multiplication-and-division-student.pdf

Multiplication

and Division

My name

Student

Series

E

First edition printed 2009 in Australia.

A catalogue record for this book is available from 3P Learning Ltd.

ISBN 978-1-921860-58-4

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Series E – Multiplication and Division

Contents

Topic 1 – Mulplicaon facts (pp. 1–14)

• 5 and 10 mes tables

__________________________

• 2 and 4 mes tables

___________________________

• 8 mes table

_________________________________

• 3 and 6 mes tables

___________________________

• 6 mes tables

________________________________

• 7 mes tables

________________________________

• 9 mes table

_________________________________

• 11 mes table

________________________________

• 12 mes table

________________________________

Topic 2 – Using known facts (pp. 15–16)

• factors and mulples

___________________________

Topic 3 – Mental mulplicaon strategies (pp. 17–29)

• mulplying by 10 and 100

_______________________

• mulplying/dividing by 0 and 1

___________________

• mulplying 3 numbers

_________________________

• doubling strategy

______________________________

• split strategy

_________________________________

• compensaon strategy

_________________________

• choose a strategy

______________________________

• doubling and halving

___________________________

• word problems

_______________________________

Topic 4 – Division (pp. 30–34)

• division is sharing and grouping

__________________

• division is repeated subtracon

__________________

• linking mulplicaon and division facts

____________

Date completed

/ /

Series E – Multiplication and Division

Contents

Topic 5 – Mental division strategies (pp. 35–41)

• dividing by 10 and 100

_________________________

• halving strategy

_______________________________

• split strategy

_________________________________

• word problem

________________________________

Topic 6 – Wrien methods (pp. 42–46)

• short mulplicaon

____________________________

• short division

_________________________________

• short division with 3-digit numbers

_______________

Topic 7 – Paerns and algebra (pp. 47–58)

• skip counng

_________________________________

• compleng and describing paerns

_________________

• predicng repeang paerns

____________________

• predicng growing paerns

_____________________

• funcon machines

_____________________________

• understanding equivalence

______________________

• balanced equaons using + and ×

_________________

• using symbols for unknowns

_____________________

Topic 8 – Games and invesgaons (pp. 59–63)

• triple product – apply

__________________________

• factor bingo – apply

____________________________

• doubling strategy to 20 – apply

___________________

• symbols – solve

_______________________________

Date completed

/ /

Series Author:

Nicola Herringer

SERIES TOPIC

1

E 1

Multiplication and Division

Count in 5s down the ladders:

Fill in the missing number for each mes

table fact:

Answer the 5 mes table:

1 × 5 =

2 × 5 =

3 × 5 =

4 × 5 =

5 × 5 =

6 × 5 =

7 × 5 =

8 × 5 =

9 × 5 =

10 × 5 =

11 × 5 =

12 × 5 =

Complete the 5 mes table turnarounds.

Multiplication facts – 5 and 10 times tables

The 5 and 10 mes tables are easier if you learn them together.

1

4

2

3

Turnaround facts

are the mes tables

turned around!

3 × 5 = 15 5 × 3 = 15

a 5 × 8 =

c 5 × 10 =

b 5 × 3 =

d 5 × 4 =

a × 5 = 25

c

× 5 = 30

e

× 5 = 35

b

× 5 = 45

d

× 5 = 50

f

× 5 = 40

a b c

755 40

SERIES TOPIC

E 1

2

Multiplication and Division

Answer the 10

mes table:

1 × 10 =

2 × 10 =

3 × 10 =

4 × 10 =

5 × 10 =

6 × 10 =

7 × 10 =

8 × 10 =

9 × 10 =

10 × 10 =

11 × 10 =

12 × 10 =

Follow the arrows by counng up in 10s:

Multiplication facts – 5 and 10 times tables

5

8

9

6

Mulply each number in the top row by 5 and then by 10:

What do you noce? __________________________________________________

×

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

5

10

Write the missing

numbers for these

5 mes table facts:

a

× 5 = 35

b 5 × 5 =

c × 5 = 30

d 5 ×

= 45

e

× 5 = 15

f 5 ×

= 10

g 5 ×

= 20

Write the missing

numbers for these

10 mes table facts:

a

× 10 = 30

b 10 × 5 =

c × 10 = 20

d 10 × 9 =

e × 10 = 60

f

× 10 = 70

g 10 × 10 =

7

SERIES TOPIC

3

E 1

Multiplication and Division

a b

Multiplication facts – 2 and 4 times tables

The 2 and 4 mes tables are good facts to learn together.

