15.04.2015 |
## Number for names numerology |

Special 20% Discount on our downloadable worksheet subscription plan, offer valid till Jan 31 2016. Noah has unseated Jacob to become the new Number 1 name for boys – the first new top boys’ choice of the 21st century. The girls’ Top 10 is comparatively stable, with Sophia and Emma maintaining their status of Number 1 and Number 2. Olivia and Isabella switched places at 3 and 4, while Mia moved up and the traditional Emily and Abigail slid down.

The most popular baby names of 2012 are officially here, with Sophia and Jacob holding onto their Number 1 spots. Jacob remains the most popular name for boys for the 14th year in a row. An Old Testament name that means “supplanter” and a cousin of James, Jacob has been in the Top Ten for nearly two decades. The Social Security Administration announced the 2012 Most Popular Baby Names on their website this afternoon. Students will learn to use the half and a quarter inch markings on their rulers: to take measurements down to half or quarter inches, to record their data appropriately, and to represent that data on line plots. Once youa€™ve gone through what theya€™ve learned about fractions, tell them that this lesson we arena€™t going to learn anything new about fractions.

They are likely to begin by rounding up or down, so when you get your first data points youa€™ll want to challenge that and ask them to be more specific.

Teacher: This fork I just drew here is a little over one inch long, but if I want to be exact, I have to look at the little markings on the ruler.

Teacher: Yes, the shaded area is half of the area between one and two, so this mark here is the half mark. When they have a good grasp of these chalkboard measurements, go back to the thumb problem and list the middle finger measurements they give you.

When youa€™ve got the list down, draw a line plot on the board (a number line) and place an x to represent each childa€™s thumb measurement. Erase the board, draw a second line plot, and have the children measure their pencils, then take turns coming up to he front, noting down their measurement, and filling out an x on the graph. For instance, to make number lines like those in the worksheet you can use our Number Line Maker : it creates custom number lines as images you can download.

Many 2nd graders and early 3rd graders will consider fractions and whole numbers to be entirely different animals.

But third grade is the time when children come to terms with the continuity between fractions and whole numbers.

This lesson also builds on the concept of ordering fractions, a topic that is introduced in a previous MathWarehouse lesson. That students would be comfortable relating fractions and whole numbers, going from fractions to whole numbers and back again. Draw a half circle on the board, and ask your student if they can tell you some of its names. Now tell your students you have a very long list of numbers; suggest you put them all on a numberline. This is, in a way, a trick question; because the way the question is set up assumes that the names are separate numbers and will go to different points. If no one objects to the graphing of the a€?numbersa€™ give chalk to three or four volunteers and divide the list up between them, asking them to mark each of those numbers on the number line.

It is important that you give them the time they need to discover the locations of these a€?cognates of 1a€™ on the number line, by whatever circuitous route they take. When your volunteer discoverers have come to the conclusion that every one of the a€?numbersa€™ is one, follow up on the concept of equivalence.

If your students have immediate suggestions, begin writing them down, illustrating with dividing lines drawn through your circles to allow any slower students to follow. Give each student a copy of the Number Names worksheet, and encourage them to make their list of names for 3 and 4 as long as they can. This nextA part of thisA lesson plan can be taught as a separate lesson if your students go slowly through the whole number section. Ask them what went wrong in their thinking; orA why the method they used for comparing parts of snicker bars didna€™t work for comparing parts of cake. Let them know, though, that when they see fractions without designation in math problems, they may assume they are referring to identical wholes unless told differently. This is only the beginning: your students need to cement their understanding of ordering and comparing fractions by doing lots of games and exercises. What does it mean when a fraction is the same as another, and what does it mean when it is different? This 3rdA grade lesson plan will give students the tools they need to understand A the concepts of same and different A applied to fractions. Ita€™s important that you introduce this topic with real world, dynamic, easily understandable examples rather than with mathematical equations and manipulations.

Students will understand that two fractions are equivalent if they are the same size, or the same point on a number line. InviteA any students who point out one or the other as wrong to explain why it is wrong, using the picture flashcards and comparing sizes.

If any students have suggestions, invite them to come up and demonstrate equivalence on the board with pictures. Hand out the remaining card sets, and ask the students to match the number cards to the visual cards and then order all the cards by portion size, from smallest to largest. The beautiful flashcards A your students used in this lesson are made with the help of Mathwarehousea€™s nifty Visual Fraction applet. Thata€™s all they need to learn today, but you want them to know it backwards, forwards, and inside-out.

Three types of stickers (ideally, small stars in red, yellow, or green; but other simple colored stickers can substitute). If he doesna€™t, or if the idea still seem counterintuitive to many of your students, go back to the idea of distance.

Then have the children help you move tables and chairs to the back, so that you have a large empty space to work. They will soon discover that after theya€™ve been called once future calls are easier, as they will have marked off some (maybe all) of their fractions on the number line. Throughout the game, continue to interweave your class objectives with the game by asking at intervals, randomly, but of every student at least once: How far did you jump?

This lesson plan gives youA A one fun way of making fractions come alive, but ita€™s best to approach every topic from multiple angles. Up to this point fractions have simply been discrete portions of tangible wholes; real parts that can be felt, seen, and tested. Tell your students that theya€™ve become so good at identifying and dealing with fractionsa€”portions of pie, pizza, or apples and orangesa€”that today they can take what theya€™ve learned to a whole new sphere. Then ask them if there are other things they could divide in half, things they cana€™t touch, feel, or cut with a sharp knife. Validate each addition to the list as you write it down, and then tell them that today youa€™re going to look at fractions of three special things: portions of time, space, and mathematical units. Draw a diagram of your day on the blackboard; essentially, a number line that describes your day. Tell your students that the area between waking up and lunch is your morning; and then shade the first half, and tell them it is half your morning. Now erase everything from the blackboard and draw a simple number line going from zero to three.

Take a strip of paper exactly as long as the distance between zero and one; fold it in half, lay it on the number line from 0 to A?, and draw your a€?half pizzaa€™ dot.

Here are some links to helpful web resources that mightA help your students learn to enjoy fractions. Tell your students that youa€™re not going to do much regular math today; today is going to be a fun day. When theya€™ve got it, tell them they have, and tell them youa€™re proud of the speed with which they can fold.

Tell them that another special thing about secret codes is that theya€™re often short and concise, allowing their writers to put a lot of information in a very little space.

