PR1ME Mathematics – Year 5 Coursebook

For Aotearoa New Zealand Schools

5

Coursebook

and

eal Z w f Ne istics o e g t vera and Sta 1-3 o c 100%ematics r Phases Mathculum fo i Curr Proven results in Aotearoa New Zealand schools for over a decade Clear, step-by-step lessons for consistent, explicit teaching Structured problem solving and reasoning for deep understanding

Multiplication Tables Let's Remember 1.

Complete the multiplication sentences. a)

b)

8 × 5 =

40

Complete the related multiplication and division facts.

7 a) 2 × = 14 b) 4 × 9 =

36

6×3= 2.

14 ÷ 2 =

18

7

36

÷9=4

EXPLORE Ella donated 5 cartons of water bottles in a charity.

There were 12 bottles in each carton. How many water bottles did Ella donate? 60

© 2027 Scholastic Education International (S) Pte Ltd

How can we solve this problem? Discuss in your group and fill in columns 1 and 2.

1. What I already know that will help me solve the problem

Multiply by 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Chapter 3: Multiplication Tables This edition is for QA submission only.

2. What I need to find out and learn

Multiply by 12.

3. What I have learnt

Answer varies.

71

Unit 1 Multiplication and Division Facts for 2s to 10s You will learn to...

• recall multiplication facts up to 10 × 10 and corresponding division facts

1.1 M ultiplication and division facts up to 10 × 10 Let's Learn

a)

×

1

2

3

4

5

6

7

8

9

10

1

1

2

3

4

5

6

7

8

9

10

2

2

4

6

8

10

12

14

16

18

20

3

3

6

9

12

15

18

21

24

27

30

4

4

8

12

16

20

24

28

32

36

40

5

5

10

15

20

25

30

35

40

45

50

6

6

12

18

24

30

36

42

48

54

60

7

7

14

21

28

35

42

49

56

63

70

8

8

16

24

32

40

48

56

64

72

80

9

9

18

27

36

45

54

63

72

81

90

10

10

20

30

40

50

60

70

80

90 100

2×5= 10

10

5×2= 10

÷5=2 10

To find the product of 2 and 5, we move along the row from the number 2 to the column with the number 5 .

We can also move along the row from the number 5 to the column with the number 2 .

÷2=5 10 2 and 5 are factors of .

10 is a multiple of 2 and 5.

72

Year 5: Number — Operations

This edition is for QA submission only.

Chapter 3: Multiplication Tables

© 2027 Scholastic Education International (S) Pte Ltd

We can use a multiplication chart to complete related multiplication and division facts.

8

b)

72 ÷ 9 =

9 72 ÷ 8 =

× 9 = 72 8

We move down the column with the number 9 to reach 72 and then move left to get the number in the 1st blue column.

× 8 = 72 9

We move down the column with the number 8 reach 72 and then move left to get the number in the 1st blue column.

8

and 9 are factors of 72.

72 is a multiple of 8 and 9.

Let's Do 1.

Complete the related multiplication and division facts.

8 a) 2 × 4 = b) 6 ×

8

÷ 4 = 2

c)

8

× 3 = 24 d) 8

24 ÷ 3 =

40

e)

4 × 10 = 40

6

= 36

6

36 ÷ 4

=6 × 7 = 28 4

28 ÷ 7 = 5

f)

9×

÷ 10 = 4

45 ÷

= 45

5

=9

Let's Practise 1.

Complete the related multiplication and division facts.

9 a) 2 × = 18 b) 3 × 6 =

18 ÷

9

= 2

c)

7

= 28

4×

7

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28 ÷ e)

g)

6 30 ÷ 5 =

7×8= 56

d)

= 4 × 5 = 30 f) 6

56

h)

÷ 8 = 7

18

18

÷6=3 5

7×

= 35

5

35 ÷ 6 54 ÷ 9 =

=7 × 9 = 54 6

9

× 10 = 90 9 90 ÷ 10 =

I have learnt to... recall multiplication facts up to 10 × 10 and corresponding division facts PB

Chapter 3: Multiplication Tables This edition is for QA submission only.

Chapter 3: Exercise 1.1, page 47

73

Unit 2 Multiplying and Dividing by 11 You will learn to...

• Multiply numbers within the multiplication table of 11 • Divide numbers using the multiplication table of 11

2.1 M ultiplying by 11 Let's Learn a)

Multiply 2 by 11.