Complete these

doubling wheels as

quickly as you can.

Mulplying by 2

is the same as

doubling.

1

2 3

4

Complete the skip counng paern of 2:

Answer the 2 mes table. One is in order, the

other is mixed up.

42

1 × 2 =

2 × 2 =

3 × 2 =

4 × 2 =

5 × 2 =

6 × 2 =

7 × 2 =

8 × 2 =

9 × 2 =

10 × 2 =

11 × 2 =

12 × 2 =

7 × 2 =

10 × 2 =

6 × 2 =

8 × 2 =

1 × 2 =

9 × 2 =

4 × 2 =

3 × 2 =

2 × 2 =

5 × 2 =

11 × 2 =

12

18

1320

16

15

Double

50

17

10019

14

24

Double

It is useful to be able to

mulply numbers above

10 by 2. Try these:

13 × 2 =

14 × 2 =

15 × 2 =

16 × 2 =

17 × 2 =

18 × 2 =

19 × 2 =

20 × 2 =

SERIES TOPIC

E 1

4

Multiplication and Division

Multiplication facts – 2 and 4 times tables

Now for the 4 mes table. The 4 mes table is just double the 2 mes table.

This is handy to remember if you forget a 4 mes table fact.

The 2 mes

table should

be easier, so

complete it

rst. Then

double each

of the 2

mes table

facts to get

the 4 mes

table facts:

Write the missing

numbers for these

4 mes table facts:

a

× 4 = 8

b

× 4 = 16

c

× 4 = 40

d

× 4 = 24

e

× 4 = 12

f

× 4 = 36

g

× 4 = 20

h

× 4 = 28

Use the hint to get the answer. Then ll in the missing digit to make the 4 mes

table fact complete:

Look at the numbers in the grid

and circle 3 numbers that would

make a mulplicaon fact. Look

for × 2 and × 4 facts. They are

either le to right or top to

boom. The rst one has been

done for you. There are 10 to nd.

5 6

7

8

a

Hint: Double 16

× 4 =

b

Hint: Double 12

× 4 =

c

Hint: Double 18

× 4 =

4 3 12 4 8 32

4 1 3 2 7 1

16 5 3 8 2 9

3 4 6 24 14 4

2 8 16 7 9 36

9 2 18 10 2 20

1 × 2 =

2 × 2 =

3 × 2 =

4 × 2 =

5 × 2 =

6 × 2 =

7 × 2 =

8 × 2 =

9 × 2 =

10 × 2 =

11 × 2 =

12 × 2 =

1 × 4 =

2 × 4 =

3 × 4 =

4 × 4 =

5 × 4 =

6 × 4 =

7 × 4 =

8 × 4 =

9 × 4 =

10 × 4 =

11 × 4 =

12 × 4 =

SERIES TOPIC

5

E 1

Multiplication and Division

Multiplication facts – 8 times table

Here is the 8 mes table. You can double the 4 mes table to get the 8 mes table.

Complete the

4 mes table as

quickly as you

can. Then aer

you have checked

them, double them

to complete the

8 mes table facts:

Use double, double and double again for these problems:

a

6 × 8 =

b

4 × 8 =

c

9 × 8 =

On Mia’s calculator, the 8

key is broken. Show her the

steps she could follow to nd

the answer to 16 × 8. Use a

calculator to test the steps.

1

2

3

1 × 4 =

2 × 4 =

3 × 4 =

4 × 4 =

5 × 4 =

6 × 4 =

7 × 4 =

8 × 4 =

9 × 4 =

10 × 4 =

11 × 4 =

12 × 4 =

1 × 8 =

2 × 8 =

3 × 8 =

4 × 8 =

5 × 8 =

6 × 8 =

7 × 8 =

8 × 8 =

9 × 8 =

10 × 8 =

11 × 8 =

12 × 8 =

If you get stuck on the 8s,

think double, double and

double again.

For example, 3 × 8

Think: double 3 is 6

double 6 is 12

double 12 is 24

SERIES TOPIC

E 1

6

Multiplication and Division

Multiplication facts – 3 and 6 times tables

Here are the 3 mes and 6 mes tables together. Can you think of why it’s

beer to learn these facts together?