Then tell them that there are people called mathematicians who decided what the main secret code was going to be for math, and youa€™ll tell them that secret. If you have any volunteers, have them come up to the blackboard try out their ideas, and explain them to the class. Pass out the flashcards, and tell the students that when you display your secret code flashcard you want them to pick up and show you the equivalent pie flashcard, without looking at any of their classmates. Tell them that when soldiers or intelligence agents use secret codes in war, it is very important that every member of the team is able to do his part well and convey the message without losing any of the meaning. Give them five minutes to review the secret code together, and tell the leaders they are responsible for making sure every member of the team understands how to write and decipher the secret code of fractions. To avoid bad feelings and loser mentality, you can let the other team continue working till theya€™ve got the message passed down correctly also, and offer them a consolation prize or a€?silver medal finalistsa€™ headbands. Tell your students they have learned something incredibly useful today; a secret code with which they can communicate with other math people all over the world. Don’t forget to encourage them toA practiceA this special code A any chance they get. Our graphing units in third grade used to be focused primarily on circle graphs (pie charts), but under the Common Core, bar charts are given a new prominence. But just because bar charts are taking center stage , doesn’t mean we can stop teaching pie charts altogether. To understand a pie chart (circle graph) and to be able to deduce information about the relative size of the parts shown in it. Paper cutouts: a large circle cut out of thick white paper, and A?, A?, and \( A frac{1}{8} \) sectors of circles cut out of different colors of construction paper.

Cover half of your circle up with your A? circle construction paper cut out, and ask how much of the circle is colored now. Ask half the class to hold up their hands; the front half, the back half, or the side half.

Go on to \( frac{1}{8}\), introducing it the same way with your \( frac{1}{8}\)A construction paper sector. Now tell them the class was made up of twenty students, and ask them how many students liked blue.

At this point you dona€™t want to focus on the nitty grittya€”for instance, it would be counterproductive to divide your circle into sixteen, twenty, or thirty equal portionsa€”as many portions as you have students in your classa€”and make an exact circle graph by coloring in the appropriate number of sectors. When your students have all created their own graphs have them take turns explaining what they drew and what different sectors mean.

These exercises should give your students a new familiarity with and perspective on fractions, as well as A opening the doors to understandingA data representation with pie charts. In third grade we get to liven up our bar chart lessons by taking advantage of our studentsa€™ new familiarity with multiplication and division. In this 3rd grade bar chart lesson, students will learn to analyze and understand data presented on a scaled bar chart.

Once upon a time, far away, in the wild open steppe land of Mongolia, two children lived with their old grandfather and grandmother in a little round tent made of felt. Click the worksheet preview for the full printable version of Number Words 1-20 Worksheets A-B.

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Palmer Notation For Numbering Teeth: Palmer's notation is a widely used method to designate individual teeth.

Quadrants: The four parts of your mouth, that is the upper left, the upper right, the lower left, and the lower right. Numerical Notation For Teeth: The numerical notation for teeth is an alternate to Palmer's notation.

Universal or International Numerical Notation For Teeth: The universal or international numerical notation is the most common numerical notation for teeth used by general dentists in the United States.

This website is designed to give you more accurate information on dental malpractice issues.

This will also provide students with a visual representation of what fractions mean in real life.

Since this space (point out the space between 1 and 2) is one inch long, how much is this space? So if I have a little tiny pencil that reaches just to here (draw your pencil on the board) ita€™ll be exactly 1 A? inch long. Then draw a number of objects along your chalkboard ruler and get the students to label the lengths.

Ask them to start by measuring all the items in their desk and writing them down on a list. Show the data by making a line plot, where the horizontal scale is marked off in appropriate unitsa€” whole numbers, halves, or quarters.

Youa€™ll find a large bank of high quality free lesson plans, all aligned with the common core, and a variety of helpful tools to make teaching easier. That there are fractions which are simply a€?namesa€™ of whole numbers will surprise some of your students, but it will be a good surprise that can open the doors into future ease in fractional manipulation.

That they would also gain familiarity in ordering fractions and comparing the sizes of any fractions that have either the same numerator or the same denominator. Encourage your students to continue mentally dividing the filled circle to create more fractions.

Draw a large numberline on the board and write on designations from one to ten, leaving room for continued expansion on the right. If your students are awake and used to thinking through problems rather than parroting answers you should have at least one willing to challenge your statement: pointing out that the list is not a list of numbers, but a list of names of one single number. They may stare at the board confusedly, they may begin marking the integers they see on the numerators, they may try to do fancy calculations, or they may all dash for the point a€?1a€™.

They will learn much more by making mistakes and following through to the dead ends that followa€”and then rethinking the problem and finding the right answera€”then they would if they were given the correct interpretation straight off. Ask if these numbers are really one and the same quantity, or if each is just a little bit different. Write 2 on the board, draw two circles, fully shaded, and tell your students a€?This is 2, and this is its name, 2. If there are no suggestions, ask your students what would happen if you divide each circle in half. If they have difficulty keeping track of multiple lines on their strawberry cakes, encourage them to draw their own sets of three or four circles and make the divisions on separate pictures. Remember, going slowly is not necessarily a bad thing; it may mean your students really are taking the time to think things through and really cementing these concepts in their minds.

Tell your students these are portions of two differentA regular sized snickers bar at your house, and ask them which is larger.

Bring them to observe that you can only compare fractions if they refer to identical wholes. A Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Through visual ordering exercises your students will become adept at recognizing fractions that are the same, and by the end of todaya€™s session they should be able to make up their own simple lists of equivalent fractions. They will be able to explain why fractions are equivalent, and will be able to recognize and make up lists of simple equivalent fractions. Pass out the folding paper, and have your students fold fractionsa€”as fast as possible; first one done is the winnera€”as you call them out. Help any who have had trouble, encouraging them to look at the picture cards and compare relative sizes.

Draw on the board the visual circle fractions, and demonstrate how the two parts are exactly the same. Let them think about and discuss this, and then demonstrate how each portion will have an infinite number of names, because you can always divide the existing pieces each in half again to get twice the amount of smaller pieces. Suggest they show equivalence by placing equivalent fractions at the same level in their orderings. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. This applet is a really fun way to generate classroom graphics, and also an enjoyable way for students who might be having difficulty visualizing fractions to see pizza portions generated before their eyes as they type in the fractions they are curious about. Since therea€™s no better way to get to that point than with a fun de-stressing game, youa€™ll do this by gettingA your students up out of their chairs A for a rousing game of a€?hopscotch fractionsa€™.

These can also be prepared by taping standard printing paper end to end and drawing the number lines with markers, using rulers for uniformity. Remind the students that we talked about what fractions of abstract numbers mean, and we learned that they work in exactly the same way as fractions of tangible, concrete things like apples.

Give them permission to discuss it with their neighbors, then ask for a volunteer to come and demonstrate it on the board. If a gym or other large empty room is available, you may want to move there for the rest of this class. Each number line will have four children manning it, so youa€™ll need to have as many number lines as the number of children in your class divided by four.

