Matholia Mathematics Primary 3B by Blue Ring Media Pty Ltd

M AT H E M AT I C S Workt ext

for learners 8 - 9 years old

Aligned to the US Common Core State Standards

Matholia Mathematics Matholia Mathematics is a series covering levels K-6 and is fully aligned to the United States Common Core State Standards (USCCSS). Each level consists of two books (Book A and Book B) and combines textbook-style presentation of concepts as well as workbook practice. Central to the USCCSS is the promotion of problem-solving skills and reasoning. Matholia Mathematics achieves this by teaching and presenting concepts through a problem-solving based pedagogy and using the concrete-pictorial-abstract (CPA) approach. Learners acquire knowledge and understanding of concepts through a guided progression beginning with concrete examples and experiences which then flow into pictorial representations and finally mastery at the abstract and symbolic level. This approach ensures that learners develop a fundamental understanding of concepts rather than answering questions by learned procedures and algorithms. Key features of the series include:

Anchor Task

Numbers to 10,000

Anchor Task

Open-ended activities serve as the starting point for understanding new concepts. Learners engage in activities and discussions to form concrete experiences before the concept is formalized.

3 2

Let’s Learn

Concepts are presented in a clear and colorful manner. Worked problems provide learners with guided step-by-step progression through examples. Series mascots provide guidance through helpful comments and observations when new concepts are introduced.

When we take a whole and divide it into equal parts, we get fractions. The whole orange is cut into 2 equal pieces. Each piece is a half which we write as 1 .

Let’s cut an apple

into 4 equal pieces

. Each piece is a quarte r.

2 halves make 1 whole.

1 2

1 whole

half

The numbers of a

1 2

half

fraction have specia l names.

1 2

1 4

1 whole

quarter

1 4

quarter

1 2

The top number is called the numerator.

The bottom numb er is called the denom inator. A half has a numerator of 1. ...and a denominator of 2!

1 4

quarter

1 4

quarter

4 quarters make 1 whole.

Ethan eats 3 pieces of the apple. We say he eats 3 quarte apple. We can write rs of the this as a fraction 3 . 4

1 4

I ate 3 quarters of the apple!

1 4

212

213

Let’s Practice

and her baby A mother elephant of 4,670 kg. have a combined mass of 482 kg The baby has a mass is the mother? How much heavier

Let’s Practice

drive 1,205 km A truck driver has to stops for a to deliver his load. He destination. rest 478 km from his d? How far has he travele

Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment. Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.

Step 1 mother. Find the mass of the ?

478 km trip remaining

trip traveled

–

1,205 km

– The truck driver has 2.

mother

baby

–

km.

traveled

kg.

The mother has a mass

s carnival, At the school athletic 4,675 the red team scored scored points. The blue team more many How 3,858 points. score points did the red team than the blue team?

Step 2 . difference in masses Subtract to find the ? baby

–

mother red team blue team ?

–

kg heavier than her

The mother is

–

more points than the

The red team scored

baby. 139

blue team.

138

(b) Home At 1.

Count the number of different creatu re in the garden. Record your data on the next page.

At Home Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.

Represent your data in the

bar graph below.

Number of Creatu res

14 12 10 8 6

2 0

272

Hands On

do an activity.

Tell your friends the time you

One friends shows the time

time on a clocks. The other friend shows the

Switch roles.

273

using their arms.

Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.

Solve it! Riley spent her summe r vaction in Europe. Complete the division equations and match the letters to find the first city she visited. T

Solve It!

6÷2=

6÷3=

Activities that require learners to apply logical reasoning and problem-solving. Problems are often posed which do not have a routine strategy for solving them. Learners are encouraged to think creatively and apply a range of problem-solving heuristics.

8÷2=

6÷1=

14 ÷ 2 =

15 ÷ 3 =

7 279

Looking Back

Looking Back Find the area of each figure in square (b) (a)

Find the perimeter of the figure. 9m

12 m

units.

11 m 11 m

11 m 10 m

Consolidated practice where learners demonstrate their understanding on a range of concepts taught within a unit.

Area =

square units.

17 m

square units. Perimeter =

(d)

(c)

Find the area and perimeter of each

figure. 1 cm 1 cm

Area =

square units. Area =

Find the area of the rectangles. (b) (a) 12 cm

square units.

10 m

4 cm 5m

Area =

Perimeter =

Area = Area =

191

190

iii

Contents 6 Division (2)

2 3 9 15 21 27

7 Measurement

40 40 49 61 73

8 Time

84 84 102

9 Geometry

128 129 138

10 Area and Perimeter

146 147 154 169 176 188

Dividing by 6 Dividing by 7 Dividing by 8 Dividing by 9 Word Problems Introduction to Measuring Mass Measuring Mass in Kilograms and Grams Measuring Volume Mass and Volume Word Problems Telling Time to the Minute Duration of Time Recognizing Quadrilaterals Drawing Quadrilaterals Introduction to Area Measuring Area Area of Rectangles Introduction to Perimeter Area and Perimeter

11 Fractions

200 200 218 236 244 252

12 Data and Graphs

264 264 276 282 288

Equal Parts Parts of a Whole Fractions on a Number Line Comparing Fractions Equivalent Fractions Picture Graphs With Scales Bar Graphs With Scales Reading and Interpreting Bar Graphs Generate Data for Line Plots

Division (2)

Anchor Task

Dividing by 6 Let’s Learn There are 18 strawberries. The strawberries are divided into equal groups. How many strawberries are in each group? How many groups of strawberries are there?

18 ÷ 6 = 3 There are 6 groups of strawberries. There are 3 strawberries in each group.

18 ÷ 3 = 6 There are 3 groups of strawberries. There are 6 strawberries in each group. 3

There are 42 blocks. The blocks are divided into equal groups. How many blocks are in each group? How many groups of blocks are there?

42 ÷ 6 = 7 42 ÷ 7 = 6 There are 6 groups of blocks. There are 7 groups of blocks. There are 7 blocks in each group. There are 6 blocks in each group.

Let’s Practice 1. The balloons are grouped in 6s. Fill in the blanks.

(a) There are

groups of

balloons.

(b) Complete the division equation.

2. Circle groups of 6 cubes and complete the division equation. (a)

÷6=

(b)

÷6= 5

3. Circle groups of 6 dots and write a division equation. (a)

(b)

4. Complete the division. (a) 6 ÷ 6 =

(b) 12 ÷ 6 =

(d) 24 ÷ 6 =

(e) 30 ÷ 6 =

(f) 36 ÷ 6 =

5. Fill in the missing numbers. (a) 42 ÷ (c) 60 ÷ 6 =

= 7 (b)

÷6=3

(d)

÷6=4

At Home 1. The presents are grouped in 6s. Fill in the blanks.

(a) There are

groups of

presents.

(b) Complete the division equation.

2. Circle groups of 6 cubes and complete the division equation. (a)

÷6=

(b)

÷6= 7

3. Circle groups of 6 suns and write a division equation. (a)

(b)

4. Complete the division. (a) 42 ÷ 6 =

(b) 30 ÷ 6 =

(d) 48 ÷ 6 =

(e) 60 ÷ 6 =

(f) 54 ÷ 6 =

5. Fill in the missing numbers. (a) 54 ÷ (c) 6 ÷ 6 =

= 9 (b)

÷6=4

(d)

÷6=6

Dividing by 7 Let’s Learn There are 28 pieces of candy. The candies are divided into equal groups. How many candies are in each group? How many groups of candies are there?

28 ÷ 4 = 7 There are 4 groups of candies. There are 7 candies in each group.

28 ÷ 7 = 4 There are 7 groups of candies. There are 4 candies in each group. 9

There are 56 peanuts. The peanuts are divided into equal groups. How many peanuts are in each group? How many groups of peanuts are there?

56 ÷ 8 = 7 There are 8 groups of peanuts. There are 7 peanuts in each group. 10

56 ÷ 7 = 8 There are 7 groups of peanuts. There are 8 peanuts in each group.

Let’s Practice 1. The hats are grouped in 7s. Fill in the blanks.

(a) There are

groups of

hats.

(b) Complete the division equation.

2. Circle groups of 7 cubes and complete the division equation. (a)

÷7=

(b)

÷7= 11

3. Circle groups of 7 dots and write a division equation. (a)

(b)

4. Complete the division. (a) 35 ÷ 7 =

(b) 42 ÷ 7 =

(d) 14 ÷ 7 =

(e) 49 ÷ 7 =

(f) 28 ÷ 7 =

5. Fill in the missing numbers. (a) 70 ÷ (c) 63 ÷ 7 =

= 10 (b)

÷7=4

(d)

÷7=3

At Home 1. The keys are grouped in 7s. Fill in the blanks.

(a) There are

groups of

keys.

(b) Complete the division equation.

2. Circle groups of 7 cubes and complete the division equation. (a)

÷7=

(b)

÷7= 13

3. Circle groups of 7 snowflakes and write a division equation. (a)

(b)

4. Complete the division. (a) 70 ÷ 7 =

(b) 63 ÷ 7 =

(d) 7 ÷ 7 =

(e) 56 ÷ 7 =

(f) 14 ÷ 7 =

5. Fill in the missing numbers. (a) 49 ÷ (c) 21 ÷ 7 =

= 7 (b)

÷7=5

(d)

÷7=4

Dividing by 8 Let’s Learn There are 24 starfish. The starfish are divided into equal groups. How many starfish are in each group? How many groups of starfish are there?

24 ÷ 8 = 3 There are 8 groups of starfish. There are 3 starfish in each group.

24 ÷ 3 = 8 There are 3 groups of starfish. There are 8 starfish in each group. 15

There are 32 shells. The shells are divided into equal groups. How many shells are in each group? How many groups of shells are there?

32 ÷ 4 = 8 There are 4 groups of shells. There are 8 shells in each group. 16

32 ÷ 8 = 4 There are 8 groups of shells. There are 4 shells in each group.

Let’s Practice 1. The flowers are grouped in 8s. Fill in the blanks.

(a) There are

groups of

flowers.

(b) Complete the division equation.

2. Circle groups of 8 cubes and complete the division equation. (a)

÷8=

(b)

÷8=

3. Circle groups of 8 dots and write a division equation. (a)

(b)

4. Complete the division. (a) 56 ÷ 8 =

(b) 8 ÷ 8 =

(d) 16 ÷ 8 =

(e) 72 ÷ 8 =

(f) 24 ÷ 8 =

5. Fill in the missing numbers. (a) 48 ÷ (c) 64 ÷ 8 =

= 6 (b)

÷8=8

(d)

÷8=2

At Home 1. The bags are grouped in 8s. Fill in the blanks.

(a) There are

groups of

bags.

(b) Complete the division equation.