Use the

picture of the

dice above

to complete

both the

3 mes

table and the

6 mes table:

Fill in the missing digits to make these mes table facts complete:

1

3

Now try these

mixed up:

a 3 × 6 =

b 4 × 3 =

c 8 × 3 =

d 9 × 6 =

e 4 × 6 =

f 5 × 3 =

g 8 × 6 =

h 9 × 3 =

i 5 × 6 =

2

1 × 3 =

2 × 3 =

3 × 3 =

4 × 3 =

5 × 3 =

6 × 3 =

7 × 3 =

8 × 3 =

9 × 3 =

10 × 3 =

11 × 3 =

12 × 3 =

1 × 6 =

2 × 6 =

3 × 6 =

4 × 6 =

5 × 6 =

6 × 6 =

7 × 6 =

8 × 6 =

9 × 6 =

10 × 6 =

11 × 6 =

12 × 6 =

a 3 × 3 =

d 6 × = 36

g

× 9 = 27

j 5 ×

= 30

b

× 2 = 6

e 3 ×

= 24

h 6 ×

= 42

k

× 6 = 48

c

× 3 = 18

f

× 6 = 60

i 9 ×

= 54

l 7 ×

= 21

SERIES TOPIC

7

E 1

Multiplication and Division

Multiplication facts – 3 and 6 times tables

Match the answers to the quesons. Each answer has two matching quesons.

Complete the cross number puzzle:

What number am I? I am in the 3 mes table, 4 mes table and 6 mes table.

I’m not 12.

I am

4

5

6

2 × 3 6 × 2 1 × 63 × 4 5 × 6

4 × 6 3 × 8 8 × 616 × 3 3 × 10

30 48 12 6 24

Across

2. 9 × 3

3. 3 × 6

6. 5 × 6

8. 7 × 6

Down

1. 8 × 6

4. 10 × 6

5. 9 × 6

6. 6 × 6

7. 4 × 6

9. 6 × 3

10. 7 × 3

1 2

3 4

5 6

7

8 9 10

SERIES TOPIC

E 1

8

Multiplication and Division

Change these × 5 arrays into × 6 arrays.

a

+

2 × 5 = +



2 × 6 =

b

+

4 × 5 = +



4 × 6 =

Complete this table to show how to change a × 5 array to a × 6 array by building

up. The rst one has been done for you.

1

2

You know more mes tables facts than you

realise. For example, knowing your × 5 can help

with your × 6.

The array shows 3 rows of 5. If we add another

dot to each row we can change 3 rows of 5 to 3

rows of 6. This is called building up.

3 × 5 = 15 + 3



3 × 6 = 18

Multiplication facts – 6 times table

× 5 Number to add × 6

a 3 × 5 = 15

3 3 × 6 = 18

b 2 × 5 = 10

c 7 × 5 = 35

d 4 × 5 = 20

e 6 × 5 = 30

f 9 × 5 = 45

+

SERIES TOPIC

9

E 1

Multiplication and Division

1 2

Pracse your 7 mes table.

Multiplication facts – 7 times table

Use this array to complete

the 7 mes table:

Fill in the missing

numbers:

a

× 7 = 63

b

× 7 = 42

c

× 7 = 21

d

× 7 = 28

e

× 7 = 35

f

× 7 = 49

g

× 7 = 56

4

Solve these problems.

a Boxes of oranges hold 8 oranges each. If I have

7 boxes, how many oranges do I have altogether?

× =

b Our hockey team scored 3 goals in each of our

7 games. How many goals did we score in total?

× =

c There are 35 frogs in the glass cases at the zoo.

Each case hold 7 frogs. How many cases are there?

× =

3

Complete these × 7 facts. Look out for turnarounds.

1 × 7 =

2 × 7 =

3 × 7 =

4 × 7 =

5 × 7 =

6 × 7 =

7 × 7 =

8 × 7 =

9 × 7 =

10 × 7 =

11 × 7 =

12 × 7 =

a

4 × 7 =

d

7 × 5 =

b

7 × 7 =

e

9 × 7 =

c

7 × 2 =

f

7 × 3 =

SERIES TOPIC

E 1

10

Multiplication and Division

Multiplication facts – 7 times table

5

6

7

If you get stuck on a 7 mes table fact, remember the 8 mes table fact and

build down.

Think of the × 8 table fact to get the × 7 table fact.