Give each student a strip of colored paper the size of one unit on their floor number lines.

It helps organization if you give all students representing a particular fraction the same color. They will do this with the strips of paper, folding them into appropriate sections as they did in yesterdaya€™s lesson, and using those sections as rulers.

The caller (you, if there wasna€™t an extra student) stands at the front of the room with a pile of full-sized shuffled a€?hopscotch flashcardsa€™. A Since they are using their colored markers, it will be easy to tell their intervals versus their team-mates. Thata€™s why Ia€™m recommending Mathwarehousea€™s wonderful fraction resources again— after all, theya€™re all free!

This third grade lesson plan, though, marks a water shed: we get to transfer our knowledge of a€?half a cookiea€™ to the more abstract concept of half a unit on a number line. Tell them that it is an apple; you can feel it, you can measure it with a ruler, and you can divide it into two equal parts with a sharp knife. Ask what it means when we say a€?half an houra€™, and get as many versions of the answer as possible. At this point, though, dona€™t describe it as a a€?number linea€™ to your students.A A PutA sitting up in bed, the first thing you do in the morning, away on the far left side of your diagram. If the morning was four hours long, from eight to twelve, and you were feeling miserable half the morning, ask them how long you were feeling miserable. Talk about the distance between the bed and the lunch table in your drawing, and what half of it means. Put your chalk at zero, write a small dot, and test the students on basic number line usage: Here, you see, I have no pizza. If someone suggests dividing the portion of the number line between zero and one in two parts and making a dot on the middle line, tell him you really like that idea. Since it is A?, ask them if it means A? wherever you place it on the number linea€”do you have to begin measuring off at zero, or can you start somewhere else instead? Anything to do with secret writing, dangerous espionage and top-secret missions brings up the energy in the room several points. Taught right, though, with just the right amount of fun mixed in, third grade fractions can be just as exciting as a top-secret mission in dangerous territory with a good dose of secret codes mixed in. Therea€™s no reason to make fractions dry book learning; let them be a game, a a€?break from the hard stuffa€™. That they would learn to work as a team, helping the weakest members in order to gain united success. Go on to explain that instead of doing regular arithmetic and adding or dividing (or whatever yesterdaya€™s topic was) youa€™re going to learn something really cool: a secret code that theya€™ll be able to use to write important math messages with. Tell them now theya€™ve done their work, so now ita€™s time to go on to secret codes and the new game.

Give them a chance to talk about what they know; the final thought you want to come up witha€”and you can just state it yourself if no-one has similar thoughtsa€”is that a secret code is a way of giving information to onea€™s friends in a way that onea€™s enemies cana€™t understand. After a few minutes, ask whoever has an idea to come forward and draw it on the blackboard.

After theya€™ve had a chance to express their ideas, show them how they can read it as a€?one of two equal partsa€™, and that the number on the bottom is the number of parts youa€™ve divided the whole in; the top, the number of those pieces you have. Then draw another circle on the blackboard, divide in four quarters, color one quarter, and write the word a€?quartera€™ next to it.

Validate each idea, and if anyone writes A?, tell him that he was thinking in exactly the same way as the mathematicians were. Go through your cards in random order at least twice; more if some students are having difficulty.

Divide the class in two teams, each with a team leader who has a good grasp of what youa€™ve been teaching. Ask what happens if one of the people passing on a message forgets the secret code (the message is lost). The game will be conducted like telephone; youa€™ll give the leader of each team a picture with six circles, each divided into different fractions with different parts shaded. You may want to walk up and down the lines checking the work; your responsibility is not to make sure they are doing it correctly, but just that the a€?secret codea€™ writers are not writing circles and the circle drawers are not writing code.

Bar charts are intuitively easy to understand for second and third graders, and since they build on and are closely connected to the number line, they follow logically from the other math your students are doing. While bar charts make comparing the relative size of parts a simple visual exercise, pie charts offer intuitively obvious visual comparisons between parts and the whole. After the students have answered, tell them that since the whole circle meant to you a whole of anything a€“ a whole class, a whole country, a whole bag of skittlesa€”the colored sections mean, to you, half of anything. Then tell them that you could use this circle to show how many children had their hands up; the colored section would be the children with their hands up, and the white section would be the other children. Then ask which of the three explicitly listed colors the least amount of children seem like. Ask whether fewer or more than six students have green for their favorite color, and whether or not five students have purple for a favorite color. Suggest they group the smaller amounts together under a€?othera€™; in the example above, this would be red, purple and yellow,A totalingA four. Instead, you want to focus on getting an intuitive sense of the size of different fractions. By the end of third grade, the Common Core recommends that students know from memory all products of two one digit numbers. They will learn how to do both simple and multi-step comparing problems using the bar chart.

Math and imaginative thinking go well together, and starting a new math topic with an imaginative exercise means youa€™ll have the attention not only of your technically minded, mathy children but also of those who love their English but usually a€?turn offa€™ when they come into your classroom. Their little tent was alone on the steppeland; for as far as they could see to the east, west, north and south there was nothing but waving grasses and wooded hills.

These worksheets provide practice in number and number word recognition as well as fine motor skills.

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In Palmer's notation, your mouth is divided into four parts called quadrants, that is the upper left quadrant, the upper right quadrant, the lower left quadrant, and the lower right quadrant as illustrated in the figure on the right. For example, the central on the upper right side of your mouth is called an upper right central. In this notation, the centrals are designated as 1's, the laterals as 2's, the cuspids as 3's, the first bicuspids as 4's, the second bicuspid's as 5's, etc. Here we look at a combination of measuringa€”an exciting hands on subject for most gradeschoolers- with a real-life application of fractions. Pencils, erasers, notebooks, textbooks and pencil cases are some of the items that might be measured and recorded.

Your aim is that they would be able to tell you on sight which is the greatest of two fractions, given either a similar denominator or a similar numerator. If anyone makes this objection, ask him or her to get up and demonstrate this to the class. Give them the time they need to think through the problem and make mistakes, and only call a halt on the project once they tell you they have the numbers all marked.

The circuitous, labored path will also cement the final concept in their minds in a way youa€™d never have been able to teach if you were the prime mover. Agree with them that they are all equivalent; all different names of the same absolute point.

Allow them to take it from there, and write their list of the a€?names of twoa€™ on the blackboard. Bring them to observe that the fewer pieces you divide something in, the larger the pieces are; and a third is larger than a fourth. Since the snicker bars are somewhere elseA and that isna€™t possible, you can also check by drawing diagrams, being careful to make neat thirds and quarters. Observe this is more difficult to compare by looking at the numbers because neither the numerator or denominator are the same, but ask them if they can rename A? into something else.