2. Circle groups of 8 cubes and complete the division equation. (a)

÷8=

(b)

÷8= 19

3. Circle groups of 8 triangles and write a division equation. (a)

(b)

4. Complete the division. (a) 64 ÷ 8 =

(b) 16 ÷ 8 =

(d) 48 ÷ 8 =

(e) 56 ÷ 8 =

(f) 72 ÷ 8 =

5. Fill in the missing numbers. (a) 56 ÷ (c) 32 ÷ 8 =

= 7 (b)

÷8=2

(d)

÷8=3

Dividing by 9 Let’s Learn There are 27 shuttlecocks. The shuttlecocks are divided into equal groups. How many shuttlecocks are in each group? How many groups of shuttlecocks are there?

27 ÷ 3 = 9 There are 3 groups of shuttlecocks. There are 9 shuttlecocks in each group.

27 ÷ 9 = 3 There are 9 groups of shuttlecocks. There are 3 shuttlecocks in each group.

There are 54 marbles. The marbles are divided into equal groups. How many marbles are in each group? How many groups of marbles are there?

54 ÷ 6 = 9 There are 6 groups of marbles. There are 9 marbles in each group.

54 ÷ 9 = 6 There are 9 groups of marbles. There are 6 marbles in each group.

Let’s Practice 1. The pencils are grouped in 9s. Fill in the blanks.

(a) There are

groups of

pencils.

(b) Complete the division equation.

2. Circle groups of 9 cubes and complete the division equation. (a)

÷9=

(b)

÷9= 23

3. Circle groups of 9 dots and write a division equation. (a)

(b)

4. Complete the division. (a) 18 ÷ 9 =

(b) 45 ÷ 9 =

(d) 9 ÷ 9 =

(e) 27 ÷ 9 =

(f) 90 ÷ 9 =

5. Fill in the missing numbers. (a) 54 ÷ (c) 72 ÷ 9 =

= 6 (b)

÷9=4

(d)

÷ 9 = 12

At Home 1. The soccer balls are grouped in 9s. Fill in the blanks.

(a) There are

groups of

soccer balls.

(b) Complete the division equation.

2. Circle groups of 9 cubes and complete the division equation. (a)

÷9=

(b)

÷9= 25

3. Circle groups of 9 hearts and write a division equation. (a)

(b)

4. Complete the division. (a) 27 ÷ 9 =

(b) 81 ÷ 9 =

(d) 72 ÷ 9 =

(e) 45 ÷ 9 =

(f) 90 ÷ 9 =

5. Fill in the missing numbers. (a) 63 ÷ (c) 81 ÷ 9 =

= 7 (b)

÷9=2

(d)

÷9=3

Word Problems Let’s Learn Riley reads the same number of pages of her storybook each night. If she reads 24 pages in 6 days, how many pages does she read each night?

24 pages

24 ÷ 6 = 4 Riley reads 4 pages each night. Mrs. Smith has 45 stickers. She shares the stickers equally among 9 pupils. How many stickers does each pupil receive? ?

45 stickers

45 ÷ 9 = 5 Each pupil receives 5 stickers. 27

Jordan buys a box of cupcakes for $24 to share with his friends. If one cupcake costs $3, how many cupcakes are in the box?

$24

24 ÷ 3 = 8 8 cupcakes are in the box. Keira has 50 flowers. She puts 10 flowers into each vase. How many vases does Keira need?

10 flowers

50 ÷ 10 = 5 Keira needs 5 vases. 28

? vases

Let’s Practice 1. Ethan collects 30 eggs on a farm. He helps pack them into cartons. Each carton holds 6 eggs. How many cartons does he need to pack all of the eggs?

Ethan needs

cartons to pack all of the eggs.

2. Mrs. Choi buys 27 buttons to put on shirts. Each shirt has 9 buttons. How many shirts did she make in total?

Mrs. Choi made

shirts in total.

3. Sophie buys 5 identical picture frames for $35. Find the cost of one picture frame.

One picture frame costs $

4. The school cafeteria has seats for 54 people. The seats are arranged so that there are 6 seats per table. How many tables are there in the cafeteria? Draw a model to help find the answer.

There are 30

= tables in the cafeteria.

5. Halle is saving her money to buy a ukulele. She can save $9 per week. If the ukulele costs $72, how many weeks must she save her money? Draw a model to help find the answer.

Halle must save her money for 6.

weeks.

Donuts are sold in boxes of 8. Michelle buys 48 donuts. How many boxes does she buy? Draw a model to help find the answer.

Michelle buys

= boxes of donuts. 31

At Home 1. Class 3A goes on a field trip to the dinosaur museum. They take mini vans which can seat 6 pupils. There are 36 pupils in class 3A. How many vans will they need?

Class 3A will need

mini vans.

2. Dominic is cleaning his room. He packs his 54 toy cars into boxes. If each box can hold 9 cars, how many boxes does he need?

Dominic needs 32

boxes to pack his toy cars.

Riley is baking chocolate chip cookies. She adds 5 chocolate chips to each cookie. She uses a total of 40 chocolate chips. How many cookies does she bake?

Riley baked

cookies.

4. Blake shares $24 equally amongst his three brothers. How much money does each brother receive?

Each brother receives $

. 33

Looking Back 1. The balloons are grouped in 7s. Fill in the blanks.

(a) There are

groups of

balloons.

(b) Complete the division equation.

2. The bags are grouped in 8s. Fill in the blanks.

(a) There are

groups of

(b) Complete the division equation.

bags.

3. Circle groups of 6 cubes and complete the division equation.

÷6=

4. Circle groups of 9 cubes and complete the division equation.

÷9=

5. Divide by 6. Complete the equations. (a) 24 ÷ 6 =

(b) 54 ÷ 6 =

(d) 12 ÷ 6 =

(e) 60 ÷ 6 =

(f) 36 ÷ 6 =

(g) 18 ÷ 6 =

(h) 6 ÷ 6 =

(i) 48 ÷ 6 =

(j) 30 ÷ 6 =

6. Divide by 7. Complete the equations. (a) 7 ÷ 7 =

(b) 42 ÷ 7 =

(d) 14 ÷ 7 =

(e) 21 ÷ 7 =

(f) 70 ÷ 7 =

(g) 49 ÷ 7 =

(h) 28 ÷ 7 =

(i) 63 ÷ 7 =

(j) 56 ÷ 7 =

7. Divide by 8. Complete the equations. (a) 8 ÷ 8 =

(b) 32 ÷ 8 =

(d) 56 ÷ 8 =

(e) 40 ÷ 8 =

(f) 16 ÷ 8 =

(g) 72 ÷ 8 =

(h) 80 ÷ 8 =

(i) 24 ÷ 8 =

(j) 48 ÷ 8 =

8. Divide by 9. Complete the equations. (a) 18 ÷ 9 =

(b) 45 ÷ 9 =

(d) 9 ÷ 9 =

(e) 27 ÷ 9 =

(f) 90 ÷ 9 =

(g) 63 ÷ 9 =

(h) 36 ÷ 9 =

(i) 81 ÷ 9 =

(j) 72 ÷ 9 =

9. Fill in the blanks. (a) 40 ÷ 10 = (c) 8 ÷ (e)

= 2 (d) 24 ÷ ÷ 10 = 7 (f)

(g) 49 ÷ 7 = (i) 100 ÷ (k)

=6 ÷ 7 = 6

(n) 28 ÷ 7 = = 3 (p) 24 ÷ ÷ 8 = 2 (r)

(s) 48 ÷ 8 =

(w)

÷ 5 = 3

(h) 81 ÷ 9 =

÷ 6 = 6 (l)

(o) 9 ÷

(u) 64 ÷

= 10 (j) 12 ÷

(m) 2 ÷ 2 =

(q)

(b) 32 ÷ 4 =

=3 ÷ 9 = 4

(t) 90 ÷ 10 = = 8 (v) 18 ÷

÷ 3 = 9 (x)

=9 ÷ 10 = 1 37

10. An egg carton can hold 10 eggs. How many such cartons are needed to pack 70 eggs?

egg cartons are needed to pack 70 eggs.

11. Ethan bought 6 tickets to the fair for $42. Find the cost of 1 ticket.

The cost of 1 ticket is $

12.

Sophie made pizza slices to share equally among her 4 friends. She cooked a total of 24 slices. How many slices did each friend receive? Draw a model to help find the answer.

Each of Sophie’s friends received

pizza slices.

13. Ethan buys 64 beads for an art project. The beads are sold in packs of 8 beads. How many such packs does Ethan buy?

Ethan bought

= packs of beads.

Measurement

Introduction to Measuring Mass Anchor Task

Let’s Learn Compare the mass of the ball and the toy truck. The ball is as heavy as the toy truck.

Compare the mass of the spinning top and the soft toy. The soft toy is lighter than the spinning top.

Compare the mass of the toy boat and the toy airplane. The toy airplane is heavier than the toy boat.

Each

has a mass of 1 unit. Find the mass of the pen. The pen has a mass of 2 units.

Find the mass of the book. The book has a mass of 5 units.

Find the mass of the shoe.

The shoe has a mass of 8 units.

Let’s Practice 1. Use the word groups 'is heavier than', 'is lighter than' or 'is as heavy as' to fill in the blanks. (a) (b)

(e) (f)

(g) (h)

2. Each cube has a mass of 1 unit.

(a) What is the mass of the glue stick?

units.

(b) What is the mass of the scissors?

units.

(d) What is the mass of the notepad?

units.

(e) Which object is the heaviest? (f) What is the combined mass of the glue stick and the crayons? 44

units.

Solve It! 1. Find the mass of each object. (a)

The

has a mass of

(b)

The

has a mass of

2. Check the set of balls that will make the balance level. (a)

(b)

At Home 1. Check the heavier object. If they have the same mass, circle both objects. (a) (b)

2. Check the lighter box. If they have the same mass, circle both boxes. (a) (b)

3. Each cube has a mass of 1 unit. Write the mass of each object. (a)

units

(b)

units

(c)

units

(d)

units

Measuring Mass in Kilograms and Grams Let’s Learn Dominic measures the mass of a pineapple by placing it on the scale. The pineapple weighs 1 kg.

0 4 kg 3 kg

1 kg 2 kg

We say: 1 kilogram. We write: 1 kg Here are some things that we measure in kilograms. Can you guess the mass of each object?

What is the mass of the apples?

The mass of the apples is 1 kg.

0 4 kg 3 kg

1 kg

1 kg 2 kg

2 kg

What is the mass of the oranges? The mass of the oranges is 3 kg.

0 4 kg 3 kg

1 kg

2 kg

What is the mass of the potatoes? The mass of the potatoes is 7 kg. 9 kg

9 kg

10 kg

8 kg

1 kg

8 kg

2 kg

7 kg

3 kg

2 kg

7 kg 6 kg

1 kg

10 kg

3 kg 5 kg

4 kg

6 kg

5 kg

4 kg

For objects lighter than 1 kg, we can measure their mass in grams. The cupcake weighs 80 g.

0 500 g 400 g

300 g

100 g

200 g

We say: 80 grams. We write: 80 g There are 1,000 g in 1 kg. The mass of these objects is measured in grams.

What is the mass of the popcorn?

The popcorn has a mass of 100 grams.

0 500 g 400 g

100 g

0 500 g 400 g

100 g

300 g 300 g

200 g

The bread has a mass of 300 grams.