Add the missing numbers to each fact:

Use the × 8 to complete the × 7:

a

× 7 = 28

d

× 7 = 42

b

× 7 = 35

e

× 7 = 49

c

× 7 = 21

f

× 7 = 14

× 8 table Number to subtract × 7 table

1 × 8 = 8 1 1 × 7 =

2 × 8 = 16 2 2 × 7 =

3 × 8 = 24 3 3 × 7 =

4 × 8 = 32 4 × 7 =

5 × 8 = 40 5 × 7 =

6 × 8 = 48 6 × 7 =

7 × 8 = 56 7 × 7 =

8 × 8 = 64 8 × 7 =

9 × 8 = 72 9 × 7 =

10 × 8 = 80 10 × 7 =

11 × 8 = 88 11 × 7 =

12 × 8 = 96 12 × 7 =

×

11 4 2 6 1 12 9 5 3 7 8

8

7

SERIES TOPIC

11

E 1

Multiplication and Division

1

2

3

Use this array to complete

the 9 mes table:

Complete these × 9 facts. Look out for turnarounds.

Find the cost of these items:

Pracse your 9 mes table.

Multiplication facts – 9 times table

a 3 × 9 =

d 2 × 9 =

b 9 × 4 =

e 9 × 5 =

c 6 × 9 =

f 1 × 9 =

Mango juice £3

Banana split £6

Fruit salad £9

a 6 fruit salads =

c 3 mango juices =

e 3 banana splits =

b 4 banana splits =

d 5 fruit salads =

f 7 mango juices =

1 × 9 =

2 × 9 =

3 × 9 =

4 × 9 =

5 × 9 =

6 × 9 =

7 × 9 =

8 × 9 =

9 × 9 =

10 × 9 =

11 × 9 =

12 × 9 =

SERIES TOPIC

E 1

12

Multiplication and Division

Multiplication facts – 9 times table

5

Complete the × 9:

Think of the × 10 facts and build down to get the × 9 facts. The rst one is done for you.

4

If you get stuck on a 9 mes table fact,

you can use the 10 mes table facts

and then build down.

3 × 9 =

?

3 × 10 = 30 − 3



So, 3 × 9 = 27

×

2 6 4 8 12 3 9 10 5 7 11

9

× 10 table Number to subtract × 9 table

1 × 10 = 10

1 1 × 9 = 9

2 × 10 = 20

3 × 10 = 30

4 × 10 = 40

5 × 10 = 50

6 × 10 = 60

7 × 10 = 70

8 × 10 = 80

9 × 10 = 90

10 × 10 = 100

11 × 10 = 110

12 × 10 = 120

Can you see a

paern in the

numbers in the

9 mes table?

As the numbers

get larger the

tens digit goes

up one and the

ones digit goes

down one.

If you want to

check whether a

number is in the 9

mes table add its

digits together. If

the answer is 9, then

it is! For example, if

you add the digits of

27 together, you get

9 (2 + 7 = 9), so you

know that 27 is in

the 9 mes table.

SERIES TOPIC

13

E 1

Multiplication and Division

1

2

Use this array to complete the 11 mes table:

Complete these × 11 facts. Look out for turnarounds.

Pracse your 11 mes table. Can you see the paern?

Multiplication facts – 11 times table

1 × 11 =

2 × 11 =

3 × 11 =

4 × 11 =

5 × 11 =

6 × 11 =

7 × 11 =

8 × 11 =

9 × 11 =

10 × 11 =

11 × 11 =

12 × 11 =

a

3 × 11 =

d

4 × 11 =

b

11 × 5 =

e

11 × 9 =

c

7 × 11 =

f

8 × 11 =

3

Solve these problems.

a There are 11 players in a football team and 10 teams

in the league. How many players are there in total?

× =

b On each of our 6 class tables is a pot containing

11 pencils. How many pencils are there altogether?

× =

c On our school trip we split our class of 33 into groups

of 11. How many children were in each group?

× =

SERIES TOPIC

E 1

14

Multiplication and Division

1

2

Use this array to complete the 12 mes table:

Complete these × 12 facts. Look out for turnarounds.

Pracse your 12 mes table.

Multiplication facts – 12 times table

1 × 12 =

2 × 12 =

3 × 12 =

4 × 12 =

5 × 12 =

6 × 12 =

7 × 12 =

8 × 12 =

9 × 12 =

10 × 12 =

11 × 12 =

12 × 12 =

a

3 × 12 =

d

4 × 12 =

b

12 × 5 =

e

12 × 3 =

c

7 × 12 =

f

12 × 9 =

3

Solve these problems.

a I make 3 batches of 12 cookies. How many cookies

is this altogether?

× =

b A orist is selling bunches of 12 roses. She sells

6 bunches. How many roses is this?

× =

c Eggs cost £3 for a dozen? If I spend £15 on eggs,

how many eggs have I bought in total?

× =

SERIES TOPIC

15

E 2

Multiplication and Division

Using known facts – factors and multiples

When 2 numbers are mulpled together, the answer is called a mulple.

