical terms so that you can figure out actually what the magnitude of the net force is. Say we have a ramp at an angle of q. The magnitude of the normal force is equal to the magnitude of the component of the weight force perpendicular to the slanted surface. So what is the magnitude? Well, through simple trigonometry, the magnitude of the normal force is: By the same reasoning, the magnitude of the net force is: Notice what happens when the q equals 0 (a level surface). Since cos 0 = 1 and sin 0 = 0, the equations merely simplify to: Fnet = 0 ...which is what we would expect. FrictionAll this time we have been ignoring friction, but friction plays a big role as well. Friction is a force that acts parallel to the surfaces in contact, and it turns out that it is determined by the normal force. The ratio of the frictional force to the normal force called the coefficient of friction (denoted by the Greek letter, m). To find the force of friction (Ffr): There are two types of friction that we will be dealing with, static friction and kinetic friction. Static friction is the friction between two surfaces at rest. To start moving an object, you have to overcome the force of static friction. Kinetic friction is the friction between two surfaces that are moving with respect to one another. To keep an object moving, you have to overcome the force of kinetic friction. Generally the force of static friction is greater than the force of kinetic friction. Thus, the coefficient of static friction (ms) is greater than the coefficient of kinetic friction (mk). The coefficients vary depending on the materials in contact. Okay, let's put everything you just learned into one big example. We have a 5 kg block sitting on a ramp at an incline of 30°. This time friction is acting. The coefficient of static friction between the block and the surface is 0.5. The coefficient of kinetic friction is 0.2. Will the block begin to slide? If so, how fast does it accelerate down the ramp once it begins to slide? It may look complicated at first but it really isn't too bad if you take it one step at a time. Let's first find the weight force: Now, let's find the force that makes the block move down the ramp. This time we do not call it Fnet since it doesn't take all the forces into account (we're leaving out friction). Instead, let's call it Fdown: Now let's find the force of friction. But since the force of friction depends on the normal force, we have to find the normal force first: Okay, now that we have the normal force, which coefficient of friction do we use? Well, we're trying to find out whether the block will begin sliding, so we should use the coefficient of static friction: Since the friction is acting directly opposite of the down force, we merely subtract the down force and the friction to find the net force: Now we can say for sure that the block will slide down the ramp because the net force is positive (Fdown is greater than Ffrs). What about the next part of the question? Since the block is moving now, we should find the force of kinetic friction: And then we should find the new net force with that force of friction: Now we can plug this answer back into the general definition of a force to find the acceleration: 16.0 N = (5 kg)a a = 3.2 m/s2 And there you have it! The block accelerates down the ramp at 3.2 m/s2. Check out the Vector Analyzer in our games and fun stuff section to see how vector forces interact to move a body. |Created by TQ Team 16600:|| Clyde, Chetan, Jim Melanie Krieger, Chhaya Taralekar

<urn:uuid:d8f85d8d-28c0-4752-a29f-9b3bdbf47c12>

Lesson Plans and Worksheets Browse by Subject Comparing Decimals Teacher Resources Find Comparing Decimals educational ideas and activities Students can practice sorting and rounding decimals in this review activity, which features several examples of each skill as well as twenty-two practice exercises. This worksheet will also work well in an electronic format, as each question allows students to check their answers. Fifth graders examine the process of subtracting decimals. They discuss how subtracting decimals is like subtracting money, then in small groups play a decimal subtraction game using Unifix cubes. Students then buy and sell products at a class store, and independently complete a worksheet. Knowing both the Dewey Decimal and Library of Congress Classification systems, and how to read their call numbers, facilitates information literacy, a critical skill for 21st century life. High schoolers, who may be familiar with Dewey, learn to navigate the LCC system, compare the two in a Venn diagram, and create call numbers for books and subjects in their class schedules. Links in the resource are missing; we've added 3 so everything you need is a click away. Third graders create rain gauges and take them home. Individually, they record the rainfall amounts at all of their homes over a 2-week period and then bring the data back to class so they can compare the different amounts of rainfall that occurred over a relatively small geographic area. Sixth graders observe and demonstrate a variety of problem solving strategies to solve math word problems involving addition and subtraction of decimals that represent money. They solve a problem step-by-step along with the teacher, then independently solve a similar problem.

<urn:uuid:a03b0da1-7b1f-4314-9d13-be7981410dae>

Add To Favorites How well do we know our shapes? Prior to opening this lesson, prepare an envelope of shapes for student groups. Consider putting a circle, oval, triangle, square, rectangle, etc. in the envelope. Create one envelope for each student group. Ask each group of students to lay out their shapes in a random order. Students may choose to organize their shapes into a circle. Now it is time to play! Call out a shape. Students go to that shape on the floor. For example, the teacher may name a square. All students in group should head to and stand next to the square on the floor. Repeat as is necessary to ensure all students know their shapes. As an alternate way to play, have student groups combine their shapes and lay them out in a circle on the floor. Play music for the students and allow them to begin moving around the circle, from shape to shape. When you stop the music, call out a shape, such as "square". All students standing on a square are to sit down. The game is over when all students are sitting. Let's make something! Let's find out how we know our shapes! Add To Favorites Children create shapes out of everyday materials. What does your shape look like? Extend a unit of study on neighborhoods, shapes, symbols, and transportation with the creation of a town street maze. Learn about geometric shapes and practice drawing sensational squares, terrific triangles, and other perfect polygons! This activity spans the seasons and school year! Have fun with concentric circles and mixed media! Create an abstract piece of art. Our crayons have been rolling off the assembly line since 1903, and you can see how it’s done. Visit us »

<urn:uuid:5d814988-45ea-406c-9bc0-4adb00e243d4>

Lesson Plan: For Teachers: Abortion and the Charter of Rights and Freedoms Ask students what they know about Canada's Charter of Rights and Freedoms. Record their answers on the board or Provide each student with the download sheet Abortion and the Charter of Rights and Freedoms. Compare their list with the summary and note which rights and freedoms, if any, the class did not identify. Outline the Opportunity Have students work in groups of three or four to review the clips titled "Challenging the law", "Abortion law ruled unconstitutional", "Morgentaler's controversial legacy", "Ontario jury acquits Morgentaler," "The end of a fight," and "Abortion issue, ten years later" on the topic Dr. Henry Morgentaler: Fighting Canada's Abortion Laws on the CBC Digital Archives website. As they review the clips, students should take note of all pertinent points about the legal argument over abortion. Then have students use their summary of the Charter of Rights and Freedoms and identify how the charter was applied to the issue of abortion in Dr. Morgentaler's case. Students should write a one- to two-page analysis explaining if and how the charter was used to defend Dr. Morgentaler. Revisit and Reflect Have students share their analyses in small groups. They should note whether group members have different views about if and how the charter was applied, and why that might be so. Gather the groups and ask them to share their ideas of how the Charter of Rights and Freedoms helped Dr. Morgentaler. Extend the discussion by brainstorming other issue-based court decisions where changes in the Charter of Rights and Freedoms might change the results of a legal battle. Students can write a report comparing the Canadian Bill of Rights with the Charter of Rights and Freedoms and discuss how Morgentaler's defence was different after the Charter was enacted.

<urn:uuid:6c561b13-45dd-43d3-9b41-36d2d302f600>

8.3 Skills Practice: Circles In this circles worksheet, students write an equation for a circle that meets specified criteria. They find the center and radius of a circle with the given equation and graph the circle. This one-page worksheet contains 18 multi-step problems. 10th - 12th Math 4 Views 6 Downloads Visual Study Guides Give your learners the opportunity to create visual study guides! Using the Inspiration software, show your class the diagram view and images that can be attached. After creating a study guide, students make an outline to organize the... 6th - 12th English Language Arts CCSS: Designed

<urn:uuid:16a980a9-0aa3-486f-b14a-605ee18189e6>

In this addends worksheet, students use objects to help the find the missing addend. Students then write in the missing number to solve the addition number sentence. 1st - 2nd Math 3 Views 2 Downloads Ten-Frames – A Games Approach to Number Sense "How can you help students visualize numbers in a way that is compatible with our base-ten number system?" The answer is simple: use ten-frames. Whether they're being used as a part of classroom routines or as instructional tools, this... K - 3rd Math CCSS: Adaptable Transforming Word Problems into Number Sentences Transforming Word Problems into Number Sentences Practice using problem solving strategies by breaking down word problems into a series of visual "stair" steps. Learners restate what is being asked, locate word clues, eliminate unnecessary information, and determine the operation to be... 2nd - 5th Math Activities that Build Number Sense Have fun while building the number sense of young mathematicians with this list of ten-frame learning games. From developing cardinality and counting skills to learning place value and basic addition strategies, ten-frames are excellent... K - 2nd Math CCSS: Adaptable

<urn:uuid:9436b7ac-71e0-451f-816a-93c450f1bfc2>

How Are The Properties of Covalent Compounds Influenced By Chemical Bonding? High schoolers work together to observe the bond lengths of single, double and triple bonds. They make their own predictions about the strength of the bonds and chemical reactions. They answer discussion questions to complete the lesson plan. 9th - 12th Science 6 Views 34 Downloads Matter and Energy: Equations and Formulas Using simple materials, an informative lesson demonstrates the Law of Conservation of Matter and explains how to balance chemical equations. Young chemists perform experiments, analyze reactions, and balance chemical equations on their... 9th - 12th Science CCSS: Adaptable Naming III-Identifying Problems Chemical Compound Names In this naming chemical compounds worksheet, students are given 9 lettered statements that they use to match with 10 statements about compounds. Students also review the rules for naming compounds by filling in 25 blanks to complete... 9th - 12th Science Chemistry Lesson: Identifying Ionic vs. Molecular Compounds Is that compound ionic or molecular? How can you tell? Pupils learn about naming chemical compounds and classify them as being molecular or ionic. They learn in detail as they build foundational skills in the short, yet informative, lesson. 6 mins 9th - 12th Science

<urn:uuid:0639418e-dee1-45c2-a3cb-8641f229bb4d>

Taking action against prejudice In this activity students consider the concept of respect as the basis of human rights. - Introduce the concept of respect as the basis of human rights. - Ask students to brainstorm the meaning of respect. Record students' responses on the board or on butcher's paper. - Ask students to think of examples which might illustrate respect e.g. listening to others' opinions, treating others as you would like to be treated, helping people out etc. Record students' responses on the board or on butcher's paper. - In small groups or individually, ask students to create or find images which represent respect in their school, community or town e.g. people from different backgrounds working or playing together, a time or event that celebrates diversity etc. Students may choose to draw images, create a collage, take photographs or make posters which illustrate the concept of respect. - At the conclusion of the activity, display students' artwork in the classroom or library. - This activity may be conducted during class time or over several sessions. - Dictionaries (including bilingual dictionaries) may be provided to assist students with limited English in defining respect. - Activity adapted from The Shot Competition, www.humanrights.gov.au/shot

<urn:uuid:1a3f4e80-39d2-46e0-84ea-7eee5dff184e>

Counting worksheets and resources for younger children Choose a topic Learning to count lays the foundations for future math learning. Children will usually start by learning to chant the numbers in order, "one, two, three, four, five". This can be misleading, as just because a child can say the numbers, it doesn't necessarily mean that they can count a group of objects accurately. They will need lots of practice counting real things like buttons, shoes, pencils, raisins and so on. These worksheets will help children to develop their counting skills. Cut and stick to make a number line up to 20 with a little frog to hop along and help with counting, addition and subtraction. This worksheet gives you 40 printable cards with the numbers 1 to 10, pictures, dots and words. Instructions for making different matching games included. How many blue fish can you count? How many yellow fish? How many green fish? How many red fish? How many fish are there altogether? To feed the fish, click in the pond. (c) 2007 Math Worksheets

<urn:uuid:4f6f0a1a-e865-4826-b38c-a97ce2a51898>

To be published in the journal Physical Review Letters, the research provides the blueprint for a nuclear clock that would get its extreme accuracy from the nucleus of a single thorium ion. This RF ion trap at the Georgia Institute of Technology holds individual thorium atoms while they are laser-cooled to near absolute zero temperature. Credit: Corey Campbell Such a clock could be useful for certain forms of secure communication – and perhaps of greater interest – for studying the fundamental theories of physics. A nuclear clock could be as much as one hundred times more accurate than current atomic clocks, which now serve as the basis for the global positioning system (GPS) and a broad range of important measurements. "If you give people a better clock, they will use it," said Alex Kuzmich, a professor in the School of Physics at the Georgia Institute of Technology and one of the paper's co-authors. "For most applications, the atomic clocks we have are precise enough. But there are other applications where having a better clock would provide a real advantage." Beyond the Georgia Tech physicists, scientists in the School of Physics at the University of New South Wales in Australia and at the Department of Physics at the University of Nevada also contributed to the study. The research has been supported by the Office of Naval Research, the National Science Foundation and the Gordon Godfrey fellowship. Early clocks used a swinging pendulum to provide the oscillations needed to track time. In modern clocks, quartz crystals provide high-frequency oscillations that act like a tuning fork, replacing the old-fashioned pendulum. Atomic clocks derive their accuracy from laser-induced oscillations of electrons in atoms. However, these electrons can be affected by magnetic and electrical fields, allowing atomic clocks to drift ever so slightly – about four seconds in the lifetime of the universe. Because neutrons are much heavier than electrons and densely packed in the atomic nucleus, they are less susceptible to these perturbations than the electrons. A nuclear clock should therefore be less affected by environmental factors than its atomic cousin. "In our paper, we show that by using lasers to orient the electrons in a very specific way, we can use the neutron of an atomic nucleus as the clock pendulum," said Corey Campbell, a research scientist in the Kuzmich laboratory and the paper's first author. "Because the neutron is held so tightly to the nucleus, its oscillation rate is almost completely unaffected by any external perturbations." To create the oscillations, the researchers plan to use a laser operating at petahertz frequencies -- 10 (15) oscillations per second -- to boost the nucleus of a thorium 229 ion into a higher energy state. Tuning a laser to create these higher energy states would allow scientists to set its frequency very precisely, and that frequency would be used to keep time instead of the tick of a clock or the swing of a pendulum. The nuclear clock ion will need to be maintained at a very low temperature – tens of microkelvins – to keep it still. To produce and maintain such temperatures, physicists normally use laser cooling. But for this system, that would pose a problem because laser light is also used to create the timekeeping oscillations. To solve that problem, the researchers include a single thorium 232 ion with the thorium 229 ion that will be used for time-keeping. The heavier ion is affected by a different wavelength than the thorium 229. The researchers then cooled the heavier ion, which also lowered the temperature of the clock ion without affecting the oscillations. "The cooling ion acts as a refrigerator, keeping the clock ion very still," said Alexander Radnaev, a graduate research assistant in the Kuzmich lab. "This is necessary to interrogate this clock ion for very long and to make a very accurate clock that will provide the next level of performance." Calculations suggest that a nuclear clock could be accurate to 10 (-19), compared to 10 (-17) for the best atomic clock. Because they operate in slightly different ways, atomic clocks and nuclear clocks could one day be used together to examine differences in physical constants. "Some laws of physics may not be constant in time," Kuzmich said. "Developing better clocks is a good way to study this." Though the research team believes it has now demonstrated the potential to make a nuclear clock – which was first proposed in 2003 – it will still be a while before they can produce a working one. The major challenge ahead is that the exact frequency of the laser emissions needed to excite the thorium nucleus hasn't yet been determined, despite the efforts of many different research groups. "People have been looking for this for 30 years," Campbell said. "It's worse than looking for a needle in a haystack. It's more like looking for a needle in a million haystacks." But Kuzmich believes that that problem will be solved, allowing physicists to move to the next-generation of phenomenally accurate timekeepers. "Our research shows that building a nuclear clock in this way is both worthwhile and feasible," Kuzmich said. "We now have the tools and plans needed to move forward in realizing this system." John Toon | EurekAlert! Mars 2020 mission to use smart methods to seek signs of past life 17.08.2017 | Goldschmidt Conference Gold shines through properties of nano biosensors 17.08.2017 | American Institute of Physics Whether you call it effervescent, fizzy, or sparkling, carbonated water is making a comeback as a beverage. Aside from quenching thirst, researchers at the University of Illinois at Urbana-Champaign have discovered a new use for these "bubbly" concoctions that will have major impact on the manufacturer of the world's thinnest, flattest, and one most useful materials -- graphene. As graphene's popularity grows as an advanced "wonder" material, the speed and quality at which it can be manufactured will be paramount. With that in mind,... Physicists at the University of Bonn have managed to create optical hollows and more complex patterns into which the light of a Bose-Einstein condensate flows. The creation of such highly low-loss structures for light is a prerequisite for complex light circuits, such as for quantum information processing for a new generation of computers. The researchers are now presenting their results in the journal Nature Photonics. Light particles (photons) occur as tiny, indivisible portions. Many thousands of these light portions can be merged to form a single super-photon if they are... For the first time, scientists have shown that circular RNA is linked to brain function. When a RNA molecule called Cdr1as was deleted from the genome of mice, the animals had problems filtering out unnecessary information – like patients suffering from neuropsychiatric disorders. While hundreds of circular RNAs (circRNAs) are abundant in mammalian brains, one big question has remained unanswered: What are they actually good for? In the... An experimental small satellite has successfully collected and delivered data on a key measurement for predicting changes in Earth's climate. The Radiometer Assessment using Vertically Aligned Nanotubes (RAVAN) CubeSat was launched into low-Earth orbit on Nov. 11, 2016, in order to test new... A study led by scientists of the Max Planck Institute for the Structure and Dynamics of Matter (MPSD) at the Center for Free-Electron Laser Science in Hamburg presents evidence of the coexistence of superconductivity and “charge-density-waves” in compounds of the poorly-studied family of bismuthates. This observation opens up new perspectives for a deeper understanding of the phenomenon of high-temperature superconductivity, a topic which is at the core of condensed matter research since more than 30 years. The paper by Nicoletti et al has been published in the PNAS. Since the beginning of the 20th century, superconductivity had been observed in some metals at temperatures only a few degrees above the absolute zero (minus... 16.08.2017 | Event News 04.08.2017 | Event News 26.07.2017 | Event News 17.08.2017 | Physics and Astronomy 17.08.2017 | Earth Sciences 17.08.2017 | Physics and Astronomy