2 groups of 11 = 22 2 × 11 = 22 Multiply 9 by 11.

9 × 11 = 99 11 × 9 = 99

74

Year 5: Number — Operations

This edition is for QA submission only.

9 × 11 = 99 and 11 × 9 = 99 are related multiplication facts.

Chapter 3: Multiplication Tables

© 2027 Scholastic Education International (S) Pte Ltd

b)

c)

Multiply 11 and 11.

1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 1 2 3 Add 1 group 4 of 11 5 6 7 8 9 10 11

11 × 11 is 11 more than 10 × 11.

10 × 11 = 110 d)

11 × 11 = 121

Multiply 12 and 11.

1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 1 2 3 Add 2 groups 4 of 11 5 6 7 8 9 10 11 12

12 × 11 is 22 more than 10 × 11.

10 × 11 = 110

12 × 11 = 132

Multiplication Table of 11 1 × 11 = 11 2 × 11 = 22 3 × 11 = 33 4 × 11 = 44 5 × 11 = 55 6 × 11 = 66

7 × 11 = 77 8 × 11 = 88 9 × 11 = 99 10 × 11 = 110 11 × 11 = 121 12 × 11 = 132

When you multiply 11 by a 1-digit number, the tens and ones places in the product have the same digits as the 1-digit number.

© 2027 Scholastic Education International (S) Pte Ltd

Let's Do 1.

Complete the multiplication sentences. a)

b)

3 × 11 = 11 × 3 =

33 33

Chapter 3: Multiplication Tables This edition is for QA submission only.

11 × 5 = 5 × 11 =

55 55

75

Let's Practise 1.

Complete the multiplication sentences.

1 × 11 = 2 × 11 = 3 × 11 = 4 × 11 =

11

5 × 11 =

22

6 × 11 =

33

7 × 11 =

44

8 × 11 =

55

9 × 11 =

66

10 × 11 =

77

11 × 11 =

88

12 × 11 = PB

99 110 121 132

Chapter 3: Exercise 2.1, page 48

2.2 D ividing by 11 Let's Learn We use related multiplication facts when we divide. a)

b)

6 × 11 = 66 11 × 6 = 66

66 ÷ 11 = 6

9 × 11 = 99 11 × 9 = 99

99 ÷ 11 = 9

Let's Do 1.

Complete the related multiplication and division facts. a)

3 × 11 = 33 11 × 3 = 33

b)

12 × 11 = 132

33 ÷ 11 = 3

11 × 12 = 132

132 ÷ 11 = 12

1.

Divide. a)

55 ÷ 11 =

5

c)

88 ÷ 11 =

8

d) PB

110 ÷ 11 =

11

Chapter 3: Exercise 2.2, page 49

I have learnt to...

Multiply numbers within the multiplication table of 11 Divide numbers using the multiplication table of 11

76

>> Look at EXPLORE on page 71 again.

Can you solve the problem now?

What else do you need to know?

Chapter 3: Multiplication Tables This edition is for QA submission only.

© 2027 Scholastic Education International (S) Pte Ltd

Let's Practise

Unit 3 Multiplying and Dividing by 12 You will learn to...

• Multiply numbers within the multiplication table of 12 • Divide numbers using the multiplication table of 12

3.1 M ultiplying by 12 Let's Learn a)

Arrange 12 square units into equal groups.

1 × 12 = 12 12 × 1 = 12

1 × 12 = 12 12 × 1 = 12 These are related multiplication facts.

2 and 6 are factors of 12.

So, the multiplication table of 12 is related to the multiplication tables of 2 and 6.

2 × 6 = 12 6 × 2 = 12 3 and 4 are factors of 12.

So, the multiplication table of 12 is related to the multiplication tables of 3 and 4.

3 × 4 = 12 © 2027 Scholastic Education International (S) Pte Ltd

4 × 3 = 12 The multiplication table of 12 is related to the multiplication tables of 2, 3, 4 and 6.

Chapter 3: Multiplication Tables This edition is for QA submission only.

Year 5: Number — Operations

77

b)

When we double the products in the multiplication table of 6, we get the products in the multiplication table of 12.