What is the mass of the bread? 0 500 g 400 g

100 g

0 500 g 400 g

100 g

300 g 300 g

200 g

The eggs have a mass of 450 grams.

What is the mass of the eggs?

0 500 g 400 g

100 g

0 500 g 400 g

100 g

300 g 300 g

200 g

Let’s Practice 1. Fill in the blanks. (a) (b)

0 4 kg 3 kg

0 4 kg 1 kg

3 kg

2 kg

1 kg 2 kg

The washing powder

The pumpkin has a

has a mass of

mass of

kg.

9 kg

10 kg

1 kg

9 kg

10 kg

1 kg

8 kg

2 kg

8 kg

2 kg

7 kg

3 kg

7 kg

3 kg

6 kg

5 kg

4 kg

6 kg

5 kg

4 kg

The roast turkey has a

The bag of potting mix

mass of

has a mass of

kg.

kg. 53

(e) (f)

0 500 g 400 g

0 500 g 100 g

300 g

400 g

200 g

100 g

300 g

200 g

The bowl of noodles has

The pencil case has a

a mass of

mass of

(g) (h)

0 500 g 400 g

100 g

300 g

0 500 g

200 g

400 g

300 g

100 g

200 g

The orange has a mass

The tablet computer has

a mass of

2. Some boxes are placed on scales to measure their masses. A

0 500 g 400 g

3 kg 200 g

400 g

300 g

2 kg

400 g

0 4 kg

100 g

1 kg 2 kg

200 g

0 500 g

0 4 kg

100 g

1 kg

3 kg

0 500 g

0 4 kg

100 g

300 g

3 kg 300 g

200 g

1 kg 2 kg

(a) What is the mass of Box E? (b) What is the mass of Box C? (c) What is the mass of Box F? (d) Which box is the heaviest? (e) Which box is the lightest? 55

3. Check the mass that is the best estimate for each object. (a) (b)

8 kg

10 g

250 g

4 kg

100 g

2 kg

1 kg

50 g

(e) (f)

600 kg

600 g

5 kg

(g) (h)

2 kg 56

2 g

10 g

10 kg

Hands On

0 500 g

Use a scale to measure the mass of objects found in your classroom. Estimate the mass of each object before measuring.

Object

Estimated Mass

400 g

300 g

100 g

200 g

Actual Mass

pencil notebook textbook scissors eraser pencil case 57

At Home 1. Fill in the blanks. (a) (b)

9 kg

10 kg

8 kg

2 kg

7 kg

3 kg

6 kg

0 4 kg

1 kg

3 kg

1 kg

4 kg

5 kg

2 kg

The kettle bell has a

The blender has a mass

mass of

kg.

0 500 g

0 500 g 400 g

300 g

100 g

400 g

200 g

300 g

100 g

200 g

The snow globe has a

The toy robot has a

mass of

2. Draw to show the mass on the scales. (a) 400 g (b) 1 kg

0 500 g 400 g

0 4 kg

100 g

3 kg 300 g

200 g

1 kg 2 kg

9 kg

10 kg

8 kg

2 kg

7 kg

3 kg

6 kg

5 kg

0 500 g

1 kg

4 kg

400 g

300 g

100 g

200 g

3. Check the mass that is the best estimate for each object. (a) (b)

1 kg

10 g

500 g

15 kg

250 g

25 kg

1 kg

7 g

4. Circle the appropriate unit of mass to measure each object. (a) A television grams kilograms (b) A sandwich grams kilograms (c) A cookie grams kilograms (d) A stapler grams kilograms (e) A brick grams kilograms (f) A person grams kilograms (g) A mango grams kilograms (h) A microwave grams kilograms 60

Measuring Volume Anchor Task

Let’s Learn Each of the containers below have an amount of colored water.

The amount of water in each container is called the volume of water. Halle poured the water from Container A into Container B. She then poured the water back into Container A. Did the volume of water change?

Container A

Container B

Container A

When the water is poured into different containers, the volume remains the same!

Container A and Container B are the same size. Compare the volume of water in the containers.

Container A

Container B

The volume of water in Container A is less than the volume of water in Container B. The volume of water in Container B is greater than the volume of water in Container A. The glasses below are of the same size. Compare the volume of water in each glass. Arrange the glasses in order from the smallest volume to the greatest volume.

smallest volume

greatest volume

The carton below contains 1 l of orange juice. This is the symbol for liters. We write 1 liter as 1 l.

l These containers contain more than 1 liter of liquid.

These containers contain less than 1 liter of liquid.

Let’s Practice 1. Some water was poured into identical beakers. Check the beaker with the greater volume of water. (a) (b)

2. Circle the beaker with the smallest volume of liquid. (a)

(b)

(c)

3. The liquid in each container was poured into 1-liter beakers. Find the volume of liquid from each container. (a)

(b)

(c)

4. Check to describe the volume of liquid in each container. (a) Large bottle of sports drink

less than 1 l more than 1 l about 1 l (b) Bath tub less than 1 l more than 1 l about 1 l (c) Small packet of ketchup

less than 1 l more than 1 l about 1 l (d) Perfume bottle less than 1 l more than 1 l about 1 l 67

Solve It! 1. Find the volume of water in each container.

2. Arrange the containers from the smallest volume to the greatest volume. smallest

greatest

3. Tick the bottles used to fill the containers. (a) Dominic poured 13 l of water into the blue container.

12 l

13 l

(b) Keira poured 16 l of water into the yellow container.

13 l

16 l

12 l

28 l

At Home 1. Some water was poured into identical glasses. Check the glass with the smaller volume of water. (a) (b)

2. Circle the glass with the greatest volume of water. (a)

(b)

3. The liquid in each container was poured into 1-liter beakers. Find the volume of liquid from each container. (a)

l (b)

l (c)

4. Check to describe the volume of liquid in each container. (a) Bottle of hand wash less than 1 l more than 1 l about 1 l (b) Water cooler bottle

less than 1 l more than 1 l about 1 l (c) Cup of tea less than 1 l more than 1 l about 1 l (d) Bottle of eye drops less than 1 l more than 1 l about 1 l 72

Mass and Volume Word Problems Let’s Learn Riley buys an apple and a mango for lunch. The apple has a mass of 125 grams and the mango has a mass of 236 grams. What is the combined mass of the fruits? 125

236

mass of apple

mass of mango ?

2 5

+ 2 3 6 3 6

125 + 236 = 361 So, the combined mass of the fruits is 361 grams. A brick has a mass of 5 kg. Mr. Cordner orders 9 such bricks to fix a wall. What is the total mass of the bricks? 5 kg

? 5 x 9 = 45 The total mass of the bricks is 45 kg.

The elephant has a mass of 2,750 kg. The car has a mass of 1,349 kg. How much heavier is the elephant than the car?

2,750 kg 4

– 1 3 4 9

mass of car 1,349 kg

2,750 – 1,349 = 1,401 The elephant is 1,401 kg heavier than the car. 8 identical paper clips are joined in a chain. The mass of the chain is 24 g. Find the mass of 1 paper clip. ?

24 g

24 ÷ 8 = 3 The mass of 1 paper clip is 3 g. 74

2 7 5 0

mass of elephant

4 0 1

Ethan's bucket holds 9 liters of water. He uses 8 buckets to help wash his father's car. How many liters of water does he use in total?

? 9 x 8 = 72 Ethan uses 72 l of water in total to wash his father's car. An inflatable swimming pool holds 2,150 l of water. Some children jump in the pool and spill 270 l of water. What volume of water remains in the pool?

2,150 l 1

volume before spill volume after spill ?

spilled 270 l

–

1 5 0

2 7 0 1

8 8 0

2,150 – 270 = 1,880 There is 1,880 l of water remaining in the pool. 75

A store has 844 l of milk. An order of 1,260 l is delivered to the store. Find the total volume of milk. 844 l milk in store

1,260 l milk delivered

2 6 0 8 4 4

1 0 4

844 + 1,260 = 2,104 The store has a total of 2,104 l of milk. Mrs. Kim needs to buy 28 liters of paint to paint her garden fence. She buys the paint in 4 identical tins. What is the volume of paint in each tin?

28 l

28 ÷ 4 = 7 Each tin contains 7 l of paint.

Let’s Practice 1. A dairy farmer gets 27 l of milk from his cows in the morning. He pours the milk into identical containers that hold 9 l. How many containers does he need to hold all of the milk?

The dairy farmer needs

containers.

2. A pickup truck has a mass of 2,087 kg. 963 kg of soil is loaded into the back of the truck. What is the mass of the truck now?

pickup truck

soil

The pickup truck now has a mass of

. 77

3. In 1 day, a juice shop sells 563 l of orange juice and 395 l of carrot juice. How many more liters of orange juice does the shop sell than carrot juice?

orange juice carrot juice ?

–

The juice shop sells

l more orange juice than carrot juice.

4. A bakery orders 8 bags of flour. Each bag has a mass of 5 kg. Find the total mass of flour ordered.

The total mass of flour ordered is 78

kg.

At Home 1. Halle's fish tank can hold 24 l of water. She cleans the tank and refills it using a 4 l container. How many such containers of water must she pour to fill the tank? Draw a model to help find the answer.

containers are needed to fill the fish tank.

2. A chocolate factory orders ingredients to make their chocolate. They order 980 kg of sugar and 1,865 kg of cocoa. What is the total mass of the ingredients? Draw a model to help find the answer.

The total mass of the ingredients is

kg. 79

3. Julian buys 1,550 kg of concrete and 865 kg of stones to repair the driveway to his house. How many more kilograms of concrete did he buy than stones? Draw a model to help find the answer.

Julian bought

more kilograms of concrete than stones.

4. Dominic fills a tub using a 6 l bucket. He pours 7 buckets of water into the tub. What volume of water is in the tub? Draw a model to help find the answer.

There are 80

l of water in the tub.

Looking Back 1. Check the heavier box. If they have the same mass, circle both boxes. (a) (b)

2. Fill in the blanks. (a) (b)

9 kg

10 kg

0 500 g

1 kg

8 kg

2 kg

7 kg

3 kg

6 kg

5 kg

400 g

300 g

4 kg

100 g

200 g

The school bag has a

The cake has a

mass of

kg.

g. 81

3. Circle the appropriate unit of mass to measure each object. (a) A table grams kilograms (b) A cupcake grams kilograms (c) A cherry grams kilograms (d) A bookshelf grams kilograms 4. Check the beaker with the greater volume of liquid. (a) (b)

5. Check the beaker with the smallest volume of liquid.

6. The water from the watering can was poured into 1-liter beakers. Find the volume of water that was in the can.

l 82

7. Circle to describe the volume of a kitchen sink. less than 1 l more than 1 l about 1 l 8. Circle to describe the volume of a coffee cup. less than 1 l more than 1 l about 1 l 9.

Sugar comes in a box containing 8 packs. The total mass of the box is 32 kg. What is the mass of 1 such pack of sugar? Draw a model to help find the answer.