<urn:uuid:83693e08-87ec-4334-adcf-abf40f6404b9>

Introduction To Solving Equations Use manipulatives (film cans and balance scales) to visualize and solve equivalent equations with your math class. After a lecture/demo, they utilize handouts and solve various equations using the methods learned. 3 Views 14 Downloads Deciphering Word Problems in Order to Write Equations Help young mathematicians crack the code of word problems with this three-lesson series on problem solving. Walking students step-by-step through the process of identifying key information, creating algebraic equations, and finally... 5th - 8th Math CCSS: Adaptable Relationships Between Quantities and Reasoning with Equations and Their Graphs Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving... 6th - 10th Math CCSS: Designed Comparing Tape Diagram Solutions to Algebraic Solutions Learners solve vacation equations with tape in a instructional activity that uses tape diagrams to aid in the understanding of the algebraic steps used to solve two-step linear equations. Groups work together to solve seven scenarios... 7th Math CCSS: Designed Solving Equations Using the Addition Property Challenge your mathematicians to simplify and solve a variety of different equations. This worksheet focuses on multi-step problems that begin with combining like terms and advance toward solving equations with variables on both sides. A... 6th - 10th Math CCSS: Adaptable New Review Solving Basic Equations Part Two Some equations require inverses of multiplication and division. Solving equations use inverse operations to isolate the variable. The video shows how to solve one-step equations involving multiplication and division and works several... 10 mins 6th - 9th Math CCSS: Adaptable

<urn:uuid:f9249571-a462-429b-b7d0-a96a1672ef42>

Notes On Basic Equations In this math worksheet, students read the notes about solving equations. They focus upon how one could use the order of operations to simplify expressions. 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: Introduction to Systems of Linear Equations Here is a lesson that really delivers! Middle schoolers collaborate to consider pizza prices from four different pizza parlors. Using systems of simultaneous equations, they graph each scenario to determine the best value. Developed for... 7th - 9th Math CCSS: Designed Relationships Between Quantities and Reasoning with Equations and Their Graphs Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving... 6th - 10th Math CCSS: Designed Module 2: Systems of Equations and Inequalities The brother-sister pair Carlos and Clarita need your class's help in developing their new pet sitting business. Through a variety of scenarios and concerns presented to the siblings, the learners thoroughly explore systems of equations... 8th - 10th Math CCSS: Designed Systems of Equations and Inequalities This is a comprehensive lesson on creating and solving equations and systems of equations and inequalities. Problems range from basic linear equations to more complex systems of equations and inequalities based on a real-world examples.... 8th - 12th Math CCSS: Adaptable Solving Basic Equations Part Two Some equations require inverses of multiplication and division. Solving equations use inverse operations to isolate the variable. The video shows how to solve one-step equations involving multiplication and division and works several... 10 mins 6th - 9th Math CCSS: Adaptable

<urn:uuid:5f02ccb4-9047-4948-a4f8-259164158285>

Valid assessment of higher order thinking skills requires that students be unfamiliar with the questions or tasks they are asked to answer or critical thinking. Parents and teachers can do a lot to encourage higher order thinking answer children's questions teachers should make sure students understand the critical. I see both creative and critical thinking emerge as the students themselves imitate my thinking questions short teaches art at westview elementary. Teaching strategies to promote critical thinking a number of techniques that can help students learn critical thinking a lot questions. Work sheet library: critical thinking: grades 3 use with your students to build a wide variety of critical thinking questions about a graph that show. Checkout the 50 questions to help students ti ask great questions mathematics enhances critical thinking in 50 questions to help students think. How and when to fit them into our limited time with students see that critical thinking is a type of questions we ask students critical thinking. Glossary of critical thinking terms the role of questions in teaching for young students (elementary/k-6) children's guide video series (k-6. Ask students questions to assess their understanding model critical thinking for students by sharing your own 81 fresh & fun critical-thinking activities. See frequently asked questions jumpstart’s critical thinking activities are therefore a great way to engage students and encourage critical thinking and. Check out these 10 great ideas for critical thinking activities and see thinking activities that engage your students these questions to themselves. Thinking skills for tests: upper elementary effective critical thinking skills and other of the test questions had more to do with critical thinking. Critical thinking worksheets for teachers used in engaging students in the advanced levels of thinking we have brain teasers and mad libs too. Here's how to teach some basic critical thinking skills to young children in a way to your students critical thinking questions about stories. Background beliefs when two people have radically different background beliefs (or worldviews), they often have difficulty finding any sort of common ground. Critical thinking in the elementary classroom: and questions to inspire you to begin thinking critically problems through critical thinking students will. Critical thinking is a skill that students develop gradually as they if you try to answer these questions critical thinking exercises. Getting students to dig deeper and answer questions using higher-level thinking can be a challenge here are our favorite tips for teaching critical thinking skills. Math downloadable and printable help pages designed for students critical thinking - worksheets math vocabulary and thinking process to answer the questions. Critical thinking, on the other hand (elementary ed) waco, tx the teacher later categorized or clustered the students' questions into groups and used them. The critical thinking company publishes prek-12+ books and software to develop critical thinking in want more critical thinking quiz questions of critical. Readwritethink couldn't publish all of this great content developing students' critical thinking skills through students generate many questions. Teaching critical reading with questioning strategies it is time—actually past time—to address critical-thinking and analytic i send students' questions. Questions give students questions before reading, so the purpose of the reading is set cue questions based on bloom’s taxonomy of critical thinking. Explore sarah ashton's board critical thinking for elementary students on pinterest | see more ideas about gym, thoughts and critical thinking. Tools for thought 1 © the critical thinking consortium provide each pair of students with a copy of sample guiding questions (activity sheet: secondary or elementary. Teachers use a number of techniques to help students learn critical thinking critical thinking: ask open-ended questions elementary school. Let's look at the qualities of questions that call on higher order thinking skills and math questions worth asking in asking students good questions. Critical thinking elementary brain teaser version 6: students might actually come across these problems in everyday life these questions make you think fast. Here are some wonderful tools and strategies for beginning to foster a critical thinking mindset in your elementary school students. Mathematics critical thinking guiding questions for teachers to use to stimulate challenge and interest elementary students in algebraic thinking.

<urn:uuid:c680eb7f-0f9b-41f9-b44e-ee1c8e429a54>

One of the hardest parts of chemistry is understanding how electrons orbit the nucleus and fill in their shells (S, P, D, and F). On top of that you add the spin (up or down) to model uncertainty. It was hard for me to organize and process how to combine all these facets of the electron. For this I combined an orbital diagram worksheet with other orbital diagrams to show how the electrons fill in order. https://www.youtube.com/watch?v=cPDptc0wUYI has a great video on orbitals. While you can waste paper filling out orbital diagrams, I figured a way to model the shell levels, numbers and spin into one manipulative. If you have the Photographic Card Deck of the Elements (periodictable.com) you can use the cards to help your class study, or challenge and review the elements with this board. THIS IS A WORK IN PROCESS This will require 118 (16 mm) marbles.If you can find decent quality marbles that have a consistent size, that will help. This is good for a AP Chem or College chem class. Print 2-6 sets for a class to do as a small group activity. Speed games can be developed as well to test students The lesson plan will be for sale on TeacherPayTeacher.com. Overview and Background Explore the shell shapes, then the order in how they fill. Explore the numbering system, and the Up and Down spin of electrons. Lesson Plan and Activity 1-5 class periods based on depth of lesson. Watch students to make sure they don't inhale marbles. Tape down to table if you worry about students knocking them off. To prevent flying marbles, have a rule like "It fly's you fail ". This would make for a small group (3-4 students) activity. They can challenge others to find the element and label the electron orbitals.

<urn:uuid:826b14c2-226f-4f1d-a322-96194ea48670>

Three Questioning Strategies for Any Lesson Teachers know—questions play a different role, depending on when they’re used. - Before a lesson: Questions are a way to motivate, set goals, stimulate thinking, convey purpose, and create a positive learning environment. - During a lesson: Questions inspire thinking and reflection, allow students to review what they’re learning, involve students in evaluating their understanding of implicit and explicit learning, and encourage students to think ahead – to predict, anticipate, problem solve, and identify trends and patterns. - After a lesson: Questions prompt students to summarize what they learned, make analogies, reflect, draw conclusions, incorporate new learning with prior learning, and extend learning. In her ASCD Annual Conference session, Sandra Page presented several questioning strategies that can be used at all stages of a lesson: Student Sort Cards On one side of an index card, students write their name large enough to be seen across the room. On the other side, students complete a brief inventory of their interested and learning preferences (group work, visual, etc.). Teachers can use this stack of cards to randomly call on students, and when appropriate, target questions to students’ interests. With differentiation for readiness-level, for students who need practice with a question before answering it in front of the class, Page writes their question on a sticky note she affixes to their name card. She shares the question with the students in advance, so there are no surprises when she asks it. Page gradually removes this scaffold as students become more proficient with their responses. Student sort cards are also useful for getting students to discuss a topic with one another. “A discussion is not teacher-student, teacher-student,” Page said. Instead of calling out students’ names to respond to a question, she asks a question and holds a name card up to her face, so that students can see who is expected to respond. While the student responds, she is careful not to look at the student giving the response. Page looks around the room, so that the speaker will also direct their response to his classmates, not just the teacher. A minute or so into a response, Page holds another students’ name card to her face to signal the student who is expected to build on, clarify, or dissent to what the previous student said. This technique requires students to actively listen to their peers’ responses, and practice making transitional statements—a skill they’ll use not only conversationally, but also in academic essays and response papers. If this strategy stresses students out—so much so that they are just focusing on whether they’ll be called on next, and not listening to the speaker—try some test-runs on a topic all kids are familiar with. Pair this strategy with the sticky-note strategy, so students know the question in advance and have some time to formulate responses. Display transitional statement stems on the board or around the classroom. Even further, students can, as a class, brainstorm potential stances on a topic, and record these in a chart or matrix that is visible during the discussion. Question Stem Cards Laminate these sheets of question stems, and then cut the sheets into individual question prompts. Have students use these stems to write their own questions about what they just read or learned. Page has students write and display their questions in dry-erase marker on a sort of DIY white board—stiff card stock covered by a plastic page protector. She will focus on a specific category of question stem (i.e, analysis, evaluation, application) when she wants to reinforce a particular thinking skill. When students write their own questions, Page added, it invites the novelty of discovery, reveals misconceptions, and gets students thinking in questions During discussion, Page often asks students to “FY3” their responses. FY3 is shorthand for diversify, verify, and amplify. She’s asking students to enhance the discussion with a response that - Diversifies: provides more than one perspective - Verifies: offers evidence - Amplifies: elaborates on an idea These strategies provide scaffolds that encourage students to ask and answer questions. How do you encourage questions in your classroom? How do you get students discussing topics with one another?