Although your students have discovered informally that the slab of pie represented by those two fractions— and the point on the number linea€”looks, feels, and acts the same, they still need to take this one step further and realize that these two fractions are actually one and the same quantity.

Find two students who have chosen different orderings, and give them the scrabble tile holders. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Games have a way bringing book learning from the a€?theoreticala€™ category into a€?real lifea€™, and this one is no exception. Before the game is halfway done, you should have no measuring at all; just quick, sure hopping when a new fraction is called. Remind them you can do the same with pizza, and with almost any physical object, provided your knife is sharp enough. If no-one suggests it, tell them that one way of thinking about it is as half the distance from one hour to the other. If I buy two pizzasa€”one peperoni and one sausagea€”where would I show that on the number line?

Get feedback as to why or why not before you explain that since A? is just half of one, and you have no a€?wholesa€™ to add it to, you always have to start on zero when you measure its placement. And that if they learn it well, theya€™ll be able to use it right away, in an exciting game that they can play in the classroom. Ask what a third is (one of three equal parts) and how many thirds are in a whole (3); then go on to fourths. Provide chalk for each child, and have them write down their secret codes.A A Ask whoever has a unique notation to explain their secret code and why they chose it to the class.

Tell them that the team that wins will get whatever prize youa€™ve prepared, or get the honor of wearing a€?winning teama€™ headbands for the rest of the week in school. Tell the teams that the same thing will happen if one of their members musses up or forgets the code: they will lose all chance of winning. Theya€™ll a€?translate thisa€™ on to their missive sheet, writing in matha€™s secret codes. Teaching circle graphs also enables our students to practice fractions in a fun, easy-to-grasp way. Give them some time to discuss what a circle means to them, and validate their feelings and opinions as they share them. They will probably be ready with the right answer; if anyone is unsure, show that A? is half of a half, and that four quarters cover the whole circle.

Ask if four students might have purple for a favorite color, and then whether two might have liked purple best. Then start with the color most children like, and ask what fraction of the total number of children like that color. Your students will A do this by relating the fractions they are unsure ofa€”how much is \(frac{5}{16}\), anyway? Ask them how the graphs would change if one child changed his favorite color– for instance, if Madeline decided she preferred blue or Jordan switched to green.

By the time you schedule your bar chart lesson, your students should be comfortable doing skip counting by twos, threes, fives or tens; and that means they shouldna€™t have any difficulty interpreting a scaled bar chart. No worksheet or portion thereof is to be hosted on, uploaded to, or stored on any other web site, blog, forum, file sharing, computer, file storage device, etc. The concepts presented here are simple and your students shouldna€™t have much trouble with them, but, done right, they will provide an invaluable intuitive understanding of fractional parts. Take time to elucidate any concepts they are hazy on; this is your chance to get everyone started on the same page. Discuss how it is a list that can go on forever, because you can always divide every portion into smaller and smaller portions. Then, give appropriate feedback: if theya€™ve marked it correctly, tell them so, and ask them to explain to the rest of the class why all those points are one point. Each name is just as true and accurate as any other, and no name is bigger or smaller than any other name. Note that since the numerators are the same, the denominators will tell which is larger; and the smaller the denominator, the larger the portion.

Suggest they draw a diagram of A?, and divide each portion in half again to find the a€?new namea€™. Introduced with fancy manipulation, fractions become a complicated numerical puzzle that will leave many of your students feeling confused and helpless.

Ask them to match the cards to the pie pictures, and then to order both sets according to size, smallest to largest. Ask them to place their numerical cards carefully on the tile holder, then go to the front of the room and display their ordering to the class.

These strips are their a€?shoesa€™, and theya€™ll be needed again and again throughout the game. Immediately the students representing that fraction take their a€?shoea€™ a€“ the paper stripa€”mark off the appropriate number of intervals, and then jump, once in each interval, to the fraction marker.

Walk four steps away from your desk, counting as you go, and ask how many steps it is to your desk.

We get to use the same number line, in exactly the same way, whether wea€™re talking about cookies, pizza, time, or distance.

But I wasna€™t feeling very hungry and didna€™t have much spare money, so I only bought half. If they have forgotten any of this or it seems even a little rusty, give them a bit of a refresher.

Ask them whether they have any guesses as to how you would write it in matha€™s secret code. These opinions can be as simple as a€?pizza!a€™ or as abstruse as a€?unendinga€™; there is no one answer. Ask a quarter of the class to raise their hands; you will probably have to mark off the demarcation lines for the quarter. Then ask them what would happen to the graph if your class was merged with another third grade class of the same size, and all the children in that class liked yellow best. For example, the two upper and two lower teeth at the center of your mouth are called central's. In fact, this lesson might be considered a foundation stone for future work in three important fields: measurement, fractions, and data representation on line plots.

The numbers on the top and bottom of your fractionsa€”always the samea€”will just keep on getting larger and larger and larger, and there is no end. If they have marked the a€?numbersa€™ on separate points, ask them to demonstrate their a€?orderingsa€™ with pictures. Bring them to observe that if the denominators are the same, the fraction with the larger number in the numerator is larger.

When demonstrated with visual examples, though, equivalent fractions will speedilyA seem intuitive to your students; nothing less than common sense. If they do not come up with their own examples, remind them of a common acquaintancea€”the principal, perhaps, who is called Mr.

Continue with other volunteers and other fractions until your students are comfortable with the idea.

Ask how many steps you would need to walk if you wanted to walk only half the way back to the desk (2). Give them each a rectangle and as you call out a€?half!a€™ a€?quarter!a€™ or a€?third!a€™ have them race to fold it and display the portion you called. If they are not correct and the other team has not yet won, he can walk down his line, checking the papers, and find where the mistake began.

When they have all had a chance to share how they feel about it,A explain that to you, since it is a whole, entire circle, it can mean a a€?wholea€™ of anythinga€”a whole class of children, a whole country, a whole family, a whole bag of skittles. Tell them that if the whole white circleA representsA the class, that construction paper quarter is the part of the class with their hands up. In this case \( frac{4}{16} = frac{1}{4} \) which is a nice solid quarter, and the \(frac{1}{16}\)A it goes over is less than \(frac{1}{8}\), which is a fat sliver. This is because the identical denominator means the pieces are the same size, and the larger numerator means you have more pieces. Each student will be called on the same number of times, but students with smaller fractions will have to do more counting and hopping.

The first three to successfully measure and jumpA are awarded stickers on their fraction nametags: red for the first to hop to place, yellow for the second, and green for the third. If he corrects that mistake, the message begins again at that person and is passed on again down the line until it comes to the end. Have the students color a generous quarter on their circles, and go on to the next color: in this graph, blue, \( frac{4}{16} \) or exactly \(frac{1}{4} \)A of a circle. Point out that the man these names this refers to is the same, no matter what name he is called, and that all of these names belong to him equally.