Multiplication Table of 6

×2

1×6=6 2 × 6 = 12 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 10 × 6 = 60

c)

1 × 12 = 12 2 × 12 = 24 3 × 12 = 36 4 × 12 = 48 5 × 12 = 60 6 × 12 = 72 7 × 12 = 84 8 × 12 = 96 9 × 12 = 108 10 × 12 = 120

5 × 6 = 30 ×2

×2

5 × 12 = 60 The product of 5 × 12 is double the product of 5 × 6.

Double 30 is 60.

When we triple the products in the multiplication table of 4, we get the products in the multiplication table of 12.

Multiplication Table of 4

×3

Multiplication Table of 12 1 × 12 = 12 2 × 12 = 24 3 × 12 = 36 4 × 12 = 48 5 × 12 = 60 6 × 12 = 72 7 × 12 = 84 8 × 12 = 96 9 × 12 = 108 10 × 12 = 120

5 × 4 = 20 ×3

×3

5 × 12 = 60 The product of 5 × 12 is triple the product of 5 × 4.

© 2027 Scholastic Education International (S) Pte Ltd

1×4=4 2×4=8 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 10 × 4 = 40

78

Multiplication Table of 12

Chapter 3: Multiplication Tables This edition is for QA submission only.

d)

Multiply 11 and 12.

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 12

Add 1 group of 12

1 2 3 4 5 6 7 8 9 10 11

11 × 12 is 12 more than 10 × 12.

10 × 12 = 120 e)

11 × 12 = 132

Multiply 12 and 12.

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 Add 2 groups 4 of 12 5 6 7 8 9 10 11 12

12 × 12 is 24 more than 10 × 12.

10 × 12 = 120

12 × 12 = 144

Let's Do 1.

Complete the multiplication sentences.

© 2027 Scholastic Education International (S) Pte Ltd

a)

b)

4 × 12 =

48

12 × 7 =

84

12 × 4 =

48

7 × 12 =

84

Chapter 3: Multiplication Tables This edition is for QA submission only.

79

Let's Practise 1.

Complete the multiplication sentences.

1 × 12 = 2 × 12 = 3 × 12 = 4 × 12 =

12

5 × 12 =

24

6 × 12 =

36

7 × 12 =

48

8 × 12 =

60

9 × 12 =

72

10 × 12 =

84

11 × 12 =

96

12 × 12 = PB

108 120 132 144

Chapter 3: Exercise 3.1, page 50

3.2 D ividing by 12 Let's Learn We use related multiplication facts when we divide. a)

3 × 12 = 36

36 ÷ 12 = 3

12 × 3 = 36 b)

9 × 12 = 108

108 ÷ 12 = 9

12 × 9 = 108

Let's Do Complete the related multiplication and division facts. a)

4 × 12 = 48 12 × 4 = 48

b)

10 × 12 = 120

48 ÷ 12 = 4

12 × 10 = 120

120 ÷ 12 = 10

Let's Practise 1.

Divide. a)

72 ÷ 12 =

6

b)

60 ÷ 12 =

5

d) PB

144 ÷ 12 =

12

Chapter 3: Exercise 3.2, page 51

I have learnt to...

Multiply numbers within the multiplication table of 12 Divide numbers using the multiplication table of 12

80

Chapter 3: Multiplication Tables This edition is for QA submission only.

© 2027 Scholastic Education International (S) Pte Ltd

1.

Unit 4 Problem Solving You will learn to...

• solve 1-step word problems involving multiplication and division • solve non-routine problems involving multiplication tables

4.1 Word problems Let's Learn A shop has 3 packets of pens. Each packet has 12 pens. How many pens does the shop have in all?

1U

nderstand the problem.

How many packets of pens are there?

How many pens are there in each packet?

What do I need to find?

Mārama

2P

lan what to do.

I should multiply to find the total number of pens in the shop.

Whakaaro

3A

Work out the

12

nswer.

Whakaatu

?

© 2027 Scholastic Education International (S) Pte Ltd

3 × 12 = 36 The shop has 36 pens in all.

4

Check

if your answer is correct.

36 ÷ 12 = 3 My answer is correct.

Tirohia

Chapter 3: Multiplication Tables This edition is for QA submission only.

Year 5: Number — Operations

81

5

Draw pictures to represent the packets of pens.

+ Plus

Solve the problem in another way.

Tāpiri

3 × 12 = 36 The shop has 36 pens in all.

Compare the methods in steps 3 and 5.

Which method do you prefer? Why? 1. Understand

2. Plan

3. Answer

4. Check

5. Plus

Let's Do Solve the word problems. Use the bar models to help you. Show your work clearly.