The mass of 1 pack of sugar is

10. A swimming pool contains 3,875 l of water. After some heavy rain, the volume of water in the pool increases to 4,183 l. What volume of water did the rain add to the pool? Draw a model to help find the answer.

The rain added

of water to the pool. 83

Time

Telling Time to the Minute Anchor Task It’s 23 minutes past 10.

It’s ten twenty-three.

It’s 23 minutes after 10 o’clock.

Let’s Learn 1 minute

On a clock, it takes the minute hand 1 minute to move from one marking to the next. It takes 5 minutes to move from one number to the next. There are 60 minutes in one hour. It takes the minute hand 1 hour to move once around the clock. It’s 10:13.

It’s 7:56.

It is 6:12 a.m. It is 12 minutes past 6 o’clock in the morning. Jordan wakes up at 12 minutes past 6.

It is 3:26 p.m. It is 26 minutes past 3 o’clock in the afternoon. Jordan rides home at 26 minutes past 3. 86

It is 10:47 a.m. It is 13 minutes until 11 o’clock in the morning. Halle plays the piano at 13 minutes to 11.

It is 8:52 p.m. It is 8 minutes until 9 o’clock at night. Halle watches television at 8 minutes to 9. 87

Let’s Practice 1. Match.

6:13

5:39

1:07

9:33

8:55

2. Match.

8 minutes past 10

12 minutes to 7

18 minutes to 9

12 minutes past 7

3 minutes past 12

3. Fill in the blanks. (a)

It is It is

. minutes past

(b)

It is It is

. minutes to

(c)

It is It is 90

. minutes to

(d)

It is It is

. minutes to

(e)

It is It is

. minutes past

(f)

It is It is

. minutes to

4. Write ‘past’ or ‘to’. (a) (b)

6 minutes

5. 12 minutes

16 minutes

10. 23 minutes

(e) (f)

9 minutes

1. 17 minutes

5. Draw hands on the clocks to show the time. (a) 11 minutes past 6 (b) 15 minutes to 11

(e) 22 minutes to 3 (f) 12 minutes past 9

6. Fill in the blanks. (a) 4 minutes to 8 is

(b) 24 minutes past 12 is (c) 16 minutes to 1 is (d) 7:39 is

. .

minutes to

(e) 12:02 is

minutes past

(f) 10:47 is

minutes to

. . . 93

Hands On 1. Tell your friends the time you do an activity. 2. One friends shows the time using their arms. 3.

The other friend shows the time on a clock.

4. Switch roles.

I play the violin at 25 minutes past 9.

(b) Home At 1. Match.

12:22

12:11

2:55

1:07

11:51

2. Match.

9 minutes to 4

9 minutes past 4

26 minutes to 11

2 minutes past 2

14 minutes to 12

3. Fill in the blanks. (a)

It is It is

. minutes past

(b)

It is It is

. minutes to

(c)

It is It is

. minutes past

. 97

4. Draw the minute and hour hands to show the time. (a) 1 minute past 8 (b) 27 minutes to 11

(e) 21 minutes to 5 (f) 4 minutes past 7

5. Fill in the blanks. (a) 16 minutes to 2 is (b) 4 minutes to 11 is

. .

minutes to

(e) 8:29 is

minutes past

(f) 10:33 is 98

minutes to

. . . .

Hands On 1. Roll the dice. Move your counter the number of spaces shown on the dice. 2. Say the time using ‘past’ and ‘to’. If you say the incorrect time, go back to the start. 3.

The first player to the finish is the winner.

Solve It! Check the correct clock. (a) Wyatt worked in the garden for 25 minutes. He finished gardening at 5:00 p.m. What time did Wyatt start gardening?

(b) Riley started playing the guitar at midday. She played the guitar for 18 minutes. What time did Riley stop playing the guitar?

100

(c) Jordan started fishing at 4 o’clock. He caught his first fish 46 minutes later. What time did Jordan catch his first fish?

(d) Chelsea watched a 30-minute television show. She finished watching the show at 8:15 p.m. What time did the show start?

1 01

Duration of Time Let’s Learn Mr. Jenkins puts a pizza in the oven at 7:30 p.m. He removes the pizza at 7:48 p.m. How long does it take Mr. Jenkins to cook a pizza?

5, 10, 15, 16, 17, 18.

18 17 16 15

10 5

It takes Mr. Jenkins 18 minutes to cook a pizza. +5

7:30 1 02

7:45

7:48

Riley started running at 9:10 a.m. She ran for 5 kilometers. She finished at 9:47 a.m. How long does it take Riley to run 5 kilometers? 47 – 10 = 37

37 minutes

9:10

9:47

Riley took 37 minutes to run 5 kilometers. How long is it from 4:30 p.m. to 5:15 p.m.? 30 minutes

15 minutes

45 minutes

30 min

4:30

15 min

5:00

5:15

30 + 15 = 45 It is 45 minutes from 4:30 p.m. to 5:15 p.m. 103

Let’s Practice 1. Fill in the blanks. (a) How many minutes are there from 6:25 a.m. to 6:48 a.m.?

minutes

(b) How many minutes are there from 1:20 p.m. to 1:48 p.m.?

minutes

104

minutes

(d) How many minutes are there from 12:35 a.m. to 12:56 a.m.?

minutes

(e) How many minutes are there from 11:05 p.m. to 11:23 p.m.?

minutes

(f) How many minutes are there from 10:10 a.m. to 10:36 a.m.?

minutes

105

2. Fill in the blanks. Use the time line to count on. (a) How many minutes are there from 1:05 p.m. to 1:48 p.m.?

minutes

(b) How many minutes are there from 3:15 a.m. to 3:56 a.m.?

106

minutes

3. How many minutes are there between the times? Fill in the blanks. (a) 3:45 a.m. and 3:52 a.m. (b) 2:45 p.m. and 12:59 p.m. (c) 1:05 a.m. and 1:43 a.m. (d) 4:20 a.m. and 4:42 a.m. 4. Fill in the blanks. (a) What time is it 14 minutes after 2:30 p.m.? (b) What time is it 41 minutes after 8:10 p.m.? (c) What time is it 19 minutes after 9:05 p.m.? (d) What time is it 38 minutes after 11:10 p.m.? 107

5. Fill in the blanks. (a) Riley leaves her home at 7:25 a.m. She arrives at school at 7:52 a.m. How long did it take Riley to get to school?

It took Riley

minutes to get to school.

(b) Science class starts at 2:10 p.m. and finishes at 2:55 p.m. How long is the science class?

The science class is 108

minutes long.

Ethan finished jogging at

(d) Chelsea goes into her garden at 5:05 p.m. She plays with her ducks for 52 minutes, then goes inside. What time does Chelsea go inside?

Chelsea goes inside at

. 109

(b) Home At 1. Fill in the blanks. (a) How many minutes are there from 3:05 a.m. to 3:21 a.m.?

minutes

(b) How many minutes are there from 2:45 p.m. to 3:18 p.m.?

minutes

110

minutes

(d) How many minutes are there from 7:35 a.m. to 8:12 a.m.?

minutes

(e) How many minutes are there from 3:30 p.m. to 3:45 p.m.?

minutes

(f) How many minutes are there from 1:50 a.m. to 2:28 a.m.?

minutes

111

2. Fill in the blanks. Use the time line to count on. (a) How many minutes are there from 4:15 p.m. to 4:41 p.m.?

minutes

(b) How many minutes are there from 9:55 a.m. to 10:10 a.m.?

112

minutes

3. How many minutes are there between the times? Fill in the blanks. (a) 1:45 a.m. and 1:52 a.m. (b) 12:15 p.m. and 12:59 p.m. (c) 5:15 a.m. and 5:39 a.m. (d) 9:20 a.m. and 9:43 a.m. 4. Fill in the blanks. (a) What time is it 29 minutes after 2:30 p.m.? (b) What time is it 41 minutes after 2:05 p.m.? (c) What time is it 38 minutes after 11:10 p.m.? (d) What time is it 16 minutes after 12:35 p.m.? 113

5. Fill in the blanks. (a) Blake takes a nap at 3:05 p.m. He wakes up at 3:48 p.m. How long was Blake asleep?

Blake was asleep for

minutes.

(b) Sophie started making a pizza at 5:15 p.m. She finished making the pizza at 5:51 p.m. How long did it take Sophie to make the pizza?

Sophie took 114

minutes to make the pizza.

Wyatt reached the waterfall at

(d) Halle’s English exam started at 10:15 a.m. She finished the exam in 43 minutes. What time did Halle finish the English exam?

Halle finished the English exam at

. 115

Let’s Practice 1. Fill in the blanks. (a) How many minutes are there from 9:25 p.m. to 10:15 p.m.?

min 9:25 p.m. +

min 10:00 p.m.

10:15 p.m.

minutes (b) How many minutes are there from 5:50 a.m. to 6:30 a.m.?

min 5:50 a.m. +

minutes 116

min

1:35 p.m. +

minutes (d) How many minutes are there from 11:45 a.m. to 12:40 p.m.?

min

11:45 a.m. +

minutes

117

2. Fill in the blanks. (a) Ethan started opening his birthday presents at 11:50 a.m. He finished opening his presents at 12:35 p.m. How long did Ethan spend opening his presents?

Ethan spent

minutes opening his presents.

(b) Sophie started cleaning her bedroom at 4:45 p.m. Her bedroom was spotlessly clean at 5:25 p.m. How long did it take Sophie to clean her bedroom?

It took Sophie 118

minutes to clean her bedroom.

Wyatt reached the cave at

(d) Halle’s science exam started at 2:10 p.m. She finished the exam in 58 minutes. What time did Halle finish the science exam?

Halle finished the science exam at

. 119

Solve It! Use the map on the next page to answer the questions. 1. Sophie left the camp site at midday. She hiked via the cave to the waterfall. What time did she arrive at the waterfall?

Sophie arrived at the waterfall at

2. Blake left the camp site at 3:10 p.m. He hiked past the pond and the waterfall to the forest. What time did Blake arrive at the forest?

Blake arrived at the forest at

3. Keira left the camp site at 8:00 a.m. She passed the pond, rocks and forest on the way to the waterfall. What time did Keira arrive at the waterfall?

Keira arrived at the waterfall at 120

35 min

25 min

10 min

15 min

25 min 30 min

35 min

121

(b) Home At 1. Fill in the blanks. (a) How many minutes are there from 6:35 p.m. to 7:20 p.m.?

min 6:35 p.m. +

min

7:00 p.m.

7:20 p.m.

minutes (b) How many minutes are there from 11:45 a.m. to 12:30 p.m.?

min 11:45 a.m. +

12:00 p.m. =

minutes 1 22

min 12:30 p.m.

min 3:20 p.m. +

min 4:00 p.m. 4:10 p.m.

minutes (d) How many minutes are there from 10:45 a.m. to 11:40 a.m.?

min

10:45 a.m. +

minutes 123

2. Fill in the blanks. (a) Riley arrived at her grandmother’s house at 9:40 a.m. She left at 10:15 a.m. How long did Riley spend at her grandmother’s house?

