- model, compare, and order fractions and mixed numbers explore and model tenths and hundredths as decimals compare and order decimals add and subtract decimals add and subtract money 270
The Grade 4 students are holding an Activities Day to celebrate the arrival of spring. In the Egg Race, the winner is the person who puts the most plastic eggs into the cartons. Here are some results. Name Penny Maria Brady Carton Filled H 12 11 12 7 12 What does the fraction jj mean? Where have you seen fractions like those in the table? How were they used? What are some questions you can ask about the Egg Race? tenths numerator denominator proper fraction equivalent fractions improper fraction mixed number decimal decimal point hundred hhs
Fractions of a Whole Pioneers made quilts from scraps of material sewn together. Square pieces are easy to fit together. xplore J You will need Colour Tiles or congruent squares, and 1 -cm grid paper. Design a quilt that uses squares of at least 3 colours. Record your quilt on grid paper. Use fractions to describe your quilt. Show and Share 2x6 5x6 -,_,..., ^ 7 X 6 4 X 6 Trade quilts with your partner. Describe your partner's quilt using words and fractions. How did you know which fractions to use? 272 LESSON FOCUS I Represent fractions of a whole using materials, pictures, and symbols.
Connect J Fractions name equal parts of a whole. / CA 2 equal parts are halves. j or one-half is blue. 4 equal parts are fpjujlhs. f or two-fourths are green. 10 equal parts are tenths. jo or four-tenths are red. IQ of the rectangle are red. ^ of the rectangle are white ^ 10 is the denominator. It tells how many equal parts are *~ j Q 4 is the numerator. It tells how many eajjajjpajts are cojunted. A fraction is a number, jq is a proper fraction. It represents an amount less than 1 whole. Practice J 1. Write a fraction to tell what part of each quilt is striped. a) i [ I i III ii b) c) 273
v/ 2. Use coloured squares to show each fraction. Record your work on grid paper. a) b) jo c) one-eighth d) five-fifths J 3. About what fraction is left? / S. Does this diagram show f? Explain. 6. Use grid paper. Design a place mat by colouring squares in a rectangle. Use fractions to describe your place mat design. 7. Nadia shares her square brownie with Tran. Here are two ways to cut the brownie. Are the pieces the same size? Show your work. Use pictures, words, or numbers to explain the fraction f. Physical Education A volleyball court is divided into 2 equal parts. What other sports are played on an area that is divided into equal parts? 274 ASSESSMENT FOCUS I Question 7
Fraction Benchmarks Explore J You will need 6 paper strips the same length as this strip. > Fold and colour a paper strip to show -f. Line up your strip with the strip above. Is j closer to 0,^,or 1? > Estimate if each fraction in the box is closer to 0,j,or 1. Use paper strips to check your estimates. Record your findings in a table. 2 3 7 3 8 8 1 5 1 6 6 8 Closer Closer Closer too toi Show and Share Talk with your partner about the fractions. Which fraction is closest to 0? Closest to jl Closest to 1? Connect J j is closer to 1. j$ is closer to j. It is a little less than y. is closer to 0. LESSON FOCUS I Use 0, ^ and 1 as reference points for fractions. 275
Practice J \ Is the fraction of juice left in each glass closer to 0, \, or 1? a) =9 b) c) d) 2. Is the fraction of eggs in each carton closer to 0, \, or 1? How do you know? C) 3. Name a fraction between \ and 1, but closer to 1. Draw a picture to show the fraction. Tell how you chose which fraction to draw. 4. Gary poured a little more than \ a glass of milk. Name a fraction that might tell how much milk that is. Number Strategies Write two different fractions close to 0. Use paper strips to show which fraction is closer to 0. Estimate each sum. 59 + 72 24 + 86 373 + 109 281+410 Which strategies did you use? 276 ASSESSMENT FOCUS I Question 3