<urn:uuid:f497f805-f201-4e07-95fb-d5dce2770964>

About This Chapter Below is a sample breakdown of the Waves, Sound & Light chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs. |Day||Topics||Key Terms and Concepts Covered| |Monday||How does energy move?||Identify energy waves and vibrations, describe how waves and vibrations operate, and define the following terms with examples: medium, wave parameters, wave amplitude, frequency, wavelength, speed, period, longitudinal waves and transverse waves| |Tuesday||The movement of sound||Explain longitudinal wave properties in relation to sound; identify how mass density, wave equation, and elasticity affect the speed at which sound travels; analyze sound wave parameters in relation to volume and pitch; review the following terms: musical pitch, the decibel scale, intensity and frequency| |Wednesday||Electromagnetic waves and light||Point out the sources and properties of electromagnetic waves, review the categories of electromagnetic waves, discuss the electromagnetic spectrum, identify the origin of light, explore the various colors and frequencies of the light spectrum, and discuss the following concepts: reflection, angles of incidence, rough surface reflections, resonance, transparent objects, opaque objects and wave transmission mechanisms| |Thursday||Light and color||Explain the composition of white light, review how we perceive color, identify light refraction properties and define the following terms: Snell's law, index of refraction, dispersion, diffraction, wave length effects, destructive interference, constructive interference, standing wave, reflection, transmission and absorption| |Friday||Energy concepts||Doppler Effect, wave-particle duality, major regions of the electromagnetic spectrum and diffuse reflection| 1. Vibrations and Waves: Energy and Motion What is a wave? What causes waves, and how do they travel from one place to another? This lesson will guide you through the basics of waves. We'll discuss their origins from vibrations and investigate how they carry energy through a medium. 2. Wave Parameters: Wavelength, Amplitude, Period, Frequency & Speed How do we measure and describe waves? How do waves differ based upon their shapes? This lesson will guide you through the five wave parameters - period, frequency, amplitude, wavelength, and speed - that we use to characterize waves. 3. Transverse & Longitudinal Waves: Definition & Examples What comes to mind when you think of a wave? Chances are your mental image takes the form of a transverse wave. But, longitudinal waves are just as important, and understanding the difference is vital to learning about waves. In this lesson, explore both types of waves and the unique characteristics of each. 4. What is Sound? - Definition and Factors Affecting the Speed of Sound Explore the minute workings of sound waves and how they travel. We'll discuss the main factors that affect the speed of sound waves, and we'll try some mathematical problems involving the wave equation. 5. Pitch and Volume in Sound Waves What do pitch and volume mean when talking about sound waves? Further your understanding of sound waves in this lesson as we explore the more familiar aspects of sound. We'll learn about pitch and volume and how they relate to sound wave parameters. 6. Electromagnetic Waves: Definition, Sources & Properties In this lesson, learn the basics of electromagnetic waves and how they make up the electromagnetic spectrum. We will explore the major trends and categories within the spectrum, as well as the various sources of electromagnetic waves. 7. The 7 Major Regions of the Electromagnetic Spectrum This lesson will walk you through each of the major regions of the electromagnetic spectrum. Explore the unique characteristics of X-rays, microwaves, radio waves, UV rays, infrared, gamma rays, and of course, visible light. 8. The Nature of Light: Origin, Spectrum & Color Frequency This lesson introduces the basics of visible light and color. Learn how the visible light spectrum is divided into the six color ranges. We'll also discuss why different people name colors in different ways. 9. Reflection: Angle of Incidence and Curved Surfaces How do waves reflect off of surfaces? How do we account for the images that we see reflected in various objects? Discover the answers to these questions as we investigate the rays and angles defining the law of reflection. 10. Diffuse Reflection: Definition, Examples & Surfaces This lesson explores the law of reflection and how it applies to different surfaces and wave types. We'll learn the difference between specular and diffuse reflection and investigate how diffuse reflection affects our perception of sound and light. 11. Resonance: Definition & Transmission of Waves This lesson describes how sound and light waves are affected by the principle of resonance. Learn how resonance occurs through the vibrations and resonant frequencies of objects. You'll investigate everyday examples of resonance and learn how to break a wine glass with your voice! 12. Transparent and Opaque Materials in Electromagnetic Waves What makes an object transparent or opaque? How does light pass through some objects and not others? And what about the other types of electromagnetic waves? We'll investigate all these questions in this lesson about the transparency and opacity of materials. 13. Color: White Light, Reflection & Absorption What gives color to objects? How do light waves interact with materials to produce red and green or white and black? In this lesson, learn how white light is composed of all colors and how absorption and reflection influence our color perception. 14. Refraction & Dispersion: Definition, Snell's Law & Index of Refraction Refraction explains why light bends in water. But, did you know that mathematical laws determine exactly how light waves are bent? In this lesson, we'll explore the mechanics of wave refraction, including Snell's Law and the index of refraction. 15. Diffraction: Relation to Sound & Light and Effects of Wavelength This lesson explores diffraction as one of the many behaviors of waves. Learn how diffraction occurs in sound and light waves and how it is affected by the wavelength of a wave. Find out how animals use diffraction to communicate and how scientists use it to study molecules. 16. Constructive and Destructive Interference What happens when one wave meets another? Do the waves converge to make one giant wave? Or, do they destroy each other? In this lesson, we'll explore the workings of wave interference. 17. The Doppler Effect: Definition, Examples & Applications What is the Doppler effect? How does it affect our perceptions of sound and light? In this lesson, learn how traveling wave sources can change the way we observe sound and light waves. Explore the applications of the Doppler effect on shock waves, sonic booms, and the movements of distant galaxies. 18. Wave-Particle Duality: Concept, Explanation & Examples Is light a particle with mass and substance? Or, is it just a wave traveling through space? Most scientists say light is both a particle and a wave! Find out how they came to this strange conclusion as we learn about the theory of wave-particle duality. 19. Reflection in Physics Project Ideas Reflection is the change of direction that takes place when a wave hits a boundary. This asset contains projects that encourage students to explore and discuss reflection. Earning College Credit To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Other chapters within the High School Physics Curriculum Resource & Lesson Plans course - Introduction to Physics Lesson Plans - Vectors in Physics Lesson Plans - Kinematics Lesson Plans - Newton's Laws in Physics Lesson Plans - Work, Energy & Power Lesson Plans - Linear Momentum Lesson Plans - Rotational Motion Lesson Plans - Circular Motion & Gravitation Lesson Plans - Oscillations Lesson Plans - Electrical Forces & Fields Lesson Plans - Potential & Capacitance in Physics Lesson Plans - Direct Current Circuits Lesson Plans - Magnetism in Physics Lesson Plans - Atomic & Nuclear Physics Lesson Plans - Fluid Mechanics Lesson Plans - Thermal Physics & Thermodynamics Lesson Plans - The Universe Lesson Plans - Relativity & Quantum Theory Lesson Plans - Motion - Physics Lab Lesson Plans - Matter & Light - Physics Lab Lesson Plans - Electricity - Physics Lab Lesson Plans

<urn:uuid:b16047e6-c57b-4010-ae4d-808bdc65342b>

This section discusses all the English verbs, including the conjugation of the verbs in different tenses, modal verbs, infinitives, regular and irregular verbs and many more. This chapter will give you a general overview of the topics discussed in the subchapters of this course. Verbs are words that describe what happens during an action and when (present, past or future) this action happened. A verb can also suggest something, express a possibility or obligation using modal verbs. The English language consists of 12 tenses, all having a different conjugation. Take a look at the table below to see an overview of the 12 tenses. |Simple||I study in Spain.||I lived in England.||I will come to the party.| |Continuous||I am studying in Spain.||I was living in England.||I will be coming to the party.| |Perfect||I have studied in Spain.||I had lived in England.||I will have come to the party.| |Perfect continuous||I have been studying in Spain.||I had been living in England.||I will have been coming to the party.| The English auxiliary verbs are used for the different verb tenses. The three auxiliary verbs are 'to be', 'to have', and 'to do'. The auxiliary verbs 'will' and 'would' are also modal verbs, and will be discussed in that chapter. |Verb 'to be'|| |Verb 'to have'|| |Verb 'to do'|| The English participles are used for the different tenses. The present participle is used to show a continuous action. The past participle is used to form the present perfect, past perfect and future perfect. I was talking to her. |Present participle||She has played soccer.| Modal verbs are used to give a certain attitude towards another verb in English. These modal verbs are not conjugated. |Can||Ability, permission, possibility||She can come tonight.| |Could||Ability, permission, possibility||They could help you later.| |May||Permission, possibility||The customers may use the staff bathroom.| |Might||Permission, possibility, probablity||It might snow next weekend.| |Will||Prediction, promise, habits||I will finish the assignment.| |Would||Wish, habits in the past||They wish you would study with them.| |Shall||Suggestion||Shall I carry that for you?| |Should||Advice, obligation||You should stop smoking.| |Must||Obligation, prohibition||You must clean your room.| The phrasal verbs are made up of a main verb and a proposition or an adverb. The English phrasal verbs have different meanings than the verb on its own. The English regular verbs are all conjugated with the same structure for the present and past tense. The English irregular verbs all have their own form in the present and past tense. The gerund in English is a verb used as a noun. It looks the same as the present participle, but the function is different. The infinitives in English are the base forms of the verbs, with 'to' in front of them. The English imperative is used to give orders and instructions. The imperative is formed with the infinitive of the verb. The reported speech in English is used to talk about what someone said in the past. The English active and passive voice are not tenses, but are about the structure of the sentence and differ in who performs the action. If you study these chapters, you will improve your English speaking and writing skills. There are exercises in every chapter to practice what you have learned in that chapter. |1 Present tenses in English| |2 Past tenses in English| |3 Future tenses in English| |4 Auxiliary verbs in English| |5 Present participle in English| |6 Past participle in English| |7 Modal verbs in English| |8 Phrasal verbs in English| |9 Regular verbs in English| |10 Irregular verbs in English| |11 Gerund (-ing form) in English| |12 Infinitive verbs in English| |13 Imperative in English| |14 Reported speech in English| |15 Active and passive voice in English| 4.6/5 from 2 reviews Me as a Teacher I am a Serbian native speaker and a language teacher. I have been teaching online for 5 years. I live in Belgrade. I've been... teaching online for 5 years (officially). I love teaching because it's a dynamic and an interesting job. You can teach your students and you can learn from them as well. The happiness and joy of the student + their progresses with their target language = my biggest prize (so my students are the ones who motivate me to work better)and I try to combine: a bit of reading, a bit of writing, a bit of conversation, a bit of grammar and a bit of listening by using different resources. About Me My favorite topics are: 1. Travelling , 2. Foreign languages, 3. TV programs, 4. Films and TV series, 5. Culture, 6. sport, 7. IT, 8. Science My hobbies are: learning foreign languages, horse- riding, reading, travelling, ... I am open-minded, flexible and very positive. If you come up with something interesting to talk about, please, don't hesitate to suggest me and I'll gladly discuss with you about that. I visited: Montenegro, Croatia, Bosnia and Herzegovina, Greece, Hungary, Italy, Slovakia and Slovenia. My Lessons & Teaching Style Firstly, I test the level of the target language... I have two parts: 1) Conversational part (here I check their vocabulary and their fluency + I find out their language goals and their needs) 2) Writing part (with that I focus much more on grammar and spelling) For each part, I take notes (I have my notebook for that). Secondly, I personalize my lessons to their goals and needs. I can cover a lot of topics: business, travelling, culture, etc. My Teaching Material Text Documents Audio Recordings Images and Visuals Video News Articles and Magazines Quizzes Example Test Templates Graphs and Charts Homework Assignments PowerPoint Presentations Read more Hello, my name is Corinne and I am a qualified ESL English teacher from England. I have been teaching in classrooms and online for over 2 years... and I have many satisfied students. My lessons generally consist of a mixture of conversation and set exercises to help to improve both vocabulary and grammar. I encourage a lot of talking from my students and I give instant written correction so that they are able to recognize any grammatical errors they are making. I take note of repeated mistakes and set exercises for following lessons to address these mistakes accordingly. You will quickly notice an increase in your confidence in speaking English from our lessons, your vocabulary will increase and your grammar and sentence structure will improve. Together, we will reach your goals. Read more Hi! I've been teaching Dutch, Spanish and Italian for many years, in The Netherlands, for private institutes, for the integration of foreigners... into society, and online from Italy, where I currently live. Today I can also help you with English! I will help you, in a simple but effective way, to learn your favorite language(s). By focusing on conversation, I will help you in becoming confident with the language so that you will learn it faster. Learning a foreign language is not a matter of doing much effort, but rather of being consistent, enjoying the lessons and allowing your intuition to work with you. You will book immediate results while having fun! I offer you general language courses Italian (A1-C2), Dutch (A1-C1) as well as courses "Basisinburgering" "Inburgeringsexamen A1 and A2", Spanish (A1-C1), and English (A1-A2). So if you want to learn a language or improve the one you already speak, whether it is for work, to move abroad or just because you love languages, contact me for a free trial and let me know how I can help you. I'm looking forward to meeting you! Read more

<urn:uuid:80146f8b-6f20-4116-94ee-f7e03230e50d>

Lesson Plan Template: General Lesson Plan Learning Objectives: What should students know and be able to do as a result of this lesson? When given 3 index cards containing addition and subtraction equations through the thousands, the student will be able to determine if the equations are true or false. Students will justify their reasoning as they work in partners to explain how they know these equations are true or false. Students will use comparative relational thinking, without computing. Prior Knowledge: What prior knowledge should students have for this lesson? Prior to this lesson, students should have a thorough understanding of the place value system and numbers that add to 10. Students should be able to compute mentally through the thousands, using relational thinking, without using paper and pencil. Guiding Questions: What are the guiding questions for this lesson? What does it mean for an equation or number sentence to be true or false? Possible student answer: both sides of the equal sign have to be the same, or one side has to equal the other side like a balance scale. Essential Question-How can you use relational thinking to solve a set of problems, without actually using paper and pencil computation? Students need to be able to orally answer this at the end of the lesson. Teaching Phase: How will the teacher present the concept or skill to students? 1. The teacher will begin the lesson by introducing equations to students. Is the number sentence 12-9=3 true or false? How do you know? Suggested answer: It is true because if I have 12 snickers and I eat 9, then I am left with 3. Is the number sentence 14+16=30 true or false? How do you know? Suggested answer: It is true. Possible reasons: I know because 10+10= 20 and 6+4=10, so 20+10=30 or "I can move one from the 16 over to the 14 and make the problem 15+15=30. Is the number sentence 13-3=9 true or false? How do you know? Suggested answer: It is false because when I take away 3 from 13, I have 10 left over, not 9. **The teacher should notice which children are computing and which children are using relationships to determine which problems are true and which problems are false. 2. Now students need to be given problems in which there are two addends on each side of the problem. How do we know if 60+74=72+62 is true or false? Possible answer includes students stating they used mental math to add their ones column and then their tens column on each side of the equation to figure out the equation is equal. Let’s do some additional practice. Tell me how we know that 44+29=45+28 is true or false? Possible answers: 44+29=45+28 is true because I can take one away from the 44, add it to 29 so now I'm working with 43+30 and that is 73 and 45+28 is also equal to 73 because if I take away 5 from the 28 and add it to the 45, I have 50+23 which also equals 73. **Children must recognize they can use relational thinking to solve these problems without the use of all the calculations. Give an example through the thousands place. The teacher will use the several examples mentioned and build upon them into multi-digit numbers through the thousands place. (Some student will have to use paper/pencil or white board/marker to show their thinking process before they begin using comparative relational thinking) Guided Practice: What activities or exercises will the students complete with teacher guidance? The teacher will then have students work in pairs with the three provided teacher-made index cards (see attachments). During this time the students will try and determine for each card whether the equation is true or false, and then share their thinking with their partner. The teacher will guide the struggling students with their relational thinking (if needed, use the individual white boards to model the students thinking so they can understand their own thinking process). Students will document their answers (on paper or white boards) so a whole group check can be done. The teacher should remind students to "Keep in mind the strategies we have used when solving these "warm up" problems today, throughout the rest of math today." While the teacher is walking around monitoring students working in their pairs to solve the example problems, the teacher might ask some of the following probing questions: 1. Can you explain to me what you are thinking? 2. Why do you say that this equation is true but this one is false? 3. How is this equation false? What is it missing to make it true? 4. Did your partner use a different method to figure out if it was true or false? 5. Ok, now explain that to your partner again because I don't think he understood that. 6. Can you share that thinking with the whole class please? Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson? After working in pairs with index cards, students will then work on an additional three index cards (see attachments) independently to solve for true or false. The students will not only solve true or false, but also demonstrate their relational thinking through a written justification for their true or false answer. (15-20 min) Independent Practice Instructions 1. I am going to provide you with three additional Independent Practice Index Cards. 2. I want you to write on these because I want you to explain and justify your thinking in writing. 3. So, you are going to write TRUE or FALSE AND I want you to explain in writing your relational thinking on how you figured out the answer. Closure: How will the teacher assist students in organizing the knowledge gained in the lesson? The teacher will collect student work and use student responses to their index cards as examples on the board (without using student names) to ask if the methods used make sense and compare them to other student responses- while asking the students if both responses are reasonable. (Use of a document camera is possible here or the teacher can just copy the student work on to the board) Once the teacher collects and begins to review student answers she/he will ask: 1. Can this person’s method be used AND this person method be used to solve for true or false? Why? Why not? 2. Is one strategy better than the other? Or is it depending on how you think about numbers? 3. How does knowing what numbers add up to ten help you with this skills? 4. Now I will give you the correct answers so you can check and see if you were correct before we do our independent practice. FINAL QUESTION- REFER BACK TO THE ESSENTIAL QUESTION- How can you use relational thinking to solve the next set of problems, without actually using paper and pencil computation? HAVE STUDENTS ORALLY RESPOND TO THIS QUESTION At the completion of the three independent practice index cards and the teacher reviews/compares student answers, index cards will be used as a summative assessment. The teacher should be looking for how the student uses written form to verbalize their relational thinking. Although there is no "right" or "wrong" answer to a student's relational thinking, the teacher is looking for the students' use of mental math strategies as modeled in the guiding questions and reasonableness. While teaching whole group, the teacher will pose a situational story problem on the board to students. Using white boards and markers, or paper and pencil, the students will write the answer to the question that has been posed with the words true or false, followed by either a written or oral description of their relational thinking. The teacher will walk around and put a sticker on the desk (stickers are not necessary, a high five or some acknowledgment is all that is necessary) for the students who are correct and ask the students who are still struggling what their relational thinking process is. If needed, the teacher will use manipulatives or numerical representations to demonstrate to those students how they can make groups of ten to solve the problems with comparative relational thinking. Feedback to Students During the whole group lesson, the teacher will provide students stickers for their correct answer for the true/false answer. The students who are struggling will get immediate feedback from the teacher by reviewing the lesson, reminding them of the other examples that were given and asking them to explain what their relational thinking process is. Once students have been given their independent practice assignment in pairs, they will solve the equations independently and then share with their partner their method of thinking and explain how they figured out if the equation is true or false and why. The teacher will be walking around listening to the students talk, and participating with them as she/he deems necessary. The teacher will remind students to stay on task, provide probing/guiding questions, and use phrases with the class "I like the way student a and b are working and talking about their true and false equations" Students will write their "true" "false" answers to the index cards on a piece of paper or a dry erase board (depending on available teacher resources or teacher preference)