The most popular baby names of 2012 are officially here, with Sophia and Jacob holding onto their Number 1 spots. Jacob remains the most popular name for boys for the 14th year in a row. An Old Testament name that means “supplanter” and a cousin of James, Jacob has been in the Top Ten for nearly two decades. The Social Security Administration announced the 2012 Most Popular Baby Names on their website this afternoon. Students will learn to use the half and a quarter inch markings on their rulers: to take measurements down to half or quarter inches, to record their data appropriately, and to represent that data on line plots. Once youa€™ve gone through what theya€™ve learned about fractions, tell them that this lesson we arena€™t going to learn anything new about fractions.

They are likely to begin by rounding up or down, so when you get your first data points youa€™ll want to challenge that and ask them to be more specific.

Teacher: This fork I just drew here is a little over one inch long, but if I want to be exact, I have to look at the little markings on the ruler.

Teacher: Yes, the shaded area is half of the area between one and two, so this mark here is the half mark. When they have a good grasp of these chalkboard measurements, go back to the thumb problem and list the middle finger measurements they give you.

When youa€™ve got the list down, draw a line plot on the board (a number line) and place an x to represent each childa€™s thumb measurement. Erase the board, draw a second line plot, and have the children measure their pencils, then take turns coming up to he front, noting down their measurement, and filling out an x on the graph. For instance, to make number lines like those in the worksheet you can use our Number Line Maker : it creates custom number lines as images you can download.

Many 2nd graders and early 3rd graders will consider fractions and whole numbers to be entirely different animals.

But third grade is the time when children come to terms with the continuity between fractions and whole numbers.

This lesson also builds on the concept of ordering fractions, a topic that is introduced in a previous MathWarehouse lesson. That students would be comfortable relating fractions and whole numbers, going from fractions to whole numbers and back again. Draw a half circle on the board, and ask your student if they can tell you some of its names. Now tell your students you have a very long list of numbers; suggest you put them all on a numberline. This is, in a way, a trick question; because the way the question is set up assumes that the names are separate numbers and will go to different points. If no one objects to the graphing of the a€?numbersa€™ give chalk to three or four volunteers and divide the list up between them, asking them to mark each of those numbers on the number line.

It is important that you give them the time they need to discover the locations of these a€?cognates of 1a€™ on the number line, by whatever circuitous route they take. When your volunteer discoverers have come to the conclusion that every one of the a€?numbersa€™ is one, follow up on the concept of equivalence.

If your students have immediate suggestions, begin writing them down, illustrating with dividing lines drawn through your circles to allow any slower students to follow. Give each student a copy of the Number Names worksheet, and encourage them to make their list of names for 3 and 4 as long as they can. This nextA part of thisA lesson plan can be taught as a separate lesson if your students go slowly through the whole number section. Ask them what went wrong in their thinking; orA why the method they used for comparing parts of snicker bars didna€™t work for comparing parts of cake. Let them know, though, that when they see fractions without designation in math problems, they may assume they are referring to identical wholes unless told differently. This is only the beginning: your students need to cement their understanding of ordering and comparing fractions by doing lots of games and exercises. What does it mean when a fraction is the same as another, and what does it mean when it is different? This 3rdA grade lesson plan will give students the tools they need to understand A the concepts of same and different A applied to fractions. Ita€™s important that you introduce this topic with real world, dynamic, easily understandable examples rather than with mathematical equations and manipulations.

Students will understand that two fractions are equivalent if they are the same size, or the same point on a number line. InviteA any students who point out one or the other as wrong to explain why it is wrong, using the picture flashcards and comparing sizes.

If any students have suggestions, invite them to come up and demonstrate equivalence on the board with pictures. Hand out the remaining card sets, and ask the students to match the number cards to the visual cards and then order all the cards by portion size, from smallest to largest. The beautiful flashcards A your students used in this lesson are made with the help of Mathwarehousea€™s nifty Visual Fraction applet. Thata€™s all they need to learn today, but you want them to know it backwards, forwards, and inside-out.

Three types of stickers (ideally, small stars in red, yellow, or green; but other simple colored stickers can substitute). If he doesna€™t, or if the idea still seem counterintuitive to many of your students, go back to the idea of distance.

Then have the children help you move tables and chairs to the back, so that you have a large empty space to work. They will soon discover that after theya€™ve been called once future calls are easier, as they will have marked off some (maybe all) of their fractions on the number line. Throughout the game, continue to interweave your class objectives with the game by asking at intervals, randomly, but of every student at least once: How far did you jump?

This lesson plan gives youA A one fun way of making fractions come alive, but ita€™s best to approach every topic from multiple angles. Up to this point fractions have simply been discrete portions of tangible wholes; real parts that can be felt, seen, and tested. Tell your students that theya€™ve become so good at identifying and dealing with fractionsa€”portions of pie, pizza, or apples and orangesa€”that today they can take what theya€™ve learned to a whole new sphere. Then ask them if there are other things they could divide in half, things they cana€™t touch, feel, or cut with a sharp knife. Validate each addition to the list as you write it down, and then tell them that today youa€™re going to look at fractions of three special things: portions of time, space, and mathematical units. Draw a diagram of your day on the blackboard; essentially, a number line that describes your day. Tell your students that the area between waking up and lunch is your morning; and then shade the first half, and tell them it is half your morning. Now erase everything from the blackboard and draw a simple number line going from zero to three.

Take a strip of paper exactly as long as the distance between zero and one; fold it in half, lay it on the number line from 0 to A?, and draw your a€?half pizzaa€™ dot.

Here are some links to helpful web resources that mightA help your students learn to enjoy fractions. Tell your students that youa€™re not going to do much regular math today; today is going to be a fun day. When theya€™ve got it, tell them they have, and tell them youa€™re proud of the speed with which they can fold.

Tell them that another special thing about secret codes is that theya€™re often short and concise, allowing their writers to put a lot of information in a very little space.