Fractions of a Set Explore J You will need 25 two-colour counters 8 fraction cards You will use the counters to model a fraction of a set. > Shuffle the cards. Put them face down in a pile. > Take turns. One person takes a fraction card. Do not show the card. > Count out the counters you need to match your card. Place all the counters red side up. Turn some groups of counters yellow side up to show your fraction. > Have your partner tell you the fraction. > Continue until you have used all the cards. 3 8 of 16 4 5 of 10 Show and Share Talk to your partner about your strategy. How did you know how many equal groups to make? LESSON FOCUS I Represent fractions of a set using materials, pictures, and symbols. 277
ft ConnectJ Fractions can show equal parts of a set. O O S 5 of 6. 2 j o ( of 6 = 6 of 6 = 4 ^ Here is a way to find f of 10. The denominator tells us we are counting fifths. Divide 10 counters into 5 equal groups to show fifths. 3 3 3 ) ) ) 1 1 1 1 1 5 5 5 5 5 of 10 = 2 of 10 = 6 Practice J Use counters in questions 1 to 3. Find the fraction of each set. / 1. a) ^of8 s 2. a) jof12 b) 4 of 8 b) of 12 c) of 8 c) of 12 v/ 3. a) of 16 b) 10 of 20 c) fof12 Your World Scientists say we spend ^ of our lives sleeping. About how many years have you spent sleeping? 278 i
4. Draw a picture to show the fraction of each set. a) of 10 b) of 16 c) 4 of 10 5. Find: a) \ of 10 b) of 12 c) yof5 6. Print your first name. Use fractions to describe the letters in your name. The pie shop sold 16 pies. One-half of them were apple pies. One-fourth of them were blueberry pies. How many pies were not apple or blueberry? Show your work. 8. 5 is 4 of a set. How many are in the set? 9. There are 10 boys in a class. Two-fifths of the class are boys. How many students are in the class? How do you know? Mental Math Explain why both pictures show jq. Which numbers of markers can you share equally among \ 6 friends?» < 4 t A» \ 10 15 18 20 24 * 4 How do you know? ASSESSMENT FOCUS I Question 7 279
Explore J Nawar had 24 stickers. He kept \ of the stickers and divided the rest equally among his 5 friends. How many stickers did each friend receive? Show and Share Describe how you solved this problem. Connect J Kalpana had 40 prizes to award at the school fair. She put \ of the prizes in the raffle. She divided the rest equally among the 6 races. How many prizes were there for each race? What do you know? There are 40 prizes. The raffle used \ of the 40 prizes. The rest of the prizes were for the winners of the 6 races. Think of a strategy to help you solve the problem. You can use a model. Use counters to represent the prizes. Make a table. Use a model. Draw a picture. Solve a simpler problem. Work backward. Guess and check. Make an organized list. Use a pattern. 280 LESSON FOCUS I Interpret a problem and select an appropriate strategy.
How many counters will you start with? Remove the counters for the raffle. How many counters are left? Arrange them to show the prizes for the 6 races. How many prizes are there for each race? How could you solve this problem another way? Try it, and use your answer to check your work. Practice J Choose 1. Gabriella bought 20 batteries. She put 2 batteries in her radio. Her 3 brothers divided the rest equally. How many did each brother receive? 2. Ms. Logan had gel pens to award after BINGO. She gave 4 to Tip, and said that he had \ of them. How many gel pens did Ms. Logan have to start? 3. Mabel coloured a rectangular sheet of paper \ purple, \ blue, and the rest yellow. What fraction of the paper is yellow? How can counters help you solve fraction problems? Use words, pictures, or numbers to explain.
You will need Cuisenaire rods or strips of coloured paper. > Use the orange rod to represent 1 whole. Line up other rods beneath the orange rod to show fractions of 1 whole. Do this in as many ways as you can. Draw a picture to record your work. 282 LESSON FOCUS! Explore equivalent fractions.
> Label the orange rod 1 whole. Label each of the other rods with a fraction. > Repeat the activity using the brown rod as 1 whole. Show and Share Share your pictures with another pair of students. What fractions in your pictures name the same amount? ConnectJ Fractions that name the same amount are called equivalent fractions. 4 4 4 4 Here are some more equivalent fractions. 9 9 9 9 9 9 9 9 9 1. 3 > ^ and f are equivalent fractions. and f are equivalent fractions.