<urn:uuid:007fdd24-0b29-437b-8b20-9b407189cdb9>

In a typical dissociation reaction, a bond in a molecule splits ruptures resulting in two molecular fragments. The splitting can be homolytic or heterolytic. In the first case, the bond is divided so that each product retains an electron and becomes a neutral radical. In the second case, both electrons of the chemical bond remain with one of the products, resulting in charged ions. Dissociation plays an important role in triggering chain reactions , such as hydrogen—oxygen or polymerization reactions. For bimolecular reactions, two molecules collide and react with each other. Their merger is called chemical synthesis or an addition reaction. Another possibility is that only a portion of one molecule is transferred to the other molecule. This type of reaction occurs, for example, in redox and acid-base reactions. In redox reactions, the transferred particle is an electron, whereas in acid-base reactions it is a proton. This type of reaction is also called metathesis. Most chemical reactions are reversible, that is they can and do run in both directions. The forward and reverse reactions are competing with each other and differ in reaction rates. These rates depend on the concentration and therefore change with time of the reaction: the reverse rate gradually increases and becomes equal to the rate of the forward reaction, establishing the so-called chemical equilibrium. The time to reach equilibrium depends on such parameters as temperature, pressure and the materials involved, and is determined by the minimum free energy. In equilibrium, the Gibbs free energy must be zero. The pressure dependence can be explained with the Le Chatelier's principle. For example, an increase in pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas. The reaction yield stabilizes at equilibrium, but can be increased by removing the product from the reaction mixture or changed by increasing the temperature or pressure. A change in the concentrations of the reactants does not affect the equilibrium constant, but does affect the equilibrium position. Chemical reactions are determined by the laws of thermodynamics. Reactions can proceed by themselves if they are exergonic , that is if they release energy. The associated free energy of the reaction is composed of two different thermodynamic quantities, enthalpy and entropy : . Typical examples of exothermic reactions are precipitation and crystallization , in which ordered solids are formed from disordered gaseous or liquid phases. In contrast, in endothermic reactions, heat is consumed from the environment. This can occur by increasing the entropy of the system, often through the formation of gaseous reaction products, which have high entropy. Since the entropy increases with temperature, many endothermic reactions preferably take place at high temperatures. On the contrary, many exothermic reactions such as crystallization occur at low temperatures. Changes in temperature can sometimes reverse the sign of the enthalpy of a reaction, as for the carbon monoxide reduction of molybdenum dioxide :. This reaction to form carbon dioxide and molybdenum is endothermic at low temperatures, becoming less so with increasing temperature. Changes in temperature can also reverse the direction tendency of a reaction. For example, the water gas shift reaction. Reactions can also be characterized by the internal energy which takes into account changes in the entropy, volume and chemical potential. The latter depends, among other things, on the activities of the involved substances. The speed at which reactions takes place is studied by reaction kinetics. The rate depends on various parameters, such as:. Several theories allow calculating the reaction rates at the molecular level. This field is referred to as reaction dynamics. The rate v of a first-order reaction , which could be disintegration of a substance A, is given by:. The rate of a first-order reaction depends only on the concentration and the properties of the involved substance, and the reaction itself can be described with the characteristic half-life. More than one time constant is needed when describing reactions of higher order. The temperature dependence of the rate constant usually follows the Arrhenius equation :. One of the simplest models of reaction rate is the collision theory. More realistic models are tailored to a specific problem and include the transition state theory , the calculation of the potential energy surface , the Marcus theory and the Rice—Ramsperger—Kassel—Marcus RRKM theory. In a synthesis reaction, two or more simple substances combine to form a more complex substance. These reactions are in the general form:. Two or more reactants yielding one product is another way to identify a synthesis reaction. One example of a synthesis reaction is the combination of iron and sulfur to form iron II sulfide :. Another example is simple hydrogen gas combined with simple oxygen gas to produce a more complex substance, such as water. A decomposition reaction is when a more complex substance breaks down into its more simple parts. It is thus the opposite of a synthesis reaction, and can be written as . One example of a decomposition reaction is the electrolysis of water to make oxygen and hydrogen gas:. In a single replacement reaction , a single uncombined element replaces another in a compound; in other words, one element trades places with another element in a compound These reactions come in the general form of:. One example of a single displacement reaction is when magnesium replaces hydrogen in water to make magnesium hydroxide and hydrogen gas:. In a double replacement reaction , the anions and cations of two compounds switch places and form two entirely different compounds. Another example of a double displacement reaction is the reaction of lead II nitrate with potassium iodide to form lead II iodide and potassium nitrate :. Redox reactions can be understood in terms of transfer of electrons from one involved species reducing agent to another oxidizing agent. In this process, the former species is oxidized and the latter is reduced. Though sufficient for many purposes, these descriptions are not precisely correct. Oxidation is better defined as an increase in oxidation state , and reduction as a decrease in oxidation state. In practice, the transfer of electrons will always change the oxidation state, but there are many reactions that are classed as "redox" even though no electron transfer occurs such as those involving covalent bonds. In the following redox reaction, hazardous sodium metal reacts with toxic chlorine gas to form the ionic compound sodium chloride , or common table salt:. Because the chlorine is the one reduced, it is considered the electron acceptor, or in other words, induces oxidation in the sodium — thus the chlorine gas is considered the oxidizing agent. Conversely, the sodium is oxidized or is the electron donor, and thus induces reduction in the other species and is considered the reducing agent. Which of the involved reactants would be reducing or oxidizing agent can be predicted from the electronegativity of their elements. Elements with low electronegativity, such as most metals, easily donate electrons and oxidize — they are reducing agents. The number of electrons donated or accepted in a redox reaction can be predicted from the electron configuration of the reactant element. Elements try to reach the low-energy noble gas configuration, and therefore alkali metals and halogens will donate and accept one electron respectively. Noble gases themselves are chemically inactive. An important class of redox reactions are the electrochemical reactions, where electrons from the power supply are used as the reducing agent. These reactions are particularly important for the production of chemical elements, such as chlorine or aluminium. The reverse process in which electrons are released in redox reactions and can be used as electrical energy is possible and used in batteries. In complexation reactions, several ligands react with a metal atom to form a coordination complex. Chlorine-hydrocarbon photochemistry in the marine troposphere and lower stratosphere This is achieved by providing lone pairs of the ligand into empty orbitals of the metal atom and forming dipolar bonds. The ligands are Lewis bases , they can be both ions and neutral molecules, such as carbon monoxide, ammonia or water. The number of ligands that react with a central metal atom can be found using the electron rule , saying that the valence shells of a transition metal will collectively accommodate 18 electrons , whereas the symmetry of the resulting complex can be predicted with the crystal field theory and ligand field theory. Complexation reactions also include ligand exchange , in which one or more ligands are replaced by another, and redox processes which change the oxidation state of the central metal atom. When a proton is removed from an acid, the resulting species is termed that acid's conjugate base. When the proton is accepted by a base, the resulting species is termed that base's conjugate acid. The equilibrium is determined by the acid and base dissociation constants K a and K b of the involved substances. A special case of the acid-base reaction is the neutralization where an acid and a base, taken at exactly same amounts, form a neutral salt. Acid-base reactions can have different definitions depending on the acid-base concept employed. Some of the most common are:. Precipitation is the formation of a solid in a solution or inside another solid during a chemical reaction. It usually takes place when the concentration of dissolved ions exceeds the solubility limit and forms an insoluble salt. This process can be assisted by adding a precipitating agent or by removal of the solvent. Rapid precipitation results in an amorphous or microcrystalline residue and slow process can yield single crystals.guai.im/naki-chloroquine-vs-hydroxychloroquine.php A Brief Introduction to the History of Chemical Kinetics The latter can also be obtained by recrystallization from microcrystalline salts. Reactions can take place between two solids. However, because of the relatively small diffusion rates in solids, the corresponding chemical reactions are very slow in comparison to liquid and gas phase reactions. They are accelerated by increasing the reaction temperature and finely dividing the reactant to increase the contacting surface area. Reaction can take place at the solid gas interface, surfaces at very low pressure such as ultra-high vacuum. Via scanning tunneling microscopy , it is possible to observe reactions at the solid gas interface in real space, if the time scale of the reaction is in the correct range. In photochemical reactions , atoms and molecules absorb energy photons of the illumination light and convert into an excited state. They can then release this energy by breaking chemical bonds, thereby producing radicals. Photochemical reactions include hydrogen—oxygen reactions, radical polymerization , chain reactions and rearrangement reactions. Many important processes involve photochemistry. The premier example is photosynthesis , in which most plants use solar energy to convert carbon dioxide and water into glucose , disposing of oxygen as a side-product. Humans rely on photochemistry for the formation of vitamin D, and vision is initiated by a photochemical reaction of rhodopsin. In catalysis , the reaction does not proceed directly, but through reaction with a third substance known as catalyst. Although the catalyst takes part in the reaction, it is returned to its original state by the end of the reaction and so is not consumed. However, it can be inhibited, deactivated or destroyed by secondary processes. Catalysts can be used in a different phase heterogeneous or in the same phase homogeneous as the reactants. In heterogeneous catalysis, typical secondary processes include coking where the catalyst becomes covered by polymeric side products. Additionally, heterogeneous catalysts can dissolve into the solution in a solid—liquid system or evaporate in a solid—gas system. Catalysts can only speed up the reaction — chemicals that slow down the reaction are called inhibitors. With a catalyst, a reaction which is kinetically inhibited by a high activation energy can take place in circumvention of this activation energy. Heterogeneous catalysts are usually solids, powdered in order to maximize their surface area. Of particular importance in heterogeneous catalysis are the platinum group metals and other transition metals, which are used in hydrogenations , catalytic reforming and in the synthesis of commodity chemicals such as nitric acid and ammonia. Acids are an example of a homogeneous catalyst, they increase the nucleophilicity of carbonyls , allowing a reaction that would not otherwise proceed with electrophiles. The advantage of homogeneous catalysts is the ease of mixing them with the reactants, but they may also be difficult to separate from the products. Therefore, heterogeneous catalysts are preferred in many industrial processes. In organic chemistry, in addition to oxidation, reduction or acid-base reactions, a number of other reactions can take place which involve covalent bonds between carbon atoms or carbon and heteroatoms such as oxygen, nitrogen, halogens , etc. Many specific reactions in organic chemistry are name reactions designated after their discoverers. In a substitution reaction , a functional group in a particular chemical compound is replaced by another group. In the first type, a nucleophile , an atom or molecule with an excess of electrons and thus a negative charge or partial charge , replaces another atom or part of the "substrate" molecule. The electron pair from the nucleophile attacks the substrate forming a new bond, while the leaving group departs with an electron pair. The nucleophile may be electrically neutral or negatively charged, whereas the substrate is typically neutral or positively charged. Examples of nucleophiles are hydroxide ion, alkoxides , amines and halides. This type of reaction is found mainly in aliphatic hydrocarbons , and rarely in aromatic hydrocarbon. The latter have high electron density and enter nucleophilic aromatic substitution only with very strong electron withdrawing groups. Nucleophilic substitution can take place by two different mechanisms, S N 1 and S N 2. In their names, S stands for substitution, N for nucleophilic, and the number represents the kinetic order of the reaction, unimolecular or bimolecular. The S N 1 reaction proceeds in two steps. First, the leaving group is eliminated creating a carbocation. This is followed by a rapid reaction with the nucleophile. In the S N 2 mechanism, the nucleophile forms a transition state with the attacked molecule, and only then the leaving group is cleaved. These two mechanisms differ in the stereochemistry of the products. In contrast, a reversal Walden inversion of the previously existing stereochemistry is observed in the S N 2 mechanism. Electrophilic substitution is the counterpart of the nucleophilic substitution in that the attacking atom or molecule, an electrophile , has low electron density and thus a positive charge. Typical electrophiles are the carbon atom of carbonyl groups , carbocations or sulfur or nitronium cations. This reaction takes place almost exclusively in aromatic hydrocarbons, where it is called electrophilic aromatic substitution. Then, the leaving group, usually a proton, is split off and the aromaticity is restored. An alternative to aromatic substitution is electrophilic aliphatic substitution. It is similar to the nucleophilic aliphatic substitution and also has two major types, S E 1 and S E 2 . In the third type of substitution reaction, radical substitution, the attacking particle is a radical. In the first step, light or heat disintegrates the halogen-containing molecules producing the radicals. Then the reaction proceeds as an avalanche until two radicals meet and recombine. The addition and its counterpart, the elimination , are reactions which change the number of substituents on the carbon atom, and form or cleave multiple bonds. Double and triple bonds can be produced by eliminating a suitable leaving group. Similar to the nucleophilic substitution, there are several possible reaction mechanisms which are named after the respective reaction order. In the E1 mechanism, the leaving group is ejected first, forming a carbocation. The next step, formation of the double bond, takes place with elimination of a proton deprotonation. The leaving order is reversed in the E1cb mechanism, that is the proton is split off first. This mechanism requires participation of a base. The E2 mechanism also requires a base, but there the attack of the base and the elimination of the leaving group proceed simultaneously and produce no ionic intermediate. - Photodecomposition of hydrogen peroxide in highly saline aqueous medium. - Lipids in Foods. Chemistry, Biochemistry and Technology. - Chlorine and Hydrogen Chloride? - US20110086247A1 - Redox flow cell rebalancing - Google Patents. In contrast to the E1 eliminations, different stereochemical configurations are possible for the reaction product in the E2 mechanism, because the attack of the base preferentially occurs in the anti-position with respect to the leaving group. Because of the similar conditions and reagents, the E2 elimination is always in competition with the S N 2-substitution. The counterpart of elimination is the addition where double or triple bonds are converted into single bonds. Similar to the substitution reactions, there are several types of additions distinguished by the type of the attacking particle. For example, in the electrophilic addition of hydrogen bromide, an electrophile proton attacks the double bond forming a carbocation , which then reacts with the nucleophile bromine. The carbocation can be formed on either side of the double bond depending on the groups attached to its ends, and the preferred configuration can be predicted with the Markovnikov's rule. Hg, and the pressure of the mercury vapor is 1,, mm. PHOTOCHEMICAL REACTIONS LEADING TO UNSTABLE SPECIES A method according to claim 1 wherein the pressure of the thallium iodide vapor is mm. Hg and the pressure of the mercury vapor is mm. Much, 3. The following examples are given for a better understanding of the invention. What is claimed is: 1. USA true USA en. Adams et al. On the mechanism of the radiation-induced inactivation of lysozyme in dilute aqueous solution. Rabe et al. Lukes et al. Generation of ozone by pulsed corona discharge over water surface in hybrid gas—liquid electrical discharge reactor. GBA en. Forrestal et al. Chemical reaction - Wikipedia Burton et al. Williams et al. Shinzawa et al. JPHA en. Flynn et al. Photochemical preparation of o-xylylene from 1, 3-dihydrophthalazine in rigid glass. Kubodera et al. ESR evidence for the cation radicals of tetrahydrofurans and dimethyl ether produced in a. TWB en. A process for the production of methylbenzofuran MBF impurities in phenol obtained from decomposition product of cumene hydroperoxide. Bancroft et al. Stevens et al. Photoperoxidation of unsaturated organic molecules. Sensitizer yields of O