Riley spent

minutes at her grandmother’s house.

(b) Jordan started his homework at 4:25 p.m. He finished at 5:20 p.m. How long did Jordan spend doing his homework?

Jordan spent 124

minutes doing his homework.

(c) Halle started playing her ukulele at 10:25 a.m. She played the ukulele for 50 minutes. What time did Halle stop playing the ukulele?

Halle stopped playing the ukulele at

(d) Ethan arrived at the swimming pool at 12:45 p.m. He swam for 55 minutes, then left. What time did Ethan leave the swimming pool?

Ethan left the swimming pool at

. 125

Looking Back 1. Fill in the blanks. (a)

It is It is

. minutes past

(b)

It is It is

. minutes to

2. Draw the clock hands to show the time. (a) 27 minute past 8 (b) 12 minutes to 12

126

3. Fill in the blanks. (a) 21 minutes to 7 is

(b) 18 minutes to 3 is

4. Fill in the blanks. (a) There are

minutes between 4:45 a.m. and 4:52 a.m.

(b) There are

minutes between 12:30 p.m. and 12:54 p.m.

5. Fill in the blanks. (a) How many minutes are there from 6:45 p.m. to 7:35 p.m.?

minutes.

(b) How many minutes are there from 12:40 p.m. to 1:25 p.m.?

minutes. 127

Geometry

Anchor Task

1 28

Recognizing Quadrilaterals Let’s Learn Observe the lines on each side of the ruler. Notice that the distance between the two lines is the same at any point. Lines that are an equal distance apart and do not meet are called parallel lines.

G C

D F H

We say: AB is parallel to CD. We write: AB CD

We say: EF is parallel to GH. We write: EF GH

The distance between IJ and KL does not stay the same. IJ is not parallel to KL.

129

Identify the pairs of parallel lines. M

MN is parallel to OP. MN OP

A X

U Q

QR is parallel to ST. QR ST

AB is parallel to CD. AB CD

Recall that squares, rectangles, trapezoids and parallelograms are quadrilaterals. A quadrilateral has 4 straight sides and 4 angles. square

rectangle

side angle

trapezoid

parallelogram side

angle

130

Let’s look at some different types of quadrilaterals. quadrilaterals trapezoids

parallelograms

• at least 1 pair of parallel sides

• 2 pairs of parallel sides

• no parallel sides

rectangles

rhombi

• opposite sides of equal length

• all sides of equal length

squares

• all angles and sides are equal

131

Let’s Practice 1. Check the pairs of lines that are parallel. W Y A

L N

O X

E Q S

K G

2. How many pairs of parallel lines does each shape have? (a) (b) (c)

(d) (e) (f)

1 32

3. (a) Check the shapes that are quadrilaterals.

(b) Explain why a square is a type of rectangle. (c) Explain why a triangle is not a quadrilateral.

133

4. Choose a word from the box that best describes each shape. square rectangle rhombus parallelogram trapezoid quadrilateral

(a)

(b)

(c)

(d)

(e)

(f)

1 34

Hands On Work in pairs and identify objects around the schoolyard that have a quadrilateral shape. List them in the table below.

Object

Quadrilateral

135

At Home 1. Complete the key and color the shapes. squares

136

rectangles

rhombi

trapezoids

2. Circle the word that best describes the shape. (a) square rectangle

(b)

rectangle rhombus

(d) parallelogram square

137

Drawing Quadrilaterals Let’s Learn Keira uses dot paper to draw some quadrilaterals. She chooses 4 dots. Then she uses a pencil and ruler to draw lines and connect the dots. Can you name the pink shape?

Michelle draws some quadrilaterals on a piece of grid paper. She chooses 4 points where the grid lines cross. Then she uses a pencil to connect the points.

What color is the rectangle?

138

Let’s Practice 1. Draw 3 squares on the dot paper.

2. Draw 3 rectangles on the grid paper.

139

3. Draw 3 parallelograms on the dot paper.

4. Draw 2 quadrilaterals on the grid paper that are not squares, rectangles or parallelograms. Explain how they are different.

140

Hands On Work in pairs. 1. Draw a quadrilateral on the dot paper below. 2. Have your partner name the shape and make it on a geoboard. Switch turns.

1 41

At Home 1. On the dot paper, draw a square, a rectangle and a rhombus. Label each shape.

142

2. On the grid paper, draw a parallelogram, a square and a trapezoid. Label each shape.

143

Looking Back 1. Check the shapes that are quadrilaterals.

144

2. Check 1 or more names for each shape. (a)

(b)

(c)

quadrilateral

square

rectangle

trapezoid

rhombus

parallelogram

quadrilateral

square

rectangle

trapezoid

rhombus

parallelogram

quadrilateral

square

rectangle

trapezoid

rhombus

parallelogram

3. (a) Draw a trapezoid. (b) Draw a parallelogram.

145

Area and Perimeter

Anchor Task

146

Introduction to Area Let’s Learn Michelle uses square tiles to make some figures. She counts the number of tiles used to make each shape. Count the squares used to make each figure!

6 square tiles

3 square tiles

5 square tiles

The amount of surface covered by a shape is called area. We say: The green figure has an area of 6 square tiles. The yellow figure has an area of 3 square tiles. The red figure has an area of 5 square tiles. Riley uses some yellow and blue tiles to make a figure.

Can you find the area of her figure?

Each blue tile has half the area of a yellow square tile.

2 blue tiles can combine to make 1 square tile. Riley’s figure has an area of 4 square tiles. 147

1 unit

The square grids below are made of squares that have a side length of 1 unit.

1 unit

Halle draws and shades a figure on a sheet of square grid paper. What is the area of the shaded figure? To find the area of the shaded figure, count the number of square units it fills up.

Area A = 20 square units. Keira draws and shades a figure on a sheet of square grid paper. What is the area of the shaded figure? To find the area of the shaded figure, add the number of square units and half square units.

Area B = 8 square units + 4 half square units. = 10 square units. 1 48

Let’s Practice 1. Find the area of each figure.

Area =

square units.

Area =

square units.

square units. Area =

Area =

square units.

square units. 149

2. The figures are inside a grid made up of square tiles.

C B A

E D F

(a) Find the area of each figure. Area A =

square units. Area B =

square units.

Area C =

square units. Area D =

square units.

Area E =

square units. Area F =

square units.

(b) Which figure has the greatest area? (c) Which figure has the smallest area?

150

Solve It! The blue figure has an area of 16 square units. Color 3 more figures that have a different shape but the same area.

Make sure the figures do not overlap or share any squares.

1 51

At Home 1. Find the area of each figure. (a)

(b)

Area =

square units.

Area =

square units.

Area =

square units.

(c)

(d)

Area =

square units.

(e)

(f)

Area =

152

Area =

square units.

2. Complete the following. N

Q R

(a) Circle 2 figures that have the same area. (b) Figure R has an area of

square units.

(d) Figure

has the smallest area.

(e) Figure

has the greatest area.

1 53

Measuring Area Let’s Learn A square centimeter is an area equal to a square with a side length of 1 cm. The symbol for square centimeters is cm2. 1 cm 1 cm

cm2

We can use square centimeters as a unit of measurement for area. The square has a side length of 3 cm. Let’s find the area of the square. 3 cm

The 3 cm square can be divided into nine 1 cm squares.

1 cm 1 cm

The area of the square is 9 square centimeters. We say: 9 square centimeters. We write: 9 cm2.

154

The pink rectangle has a height of 2 cm and width of 5 cm. 5 cm

1 cm 2 cm

1 cm

It has an area of 10 cm2. The squares in the grid below have a side length of 1 cm.

1 cm 1 cm

Each figure in the grid has an area of 12 cm2.

155

A square meter is an area equal to a square with a side length of 1 m. The symbol for square meters is m2. 100 cm 1m 100 cm

The yellow rectangle has height of 3 m and width of 4 m. 1m

1m 3m

The area of the rectangle is 12 square meters. We say: 12 square meters. We write: 12 m2. The squares in the grid below have a side length of 1 m.

1m 1m

Both figures in the grid have an area of 14 m2.

156

This square has a side length of 1 inch. It has an area of 1 square inch. 1 in 1 in

The symbol for square inches is in2.

in2

The blue rectangle has a height of 2 in and width of 3 in. 1 in

3 in

1 in 2 in

The area of the rectangle is 6 square inches. We say: 6 square inches. We write: 6 in2. The squares in the grid below have a side length of 1 in.

1 in 1 in

Both figures in the grid have an area of 8 in2.

1 57

A square foot is an area equal to a square with a side length of 1 ft. The symbol for square feet is ft2. 12 in 1 ft 12 in

1 ft

ft2

The green rectangle has height of 5 ft and width of 4 ft. 1 ft

4 ft

1 ft

5 ft

The area of the rectangle is 20 square feet. We say: 20 square feet. We write: 20 ft2. The squares in the grid below have a side length of 1 ft.

1 ft 1 ft

Both figures in the grid have an area of 13 ft 2. 158

Let’s Practice 1. Find the area of each figure.

1 cm

(a)

1 cm

Area = Area =

Area =

(b)

Area = Area =

Area =

Area = 159

1 in

(c)

1 in

Area = Area =

Area =

1 ft

(d)

1 ft

Area = Area =

Area =

160

Area =

2. Find the area of each rectangle. Make sure you write the correct area units. (a)

1 cm 1 cm

The square is made up of

1-cm squares.

Area = (b)

The rectangle is made up

1 m of

1-m squares.

Area = (c) 1 m 1m

The rectangle is made up of

1-m squares.

Area =

(d)

1 cm 1 cm

The rectangle is made up of

1-cm squares.

Area = 161

3. Find the area of each figure. (a)

The figure is made up

1 m of

1-m squares.

Area =

(b)

1 cm 1 cm

The figure is made up of

1-cm squares.

Area =

The figure is made up 1 cm

1-cm squares.

Area =

(d)

1m 1 m The figure is made up

of Area = 1 62

1-m squares.

(e)

The figure is made up of 1 cm

1-cm squares.

Area =

1 cm

(f) 1m

The figure is made up 1m

1-m squares.

Area =

(g) 1m 1m

The figure is made up of

1-m squares.

Area =

(h)

1 cm 1 cm

The figure is made up of

1-cm squares.

Area = 163

Hands On Work in pairs. Take square centimeter tiles and build squares. Start with a square of side length 1 cm. Add tiles to make a new square of side length 2 cm. Find the area of each square you make and fill in the table.

Square Side Length

Number of 1 cm squares

Area in cm2

1 cm

2 cm 3 cm 4 cm 5 cm 164

At Home 1 . Find the area of each figure. Make sure you write the correct area units. 1m

(a)

Area = (b)

(c)

1 cm 1 cm

Area =

Area = (d)

(e)

Area = Area = (f)

(g)

1 in 1 in

1 cm 1 cm

Area =

Area = 165

(h)

(i)

1 ft

1 ft 1 ft

1 ft

Area =

(j)

1 in 1 in

Area = (k)

(l)

1 cm 1 cm

1m 1m

Area =

Area = (m)

(n)

1m 1m

1 cm 1 cm

Area = Area = 166

2. Find the area of each figure.

1 in

(a)

1 in

Area = Area =

Area =

1 ft

(b)

1 ft

Area = Area =

Area =

1 67

3. The grid is made of squares that have a side length of 1 cm.

(a) What is the area of the pink figure?

