-

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

2 7 0

The Grade 4 students are hold ing an Activit ies

Day to celebrate the arrival of spring.

In the Egg Race, the winner is the person w h o

puts the most plastic eggs into the cartons.

Here are some results.

Name Carton Filled

Penny H 12

Maria 11 12

Brady 7 12

• What does the fract ion j j 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.

S h o w a n d S h a r e 2 x 6 5 x 6 -,_ , .. . , ^ 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?

2 7 2 LESSON F O C U S 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

A fraction is a number, jq is a proper fraction. It represents an amount less than 1 whole.

4 is the numerator.

It tells how many

eajjajjpajts are cojunted.

Practice J

1. Write a fraction to tell what part of each quilt is striped.

a) I i III —

i i i —

[

b) c)

2 7 3

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?

2 7 4 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.

S h o w a n d S h a r e

Talk with your partner about the fractions.

Which fraction is closest to 0? Closest to j l Closest to 1 ?

2 3 7 3 8 8

1 5 1 6 6 8

Connect J

Closer Closer Closer toO to i

j is closer to 1.

j$ is closer to j.

It is a little less than y.

is closer to 0.

LESSON F O C U S I Use 0, ^ and 1 as reference points for fractions. 2 7 5

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.

Write two different fractions close to 0.

Use paper strips to show which fraction

is closer to 0.

Number Strategies

Estimate each sum.

59 + 72 24 + 86 373 + 109 281+410

Which strategies did you use?

2 7 6 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.

S h o w a n d S h a r e

Talk to your partner about your strategy.

How did you know how many equal groups to make?

3 8

of 16 3 8

4 5 4 5

of 10

LESSON F O C U S I Represent fractions of a set using materials, pictures, and symbols. 277

ConnectJ ft Fractions can show

equal parts of a set. O O S 5 of 6 . 2 |

j o ( of 6 = 4

of 6 = 6

^ 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) ^ o f 8

s 2. a) j o f 1 2

v/ 3. a) § of 16

b) 4 of 8

b) | of 12

b) 10 of 20

c) | of 8

c) | of 12

c) f o f 1 2

Your World

Scientists say we spend ^ of our lives sleeping.

About how many years have you spent sleeping?

2 7 8

i

4. Draw a picture to show the fraction of each set.

a) | of 10

5. Find:

a) \ of 10

b) | of 16

b) | of 12

c) 4 of 10

c) y o f 5

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?

Explain why both pictures show jq.

» < 4 t A »

* 4

Mental Math

Which numbers of markers can you share equally among

\ 6 friends?

\ 10 15 18 20 24

How do you know?

ASSESSMENT FOCUS I Question 7 2 7 9

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?

S h o w and S h a r e

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.

2 8 0 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.

2 8 2 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.

S h o w a n d S h a r e

Share your pictures with another pair of students.

What fractions in your pictures name the same amount?

Fractions that name the same amount are called equivalent fractions.

ConnectJ

4 4 4 4

Here are some more equivalent fractions.

1 . 3 > ^ and f are

equivalent fractions. 9 9 9 9 9 9 9 9 9

§ 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.

--3

6.

a) l a n d 5

10 b) f and f c) T and

SJ How many different ways can you show that

j and ^ are equivalent fractions?

Show your work.

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.

d) y a n d

Write two equivalent fractions.

Use pictures to show how you know

the fractions are equivalent.

Number Strategies

Estimate each difference.

87-36 81-38 352- 148 351-152

Which strategies did you use?

2 8 4 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.

S h o w a n d S h a r e

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. 2 8 5

Connect J

Brianna arranged 8 blue Pattern Blocks.

Her arrangement shows

thirds of : I

It also shows two whole

plus 2 thirds: 2 f

f and 2 f name the same amount.

f is an improper fraction.

It shows an amount greater than 1 whole.

2y is a mixed number.

It has a whole number part andI ajraction part.

I say f wo and

wo-fhmds.

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)

2 8 6

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 2 8 7

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

<hnd T

j and |

T and 4-

2 j a n d l f l l a n d 2\

S h o w a n d S h a r e

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.

2 8 8 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 A V - J Tenths are J Q 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,

bu t - ^ -<^ r ,

so, 2JQ < 2JQ.

• From least to greatest: 1 4 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 ^ o r 1 ^ c) l i o r i f

3. Make pictures to show which is greater.

a) b) | o r i c) i o r i

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_ 1JL 10 1 10

_8_ 10

1 7 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.

a) A 11 JL 9/ 9 / 9

K \ I i O H i l l 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.

Choose two different fractions.

Draw pictures to show a friend

how to compare them.

Ivan te. fdy \ lk Fay va. Ari Fay va. £leo

2 + rioor$ j ^ r hour*

Vt Home

Look in the kitchen, the bathroom, or the laundry area. Where do you and your family use fractions at home?