<urn:uuid:fcfc1e76-13fc-4940-a074-6a9955299dcf>

Voice and Tone includes both a set of activity sheets and a slide presentation for identifying and working with this important element of reading and writing. The Voice and Tone Activity Sheet Set includes fifteen activities that allow students to practice with voice and tone in a variety of ways. The activities include lots of different tones and voices. Some are about author's voice, some are about a character's voice, some are about tone, and some combine voice and tone. The fifteen activities are: 1.Using a Character’s Voice 2.Formal and Informal Voices 3.Write a Dialog 5.Voices – Define and Write Examples 6.Voices – Find Examples in Texts 7.Voice and Tone – Match the Statements 8.Rewrite to Change the Tone 9.They Might Say . . . 10.Costumes, Sets, and Music 12.Tones – Define and Write Examples 13.Tones – Find Examples in Texts 14.Voice and Tone – Questions 15.Voice and Tone – Illustrative Poster The Voice and Tone PowerPoint introduces and explains the concepts of voice and tone in writing. The text clearly explains these concepts, which can be confusing for many students, and provided recognizable examples. Formal and informal voices are discussed, and lists of words that could describe various voices and tones in writing are provided. The idea of voice and tone in marketing is also introduced to provoke student interest. Questions along the way and a project at the end keep students involved. In addition, the last two slides provide a student notebook page of fill-in-the blank notes that students can complete while watching the presentation and a page of completed notes that can be given to students or used as a key. Studying voice and tone supports a number of the common core reading standards and helps students to strengthen their own writing as well. With the variety of activities in the set, this resource should work well with students at a variety of skill levels. From Classroom in the Middle

<urn:uuid:b9bffe30-e418-4d18-98e5-e35f48499ad7>

Radical Notation Every positive number a has two square roots, one positive and one negative. Recall that the positive square root is called the principal square root. The symbol is called the radical sign. The expression under the radical sign is called the radicand, and an expression containing a radical sign is called a radical expression. Examples of radical expressions: Example Write each expression in terms of an absolute value. a.b.c. Solution a. b. c. Example If possible, evaluate f(1) and f( 2) for each f(x). a.b. Solution a.b. Example Calculate the hang time for a ball that is kicked 75 feet into the air. Does the hang time double when a ball is kicked twice as high? Use the formula Solution The hang time is The hang times is less than double. Example Find the domain of each function. Write your answer in interval notation. a.b. Solution Solve 3 – 4x 0. The domain is b. Regardless of the value of x; the expression is always positive. The function is defined for all real numbers, and it domain is Example Write each expression in radical notation. Evaluate the expression by hand when possible. a.b. Solution a. b. Example Write each expression in radical notation. Evaluate the expression by hand when possible. a.b. Solution a. Take the fourth root of 81 and then cube it. b. Take the fifth root of 14 and then fourth it. Cannot be evaluated by hand. Objectives Solving Radical Equations The Distance Formula Solving the Equation x n = k If each side of an equation is raised to the same positive integer power, then any solutions to the given equations are among the solutions to the new equation. That is, the solutions to the equation a = b are among the solutions to a n = b n. POWER RULE FOR SOLVING EQUATIONS Example Solve Check your solution. Solution Check: It checks. Step 1: Isolate a radical term on one side of the equation. Step 2: Apply the power rule by raising each side of the equation to the power equal to the index of the isolated radical term. Step 3: Solve the equation. If it still contains radical, repeat Steps 1 and 2. Step 4: Check your answers by substituting each result in the given equation. SOLVING A RADICAL EQUATION Example Solve Solution Step 1: To isolate the radical term, we add 3 to each side of the equation. Step 2: Square each side. Step 3: Solve the resulting equation. Example (cont) Step 4: Check your answer by substituting into the given equation. Since this checks, the solution is x = −10. Example Solve Check your results and then solve the equation graphically. Solution Symbolic Solution Check: It checks. Thus 1 is an extraneous solution. Example (cont) Graphical Solution The solution 6 is supported graphically where the intersection is at (6, 4). The graphical solution does not give an extraneous solution. Example Solve Solution The answer checks. The solution is 4. Example Solve. Solution Step 1: The cube root is already isolated, so we proceed to Step 2. Step 2: Cube each side. Step 3: Solve the resulting equation. Example (cont) Step 4: Check the answer by substituting into the given equation. Since this checks, the solution is x = 29. Example Solve x 3/4 = 4 – x 2 graphically. This equation would be difficult to solve symbolically, but an approximate solution can be found graphically. Solution Example A 6ft ladder is placed against a garage with its base 3 ft from the building. How high above the ground is the top of the ladder? Solution The ladder is 5.2 ft above ground. The distance d between the points (x 1, y 1 ) and (x 2, y 2 ) in the xy-plane is DISTANCE FORMULA Example Find the distance between the points (−1, 2) and (6, 4). Solution Take the nth root of each side of x n = k to obtain 1. If n is odd, then and the equation becomes 2. If n is even and k > 0, then and the equation becomes (If k < 0, there are no real solutions.) SOLVING THE EQUATION x n = k Example Solve each equation. a. x 3 = −216b. x 2 = 17 c. 3(x + 4) 4 = 48 Solution a. b. or The value of i n can be found by dividing n (a positive integer) by 4. If the remainder is r, then i n = i r. Note that i 0 = 1, i 1 = i, i 2 = −1, and i 3 = −i. POWERS OF i Example Evaluate each expression. a.i 25 b. i 7 c. i 44 Solution a. When 25 is divided by 4, the result is 6 with the remainder of 1. Thus i 25 = i 1 = i. b. When 7 is divided by 4, the result is 1 with the remainder of 3. Thus i 7 = i 3 = −i. c. When 44 is divided by 4, the result is 11 with the remainder of 0. Thus i 44 = i 0 = 1. Example Write each quotient in standard form. a.b. Solution a.

<urn:uuid:79a4a9d6-7c34-48f5-925e-2f4641d121fb>

Show your child the shapes circle, square, rectangle and triangle. Can they identify each shape? Talk about each shapes special features such as how many sides it has. Ask your child to go on a hunt around your home looking for shapes. You made to help them at first by asking them what shape is the door? What shape are the windows? What shape is the clock? See how many different shapes you can find. Using a teddy and a chair move the teddy around and talk to your child about describing where the teddy is. Sit the teddy on the chair and say, Where is Teddy? Teddy is on the chair. Or, Where is Teddy? Teddy is under the chair. Complete the actions for the positional language on, under, in, behind, in front and next to. Then ask your child to follow some positional language instructions such as, Put Teddy on the chair.

<urn:uuid:66a7f748-1403-4bad-8961-dcaa6cec9ffc>

It involves simple algebra (multiplication or division) using conversion factor (numerical relationship between the two units). Watch How to Convert between units here Unit conversions use conversion factors to change the units of a measurement. For example, you buy a 1.7 kg smoked ham. How much is this in pounds? You use a conversion factor to change the units. What is a conversion factor? A conversion factor is a multiplying fraction that is alway equal to one. You use the conversion factor that relates grams and pounds. You may know that 1 kg = 2.2 lb (Its actually 2.204 62 kg, but we can use the approximate number here.) If you divide both sides of the equation by 2.2 lb, we get 1 kg/2.2 lb = 2.2 lb/2.2 lb =1 If you divide both sides by 1 kg, we get 1 kg/1 kg = 2.2 lb/1 kg = 1 Thus, the conversion factor can be either 1 kg/2.2 lb or 2.2 lb/1 kg because each equal to one. How do I use a conversion factor for unit conversions? Your problem is 1.7 kg = ? lb Thus, the conversion factor is either color(blue)(1 kg/2.2 lb) or color(blue)(2.2 lb/1 kg) You use the one with the desired unit (lb) on top. For this problem, you would write 1.7 color(red)(cancel(color(black)(kg))) × color(blue)(2.2 lb)/(color(blue)(1) color(red)(cancel(color(blue)(kg)))) = 3.7 lb Notice that putting kg on the bottom makes the units cancel and gives an answer with the units of lb. If you had used the other conversion factor, you would have gotten 1.7 kg × color(blue)(1 lb/2.2 kg) = 0.77 lb^2kg^-1 The units make no sense, so this choice is wrong. Heres another way to think of using unit conversions.

<urn:uuid:8dd5ce8b-a09d-4488-b2cb-5d545bd27947>

The hyphen (-) is used to join multiple words into a compound. The main goal of hyphenating a term is to prevent confusion on the part of the reader. Some hyphenated words are found in the dictionary, but others are simply formed by convention.Here are some guidelines for deciding whether to hyphenate a term that you are using in your writing. Hyphens and Dashes. A free guide from Essay UK. Using the Hyphen and the Dash The Hyphen. The hyphen (-) is the small bar found on every keyboard. It has several related uses; in every case, it is used to show that what it is attached to does not make up a complete word by itself. Hyphens are shorter than dashes and are used to connect words. Dashes are used as punctuation in sentences. Find out more in a Bitesize KS2 English guide. Hyphens are joiners. They join the words in a compound adjective (e.g., six-foot table, silver-service waitress), and they join the words in compound nouns (e.g., paper-clip, cooking-oil). They can also join prefixes to words (e.g., ultra-expensive, re-establish). Hyphens are often used to tell the ages of people and things. A handy rule, whether writing about years, months, or any other period of time, is to use hyphens unless the period of time (years, months, weeks, days) is written in plural form. A hyphen (-) is a punctuation mark that’s used to join words or parts of words. It’s not interchangeable with other types of dashes. Use a hyphen in a compound modifier when the modifier comes before the word it’s modifying. If you’re not sure whether a compound word has a hyphen or not, check your preferred dictionary. This handout explains the most common uses of three kinds of punctuation: semicolons (;), colons (:), and dashes (—). After reading the handout, you will be better able to decide when to use these forms of punctuation in your own writing. Semicolons. These resources provide guidelines for using punctuation in your writing. Hyphens (-) are used to connect two or more words (and numbers) into a single concept, especially for building adjectives. Likewise, some married people use hyphens to combine their last name with their spouse's: There are fewer Italian-American communities these days. Using Hyphens with Compound Adjectives. An adjective is a word that describes or “modifies” a noun, such as a tall tree or blue sky. A compound adjective comprises two or more adjectives strung together to modify a noun, such as light-blue sky or hard-hearted person. These adjectival forms are usually hyphenated as well; however, there are some exceptions depending on the meaning of the. Now, it’s time to focus on some of the finer points of punctuation in research papers. In this article, we will talk about how punctuation marks like dashes, hyphens, and apostrophes can help us express ideas clearly and easily. If the noun is modified by an adjective, the choice between a and an depends on the initial sound of the adjective that immediately follows the article:. a broken egg; an unusual problem; a European country (sounds like 'yer-o-pi-an,' i.e. begins with consonant 'y' sound); Remember, too, that in English, the indefinite articles are used to indicate membership in a group. Generally, hyphens are used to join two words or parts of words together while avoiding confusion or ambiguity. Consult your dictionary if you are not sure if a hyphen is required in a compound word, but remember that current usage may have shifted since your dictionary was published. Top Tip Simpler Rules for Hypens in Age Terms Here are some simple rules for using hyphens with ages: (1) There is never a hyphen after the word old. (2) There is never a hyphen before or after the word years (Note: This rule applies only to years not year.) (3) There are always hyphens around the word year (provided it's not in a predicate adjective following a or one). The quality of the When To Use Hyphens In An Essay sources used for paper writing can affect the result a lot. Knowing this, we use only the best and the most reliable sources. We are also able to give you a list of them or help you locate them if you need. Long dashes in writing. A long dash’s primary job is to tell the reader that you’ve jumped tracks onto a new (though related) subject, just for a moment. Here are some examples: After we buy toenail clippers — the dinosaur in that exhibit could use a trim, you know — we’ll stop at the doughnut shop. Using Numbers. When using numbers in essays and reports, it is important to decide whether to write the number out in full (two hundred thousand four hundred and six) or to use numerals (200,406). There are some rules to follow to make sure you use numbers in the right way. Use words if the number can be written in two words of fewer. When To Use Hyphens In Essays, personal statement of interest, where to publish an essay, how to start paragrap in narrative essay 47 We know how important it is to craft papers that are not only extremely well-written and deeply researched but also 100% original. The second use of a hyphen is to merge words together that don’t belong together and that don’t follow the other rules. If you are writing a phrase that is being used a single word then you can merge them with hyphens. He was a good-for-nothing no-good layabout. This example works with or without hyphens. It’s down, largely, to your. If you’re a great writer, you can use all sorts of things effectively. However, for us common folk, I’m going to say no. A rhetorical question is a device to place the audience in a more active role. It encourages the audience to think about the s.

<urn:uuid:eec4cede-e93a-451e-84e8-4826f25751df>

2-DIGIT PLACE VALUE Grade 1 Place Value worksheets teach children the value of each digit in 2- digit numbers. They would learn to count ‘tens’ and ‘ones’ using base ten blocks. Each block is counted as ‘ones’ and each rod (10 unit blocks) is counted as ‘tens’. Charts on International Place Value system give you a clear idea on the place of each digit in a number. Thus, children completely become familiar with number system. Large numbers could be read with ease. In this place value page, you have a variety of activities and worksheets to write numbers in expanded form and compact form. Download all these free worksheets to start learning place value.