(b) What color is the figure that has an area of 13 cm2?

(c) What shape is the figure with the largest area? (d) What is the area of the green square? (e) 2 figures have the same area. What is the area?

168

Area of Rectangles Let’s Learn Figure A is a rectangle. Find its area in square centimeters.

Figure A

To find the area of a rectangle, we multiply the length by the breadth.

3 cm

6 cm Area Figure A = length x breadth = 6 cm x 3 cm = 18 cm2

The area of Figure A is 18 cm2. Find the area of each rectangle in square centimeters. (a) (b)

Figure B

4 cm

Figure C

6 cm

5 cm Area Figure B = length x breadth = 5 cm x 4 cm = 20 cm2

5 cm Area Figure C = length x breadth = 5 cm x 6 cm = 30 cm2

169

Let’s Practice 1. Find the area of each rectangle. (a) (b) 3 cm

6 cm 1 cm

2 cm

Area = Area = 3m (c) (d)

5 cm

4 cm 6m

Area = Area = 6 cm (e) (f)

10 cm

Area = 170

Area =

8 in (g) (h)

10 ft

2 in 8 ft

Area =

Area = 3 cm (i) (j)

7 in

5 in 7 cm

Area = Area = 10 ft (k) (l)

6 in

4 ft 6 in

Area =

Area = 171

Find the area of each rectangle.

1 cm 1 cm

(a) What is the area of figure Q?

(b) Which figure has an area of 15 cm2? (c) Which figure has the largest area? What is its area?

has an area of

(d) Which 2 figures have the same area?

and

have the same area.

(e) What is the area of figures Q and T combined?

172

Solve It! The figures are made by combining 2 or more rectangles. Find the area of each figure. Divide the figure (a) into rectangles! Find the area of each rectangle and combine. 4 cm

4 cm Working 3 cm

8 cm

Area = (b)

7m 3m

7m Working

2m 8m

Area = 173

At Home 1. Find the area of each rectangle. 4m (a) (b)

4 cm

1m 3 cm

Area = Area = (c)

20 m

Area = 4m (d) (e)

10 cm

10 cm 7m

Area = Area = 174

2. In what month is Wyatt’s birthday? Find the area of each rectangle. Then match the letters to the areas below to find out.

4 cm

10 cm

12 cm 1 cm

6 cm

3 cm 2 cm

12 cm2

16 cm2

60 cm2

6 cm2

16 cm2

12 m2

6 m2

175

Introduction to Perimeter Anchor Task

176

Let’s Learn Dominic draws two figures on a sheet of 1-cm square grid paper. He adds the lengths of each side of the figures. The total distance around a figure is called the perimeter. 1 cm 1 cm

B A

The distance of a continuous line around a figure is the perimeter. Perimeter A = 7 cm + 5 cm + 7 cm + 5 cm = 24 cm Perimeter B = 5 cm + 2 cm + 3 cm + 4 cm + 2 cm + 6 cm = 22 cm

177

Find the perimeter of the triangle.

To find the perimeter of the triangle, add the lengths of the sides.

20 m 12 m

16 m

Perimeter = 20 m + 16 m + 12 m = 48 m Find the perimeter of the rectangle.

The perimeter of the rectangle is its length + breadth + length + breadth.

11 m 40 m

Perimeter = 40 m + 11 m + 40 m + 11 m = 102 m Find the perimeter of the square.

8 cm

Perimeter = 8 cm + 8 cm + 8 cm + 8 cm = 4 x 8 cm = 32 cm 178

The perimeter of the square is equal to 4 times its length.

Find the perimeter of each figure. 3 cm 2 cm

1 cm

2 cm + 3 cm + 1 cm + 3 cm + 4 cm = 13 cm The figure has a perimeter of 13 cm.

3 cm 4 cm

4 m + 6 m + 6 m + 4 m + 6 m + 6 m = 32 m The figure has a perimeter of 32 m. 6m

6m 4m

Find the perimeter of each figure formed with an elastic band on the geoboard. 1 cm

B A

1 cm

Perimeter A = 2 cm + 3 cm + 2 cm + 3 cm = 10 cm Perimeter B = 4 x 2 cm = 8 cm Perimeter C = 1 cm + 1 cm + 1 cm + 1 cm + 2 cm + 1 cm + 4cm + 3 cm = 14 cm 179

Let’s Practice 1. Find the perimeter of each figure. Show your working. (a)

Working 3 cm

5 cm

Perimeter = (b)

Working 5 cm 4 cm

3 cm

Perimeter = (c) 10 m

10 m

10 m 10 m

Perimeter = 180

Working

(d)

Working 12 cm

12 cm

Perimeter = (e)

Working 35 cm

50 cm

Perimeter = (f)

3m 2m

Working 3m

4m 3m 3m

Perimeter =

181

2. The figures below are inside 1-cm square grid paper.

A B

G 182

F H

(a) Find the perimeter of each figure. Working

Perimeter A = Perimeter B = Perimeter C = Perimeter D = Perimeter E = Perimeter F = Perimeter G = Perimeter H =

(b) Which figure has the greatest perimeter? (c) Which figure has the smallest perimeter? (d) Which 2 figures have the same perimeter? Figures

and

have the same perimeter.

(e) Which figure has the greatest number of sides? 183

Solve It! Ethan has a piece of wire that is 16 cm long. He wants to bend the wire to make a rectangle. Draw 4 different rectangles he can make that use the full length of the wire in the grid below. 1 cm

1 cm

184

At Home 1. Find the perimeter of each figure. Show your working. (a)

Working 5 cm

5 cm

Perimeter = (b)

7 cm 7 cm

7 cm

Working

7 cm

Perimeter = (c)

12 m 5m

Working

4m 5m

Perimeter =

185

2. Find the perimeter of each figure on the geoboard. 1 cm 1 cm

Perimeter = Perimeter =

186

3. Draw 2 different rectangles with a perimeter of 14 cm. 1 cm 1 cm

4. Draw a figure with 6 sides that has a perimeter of 28 cm. 1 cm 1 cm

1 87

Area and Perimeter Let’s Learn Find the area and perimeter of the rectangle. 1 cm 1 cm

Area = 5 cm x 3 cm = 15 cm2 Perimeter = 5 cm + 3 cm + 5 cm + 3cm = 16 cm Compare the areas and perimeters of the figures in the geoboard. 1 cm

A Area = 8 cm2 Perimeter = 12 cm

1 cm

B Area = 8 cm2 Perimeter = 16 cm

C Area = 5 cm2 Perimeter = 12 cm

Figures A and B have the same area but different perimeters! 1 88

Figures A and C have the same perimeter but different areas!

Let’s Practice 1. Find the perimeter and area of each figure.

1 cm 1 cm

Area = Perimeter =

189

2. Compare the areas and perimeters of the figures in the geoboard.

1 cm 1 cm

C D

(a) Find 2 figures that have the same area. Figures

and

both have an area of

cm2.

(b) Find 2 figures that have the same perimeter. Figures 190

and

both have a perimeter of

cm.

3. Fill in the blanks.

1 cm 1 cm

Figure M

Figure L

Figure O

Figure N

Figure P

(a) Each figure has a perimeter of (b) Figures

and

cm.

have the same area of

cm2. 191

Solve It! Michelle spent her vacation at her grandfather’s ranch. The map shows some of the features of the ranch.

guesthouse

games room

flower bed

herb garden

swimming pool main house

192

Use your notebook to answer the questions below. 1m 1m

tool shed

vegetable garden

(a) Find the area of the swimming pool. (b) Find the perimeter of the guesthouse. (c) What is the combined area of the guesthouse and games room? (d) What is the area of the main house? (e) Michelle’s grandfather wants to build a fence around the vegetable garden, the flower bed and the herb garden to keep the animals out. How many meters of fencing will he need? 193

At Home 1. Find the perimeter and area of each figure.

1 cm 1 cm

194

Area =

Perimeter =

Area =

Perimeter =

2. Compare the areas and perimeters of the figures in the geoboard. 1 cm 1 cm

A B

C D

(a) Find 2 figures that have the same area. Figures

and

both have an area of

cm2.

(b) Find 2 figures that have the same perimeter. Figures

and

both have a perimeter of

cm. 195

Looking Back 1. Find the area of each figure in square units. (a) (b)

Area =

square units.

Area =

square units.

Area =

square units.

Area =

square units.

Area =

square units.

(d) (e)

Area = 196

square units.

2. Find the area of each rectangle. 12 cm (a) (b)

10 m

4 cm 5m

Area =

(c)

20 in

6 in

Area = 3 cm (d) (e)

8 ft

8 ft 9 cm

Area = Area = 197

3. Find the perimeter of each figure. (a)

8 cm

12 cm

Perimeter =

(b)

5 cm 5 cm

5 cm

Perimeter = 5 cm

5 cm 5 cm

(c)

12 m

11 m 11 m

8m 11 m 10 m 17 m

Perimeter = 1 98

4. Find the area and perimeter of each figure. 1 cm 1 cm

Area =

Perimeter =

Area =

Perimeter =

199

Fractions

Equal Parts Anchor Task

2 00

Let’s Learn Sophie takes a piece of paper and divides it into 4 parts. Each part is the same size. The piece of paper is divided into equal parts.

4 equal parts

These pieces of paper have also been divided into equal parts. How many equal parts does each shape have?

4 equal parts

3 equal parts

8 equal parts

These pieces of paper have been divided into parts of unequal sizes.

2 01

Sophie and Halle make a sandwich. To share the sandwich, they cut it into two equal parts. How much of the sandwich does each child get? We get half each!

Each child gets one of two equal parts. We can express this as a fraction.

Each child gets 1 , or one-half of the sandwich. 2

A unit fraction is one equal part of the whole. The top number of a unit fraction is always 1. The bottom number of a unit fraction shows the number of equal parts. Blake folds a piece of paper into four equal parts. What unit fraction represents one equal part? 1 4

1 4

One-fourth is the same as one-quarter.

One part out of four is 1 , or one-fourth. 4

202

Let’s look at some unit fractions.

1 2 one-half

1 3 one-third

1 4 one-quarter

1 5 one-fifth

1 6 one-sixth

1 7 one-seventh

1 8 one-eighth s a whole is divided into more and more parts, the unit fraction A represents a smaller and smaller part of the whole. 203

Let’s Practice 1. Check the shapes that are divided into equal parts. Cross the shapes that are not divided into equal parts. (a) (b)

(e) (f)

(g) (h)

204

2. Draw lines to divide the shapes into equal parts. (a) (b)

two equal parts

four equal parts

five equal parts

three equal parts

(e) (f)

six equal parts

eight equal parts 205

3. Circle the unit fractions.

206

4. Color and write the unit fraction. (a) (b)

(e) (f)

(g) (h)

207

Write the unit fraction.