Then tell them that there are people called mathematicians who decided what the main secret code was going to be for math, and youa€™ll tell them that secret. If you have any volunteers, have them come up to the blackboard try out their ideas, and explain them to the class. Pass out the flashcards, and tell the students that when you display your secret code flashcard you want them to pick up and show you the equivalent pie flashcard, without looking at any of their classmates. Tell them that when soldiers or intelligence agents use secret codes in war, it is very important that every member of the team is able to do his part well and convey the message without losing any of the meaning. Give them five minutes to review the secret code together, and tell the leaders they are responsible for making sure every member of the team understands how to write and decipher the secret code of fractions. To avoid bad feelings and loser mentality, you can let the other team continue working till theya€™ve got the message passed down correctly also, and offer them a consolation prize or a€?silver medal finalistsa€™ headbands. Tell your students they have learned something incredibly useful today; a secret code with which they can communicate with other math people all over the world. Don’t forget to encourage them toA practiceA this special code A any chance they get. Our graphing units in third grade used to be focused primarily on circle graphs (pie charts), but under the Common Core, bar charts are given a new prominence. But just because bar charts are taking center stage , doesn’t mean we can stop teaching pie charts altogether. To understand a pie chart (circle graph) and to be able to deduce information about the relative size of the parts shown in it. Paper cutouts: a large circle cut out of thick white paper, and A?, A?, and \( A frac{1}{8} \) sectors of circles cut out of different colors of construction paper.

Cover half of your circle up with your A? circle construction paper cut out, and ask how much of the circle is colored now. Ask half the class to hold up their hands; the front half, the back half, or the side half.

Go on to \( frac{1}{8}\), introducing it the same way with your \( frac{1}{8}\)A construction paper sector. Now tell them the class was made up of twenty students, and ask them how many students liked blue.

At this point you dona€™t want to focus on the nitty grittya€”for instance, it would be counterproductive to divide your circle into sixteen, twenty, or thirty equal portionsa€”as many portions as you have students in your classa€”and make an exact circle graph by coloring in the appropriate number of sectors. When your students have all created their own graphs have them take turns explaining what they drew and what different sectors mean.

These exercises should give your students a new familiarity with and perspective on fractions, as well as A opening the doors to understandingA data representation with pie charts. In third grade we get to liven up our bar chart lessons by taking advantage of our studentsa€™ new familiarity with multiplication and division. In this 3rd grade bar chart lesson, students will learn to analyze and understand data presented on a scaled bar chart.

Once upon a time, far away, in the wild open steppe land of Mongolia, two children lived with their old grandfather and grandmother in a little round tent made of felt. Click the worksheet preview for the full printable version of Number Words 1-20 Worksheets A-B.

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Palmer Notation For Numbering Teeth: Palmer's notation is a widely used method to designate individual teeth.

Quadrants: The four parts of your mouth, that is the upper left, the upper right, the lower left, and the lower right. Numerical Notation For Teeth: The numerical notation for teeth is an alternate to Palmer's notation.

Universal or International Numerical Notation For Teeth: The universal or international numerical notation is the most common numerical notation for teeth used by general dentists in the United States.

This website is designed to give you more accurate information on dental malpractice issues.

This will also provide students with a visual representation of what fractions mean in real life.

Since this space (point out the space between 1 and 2) is one inch long, how much is this space? So if I have a little tiny pencil that reaches just to here (draw your pencil on the board) ita€™ll be exactly 1 A? inch long. Then draw a number of objects along your chalkboard ruler and get the students to label the lengths.

Ask them to start by measuring all the items in their desk and writing them down on a list. Show the data by making a line plot, where the horizontal scale is marked off in appropriate unitsa€” whole numbers, halves, or quarters.

Youa€™ll find a large bank of high quality free lesson plans, all aligned with the common core, and a variety of helpful tools to make teaching easier. That there are fractions which are simply a€?namesa€™ of whole numbers will surprise some of your students, but it will be a good surprise that can open the doors into future ease in fractional manipulation.

That they would also gain familiarity in ordering fractions and comparing the sizes of any fractions that have either the same numerator or the same denominator. Encourage your students to continue mentally dividing the filled circle to create more fractions.

Draw a large numberline on the board and write on designations from one to ten, leaving room for continued expansion on the right. If your students are awake and used to thinking through problems rather than parroting answers you should have at least one willing to challenge your statement: pointing out that the list is not a list of numbers, but a list of names of one single number. They may stare at the board confusedly, they may begin marking the integers they see on the numerators, they may try to do fancy calculations, or they may all dash for the point a€?1a€™.

They will learn much more by making mistakes and following through to the dead ends that followa€”and then rethinking the problem and finding the right answera€”then they would if they were given the correct interpretation straight off. Ask if these numbers are really one and the same quantity, or if each is just a little bit different. Write 2 on the board, draw two circles, fully shaded, and tell your students a€?This is 2, and this is its name, 2. If there are no suggestions, ask your students what would happen if you divide each circle in half. If they have difficulty keeping track of multiple lines on their strawberry cakes, encourage them to draw their own sets of three or four circles and make the divisions on separate pictures. Remember, going slowly is not necessarily a bad thing; it may mean your students really are taking the time to think things through and really cementing these concepts in their minds.

Tell your students these are portions of two differentA regular sized snickers bar at your house, and ask them which is larger.

Bring them to observe that you can only compare fractions if they refer to identical wholes. A Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Through visual ordering exercises your students will become adept at recognizing fractions that are the same, and by the end of todaya€™s session they should be able to make up their own simple lists of equivalent fractions. They will be able to explain why fractions are equivalent, and will be able to recognize and make up lists of simple equivalent fractions. Pass out the folding paper, and have your students fold fractionsa€”as fast as possible; first one done is the winnera€”as you call them out. Help any who have had trouble, encouraging them to look at the picture cards and compare relative sizes.

Draw on the board the visual circle fractions, and demonstrate how the two parts are exactly the same. Let them think about and discuss this, and then demonstrate how each portion will have an infinite number of names, because you can always divide the existing pieces each in half again to get twice the amount of smaller pieces. Suggest they show equivalence by placing equivalent fractions at the same level in their orderings. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. This applet is a really fun way to generate classroom graphics, and also an enjoyable way for students who might be having difficulty visualizing fractions to see pizza portions generated before their eyes as they type in the fractions they are curious about. Since therea€™s no better way to get to that point than with a fun de-stressing game, youa€™ll do this by gettingA your students up out of their chairs A for a rousing game of a€?hopscotch fractionsa€™.

These can also be prepared by taping standard printing paper end to end and drawing the number lines with markers, using rulers for uniformity. Remind the students that we talked about what fractions of abstract numbers mean, and we learned that they work in exactly the same way as fractions of tangible, concrete things like apples.

Give them permission to discuss it with their neighbors, then ask for a volunteer to come and demonstrate it on the board. If a gym or other large empty room is available, you may want to move there for the rest of this class. Each number line will have four children manning it, so youa€™ll need to have as many number lines as the number of children in your class divided by four.

Give each student a strip of colored paper the size of one unit on their floor number lines.

It helps organization if you give all students representing a particular fraction the same color. They will do this with the strips of paper, folding them into appropriate sections as they did in yesterdaya€™s lesson, and using those sections as rulers.