<urn:uuid:7e34df48-9819-4f42-99c7-d994f12aeee7>

Many key factors led to the transition from indentured servants to slavery. Indentured servants became less cost- efficient due to the fact that land owners owned multiple pieces of land or needed more than one indentured servant to work on their land. Even though working conditions were harsh and the servants were limited to what they can and cannot do, they still had rights as humans, which means they were not slaves. But as more jobs were needed on the farm, the more indentured servant demanded in wages. As the needs of indentured servants increased, the owners believed they were not obliged to commit to the request of their servant. Mildred D. Taylor took these events into consideration when writing her novel, and in doing so, gave an accurate representation of how life was for colored people in the 1930s. Despite gaining their freedom, the vast majority of African Americans became farmers as they were well experienced in the trade. However, most of them had to become a sharecropper, or a farmer who works someone else’s land for a share of the profit. Buying land was even more of a challenge for colored people, as many whites refused to sell it to them. Being a sharecropper meant that not only did one have a job, but they were also provided with a place to live on their small share of land. While Virginia’s citizens were benefitting from generous land grants that assured many an adequate space to farm tobacco, there was a disproportionate amount of land compared to the number of laborers needed to work the farms. Even though black slaves were available at that time, they were expensive, prone to fall prey to fatal communicable disease, and they were not abundant enough to fill the farmers needs. Because of these reasons, Virginia did not utilize primarily black slaves to work on their plantations. From England, white people who were convicted criminals, transient, orphans and good-for-nothings of society entered into white bondage called indentured servitude, and were shipped to Virginia to work in the tobacco fields. Some of these new indentured servants were kidnapped or deceived into bondage by ‘recruiting agents’ of merchants and ship captains looking to turn a profit. Unfree laborers in the Colonial period were the institutional turning point of having slaves and indentured servants. Slaves and indentured servants were the primary means of the wealthy in America at this time and were seen throughout many colonies. Either as a slave or an indentured servant, the person was expected and required to work in fields to maintain crops, as a house servant, or of anything else the master chose for them to do. The treatments of both had their similarities but also having their differences. During this time period indentured servants were treated more fairly, whereas the slaves were treated unfairly. The second type of economic system that can be used for such an analysis is that of slavery. In Eric Williams ' work titled “Slavery and Capitalism”, he describes how the development of slavery marked several social and economic changes in society, especially in the nature of social hierarchies and relationships. Sven Beckert, in “The Empire of Cotton”, reiterates Williams ' argument by describing cotton cultivation in America, of which the backbone was slavery. In this economic system, production thrived because of the subordination of the labour force. Slavery was a cost effective method of employing labour. Although Christians were good citizens, and people who wanted to follow Jesus, they were constantly impacted by aspects of the Roman culture. The Roman history, pertaining to the way people worshiped, the philosophy and the music all had a significant impact on the Christian church. To begin with, In most ways, I would say that the society significantly impacted them to abandon the pagan lifestyle. Although they adapted and adopted, Christian views and customs were very different from Roman society. A key example is the way in which Christians worshiped God and not the gods. In Meso-America, however, the goal was to exploit the lands in order to produce and extract new goods which they could trade. Despite the different outcomes they were trying to reach, both held a common truth: natives and African slaves were both lesser than Europeans, The differences in climate and geography caused the North and South to develop different types of economies. The rich soil and mild winters of the South led to a Southern economy which based on agriculture. They sold cotton, tobacco, rice, sugar cane, and indigo as cash crops. However, cotton became the most important crop after Eli Whitney’s invention of the cotton gin. The Northern economy was based on manufacturing. These types of agriculture are threats to the survival of small farmers. These multimillion company owned 70,129 hectares of land while three out of four farmers do not own the land they till, and also farmers from these company are treated like slaves, I see sugar cane farmers having to harvest sugar cane in the heat of the sun without proper gears to help protect them from the sun or rain. And also they work early in the morning until the afternoon without proper break and also no proper food. I just wished that these farmers are treated especially because without them, these

<urn:uuid:2edde495-bb92-409f-b0e0-4e6441ae73fd>

Python repeat function n times Use such functions very rarely for now, only if you need to repeat the print statements many times. For example, def volumep ( r , h ): pi = 3.14159 vol = pi * r ** 2 * h print "The volume of a cylinder with radius" , r , "and height" , h , "is" , vol volumep ( 1 , 2 ) volumep ( 2 , 1 ) While loop is used to executing multiple times of statement or codes repeatedly until the given condition is true once it gets a false loop will stop .which will be done by three parts initial value, condition, increment or decrement based this only while loop is working. the below parts are main. Jun 01, 2014 · The print function. Very trivial, and the change in the print-syntax is probably the most widely known change, but still it is worth mentioning: Python 2’s print statement has been replaced by the print() function, meaning that we have to wrap the object that we want to print in parantheses. The rest of the function is similar to countdown: if n is greater than 0, it displays s and then calls itself to display s n−1 additional times. So the number of lines of output is 1 + (n - 1), which adds up to n. For simple examples like this, it is probably easier to use a for loop. In this article, we show how to print out a statement any number of times you want in Python. So, basically, to do this, we are going to use a for loop with the keyword range in the statement. Using this method, we can print out a statement any number of times we want by specifying that number in the range () function. A loop allows us to execute some set of statement multiple times. Consider the following trivial problem: Let's say we want to print string "Today is Sunday" 100 times to the console. One way to achieve this is to create a Python script and call print() function 100 times as follows:while-loop in python: A while loop in python executes a group of statements or a suite of statements multiple times, till a given condition is True. Read More..... for-loop in python: Iterate over a group of statements multiple times using a for loop. But the number of times these statements will be executed by a for loop depends upon a sequence. mail.python.org Mailing Lists: Welcome! Below is a listing of all the public Mailman 2 mailing lists on mail.python.org. Click on a list name to get more information about the list, or to subscribe, unsubscribe, and change the preferences on your subscription. Results: ``` Python 3.6.8 5000000 loops, best of 3: 0.0983 usec per loop Python 3.7.6 5000000 loops, best of 5: 102 nsec per loop Python 3.8.3 5000000 loops, best of 5: 97.4 nsec per loop Python 3.9.0 5000000 loops, best of 5: 99.5 nsec per loop Python 3.10.0a2+ with co_annotations 5000000 loops, best of 5: 92.4 nsec per loop Python 3.10.0a2 ... By passing 2 for the range() function’s “step” parameter, you can get cells from every second row (in this case, all the odd-numbered rows). The for loop’s i variable is passed for the row keyword argument to the cell() method, while 2 is always passed for the column keyword argument. Practice python mcq questions on conditionals and loops which will help you to prepare for interviews, technical rounds, competitive exams etc. >> >>> Let’s Learn About Python String Test_lstrip() Test_isupper() Test_split() B. Python Unittest Assert Methods. Now, Let’s Take A Look At What Methods We Can Call Within U Nov 12, 2020 · Python is one of high-level programming languages that is gaining momentum in scientific computing. To work with Python, it is very recommended to use a programming environment. There are many Python's Integrated Development Environments (IDEs) available, some are commercial and others are free and open source. Personally, I use the following IDEs: For loop is used to iterate over elements of a sequence. It is often used when you have a piece of code which you want to repeat "n" number of time. What is While Loop? While Loop is used to repeat a block of code. Instead of running the code block once, It executes the code block multiple times until a certain condition is met. A recursive function must have some way to control the number of times it repeats. true Each time a function is called in a recursive solution, the system incurs overhead that is not incurred with a loop python print on same line in loop. Hi, I have a unique requirement in Python where I have to print data in the same line. When I am using the print() method it is printing new data in next line. So, I want to avoid this and print in the same line. Let's know how to make function in Python to print data in the same line? Python all() Function. Definition. The all() function returns True w hen all elements in the given iterable are true. If not, it returns False.. Syntax. The syntax of the all() is: Sum Of N Numbers In Python Using While Loop The time.sleep() function will suspend the execution for the number of seconds passed in the argument. In the above example, we are sleeping for 15 seconds in each loop iteration, which means that Python will only evaluate the exit condition of the loop at a rate of four times per minute, compared to as fast as it could in the previous version. Question: ANSWER IN PYTHON ONLY Write A Function: Def Repeat(string, N, Delim) That Returns The String Repeated N Times, Separated By The String Delimiter (delim). For Example: Enter A String: Ho How Many Repetitions? 3 Separated By? ... Code can be repeated using a loop. Lines of code can be repeated N times, where N is manually configurable. In practice, it means code will be repeated until a condition is met. This condition is usually (x >=N) but it’s not the only possible condition. Python has 3 types of loops: for loops, while loops and nested loops. Like the while loop the for loop is a programming language statement, i.e. an iteration statement, which allows a code block to be repeated a certain number of times. Repeat Infringers It is Company’s policy to permanently cancel the privileges and authorizations, in appropriate circumstances, of repeat copyright infringers. Indexing With range() Function range() is a function that's often used with a for loop. range(x,y) creates a list-like object starting with integer x and ending BEFORE y. The starting point x can be omitted, in which case the list starts with 0. In a looping environment range() works as expected. Sep 17, 2019 · Python Recursion is the method of programming or coding the problem, in which the function calls itself one or more times in its body. Usually, it is returning a return value of this function call. If the function definition satisfies the condition of recursion, we call this function a recursive function. What is recursion in Python Functions¶ Python comes with many built-in functions and modules that implement additional functions. Functions can be used to execute bodies of code that are meant to be re-used. Functions can optionally take arguments and can optionally return values. Python provides the def keyword, which allows you to define a function. Video created by University of Michigan for the course "Python Functions, Files, and Dictionaries". In week four the video lectures and the Runestone textbook will outline a more advanced iteration mechanism, the while loop. For the general "repeat" part, you could use itertools.cycle. The complication is the "merge the rest of the elements" part, though you can do that with islice, taking the next N-1 elements, and then advancing again to skip to the next element for the next loop. Apr 10, 2013 · You can also make a string repeat ‘n’ number of times in python by multiplying the string with that number. Here is an example : $ cat firstPYProgram.py print "5times " * 5 Observe that the code above multiplies the string “5times” with the number 5. Problem 6: Write a function to compute the total number of lines of code, ignoring empty and comment lines, in all python files in the specified directory recursively. Problem 7: Write a program split.py , that takes an integer n and a filename as command line arguments and splits the file into multiple small files with each having n lines. Thus it returns n * factorial(n-1). This process will continue until n = 1. If n==1 is reached, it will return the result. Limitations of recursions Everytime a function calls itself and stores some memory. Thus, a recursive function could hold much more memory than a traditional function. Python stops the function calls after a depth of 1000 ... def repeatfunc(func, times=None, *args): """Repeat calls to func with specified arguments. Example: repeatfunc(random.random) """ if times is None: return starmap(func, repeat(args)) return starmap(func, repeat(args, times)) Demo Esp32 Ota Slow The ESP32 Has A Few Common Problems, Specially When You Are Trying To Upload New Sketches Or Install The ESP32 Add-on On The Arduino IDE. This Guide Is ...

<urn:uuid:1717e3d6-05f4-4662-bedc-30b6ecc3f740>

Volume is defined as the space occupied by 3-Dimensional objects. For example, volume of the cylinder is defined as the space occupied by the 3-Dimensional shape of the cylinder. Cube is the 3-D shape of the square. Volume of the cube can be given by the formula as under :- Cuboid is the 3-D shape of a rectangle. Volume of the cuboid is given by formula as under:- Sphere is the 3-D shape of Circle . Volume of sphere can be given by formula as under:- Volume of cylinder is given by the formula as under: Volume of Right Circular Cone can be given by formula as under :- Que 1 :- Calculate volume of a cylindrical bucket having radius 5 cm and height 2 cm. Ans Height of cylinder, h = 2 cm Radius of cylinder, r = 5 cm Volume of cylindrical bucket = 22(5) = 20 cm3 Que 2 :- What is the volume of the right circular cone of radius 8 m and height 6 m ? Ans Height of the right circular cone, h = 6m Radius of the right circular cone, r = 8 m Thus , volume of the right circular cone = 13(8)2(6) = 128 m^3 Que 3:- Calculate volume of basketball having radius 3 cm. Ans Radius of basketball = 3 cm Volume of sphere = 4/3π(3)^3 = 4π×3×3 In the United States and Canada, typically as per school curriculum the basic geometrical concepts such as Area, Perimeter and Volume are introduced in Grade 5. This is the first time students learn fun facts about the topic of volume such as – all sides of a cube are equal and the volume is a simple cube of the length of its side. Other than learning these fun facts, volume doesn’t just introduce students to the three dimensional shapes but it also brings the more complex topics for middle school students such as different shapes have different volumes and the fact that there are multiple ways of measuring volume. One can measure the volume by the shape but in other cases we can use the density of the material to also calculate the volume. Also the fact that state of matter also matter as solids are just packed but liquids end up taking the share of the 3 dimensional space. The topic of volume can easily get tricky for students and giving them the correct support and experiences with tools can be helpful. Conceptual understanding of volume and different types of shapes can help motivate students to learn & focus on the volume formulas. Our Homework Help is designed to help middle & high school students to understand the details about the topic of volume. Our team of Math tutors is committed towards providing our students the details they need to develop an understanding of the core concepts of volume. Available 24/7, our tutors can handle all volume related questions and get you the correct solutions at the most reasonable prices. Step 1: Fill out the help homework form & post your homework questions Step 2: Choose from the multiple requests that fit your budget and timeline. Step 3: Review your final answers before releasing the payment. Our work is 100% original and we stand behind the quality of support and guidance provided. Our tutors help hundreds of kids on a daily basis to understand difficult concepts, find solutions and improve Math grades.

<urn:uuid:04f93063-1149-4067-9730-451636eeee0f>

Here is a collection of our printable worksheets for the theme And the verb Accord of the chapter Structure of sentences in the grammar section. Find the correct verb chord – There is also a paragraph with some misused verbs in this one. Worksheet > Grammar > grade 3 > verbs > subject – Verb-subject and verb-verbal – Find the verb and change it if it doesn`t work for the sentence. Use Indefinite`s pronouns correctly – you need to highlight the indefinite pronoun in the sentence, and then choose the correct form of the verb. Use singular/plural pronouns and verbs – you must not only select the correct form of the verb, but also label pluralization. In correct English, both spoken and written, a subject and a verb must agree. Just as a subject can be plural or singular, a verb or a predicate can also be plural or singular. If the subject is plural, the verb must also be plural, and so must nouns to nouns and individual subjects; The verb must be singular. The following worksheets can be displayed and downloaded to print by clicking on the title. You can use them either at home or in class. This worksheet contains some of the most commonly used verbs for the adaptation of the subject and the verb. Find the verb and verbs of Agreeing In Paragraphs – This sheet basically mixes the skills used in the other two worksheets. Can your student grant these annoying subjects and verbs? Your student decides what form the verb should be used in a sentence. Now is the time to accept these verbs with a negative contraction of the subject! Here is a more demanding worksheet on the subject and verbal agreement. The activity includes some delicate pronouns. Complete the sentence with proper Subject and Verb Agreement – Surround the right verb to complete the sentence. Here too, we advise you to display more printable worksheets in sentence structure or grammar. Find all our working sheet verbs, from verbs as action words to conjugal verbs, verbs and irregular verbs. You`re going through the Class 3 questions. Ask questions at all levels of the class. Find the verb matching and verbs In paragraphs version 2 – Continue working on the same skill that has been re-identified. Kindergarten Class 1 2 Class 3 4 Class 5 Class 5 Class 5 7 Class 8th 10th Training Cycle.

<urn:uuid:b11e4f3b-cac8-4825-b304-6f3bb7feee27>

By year 6 children should be able to describe the properties of 3D shapes and refer in their descriptions to perpendicular and parallel faces and edges. Of course much of this work is linked to work on 2D shapes, symmetry, position and direction. KS2 Maths 3D shapes learning resources for adults, children, parents and teachers. Shapes includes 3d shape pictures. Shape Lab. Y4 Sort Triangles Crickweb. Sort Quadrilaterals Crickweb. What 2d Shape am I? ngfl-cymru. What are 2D and 3D shapes? bgfl.org.. All the materials on these pages are free for homework and classroom use only. You may not redistribute. What are 3D shapes? Find out about 3D shapes such as cubes, pyramids and spheres in this Bitesize KS1 maths guide. Use these ideas and resources in your 3D shape topic to develop your children's understanding. Join our email newsletter to receive free updates!. End of year assemblies. English Time Fillers. Estimation. Fieldwork. French Colours. Full Stops and Capital Letters.. A template with a border of 3D shapes. for use in your display work or as. Welcome to the Math Salamanders 3d Shapes Worksheets. Here you will find our range of free Shape worksheets which involve naming and identifying 3d shapes and their properties. There are a range of worksheets at different levels, suitable for children from Kindergarten up to 3rd grade. Nets of 3D Shapes Homework Extension with answers for Year 6 Summer Block 1. National Curriculum Objectives. Mathematics Year 6: (6G3b) Recognise and build simple 3-D shapes, including making nets. Mathematics Year 6: (6G2b) Describe simple 3-D shapes. Year 6 Introduce Angles IWB Properties of Shapes Activity. Step 2: This Year 6 Introduce Angles IWB Activity includes three questions designed to check pupils' understanding of quarter, half, three-quarter and full turns, and applying this to different contexts. Year 6: Geometry: properties of shapes New Maths Curriculum (2014): Year 6 objectives. Pupils should draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles. Pupils should describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements. Introduce your child to our 3D shapes worksheets. Besides learning to identify various geometric shapes and important concepts like symmetry, dimensions, and plane, your young student can print, cut, and create models that bring 3D shapes to life. They will be amazed when they create their own 3D cubes, cones, and even triangular prisms and. Begin to look at 3D shape and how these can be made up of 2D shapes. Watch the above video and ask the children to look for 3D shapes, and especially their properties. Their are several activities you can do from here, you could record the different shapes and their properties, draw them from different views or even make 3D shape angry birds using this link. A worksheet designed to help build and reinforce knowledge of 3d shapes. It asks pupils to: - Draw a line from each 3D shape to its name. - Draw a line from each 3D shape to the related everyday object This resource consists of 1 page. In Year 2, children move onto identifying how many edges, faces and vertices 3D shapes have. For example: this octagonal-based pyramid has 16 edges, 9 faces and 1 vertex: They will also be asked to identify 2D shapes on 3D shapes; for example, a cylinder has two circular faces. In Year 3, children will move onto drawing 2D shapes and making 3D shapes with modelling materials. The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Search. Browse by subject and age group. A space game where you can revise the properties of 2d and 3d shapes. There are different levels of difficulty. Pupils. Flash. 7-11 year olds.. 6-11 year olds. Sorting Shapes on a Venn Diagram. Sort a variety of 2D shapes on a Venn diagram. Sort by one or two conditions.Shape, Position and Movement Games These fun maths games can help children recognise 2d and 3d shapes and understand the properties of shapes. There are maths games where children can practise finding lines of symmetry and recognise symmetrical shapes.Year 7. Shape, Space and Measure. Geometrical reasoning: lines, angles and shapes. 198-201 Use 2d representations to visualise 3d shapes and deduce some of their properties. Construction. 222-3 Use ruler and protractor to construct simple nets of 3d shapes. E.g. cuboid, regular tetrahedron, square based pyramid, triangular prism. Lesson 1 - Views.