(a) (b)

(e) (f)

(g) (h)

208

Hands On 1. Place a paper clip on the center of the circle and hold it in place with a pencil as shown. 2. Flick the paper clip to spin it. 3. Race your friends to name the unit fractions. 4. The first person to correctly name the fractions is the winner and makes the next spin.

209

Solve It! Divide each square into quarters. Use a different way each time. The first one has been done for you. (a)

(c)

210

(b)

(d)

At Home 1. Divide the shapes into equal parts. (a) 2 equal parts. (b) 4 equal parts.

(e) 6 equal parts. (f) 4 equal parts.

211

2. Match the unit fractions.

1 2 1 3 1 4 1 5 1 6 3. Check the shapes that show 1 . 2

212

4. Check the shapes that show 1 . 3

5. Check the shapes that show 1 . 4

213

6. Check the shapes that show 1 . 5

7. Check the shapes that show 1 . 6

214

8. Check the shapes that show 1 . 7

9. Check the shapes that show 1 . 8

215

10. Fill in the blanks. (a)

The shape has

equal parts.

The unit fraction of the shape is

(b)

The shape has

equal parts.

The unit fraction of the shape is

(c)

The shape has

equal parts.

The unit fraction of the shape is 216

equal parts.

The unit fraction of the shape is

(e)

equal parts.

The unit fraction of the shape is

(d)

Solve It! Michelle is having chicken and vegetables for dinner. She divides her dinner plate into five equal parts. She puts all of the peas in one equal part. What fraction of Michelle's dinner plate has peas? Draw a picture to show your understanding.

of Michelle's dinner plate has peas.

217

Parts of a Whole Anchor Task

218

219

Let’s Learn When we take a whole and divide it into equal parts, we get fractions. The whole orange is cut into 2 equal pieces. Each piece is a half, which we write as 1 . 2

2 halves make 1 whole.

1 whole

1 2

half

1 2

half

The numbers of a fraction have special names.

1 2 A half has a numerator of 1.

220

The top number is called the numerator. The bottom number is called the denominator. ... and a denominator of 2!

Let’s cut an apple into 4 equal pieces. Each piece is a quarter.

1 4

1 whole

1 4

quarter

1 4

quarter

1 4

quarter

4 quarters make 1 whole. 1 4

1 4

Ethan eats 3 pieces of the apple. We say he eats 3 quarters of the apple. We can write this as a fraction 3 . 4

1 4

I ate 3 quarters of the apple!

1 4

221

A pizza is cut into 4 equal slices. Jordan eats one slice. Let’s write the slice he ate as a fraction.

We write the fraction of pizza he ate as 1 . 4

A farmer divides his field into 5 equal parts. He plants corn in two of the parts and wheat in the remaining parts.

1 5

2 5

Let's write the quantity of each crop as a fraction. 2 of the field is corn and 3 of the field is wheat. 5 5 2 and 3 make 1 whole. 5 5

222

1 5

3 5

1 5

What fraction of the shapes are colored? What fraction is not colored? Each part represents 1 . 3 parts are colored.

So 3 of the shape is colored. 4

1 part is not colored. So 1 of the shape is not colored. 4

Each part represents 1 . 2 parts are colored.

So 2 of the shape is colored. 6

4 parts are not colored. So 4 of the shape is not colored. 6

Each part represents 1 . 4 parts are colored.

So 4 of the shape is colored. 5

1 part is not colored. So 1 of the shape is not colored. 5

223

Let’s Practice 1. Write the numerator of each fraction. (a)

1 4

(b)

3 5

(c)

2 6

(d)

4 7

(e)

1 8

(f)

2 3

(g)

1 5

(h)

3 4

(i)

5 7

2. Write the denominator of each fraction. (a)

3 4

(b)

1 2

(c)

1 3

(d)

4 5

(e)

3 6

(f)

2 4

(g)

2 3

(h)

4 7

(i)

5 8

224

3. Match the fraction to its name in words.

4 7

four fifths

2 7

one third

1 3

four sevenths

4 5

three fifths

3 5

one half

3 4

two sevenths

1 2

five eighths

5 8

three quarters

225

4. What fraction of each pizza remains? (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

226

Complete for each shape.

(a) is colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

(b)

(c)

(d)

(e)

227

(f) is colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

(g)

(h)

(i)

(j)

228

Hands On 1. Place a paper clip on the center of the circle and hold it in place with a pencil as shown. 2.

Flick the paper clip to spin it.

3. Race your friends to name the fractions. 4. The first person to correctly name the fractions is the winner and makes the next spin.

229

Hands On Play this game in pairs.

I rolled a 1 then a 5. My fraction is 51 !

1. Roll 1 dice as the numerator and another dice as the denominator. 2. Color the matching fraction below. 3. If the fraction is not below, or already colored, it's the other player's turn. 4. The first player to color all the fractions is the winner!

230

At Home 1. Complete.

1 2 2 (b) 3 1 (c) 7 3 (d) 5 6 (e) 8 3 (f) 4 (a)

has a numerator of

and a denominator of

has a numerator of

and a denominator of

has a numerator of

and a denominator of

has a numerator of

and a denominator of

has a numerator of

and a denominator of

has a numerator of

and a denominator of

2. Circle the fraction with the greatest denominator.

1 4 2 5 4 1 (b) 7 8 (a)

2 7 5 6

3 4 2 3

3. Circle the fraction with the smallest numerator.

6 5 7 8 1 2 (b) 2 5 (a)

4 6 3 4

3 5 4 5

231

4. Color to show the fraction. (a) three quarters (b) two sixths

(e) four fifths (f) four sixths

(g) three eighths (h) five sixths

232

5. Divide into equal parts and color to show the fraction. (a)

1 3 (b) 4 8

(c)

5 1 (d) 6 2

(e)

4 1 (f) 5 8

233

Write the fractions for each shape.

(a) is green.

is blue.

is orange.

is red.

is green.

is yellow.

is blue.

is purple.

is orange.

(b)

(c)

(d)

(e)

234

Solve It! Sophie, Michelle and Jordan each color a fraction of the circle with their favorite color. Together, they color the whole circle and their fractions are different from each other. Color the circle to show 1 possible way this can be done.

235

Fractions on a Number Line Anchor Task Can you show fractions on a number line?

Number Line

I think 21 should be in the center of 0 and 1.

236

Let’s Learn 1. Fold a piece of paper in half. The folded line is at the center of the paper.

1 2

1 2 folded line

We can find 1 on a number line in a similar way. 2

Divide the number line between 0 and 1 into 2 equal parts. 1 2

1 2

0 1 2

is between 0 and 1 on a number line!

2 halves make 1 whole. How many thirds make 1 whole?

237

2. Let’s divide a number line into 3 equal parts between 0 and 1. 1 3

1 3

2 3

1 3 of the way to 1. From 0, this is

2 3 of the way to 1. From 0, this is

1 3 3 of the way to 1. 3 =1 3 From 0, this is

3. The number line has been divided into 4 equal parts between 0 and 1. From 0, what is the fraction at the green arrow?

Each mark on the number line is separated by 1 . 4

1 4

1 3 4

There are 3 one quarter sections from 0 to the green arrow. So the green arrow is 3 . 4

238

Let’s Practice 1. Draw a point to show the fraction on the number line. (a) 1

(b) 1

0 (c)

1 4

(d) 5 6

(e) 3 4

(f) 3 6

1 239

2. Write the fraction shown on the number line. (a) 0

(b)

(c)

(d)

(e)

(f)

240

3. Fill in the blanks. 3 (a) is represented by point

B 2 4

1 (b) is represented by point

F 4 5

0 3 (c) is represented by point

S 4 8

4 (d) is represented by point 4

1 .

2 4

5 (e) is represented by point 7

X 0

1 . Y

Z 1 241

At Home 1. Write the fraction. (a)

(b)

(c)

(d)

242

2. Draw a point to show the fraction on the number line. (a) 1

(b) 2

3. Fill in the blanks. 2 (a) is represented by point

B 3 6

3 (b) is represented by point

S 4 5

0 5 (c) is represented by point

D 0

F 6 8

1 243

Comparing Fractions Let’s Learn Ethan and Dominic each bought a pizza of the same size for lunch. After lunch, they compared how much pizza they had left. I have 21 of the pizza left.

1 2

I have 31 of the pizza left.

1 3

Ethan has more pizza than Dominic. 1 3

1 2

We say:

1 is greater than 1 . 2 3

We write:

1 > 1 2 3

We say:

1 is smaller than 1 . 3 2

We write:

1 < 1 3 2

244

1 2

and 31 have a numerator of 1. They are unit fractions.

Let's compare some more unit fractions of the same size rectangle. 1 2 1 3 1 4 1 5

As the denominator increases, the size of the fraction decreases. We can see that 1 > 1 and 1 > 1 . 2

Compare other fractions you see. 1 4 1 > 1 2 4

1 2

1 1 5

1 < 1 5 2

We can use a number line to compare fractions! 1

1 5 1 > 1 3 5

1 2

1 3

245

4 circles of the same size are divided into 7 equal parts. Compare the colored fraction of each circle.

1 7

2 7

3 7

Each fraction has a denominator of 7.

4 7

As the numerator increases, the fraction becomes bigger!

When the denominator is the same, the size of the fraction increases as the numerator increases. We can see that 4 > 3 and 1 < 2 . 7

Showing the fractions on a number line can help us compare!

1 7

246

2 7

3 7

4 7

Let’s Practice 1. Fill in the blanks. (a)

The denominator of each fraction is

is greater than

(b)

The denominator of each fraction is

is smaller than

(c)

The denominator of each fraction is

is greater than

. 247

2. Write the unit fraction. Check the greater fraction (a)

(b)

(c)

(d)

248

3. Circle the greater fraction. (a) (c) (e)

6 7 3 5 6 8

5 7 2 5 4 8

1 4 2 (d) 7 2 (f) 5 (b)

3 4 5 7 5 5

4. Circle the smaller fraction. (a) (c) (e)

1 2 1 6 1 1

1 3 1 5 1 2

1 6 1 (d) 7 1 (f) 4 (b)

1 8 1 3 1 5

5. Compare the fractions by writing ' < ' or ' > '. (a) (c) (e)

2 6 5 5 5 8

3 6 4 5 3 8

2 7 1 (d) 7 2 (f) 3 (b)

4 7 2 7 1 3

249

At Home 1. Fill in the blanks. (a)

The denominator of each fraction is

is greater than

(b)

The denominator of each fraction is

is smaller than

(c)

The denominator of each fraction is 250

is greater than

2. Write the unit fraction. Check the greater fraction (a)

(b)

3. Compare the fractions by writing ' < ' or ' > '.

1 5 1 (c) 5 1 (e) 7 3 (g) 5 6 (i) 8 (a)

1 8 1 3 1 8 1 5 4 8

1 3 1 (d) 4 1 (f) 7 2 (h) 7 3 (j) 3 (b)

1 2 1 5 1 6 3 7 2 3

251

Equivalent Fractions Anchor Task

252

Let’s Learn Jordan, Blake and Dominic each have a paper strip of the same size. Jordan divides his paper strip into 2 equal parts. He colors 1 part. 1 of the paper 2 strip is colored.