Next, try solving each problem in a different way. Which method do you prefer? Why? 1. Understand

2. Plan

3. Answer

4. Check

5. Plus

1. A florist has 72 roses. She needs 12 roses to make a bouquet. How many bouquets can she make? 6 72

2. Jack has 11 toy cars. Noah has five times as many toy cars as Jack.

How many toy cars does Noah have? 55 11 Jack Noah ?

82

Chapter 3: Multiplication Tables This edition is for QA submission only.

© 2027 Scholastic Education International (S) Pte Ltd

12

Let's Practise Solve the word problems. Show your work clearly.

1. Wiremu bought 6 boxes of marbles. There were 11 marbles in each box.

How many marbles did he buy altogether? 66 2. Ariki saved $4 in a week. His sister saved 12 times as much money as him.

How much money did Ariki’s sister save? $48 3. Oliver jogged a total distance of 44 kilometres over 11 days. He jogged the same distance each day. How many kilometres did he jog each day? 4 km 4. 144 children were divided into teams of 12. How many teams were there? 12 PB

Chapter 3: Exercise 4.1, pages 52–53

CREATE YOUR OWN Grace

cousin

3 years

Read the given words.

Use the words and the bar model to write a multiplication word problem. How did you come up with the word problem?

Answer varies. Sample: Grace is 3 years old. Her cousin is 12 times as old as her. How old is Grace’s cousin?

12 × 3 = 36 Grace’s cousin is 36 years old.

© 2027 Scholastic Education International (S) Pte Ltd

Next, solve the word problem. Show your work clearly. What did you learn?

Chapter 3: Multiplication Tables This edition is for QA submission only.

83

4.2 Mind stretcher Let's Learn Viliami is 3 years old this year. His mother is 11 times as old as him. In how many years' time will his mother be 3 times his age?

1U

nderstand the problem.

How old is Viliami this year?

How many times is his mother as old as him?

Will the difference in their age change?

What do I have to find?

Mārama

2P

lan what to do.

First, I find his mother's age this year.

Then, I find the difference in their age.

I can draw a bar model.

Whakaaro

3A

3

Work out the nswer.

Viliami

Whakaatu

Mother ? years

33 ?

Viliami Mother

33 − 3 = 30 30 ÷ 2 = 15 Viliami will be 15 years old when his mother is 3 times his age.

15 − 3 = 12 In 12 years’ time, Viliami’s mother will be 3 times his age.

84

Chapter 3: Multiplication Tables This edition is for QA submission only.

© 2027 Scholastic Education International (S) Pte Ltd

3 × 11 = 33 Viliami’s mother is 33 years old this year.

4

Check

if your answer is correct.

Tirohia

5

15 × 3 = 45 45 − 33 = 12 My answer is correct.

Guess and check to solve the problem.

+ Plus

Solve the problem in another way.

Tāpiri

3 × 11 = 33 Viliami’s mother is 33 years old this year.

33 – 3 = 30 Difference between their age is 30 years.

Guess Viliami’s age.

Viliami’s age

Mother’s age

Mother’s age is 3 times?

10 years

40 years

✗

12 years

42 years

✗

15 years

45 years

✓

Viliami will be 15 years old when his mother is 3 times his age.

15 − 3 = 12 In 12 years’ time, Viliami’s mother will be 3 times his age.

Compare the methods in steps 3 and 5.

Which method do you prefer? Why? 2. Plan

© 2027 Scholastic Education International (S) Pte Ltd

1. Understand

Chapter 3: Multiplication Tables This edition is for QA submission only.

3. Answer

4. Check

5. Plus

85

Let's Do Look at the number pattern below.

1,000, 988, 976, 964,

,

, 928, 916, 904

What are the two missing numbers?

Strategy: Look for a pattern.

1,000, 988, 976, 964, – 12

– 12

,

, 928, 916, 904

– 12

– 12

– 12

The next number decreases by 12 from the previous number each time.

964 – 12 = 952 952 – 12 = 940

I have learnt to... solve 1-step word problems involving multiplication and division solve non-routine problems involving multiplication tables

>> Look at EXPLORE on page 71 again.

Fill in column 3. Can you solve the problem now?

86

Chapter 3: Multiplication Tables This edition is for QA submission only.

© 2027 Scholastic Education International (S) Pte Ltd

The two missing numbers are 952 and 940.