Practice J 1. Use the dark green rod as 1 whole. Use other rods to find equivalent fractions. Draw a picture to record your work. y 2. Use rods or paper strips. Find an equivalent fraction for each fraction. a) j b) \ c) \ d) e) f f) V 3. Write an equivalent fraction to name the coloured part of each figure. 4. Draw pictures to show that the fractions in each pair are equivalent. a) land 5 10 b) f and f c) T and d) yand --3 SJ How many different ways can you show that j and ^ are equivalent fractions? Show your work. 6. Roxanne cut a pizza into 8 equal slices. She ate 2 slices. a) Write two equivalent fractions to describe how much pizza Roxanne ate. b) Write two equivalent fractions to describe how much pizza was left. Number Strategies Estimate each difference. Write two equivalent fractions. Use pictures to show how you know the fractions are equivalent. 87-36 81-38 352-148 351-152 Which strategies did you use? 284 ASSESSMENT FOCUS i Question 5
More than One There is more than 1 whole sandwich on this plate. There are 5 quarter pieces of sandwich. How would you describe how much sandwich there is? Explore J You will need Pattern Blocks and triangular grid paper Use Pattern Blocks to show fractions greater than 1 whole. Use the yellow Pattern Block as 1 whole. > Take a handful of another colour of Pattern Blocks. Arrange the blocks to show how many yellow hexagons you could cover. Name the amount in different ways. Record your work on grid paper. > Repeat the activity with another colour of Pattern Blocks. Show and Share Share your work with another pair of students. Did you draw the same pictures? Explain. Which names did you use? LESSON FOCUS I Use improper fractions and mixed numbers to represent more than one. 285
Connect J Brianna arranged 8 blue Pattern Blocks. Her arrangement shows It also shows two whole thirds of : I plus 2 thirds: 2f f and 2f name the same amount. f is an improper fraction. It shows an amount greater than 1 whole. 2y is a mixed number. I say f wo and wo-fhmds. It has a whole number part andi ajraction part. Practice j 1. Describe each picture in two different ways, a) b) c) Calculator Skills The [6] key on your calculator is broken. How can you solve each problem? 132-16 12 x 6 d) 286
2. Match each improper fraction with a mixed number. Use Pattern Blocks or draw pictures to show why each match is correct. 5 9 7 4 3. The Fernandez family drank 3j bottles of juice on a picnic. Draw pictures to show the amount, and then write this mixed number as an improper fraction. Show your work. 4. Sarah and Brian used 4^ sheets of paper to cover two boxes for a project. a) Write the mixed number as an improper fraction. b) What are some ways they may have divided the 4j sheets of paper for the two boxes? 5. Casey was making pancakes by the dozen. - t Casey's family ate 2 j dozen pancakes. J How many pancakes did they eat? Show your work. 6. Suppose you have only a y-cup measuring cup. How many times would you have to fill it to measure 2y cups of sugar? Explain how you know. Explain why 1 y and f show the same amount. ASSESSMENT FOCUS I Question 5 287
Comparing and Ordering Fractions Explore J Use Pattern Blocks to explore ways to compare fractions. Use the yellow Pattern Block as 1 whole. Which number in each pair is greater? j and J and j T and 4- <hnd T 2jandlf lland 2\ Show and Share With your partner, talk about the ideas you used to choose your answers. Record your work. Mental Math There are 30 students and 4 different activity centres. Can an equal number of students go to each centre? Explain how you know. 288 LESSON FOCUS i Compare and order fractions.
Connect j > When different fractions have the same denominator, the parts being counted have the same size. 2 P^-S Tenths are Jo counted. 5 AV-J Tenths are JQ counted. The fewer the parts, the smaller the fraction. So, JQ < JQ > Here is a way to order these mixed numbers from least to greatest: 1 jo is the least, because it is less than 2. Both 2JQ and 2JQ are between 2 and 3, but-^-<^r, so, 2JQ < 2JQ. From least to greatest: 14 24 2^ You can make pictures to check your thinking. ' 10 MO 10 > When different fractions have the same numerator, the parts have different sizes. To compare \ and \, think about sharing 1 whole. One-fourth gives you a bigger piece. So, j > \ Practice J 1. Look at each pair of figures. Compare the fraction parts that are shaded. Write a fraction sentence using <, >, or =.
Make pictures to show which is greater. a) 6 or 6 b) 2^or1^ c) lior if 3. Make pictures to show which is greater. a) b) ori c) iori 4. jthis number line is divided into tenths. Which number below is closest to 1? Closest to 0? Use the number line to help you. J_ 10 1JL 1 10 _8_ 10 17 10 1 1 10 z 10 Show how you know. 5. Which pair of students had the longest chess game? Which had the shortest game? 6. Order these numbers from greatest to least. ^ Ivan te. fdy Fay va. Ari Fay va. leo \ lk 2+ rioor$ j^r hour* a) A 11 JL 9/ 9 / 9 K\ Ii OH ill D 15/ ^ 15, I 15 \ i 3 4 1 5 c) 1 y, 7, 1 y 7. When can j give you a bigger piece than y? Draw diagrams to explain. Vt Home Choose two different fractions. Draw pictures to show a friend how to compare them. Look in the kitchen, the bathroom, or the laundry area. Where do you and your family use fractions at home?