<urn:uuid:191654f9-743f-42ca-b98f-6285719aa768>

Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which. Step 1 of 1 Let the spheres spin on the table. The sphere which spins at a lower rate will be the hollow sphere. This is because in a hollow sphere, the air inside tries to get away from the axis of rotation. Therefore its moment of inertia increases causing reduction in angular velocity. As the torque is constant (torque = moment of inertia x angular velocity) for both the spheres; hence in case of a solid sphere, it will rotate more or less like a rigid body with a greater angular velocity. Textbook: Physics: Principles with Applications Author: Douglas C. Giancoli This textbook survival guide was created for the textbook: Physics: Principles with Applications, edition: 6. Since the solution to 19Q from 8 chapter was answered, more than 377 students have viewed the full step-by-step answer. Physics: Principles with Applications was written by and is associated to the ISBN: 9780130606204. The full step-by-step solution to problem: 19Q from chapter: 8 was answered by , our top Physics solution expert on 03/03/17, 03:53PM. The answer to “Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.” is broken down into a number of easy to follow steps, and 26 words. This full solution covers the following key subjects: describe, determine, experiment, Hollow, however. This expansive textbook survival guide covers 35 chapters, and 3914 solutions.

<urn:uuid:8935b8d5-daa6-4f48-b9e4-15f6199ebfc7>

Before the lesson Download classroom resources - To create a jazz motif - Children should be taught to: - Listen with attention to detail and recall sounds with increasing aural memory - Appreciate and understand a wide range of high-quality live and recorded music drawn from different traditions and from great composers and musicians - Develop an understanding of the history of music Pupils needing extra support: Use coloured dots on the notes and the corresponding colour coded Symbols used to represent music played with instruments or sung by the human voice… handout to help them learn the tune. Pupils working at greater depth: Should experiment and adapt the A regular repeated pattern of sound as necessary, ensuring that it is still a swung rhythm.

<urn:uuid:104a48af-e72b-42d1-9ac8-6cb3aae14a7d>

Absolute has more purpose than keeping the value of a function positive. It can transform a function into a piecewise function. To understand how absolute value function can turn into a piecewise function, you need to have a clear understanding of the absolute function and piecewise function. That is why, in this resource, we will cover the basics of absolute value and piecewise function and then how an absolute value function becomes a piecewise function. Absolute Value Function An absolute value function is a function that has an algebraic expression within the modulus. The modulus is a symbol of the absolute value function. Mathematicians use absolute functions to keep the value positive. There are some things that can't be a negative entity such as matter, volume, space, time, etc. To keep them in the positive range, mathematicians use the absolute value function. They are written like this: Some functions behave differently with different inputs. It means that the function has some breakage point. From that point, the function behaves differently. However, we can't break the function but we can assume that the function works differently under those inputs. To solve that, mathematicians came up with a solution and that is to call it a piecewise function. A piecewise function is a type of function that is constructed on a sequence of intervals. For example, Absolute Value Function to Piecewise Function Having a modulus on an algebraic function means that all the values of y will be positive. However, this doesn't mean that all the values of x will also be positive. We can present it into a piecewise function. An Absolute value functions become piecewise functions by following these steps: Make the function equal to zero, without the absolute value and calculate their roots. Form intervals with the roots and evaluate the sign of each interval. Define the piecewise function, taking into account that the sign needs to be changed in the intervals where x is negative. Graph the resulting function. The platform that connects tutors and students

<urn:uuid:6a52195b-eb48-432c-8a64-e48d7e035daa>

Young people use their voice to speak up for injustice and take action for the common good. Filter by subjects: Filter by audience: Filter by unit » issue area: find a lesson Unit: Courage of the Heart Native Americans, or Indigenous People, are located geographically across the entire continent of North America. There are many stereotypes of native culture, but their culture varies as much as their locations, as each group of native peoples have their own traditions. This lesson focuses on... Unit: Be the Change: Democracy Unit: Take a Stand on Bullying Students learn about the different roles people take in the cycle of bullying. They share their observations about bullying situations and discuss why taking action to address bullying behavior is good for the community. Unit: Doodle Stones In this one-period lesson, students examine the effects of using words as social action today and in history. They use words to communicate positively and build community within the school. A service project involves writing positive messages on stones and placing them strategically... After researching the life and work of a chosen philanthropist from history, the learner takes on the role of that philanthropist in writing a letter to the learner. In this letter, the philanthropist discusses his/her motivations and feelings about his/her work, and compares and contrasts his/... Learners will define prejudice, bias, racism, and stereotype so that they will have the necessary skills to analyze the effects these attitudes have on society. Learners will identify how acts of philanthropy worked... Students will learn about the work of a specific nonprofit organization through a series of interviews and by doing volunteer work for the organization.

<urn:uuid:31627f8d-6d6b-4ebf-ad5e-110cbfe5e8dc>

Provide students with subject-verb agreement practice with this worksheet focusing on using ‘is’ and ‘are’ correctly. Practise using ‘was’ and ‘were’ correctly using a set of subject-verb agreement task cards. Provide students with subject-verb agreement practice with this worksheet focusing on using ‘do’ and ‘does’ correctly. Practise counting to 100 by 1’s with upper and lowercase alphabet cards and blank hundreds board. Create a mini-book by completing the 100-item writing prompts and illustrating each page Practise identifying dependent clauses in complex sentences with a dependent clause worksheet. Improve sentence structure and grammar skills with a board game that focuses on singular and plural subject-verb agreement. Reinforce capitalisation of proper nouns, the pronoun ‘I’ and the beginning of sentences with this set of task cards. Improve students' sentence structure with a card game focusing on correct subject-verb agreement. Practise using ‘do’ and ‘does’ correctly using a set of subject-verb agreement task cards. Practise using ‘has’ and ‘have’ correctly with a set of subject-verb agreement task cards. Practise using irregular plural nouns with an irregular plural noun matching activity. A poem to promote thoughtful discussion around issues of reconciliation on National Sorry Day. Convert direct speech to indirect speech with this worksheet. Practise converting indirect speech to direct speech with this worksheet. Reinforce understanding of how to punctuate direct speech with this worksheet. Identify terminology related to prefixes, suffixes and root words in this word search. Explore direct and indirect speech with this board game. A heart template to use in a variety of ways. Investigate the differences between direct and indirect speech with this match-up activity. Explore imaginative writing in your classroom with these 3 fun story writing prompts for Easter. Consolidate understanding of direct and indirect speech with this set of worksheets. 3 worksheets teaching students how to link ideas when writing narrative paragraphs. A template to use when exploring or planning a narrative story. A template for students to use when planning the plot structure of a narrative text. A checklist for students to use when proofreading and editing their narrative writing. 50 activities in one booklet which all revolve around learning grammar in the classroom. A 3D lantern template to use with students at the beginning of the year. A set of sentence starter prompts for students to practise writing short sentences. A desk plate with helpful cues for beginning writers. A set of 12 poetry prompts for younger students.

<urn:uuid:b566dd7f-2072-48e5-b45f-30bdc0390a68>

Proper nouns worksheets explore this concept and help children differentiate between proper and common nouns. The grammar worksheets on this page can be used to help students understand nouns. Feel free to use the printable noun worksheets below in class or at home. Grade 1 common and proper nouns worksheet pdf. Then they will practice using singular plural and collective nouns in different contexts. Add to my workbooks 47 download file pdf embed in my website or blog add to google classroom. Nouns worksheets these worksheets introduce nouns as words for people places and things. Proper nouns worksheets are a handy classroom tool or homework aid. Singular and plural nouns worksheets for grade 1 pdf daily grammar practice 10th countable uncountable image result nouns exercises grade 10 first summer worksheets pronoun and for pronouns worksheet 1 proper pdf countable uncountable grammar worksheets grade 10 pdf noun worksheet nouns and printouts noun practice worksheets 1st grade. Here is a graphic preview for all the kindergarten 1st grade 2nd grade 3rd grade 4th grade and 5th grade proper and common nouns worksheets. These 30 review sheets cover the following first grade common core standards 1 l 1 common and proper nouns possessive nouns subject verb agreement pronouns verbs adjectives articles types of sentences1 l 2 capitalization punctuation commas spelling irregular words read unknown words1 l 4 affixesthe. Plural and possessive nouns are introduced. Worksheets grammar grade 1 nouns proper nouns. The focus is on identifying simple nouns either in isolation or in a sentence. Singular plural and collective nouns worksheet students will read 15 fun sentences themed around a class trip to the zoo. Using these pages encourages self confidence while reading and writing new material. Proper nouns require a capital letter and refer directly to a person or place. Topics include identifying basic nouns common and proper nouns singular and plural nouns and collective nouns. While doing this they will identify singular plural and collective nouns. Common nouns can be person place or thing but are not names of specific people places or things. Names of people places and things. 2nd and 3rd grade grades k 12 kindergarten 1st grade ccss code s. Our parts of speech alphabet worksheet is perfect for k 3rd grade but can be used where appropriate. Part of a collection of free grade 1 grammar worksheets from k5 learning. These grade 1 grammar worksheets introduce proper nouns as the name of specific people places or things. Common nouns are different from proper nouns which give a name to a noun. Click on the image to display our pdf worksheet.

<urn:uuid:5663dc22-ca5f-48e0-9226-00502bde2461>

In these geometry worksheets students identify and draw lines of symmetry. Draw all lines of symmetry for each figure. Geometry worksheets offers free printable geometry related worksheets with subjects of angles shapes polygons 3 d solids polyhedra and symmetry. Lines of symmetry worksheet geometry. These worksheets are intended for students for drawing the line of symmetry on the worksheets. Some shapes can be cut in more than one way. A shape has line symmetryif it can be folded about a line so that its two parts match exactly. Explore activities like drawing mirror images congruent figures and learning all about trapezoids. Geometry worksheets for drawing the line of symmetry. When the folded part sits perfectly on top all edges matching then the fold line is a line of symmetry. Show your little learner the importance of shapes with our lines of symmetry worksheets. Here i have folded a rectangle one way and it didn t work. Symmetry is one of the earliest geometry skills to master and it helps in many areas of math science and even art. Symmetry worksheets consist of a variety of skills for children in grade 1 through grade 5 to understand the lines of symmetry in different shapes. Symmetry worksheets here make kids understand that a line dividing an object or image into two equal halves is known as line of symmetry and these split shapes are called symmetrical shapes. Symmetry draw the line of symmetry grade 2 geometry worksheet draw a line that cuts the following shapes in half so that each half reflects the other half through your line. So this is not a line of symmetry. For lines of symmetry at angles of 45 it is often better to rotate your paper so that the line of symmetry is vertical or horizontal and the rest of the paper is at an angle. The split halves are mirror images. The basis and understanding of symmetry starts at about grade 2 and then develops further in grades 3 4 and 5. Printable exercises to identify and draw the lines of symmetry complete the shapes count the lines of symmetry in each shape to identify symmetrical or asymmetrical shapes and to determine the perimeter of shapes are given here for practice. A line of symmetry divides a figure into two mirror image halves. Geometry worksheets for 4th grade and 5th grade and middle school. Line of symmetry worksheets. You can find if a shape has a line of symmetry by folding it. A fold line or a line of symmetry divides a shape into two parts that are the same size and shape.

<urn:uuid:60f2d84a-6565-4d2f-b3c5-124b64cec997>

Students use a measuring instrument to the limit of its precision. They determine which digit in a measured value it the most certain. 3 Views 10 Downloads - Collection Types - Activities & Projects - Graphics & Images - Handouts & References - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - PD Courses - Study Guides - Unit Plans - Instructional Videos - Performance Tasks - Graphic Organizers - Writing Prompts - Constructed Response Items - AP Test Preps - Lesson Planet Articles - Online Courses - Interactive Whiteboards - Home Letters - Unknown Types - Stock Footages - News Clips - All Resource Types - Show All See similar resources: Measuring Shadows Using an Ancient MethodLesson Planet: Curated OER How did ancient peoples determine the height of really tall objects? Young scientists and mathematicians explore the concept of using shadows to measure height in a hands-on experiment. Paired pupils measure shadows, then calculate the... 8th - 12th Math Measuring UpLesson Planet: Curated OER Teach the basics of measurement and conversion with a five-lesson resource that builds an understanding of proportion and measurement conversion from elementary through high school. Initially, young scholars use ratios to determine soup... K - 12th Math CCSS: Designed General Construction Measurement and DimensionsLesson Planet: Curated OER Learners construct their understanding of measurement and dimensions in this step-by-step approach that begins with an all group vocabulary introduction, consisting of measuring objects and dialoging using measurement vocabulary.... 6th - 9th Math CCSS: Adaptable MeasurementLesson Planet: Curated OER Build a basic understanding of units of measure and create a great foundation for your learners. The lesson gives a complete overview of everything measurement, from types of measurement to rounding to conversions — it has it all! 8th - 11th Math CCSS: Adaptable Measuring LengthLesson Planet: Curated OER Your young forensic scientists add to and strengthen their measurement and conversion skills with these seven well-scaffold worksheets. Metric conversions, measuring length, area, and volume, reading thermometers, graduated cylinders,... 5th - 12th Math CCSS: Adaptable Find Radian Measure by Dividing Arc Length by RadiusLesson Planet: Curated OER In an approach that meshes higher-level thinking with approachable methods, this presentation walks that fine line between mathematical rigor and applications with skill. Not only are the specific steps for finding the radian measure of... 6 mins 9th - 12th Math CCSS: Designed Measuring Instruments for Physics-METER RULERLesson Planet: Curated OER Unfortunately a portion of the beginning of this video is cut off. Close up views of how to use a metric ruler are displayed. Percentage error is mentioned. If you have a large class, this may provide a more practical way to demonstrate... 3 mins 7th - 12th Science Radian Measure of AnglesLesson Planet: Curated OER Degrees are not the only way to measure an angle! The third lesson in a four-part series introduces the definition of a radian. The problem videos use the definition to solve problems including converting between degrees and radian and... 21 mins 10th - 12th Math CCSS: Adaptable Radian Measure: Unit Circle ConversionsLesson Planet: Curated OER Individuals investigate the relationship between radian and angle measurements by using an interactive to find the angle measurement for given radian measures. Users answer questions to convert between the two measurements. 10th - 12th Math Problem Solving Plan, Mental Math: The Perfect Lemonade 1Lesson Planet: Curated OER Find the perfect amount of water for lemonade. Scholars solve the famous problem of measuring four liters of water using a three-liter container and a five-liter container. An interactive allows users to see each step of the solution. 7th - 10th Math