The caller (you, if there wasna€™t an extra student) stands at the front of the room with a pile of full-sized shuffled a€?hopscotch flashcardsa€™. A Since they are using their colored markers, it will be easy to tell their intervals versus their team-mates. Thata€™s why Ia€™m recommending Mathwarehousea€™s wonderful fraction resources again— after all, theya€™re all free!

This third grade lesson plan, though, marks a water shed: we get to transfer our knowledge of a€?half a cookiea€™ to the more abstract concept of half a unit on a number line. Tell them that it is an apple; you can feel it, you can measure it with a ruler, and you can divide it into two equal parts with a sharp knife. Ask what it means when we say a€?half an houra€™, and get as many versions of the answer as possible. At this point, though, dona€™t describe it as a a€?number linea€™ to your students.A A PutA sitting up in bed, the first thing you do in the morning, away on the far left side of your diagram. If the morning was four hours long, from eight to twelve, and you were feeling miserable half the morning, ask them how long you were feeling miserable. Talk about the distance between the bed and the lunch table in your drawing, and what half of it means. Put your chalk at zero, write a small dot, and test the students on basic number line usage: Here, you see, I have no pizza. If someone suggests dividing the portion of the number line between zero and one in two parts and making a dot on the middle line, tell him you really like that idea. Since it is A?, ask them if it means A? wherever you place it on the number linea€”do you have to begin measuring off at zero, or can you start somewhere else instead? Anything to do with secret writing, dangerous espionage and top-secret missions brings up the energy in the room several points. Taught right, though, with just the right amount of fun mixed in, third grade fractions can be just as exciting as a top-secret mission in dangerous territory with a good dose of secret codes mixed in. Therea€™s no reason to make fractions dry book learning; let them be a game, a a€?break from the hard stuffa€™. That they would learn to work as a team, helping the weakest members in order to gain united success. Go on to explain that instead of doing regular arithmetic and adding or dividing (or whatever yesterdaya€™s topic was) youa€™re going to learn something really cool: a secret code that theya€™ll be able to use to write important math messages with. Tell them now theya€™ve done their work, so now ita€™s time to go on to secret codes and the new game.

Give them a chance to talk about what they know; the final thought you want to come up witha€”and you can just state it yourself if no-one has similar thoughtsa€”is that a secret code is a way of giving information to onea€™s friends in a way that onea€™s enemies cana€™t understand. After a few minutes, ask whoever has an idea to come forward and draw it on the blackboard.

After theya€™ve had a chance to express their ideas, show them how they can read it as a€?one of two equal partsa€™, and that the number on the bottom is the number of parts youa€™ve divided the whole in; the top, the number of those pieces you have. Then draw another circle on the blackboard, divide in four quarters, color one quarter, and write the word a€?quartera€™ next to it.

Validate each idea, and if anyone writes A?, tell him that he was thinking in exactly the same way as the mathematicians were. Go through your cards in random order at least twice; more if some students are having difficulty.

Divide the class in two teams, each with a team leader who has a good grasp of what youa€™ve been teaching. Ask what happens if one of the people passing on a message forgets the secret code (the message is lost). The game will be conducted like telephone; youa€™ll give the leader of each team a picture with six circles, each divided into different fractions with different parts shaded. You may want to walk up and down the lines checking the work; your responsibility is not to make sure they are doing it correctly, but just that the a€?secret codea€™ writers are not writing circles and the circle drawers are not writing code.

Bar charts are intuitively easy to understand for second and third graders, and since they build on and are closely connected to the number line, they follow logically from the other math your students are doing. While bar charts make comparing the relative size of parts a simple visual exercise, pie charts offer intuitively obvious visual comparisons between parts and the whole. After the students have answered, tell them that since the whole circle meant to you a whole of anything a€“ a whole class, a whole country, a whole bag of skittlesa€”the colored sections mean, to you, half of anything. Then tell them that you could use this circle to show how many children had their hands up; the colored section would be the children with their hands up, and the white section would be the other children. Then ask which of the three explicitly listed colors the least amount of children seem like. Ask whether fewer or more than six students have green for their favorite color, and whether or not five students have purple for a favorite color. Suggest they group the smaller amounts together under a€?othera€™; in the example above, this would be red, purple and yellow,A totalingA four. Instead, you want to focus on getting an intuitive sense of the size of different fractions. By the end of third grade, the Common Core recommends that students know from memory all products of two one digit numbers. They will learn how to do both simple and multi-step comparing problems using the bar chart.

Math and imaginative thinking go well together, and starting a new math topic with an imaginative exercise means youa€™ll have the attention not only of your technically minded, mathy children but also of those who love their English but usually a€?turn offa€™ when they come into your classroom. Their little tent was alone on the steppeland; for as far as they could see to the east, west, north and south there was nothing but waving grasses and wooded hills.

These worksheets provide practice in number and number word recognition as well as fine motor skills.

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In Palmer's notation, your mouth is divided into four parts called quadrants, that is the upper left quadrant, the upper right quadrant, the lower left quadrant, and the lower right quadrant as illustrated in the figure on the right. For example, the central on the upper right side of your mouth is called an upper right central. In this notation, the centrals are designated as 1's, the laterals as 2's, the cuspids as 3's, the first bicuspids as 4's, the second bicuspid's as 5's, etc. Here we look at a combination of measuringa€”an exciting hands on subject for most gradeschoolers- with a real-life application of fractions. Pencils, erasers, notebooks, textbooks and pencil cases are some of the items that might be measured and recorded.

Your aim is that they would be able to tell you on sight which is the greatest of two fractions, given either a similar denominator or a similar numerator. If anyone makes this objection, ask him or her to get up and demonstrate this to the class. Give them the time they need to think through the problem and make mistakes, and only call a halt on the project once they tell you they have the numbers all marked.

The circuitous, labored path will also cement the final concept in their minds in a way youa€™d never have been able to teach if you were the prime mover. Agree with them that they are all equivalent; all different names of the same absolute point.

Allow them to take it from there, and write their list of the a€?names of twoa€™ on the blackboard. Bring them to observe that the fewer pieces you divide something in, the larger the pieces are; and a third is larger than a fourth. Since the snicker bars are somewhere elseA and that isna€™t possible, you can also check by drawing diagrams, being careful to make neat thirds and quarters. Observe this is more difficult to compare by looking at the numbers because neither the numerator or denominator are the same, but ask them if they can rename A? into something else.

Although your students have discovered informally that the slab of pie represented by those two fractions— and the point on the number linea€”looks, feels, and acts the same, they still need to take this one step further and realize that these two fractions are actually one and the same quantity.