Blake divides his paper strip into 4 equal parts. He colors 2 parts.

2 of the paper 4

strip is colored.

Dominic divides his paper strip into 8 equal parts. He colors 4 parts.

4 of the paper 8

strip is colored. Let’s compare each strip of paper. 1 2 2 4 4 8

The fractions 21 , 42 and 48 are equal. Equal fractions are called equivalent fractions. 1 2 4 = = 2 4 8

253

What fraction of each shape is shaded?

1 3 1 2 3, 6

and

2 6 3 9

3 9 1 3

are equivalent fractions.

2 6

3 9

6 9

What fraction of each shape is shaded?

2 3 2 4 3, 6

and

4 6 6 9

6 9 2 3

are equivalent fractions.

4 6

What fraction of each shape is shaded?

3 4 3, 6 4 8

254

and

6 8 9 12

are equivalent fractions.

9 12 3 4

6 8

9 12

Let’s Practice 1. What fraction of each shape is colored? Find the equivalent fractions. (a)

and

are equivalent fractions.

and

are equivalent fractions.

(b)

255

2. Fill in the blanks to label the equivalent fractions. (a)

1 2

1 3

3 4

(b)

(c)

(d)

256

3. (a) Circle the equivalent fraction of 1 . 2

2 3

2 4

2 5

(b) Circle the equivalent fraction of 1 . 4

1 2

3 6

2 8

2 10

3 8

1 2

(d) Circle the equivalent fraction of 2 . 3

6 9

1 3

3 6

(e) Circle the equivalent fraction of 3 . 4

1 2

3 8

9 12

(f) Circle the equivalent fraction of 1 . 2

4 6

4 8

4 12 257

Solve It! Use the fraction tiles to find 4 different pairs of equivalent fractions. Color the fraction pairs and write them below.

1 5

1 4

1 3

1 2

1 5

1 4

1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 1 8 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 1 10 10 10 10 10 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 1 12 12 12 12 12 12

1 2

1 3 1 5 1 7 1 9 1 11

1 4 1 6

1 5

258

1 4

1 5

1 6 1 1 1 7 7 7 1 1 1 1 8 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 1 10 10 10 10 10 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 1 12 12 12 12 12 12

(a) (b) =

1 6

1 3

At Home 1. Find the equivalent fractions. (a) A B C D

Fractions

and

are equivalent.

and

are equivalent.

and

are equivalent.

and

are equivalent.

(b) P Q R S

Fractions (c) W X Y Z

Fractions (d) L M N O

Fractions

259

2. Fill in the blanks to label the equivalent fractions. (a)

(b)

(c)

(d)

260

3. Circle the equivalent fractions. (a)

1 3

1 4

2 5

2 6

2 4

3 4

1 2

4 5

3 9

6 9

2 12

1 6

2 5

1 2

4 10

4 7

(b)

(c)

(d)

4. Write an equivalent fraction. (a) (b)

1 3

1 2

2 3

(e) (f) 3 =

1 4

(g) (h) 4 =

6 9

4 4

261

Looking Back 1.

Color and write the unit fraction.

(a) (b) (c)

2. Check the shapes that show 1 . 4

Write the fractions for each shape.

(a) is blue.

is orange.

is yellow.

is green.

(b)

262

4. Fill in the blanks. 2 (a) is represented by point

4 (b) is represented by point

5. Compare the fractions by writing ' < ' or ' > '.

1 2 4 (c) 7 (a)

1 5 6 7

(b) (d)

1 6 1 3

1 3 2 3

6. Circle the equivalent fractions. (a)

2 3

2 4

4 5

4 6

1 2

5 10

6 12

5 6

(b)

263

Data and Graphs

Picture Graphs With Scales Anchor Task Creatures in Springfield Nature Park Spiders Ants Beetles Butterflies

264

Let’s Learn The children in class 3A made a picture graph of their favorite fruits. Favorite Fruits Apple Orange Pear Mango 1

stands for 2 children.

Let’s look at what the picture graph shows. There are 4 2

for apple. 1 6

stands for 2 children. 8

4x2=8 In class 3A, 8 children like apples. There are 8 2

for mango. 6

8 x 2 = 16 In class 3A, 16 children like mangoes. 265

Chelsea, Sophie, Halle and Riley made a picture graph to compare the number of movies they watched in a year. Movies Watched This Year

Chelsea 1

Sophie

Halle

Riley

stands for 3 movies.

There are 3 3

for Sophie. 1

stands for 3 movies.

3x3=9 Sophie watched 9 movies. There are 5 3

for Chelsea. 9

How many more movies did Chelsea watch than Sophie?

5 x 3 = 15 Chelsea watched 15 movies. 15 – 9 = 6 Chelsea watched 6 more movies than Sophie. 2 66

Let’s Practice 1. The picture graph shows the number and color of Blake’s toy cars. Toy Cars at Home Blue Red Yellow Green 1

stands for 2 toy cars.

(a) How many red cars does Blake have?

Blake has

red cars.

(b) How many yellow cars does Blake have?

Blake has

yellow cars.

–

Blake has

more red cars than green cars.

(d) How many fewer blue cars than red cars does Blake have?

–

Blake has

= fewer blue cars than red cars. 2 67

2. The picture graph shows the animals Keira spotted during a field trip to the wetlands. Wetland Animals

Fish

Birds

Crabs

Frogs

Lizards

stands for 3 animals.

(a) Which animal did Keira spot the most? (b) How many fish and crabs did Keira spot in all?

Keira spotted

fish and crabs in all.

–

Keira spotted

more fish than lizards.

(d) How many animals did Keira spot that were not birds?

Keira spotted

26 8

= animals that were not birds.

3. The picture graph shows the money Riley saved in 5 weeks. Money Saved Week 1 Week 2 Week 3 Week 4 Week 5 1

stands for $5.

(a) In which week did Riley save $15? (b) How much money did Riley save in Week 4?

Riley saved $

in Week 4.

–

Riley saved $

= more in Week 3 than in Week 5.

(d) How much money did Riley save in the first three weeks?

Riley saved $

= in the first three weeks. 269

4. Wyatt recorded the number of animals he saw at the aquarium. Use the table he made to make a picture graph to represent the data. Animals at the Aquarium

Turtles

Fish

Penguins

Seals

Animals at the Aquarium Turtles Fish Penguins Seals 1

270

stands for 2 animals.

5. A florist recorded the different types of flowers she sold on the weekend. Use the table she made to make a picture graph to represent the data. Flowers Sold on the Weekend Roses

Daisies

Petunias

Lilies

Flowers Sold on the Weekend

Roses 1

Daisies

Petunias

Lilies

stands for 5 flowers.

271

Hands On Complete this activity in groups of 3-4 pupils. Think of a question you can ask the pupils in your school. Write the question and 4 answer options in the space below. Question:

Answer Options: 1. 2. 3. 4. Create a tally to record your data.

27 2

Create a picture graph with a scale to represent your data.

What can you learn from your picture graph?

273

(b) Home At 1. The picture graph shows the pets at Jimmy’s Pet Shop Pets at Jimmy’s Pet Shop Birds Rabbits Kittens Fish 1

stands for 3 animals.

(a) There are as many

(b) How many fish are at Jimmy’s Pet Shop?

There are

fish at Jimmy’s Pet Shop.

–

There are

more fish than rabbits.

(d) How many fewer kittens are there than birds?

–

There are

2 74

= fewer kittens than birds.

2. The tally shows the number of books borrowed from the school library on Friday. Complete the tally, then use the data to create a picture graph. Books Borrowed from the School Library on Friday Science

English

Mathematics

Other

Books Borrowed from the School Library on Friday

stands for

books. 275

Bar Graphs With Scales Let’s Learn The bar graph shows the number of shells each friend collected at the beach.

12 shells

8 shells

16 shells

14 shells

We can represent the data in a vertical bar graph with a scale. Shells Collected

18 16 14 12 Number of shells

10 8 6 4 2 0

276

Halle

Riley Michelle Friends

Keira

We can also use a horizontal bar graph with a scale. Shells We Collected Halle

Riley Friends Michelle

Keira

Longer bars represent greater values.

6 8 10 12 14 Number of shells

The blue bar is the longest!

277

Let’s Practice 1. Mrs. Jones recorded the number of each type of fruit she sold at the market.

8 pears

18 peaches

10 mangoes

6 apples

14 bananas

Color to represent Mrs. Jones’ sales data in a vertical bar graph. Fruit Sold at Market

20 18

Number of Fruits

16 14 12 10 8 6 4 2 0

Pears

Peaches

Mangoes Type of Fruit

278

Apples

Bananas

2. Blake counted the number of different color cars in the school parking lot.

15 red cars

27 white cars

15 blue cars

18 green cars 9 yellow cars

Represent the data in the horizontal bar graph. Cars in School Parking Lot

24 27 30 33

279

(b) Home At 1. Count the number of different creatures in the garden. Record your data on the next page.

280

2. Represent your data in the bar graph below. 16

Number of Creatures

14 12 10 8 6 4 2 0

281

Reading and Interpreting Bar Graphs Let’s Learn A fisherman recorded the number of fish he caught at sea during the week. He recorded his data in a bar graph. Fish Caught at Sea

Number of Fish

70 60 50 40 30 20 10 0

Mon

Tue

Wed Day

Thurs

Fri

The fisherman caught the fewest fish on Monday. He caught the most fish on Friday. The fisherman caught 30 fish on Monday and 45 fish on Tuesday. 30 + 45 = 75 On Monday and Tuesday the fisherman caught 75 fish in all. The fisherman caught 45 fish on Tuesday and 55 fish on Thursday. 55 – 45 = 10 The fisherman caught 10 more fish on Thursday than on Tuesday. 2 82

The bar graph shows the number of visitors to the zoo each week over 5 weeks.

Zoo Visitors Week 1 Week 2 Week 3 Week 4 Week 5 0

100

150

200 250 300 350 Number of Visitors

400

450

500

350 people visited the zoo during Week 1. 330 people visited the zoo during Week 2. 350 + 330 = 680 In the first 2 weeks, 680 people visited the zoo in all. 460 people visited the zoo during Week 4. 250 people visited the zoo during Week 5. 460 – 250 = 210 210 fewer people visited the zoo in Week 5 than in Week 4. 283

Let’s Practice 1. Mrs. Williams recorded the sales at her cafe from Monday to Friday. Cafe Sales Amount of Money ($)

70 60 50 40 30 20 10 0

Mon

Tue

Wed Day

(a) The sales were the same on

Thurs

Fri

and

(b) How much did Mrs. Williams make on Tuesday? $

–

Mrs. Williams made $