<urn:uuid:9cdfe472-5141-412e-befa-b2307dd8f9f2>

What is Social-Emotional Learning (SEL)? Social-emotional learning (SEL) is the process through which children and adults understand and manage emotions, set, and achieve positive goals, feel and show empathy for others, establish and maintain positive relationships, and make responsible decisions. SEL is vital because it helps individuals succeed in school, work, and life. Research has shown that SEL programs can improve academic performance, reduce disciplinary issues, and increase social skills and emotional intelligence. There are many ways to incorporate SEL into the classroom, including: Teaching social skills: This can be done through role-playing, group activities, and direct instruction. Fostering a positive classroom culture: Creating a positive and supportive classroom climate can help students feel safe and valued, improving their overall well-being and academic performance. Encouraging empathy: Teaching students to identify and understand the emotions of others can help them develop strong relationships and become more compassionate individuals. Providing opportunities for decision-making: Giving students the opportunity to make their own decisions can help them develop problem-solving skills and feel more invested in their own learning. Implementing SEL in the classroom can have long-term benefits for both students and teachers. In addition to improving academic performance, SEL can help students develop the skills they need to form healthy relationships and make responsible decisions throughout their lives. It can also create a more positive and supportive classroom environment, increasing teacher job satisfaction. Overall, SEL is a vital component of education that can help students succeed in school and in life. By teaching social and emotional skills, educators can give students the tools they need to navigate the challenges of the modern world and lead fulfilling, meaningful lives. PLEASE FOLLOW AND LIKE US:

<urn:uuid:851ab35d-a20e-4d3b-a35b-bfd0bd159ae3>

Teaching a child boundaries can be done in a variety of ways: - Lead by example: Children often learn by example, so it’s important to model healthy boundaries in your own behavior and interactions with others. - Communicate clearly: Clearly communicate the boundaries and explain the reasons behind them. Use age-appropriate language and examples that the child can understand. - Use positive reinforcement: Reward children when they respect boundaries and consequences when they don’t. - Encourage them to express themselves: Encourage children to express their feelings and needs in a respectful manner, and teach them how to set boundaries themselves. - Teach them to respect others boundaries: Teach children to respect other people’s boundaries, including physical boundaries, personal space, and privacy. - Show them the importance of boundaries: Explain to children why boundaries are important for their safety, well-being and the well-being of others. - Set clear rules and consequences: Set clear rules and consequences for breaking boundaries, and enforce them consistently. - Be consistent: Be consistent in enforcing boundaries and following through with the consequences. It’s important to remember that boundaries are an ongoing process and that it’s important to make it an ongoing conversation in your household. It’s also important to adapt the boundaries as the child grows and develops.

<urn:uuid:a6faaafe-df8f-45c8-b464-26a3831099ba>

Every child has a right to education regardless of economic class, personal challenges, academic abilities, or any other peculiarity. Every child needs a supportive learning environment that encourages academic achievement, intellectual confidence and personal growth. In education parlance, this concept is referred to as inclusion. Inclusive learning provides all students with access to flexible learning choices and effective paths for achieving educational goals in spaces where they experience a sense of belonging. In an inclusive education environment, all children, regardless of abilities or challenges, learn together in the same age-appropriate classroom. It is based on the understanding that all children and families are valued equally and deserve access to the same opportunities. Inclusive educational practice provides opportunities for all young people to learn together by removing learning barriers. It also addresses the issues that concern all individuals who are vulnerable to exclusion from education. One of the most important principles of inclusive education is that no two learners are alike, and so inclusive schools place great importance on creating opportunities for students to learn and be assessed in a variety of ways. How can schools foster inclusion? Excellence in teaching and learning - Ensure that the educators have the proper training, flexibility and enough resources to teach students with diverse needs and learning styles. Teachers must also establish and implement more effective instructional practices. Promote A Positive Learning Climate - A positive climate can affect students’ learning and engagement in a good way. It is helpful to provide a welcoming atmosphere to all students regardless of their ethnicities, socio-economic backgrounds or educational preparedness. As teachers build a personal connection with their students, it can increase class participation and enthusiasm. Having a supportive environment motivates students to perform better. Embrace Students’ Diversity - It is essential to value and embrace diversity in ethnicity, religion, gender, sexual orientation, backgrounds and even academic readiness. Failing to do so can negatively affect a student’s progress. Therefore, everyone must develop cultural competence and sensitivity to promote inclusion in school. Encourage Student Interactions - Students would more likely persist if they feel academically and socially connected to their school. To support the institution’s student engagement efforts, teachers and staff should provide opportunities for students to meet and get to know each other better. By letting the students have thoughtful interactions and conversations with people from different backgrounds and life experiences, it makes them more aware of their environment. Inclusive Education Strategies To introduce an inclusive education environment into your classroom means challenging and upsetting the status quo, removing curriculum barriers and presenting educational goals in interesting ways to engage all learners and serve all students equitably. There are four important strategies for educators to consider when designing an inclusive classroom. Use universal design principles Universal Design Principles (UDP) is a set of principles that were born from the desire to offer every student an equal opportunity to learn, based on the idea that every person has their own unique and individual learning preference. According to UDP, there are three primary brain networks that are responsible for how a person learns: the recognition network, the strategic network and the affective network. The three main principles of UDP — Representation (the what of learning), Action and Expression (the how of learning), Engagement (the why of learning) — were formed based on these three brain networks. Understanding the foundation of UDP — the principles and brain networks — is imperative for teachers who wish to implement UDP in the classroom. Use a variety of instructional formats The first principle of universal design theory is the “what” of learning. It says to use “multiple means of representation.” While some students are visual learners, others may grasp information better when it is presented through text or when it is spoken orally or taught through kinaesthetic learning. Some students do best with a combination of the above. While these differentiated teaching methods may support the needs of students with disabilities, they also offer diversity of instruction to the entire classroom, giving each and every student an opportunity to learn in the way they do best. Similarly, using different mediums to present information and engage students is important in inclusive classrooms. Remember that principle two of universal design theory calls for utilising “multiple means of action and expression.” Some students may find that their best outlet and means of expression comes through writing, while others may prefer to give an oral presentation, act out a play or create a piece of art. Each student is different and should be given the opportunity to express their knowledge through the methods that work best for them. Additionally, teachers can use a diversity of materials and mediums to engage students. Examples of mediums could include theatre, art, video and computer software in addition to the traditional mediums of lecture and text. Through using varied teaching techniques and mediums, teachers can increase the engagement of their entire class, not just the students who respond to a particular style of learning and expression. Know your students’ Individual education plans (IEPs) To create an equitable learning environment for everyone, it is important to familiarise yourself with students’ IEP. If you have a student with an IEP plan, you are legally required to make any necessary accommodations as outlined in the IEP. You can work with the school counsellor or teaching specialists to better understand the student’s specific needs. Much like the concept of inclusive learning, IEPs were designed to ensure that students with disabilities are allowed to learn in a regular classroom environment, while still being provided with services, educational aids or accommodations they may require. Students with an IEP may require additional educational services outside of the regular classroom. These services are typically provided and monitored by additional support staff (like counsellors and mentors). Develop a behaviour management plan Disruptive classroom behaviour can affect not just the teacher, but the other students in the classroom as well. Developing a behaviour management plan can help you prepare for the inevitable moment a student or students exhibit disruptive behaviours — with the understanding that some behaviours are of much less consequence than others (talking out of turn vs. being defiant or aggressive). The behaviour plan should be shared with parents and students, so that everyone is aware of the expectations and consequences should those expectations not be met. The most effective plans typically involve a great deal of positive reinforcement and a clear understanding of the expectations. There are several different types of behaviour management plans you can implement depending on the needs of your classroom, including a whole group plan, a small group plan, an individual plan or an individual plan designed for particularly challenging students. How is it done in other jurisdictions and which lessons can we pick? Unique to Dwight School Seoul in South Korea, is the Quest Programme, identifying each student’s learning styles and capabilities in order to provide a supportive environment for targeted study tailored to maximize academic potential and enhance the skills of gifted students. Delivered at the helm of innovation and technology by experienced and respected professionals, the Quest Programme falls in line with the school’s ambition to provide personalized learning, on top of a diverse community and a unique, global vision. As a culturally-rich community that represents more than 38 nationalities, the school undoubtedly reflects and promotes the very essence of education inclusion. Here, students have access to the guidance they need to mould their dreams into reality, with a Learn-by-Doing approach that gives students the power to design a fulfilling and thriving future. In a hyperconnected world, Dwight’s inclusive atmosphere gives students the foundational skills needed to succeed in 21st century. The Hokkaido International School (HIS) in Japan wholeheartedly believes that education should represent so much more than just books. Here, the process of learning is making and applying connections between knowledge, skills and understandings through inquiry-based, collaborative and experiential instruction. From the start of the Early Years multi-age programme, children learn and explore through a series of activities designed to develop their confidence, character and expertise, all while reaping the benefits of studying in an inclusive learning environment. In Elementary and Middle School, HIS follows the International Primary Curriculum and the International Middle Years Curriculum, specifically developed to meet the learning needs of both age groups. The school also hosts numerous academic and fun activities outside the classroom for students, parents and teachers, allowing them to make new friends and interact with students from a diverse range of age groups, countries and cultures. The education process at the International Community School (ICS) - Singapore, extends well beyond the limits of traditional curriculum; as a Christian school, the ability to foster a ‘Caring Community’ is one of its core values. The goal is to help students learn to respectfully interact across age, cultural and ethnic boundaries. Faculty and staff work alongside each other to harbour an inclusive sense of community on campus, with many opportunities to engage with the greater Singapore as well. Students are encouraged to participate in a broad range of extra-curricular activities, ranging from bowling to taekwondo, ceramics to typography, kickboxing to percussion, and more. Not only do these activities give children the chance to make friends and become an active member of the community, they also uphold the school’s value to provide a holistic education, with highly-qualified staff on-hand to ensure no child is left out. Throughout their ICS experience, students learn to embrace the “servant-leadership” philosophy, and understand the value of investing in others, and are shaped into active community members within ICS, Singapore, and the wider world. These are lessons we can pick and interpolate to fit our context and realities. But the bottom line for every school, every educator should be; how can each learner get a fair shot at quality education regardless of their economic class, personal challenges, academic abilities, or any other peculiarity?

<urn:uuid:bc8f5e23-9822-48b3-b614-a9d3940f525d>

Matrices are math objects where the numbers are organized into a nice rectangular array of rows and columns. They are useful to learn because we can turn a system of equations into matrix form. We can manipulate matrices more easily than a collection of equations. To get you on the right track, we will look at matrices in this video lesson, their proper notation, their allowed math operations, and how to tell when two matrices are equal to each other. To begin, we look at the proper notation for matrices. Look at this properly written matrix: Proper notation for matrices Our numbers are arranged in neat rows and columns. Surrounding our matrix are square brackets. These square brackets tell us that this particular group of numbers belongs together in one matrix. We can also label our matrix by calling it matrix A. If we have labeled our matrix, we can either write out the matrix with all the numbers in it or we can write it using our label surrounded by square brackets. Our matrices are also described by their size. This particular matrix has three rows and three columns, so we can also call it a 3x3 matrix. A matrix with four rows and two columns is a 4x2 matrix. Okay, now that we know what proper matrix notation looks like, let's talk about when two matrices are equal to each other. You know how when two numbers are the same, they are the identical number, like when you have 2 and 2. Well, matrices are similar, but there is just a bit more involved. When two matrices are the same, all the numbers must be the same in the same positions and the matrices must both be the same size. For example, these two matrices are the same: They are both the same size and all the numbers are the same in the same spots. They are both 2x3 matrices. Take a look at these matrices. Are these the same? These matrices are not equal. They are not equal matrices because they are different sizes. Just because two matrices have all the same numbers does not mean they are equal. Their sizes must also be the same. Matrix Addition and Subtraction Let's cover the kinds of math operations we can do. We can do addition and subtraction. Matrix addition and subtraction is the same as number addition and subtraction. We add or subtract number by number. Because we have to match our number to number, our two matrices must be the same size, like this: Matrices must be the same size to add or subtract. We matched the numbers together. We matched the number in the first row and first column in the first matrix to the number in the first row and first column in the second matrix and so on. We can't add or subtract two matrices that are different sizes. We can however add or subtract the same number to all the numbers in a matrix. Adding the same number to all the matrix numbers We perform subtraction in the same way as addition. The two matrices must be the same size and we subtract number to number, matching the location of the numbers together. We can also subtract the same number from all the numbers in a matrix. The last math operation we can do is matrix multiplication. There is no such thing as matrix division. Matrix multiplication is more complicated than number multiplication. You can easily multiply 3 and 5 to make 15. But with matrices, when we multiply two matrices together, we have to use a combination of multiplication and addition. Also, the number of columns in the first matrix must match the number of rows in the second matrix. So, we can multiply a 1x3 matrix with a 3x2 matrix, but we can't multiply a 1x3 matrix with a 2x3 matrix. And unlike numbers where the order of multiplication doesn't matter, with matrices, which matrix comes first matters. Let's look at how we multiply two matrices together: Multiplication with matrices To multiply these two matrices, what we do is we match rows in the first matrix to columns in the second matrix. We then take each pair of numbers one by one, multiplying as we go, and then adding all the products together in the end. So for our matrices, we take the first row in the first matrix and match it up with the first column in the second matrix. This will give us the number in the first row and first column in the answer matrix. We match the 1 to the 0 and the 2 with the 2. We multiply 1 with the 0, the 2 with the 2, then add it all up. We have 1(0) + 2(2) = 0 + 4 = 4. The number in the first row and first column in the answer matrix is 4. We have two columns in the second matrix, so we need to match the first row to the second column as well. We need to match each row in the first matrix to each column in the second matrix. Matching the first row in the first column to the second column in the second matrix gives us the number in the first row and second column in the answer matrix. Matching the numbers again we have: 1(1) + 2(3) = 1 + 6 = 7. Now that we've matched the first row in the first matrix to every column in the second matrix, we now move on to the second row in the first matrix. And we do the same, matching it to every column in the second matrix. The number in the second row and first column in the answer matrix is: 3(0) + 5(2) = 0 + 10 = 10. The number in the second row and second column in the answer matrix is: 3(1) + 5(3) = 3 + 15 = 18. Our final answer is this matrix: Final multiplication answer As you can see, matrix multiplication is just a bit different than number multiplication. Remember that you are matching the rows in the first matrix to columns in the second matrix. We multiply the pairs of numbers and then we add them all up. We can also simply multiply all the numbers in a matrix by one number. In this case, every number in the matrix is multiplied by the same number. Let's review what we've learned now. Matrices are math objects where the numbers are organized into a nice rectangular array of rows and columns. We label them with either a letter surrounded by square brackets or by their size, such as a 3x2 matrix, which tells us that there are three rows and two columns. We can do addition, subtraction, and multiplication to matrices. For addition and subtraction, the matrices must be the same size, and we simply add and subtract the numbers that are in matching locations in the two matrices. For matrix multiplication, we match each row in the first matrix to each column in the second matrix. We multiply each pair of numbers and then add them all up. Watch and rewatch this lesson on matrices to be certain you can: - Provide the definition of matrices - Identify proper matrix notation - Determine when matrices are equal - Add, subtract and multiply matrices

<urn:uuid:2613c4c6-aa1e-4b79-ba31-7ada376d5c2e>