Find two students who have chosen different orderings, and give them the scrabble tile holders. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Games have a way bringing book learning from the a€?theoreticala€™ category into a€?real lifea€™, and this one is no exception. Before the game is halfway done, you should have no measuring at all; just quick, sure hopping when a new fraction is called. Remind them you can do the same with pizza, and with almost any physical object, provided your knife is sharp enough. If no-one suggests it, tell them that one way of thinking about it is as half the distance from one hour to the other. If I buy two pizzasa€”one peperoni and one sausagea€”where would I show that on the number line?

Get feedback as to why or why not before you explain that since A? is just half of one, and you have no a€?wholesa€™ to add it to, you always have to start on zero when you measure its placement. And that if they learn it well, theya€™ll be able to use it right away, in an exciting game that they can play in the classroom. Ask what a third is (one of three equal parts) and how many thirds are in a whole (3); then go on to fourths. Provide chalk for each child, and have them write down their secret codes.A A Ask whoever has a unique notation to explain their secret code and why they chose it to the class.

Tell them that the team that wins will get whatever prize youa€™ve prepared, or get the honor of wearing a€?winning teama€™ headbands for the rest of the week in school. Tell the teams that the same thing will happen if one of their members musses up or forgets the code: they will lose all chance of winning. Theya€™ll a€?translate thisa€™ on to their missive sheet, writing in matha€™s secret codes. Teaching circle graphs also enables our students to practice fractions in a fun, easy-to-grasp way. Give them some time to discuss what a circle means to them, and validate their feelings and opinions as they share them. They will probably be ready with the right answer; if anyone is unsure, show that A? is half of a half, and that four quarters cover the whole circle.

Ask if four students might have purple for a favorite color, and then whether two might have liked purple best. Then start with the color most children like, and ask what fraction of the total number of children like that color. Your students will A do this by relating the fractions they are unsure ofa€”how much is \(frac{5}{16}\), anyway? Ask them how the graphs would change if one child changed his favorite color– for instance, if Madeline decided she preferred blue or Jordan switched to green.

By the time you schedule your bar chart lesson, your students should be comfortable doing skip counting by twos, threes, fives or tens; and that means they shouldna€™t have any difficulty interpreting a scaled bar chart. No worksheet or portion thereof is to be hosted on, uploaded to, or stored on any other web site, blog, forum, file sharing, computer, file storage device, etc. The concepts presented here are simple and your students shouldna€™t have much trouble with them, but, done right, they will provide an invaluable intuitive understanding of fractional parts. Take time to elucidate any concepts they are hazy on; this is your chance to get everyone started on the same page. Discuss how it is a list that can go on forever, because you can always divide every portion into smaller and smaller portions. Then, give appropriate feedback: if theya€™ve marked it correctly, tell them so, and ask them to explain to the rest of the class why all those points are one point. Each name is just as true and accurate as any other, and no name is bigger or smaller than any other name. Note that since the numerators are the same, the denominators will tell which is larger; and the smaller the denominator, the larger the portion.

Suggest they draw a diagram of A?, and divide each portion in half again to find the a€?new namea€™. Introduced with fancy manipulation, fractions become a complicated numerical puzzle that will leave many of your students feeling confused and helpless.

Ask them to match the cards to the pie pictures, and then to order both sets according to size, smallest to largest. Ask them to place their numerical cards carefully on the tile holder, then go to the front of the room and display their ordering to the class.

These strips are their a€?shoesa€™, and theya€™ll be needed again and again throughout the game. Immediately the students representing that fraction take their a€?shoea€™ a€“ the paper stripa€”mark off the appropriate number of intervals, and then jump, once in each interval, to the fraction marker.

Walk four steps away from your desk, counting as you go, and ask how many steps it is to your desk.

We get to use the same number line, in exactly the same way, whether wea€™re talking about cookies, pizza, time, or distance.

But I wasna€™t feeling very hungry and didna€™t have much spare money, so I only bought half. If they have forgotten any of this or it seems even a little rusty, give them a bit of a refresher.

Ask them whether they have any guesses as to how you would write it in matha€™s secret code. These opinions can be as simple as a€?pizza!a€™ or as abstruse as a€?unendinga€™; there is no one answer. Ask a quarter of the class to raise their hands; you will probably have to mark off the demarcation lines for the quarter. Then ask them what would happen to the graph if your class was merged with another third grade class of the same size, and all the children in that class liked yellow best. For example, the two upper and two lower teeth at the center of your mouth are called central's. In fact, this lesson might be considered a foundation stone for future work in three important fields: measurement, fractions, and data representation on line plots.

The numbers on the top and bottom of your fractionsa€”always the samea€”will just keep on getting larger and larger and larger, and there is no end. If they have marked the a€?numbersa€™ on separate points, ask them to demonstrate their a€?orderingsa€™ with pictures. Bring them to observe that if the denominators are the same, the fraction with the larger number in the numerator is larger.

When demonstrated with visual examples, though, equivalent fractions will speedilyA seem intuitive to your students; nothing less than common sense. If they do not come up with their own examples, remind them of a common acquaintancea€”the principal, perhaps, who is called Mr.

Continue with other volunteers and other fractions until your students are comfortable with the idea.

Ask how many steps you would need to walk if you wanted to walk only half the way back to the desk (2). Give them each a rectangle and as you call out a€?half!a€™ a€?quarter!a€™ or a€?third!a€™ have them race to fold it and display the portion you called. If they are not correct and the other team has not yet won, he can walk down his line, checking the papers, and find where the mistake began.

When they have all had a chance to share how they feel about it,A explain that to you, since it is a whole, entire circle, it can mean a a€?wholea€™ of anythinga€”a whole class of children, a whole country, a whole family, a whole bag of skittles. Tell them that if the whole white circleA representsA the class, that construction paper quarter is the part of the class with their hands up. In this case \( frac{4}{16} = frac{1}{4} \) which is a nice solid quarter, and the \(frac{1}{16}\)A it goes over is less than \(frac{1}{8}\), which is a fat sliver. This is because the identical denominator means the pieces are the same size, and the larger numerator means you have more pieces. Each student will be called on the same number of times, but students with smaller fractions will have to do more counting and hopping.

The first three to successfully measure and jumpA are awarded stickers on their fraction nametags: red for the first to hop to place, yellow for the second, and green for the third. If he corrects that mistake, the message begins again at that person and is passed on again down the line until it comes to the end. Have the students color a generous quarter on their circles, and go on to the next color: in this graph, blue, \( frac{4}{16} \) or exactly \(frac{1}{4} \)A of a circle. Point out that the man these names this refers to is the same, no matter what name he is called, and that all of these names belong to him equally.

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