The rst 3 mulples of 2 are 2, 4, 6.

1 × 2 = 2 2 × 2 = 4 3 × 2 = 6

5, 10, 15, 20, 25, 30, 35, 40, 45, 50 are the rst 10 mulples of 5.

1

2

3

List the rst 12 mulples of each number:

a 6

6

b 2

2

c 10

d 3

e 4

Write these numbers in the correct spots on the Venn diagram:

Can you think of any other numbers up to 60 that could go into the overlapping

space in the Venn diagram above?

Mulples

of 2

Mulples

of 3

The space in the

diagram where the

circles overlap is where

you put numbers that are

both mulples of 2 and 3.

8 4 9 6 12 3

SERIES TOPIC

E 2

16

Multiplication and Division

Using known facts – factors and multiples

Complete each diagram to show the factors of the number in the middle circle:

Complete the number sentence for each set of arrays and then list the factors.

4

5

a

× =

c

× =

Factors are numbers that you mulply together to give a mulple.

These arrays show some of the factors of 18: 3, 6, 2 and 9.

Can you think of any other factors of 18?

3 × 6 = 18 2 × 9 = 18

b

× =

d The factors of 12 are:

______________________

a

b

c

24

12

2

30

16

SERIES TOPIC

17

E 3

Multiplication and Division

a

c

b

Mental multiplication strategies – multiplying by 10 and 100

Use paerns to solve these:

a 14 × 1 =

14 × 10 =

14 × 100 =

b 25 × 1 =

25 × 10 =

25 × 100 =

c 82 × 1 =

82 × 10 =

82 × 100 =

Use the place value tables to mulply these numbers by 10 and 100:

1

2

Th H T O

1 5 ×

10

100

Th H T O

7 2 ×

10

100

Th H T O

4 8 ×

10

100

Can you see a paern

in each of the tables?

When we mulply any whole number by 10, the number is geng 10 mes

bigger. This means that each digit moves one place value column to the le and

we use 0 as a place holder in the ones column.

When we mulply any whole number by 100 the number gets 100 mes bigger.

This means that each digit moves two place value columns to the le and we

use 0 as a place holder in the ones and tens columns.

Thousands Hundreds Tens Units

4 5 ×

4 5 0 10

4 5 0 0 100

SERIES TOPIC

E 3

18

Multiplication and Division

Mental multiplication strategies – multiplying by 10 and 100

How do you mulply by other mulples of 10? Let’s look at 8 × 20.

We can use known mes tables facts and write this as place value amounts:

8 × 2 tens = 16 tens So, 8 × 20 = 160

3

4

5

6

Draw lines from the numbers wrien as place value amounts to the mes tables facts:

Write the digit that represents each place value amount:

First complete the hints and then use them to write the facts:

Hints: Facts:

a 4 × 6 tens =

tens 4 × 60 =

b 9 × 2 tens = tens 9 × 20 =

c 2 × 7 tens = tens 2 × 70 =

Complete the

number wheels:

a 10 tens =

d 15 tens =

g 19 tens =

b 36 tens =

e 22 tens =

h 16 tens =

c 12 tens =

f 8 tens =

i 18 tens =

10 tens 14 tens 36 tens 27 tens 12 tens 16 tens

a b

3 × 4 tens 4 × 4 tens 5 × 2 tens 7 × 2 tens 6 × 6 tens 9 × 3 tens

2

10

8

7

4

3

95

× 30

2

7

4

8

6

9

35

× 40

SERIES TOPIC

19

E 3

Multiplication and Division

Solve these calculaons:

Mental multiplication strategies – multiplying/dividing

by 0 and 1

If you mulply by 0 the answer will always be 0.

5 × 0 means ‘5 lots of 0’, which is nothing.

The answer is not going to change, whether you have 5 or 35 or 3,005 lots of

nothing. The answer will always be zero.

Mulplying by 1 is also very simple.

8 × 1 means ‘8 lots of 1’. 73 × 1 means ‘73 lots of 1’, which is 73.

So if you mulply any number by 1 the answer will always be the number with

which you started.

Dividing by 1 is straighorward too. If we divide a number, we are working out

how many equal groups can be made from that number. So, 10 ÷ 1 means ‘we

have 10 and we want to make one group with it’. How many will be in that one

group? The answer is 10. So, as with mulplying by 1, you always end up with

your starng number when you divide by 1.

3 ÷ 1 = 3 333 ÷ 1 = 333 33 333 ÷ 1 = 33 333

(In case you are wondering, you can’t divide by 0. We can’t split, say, a bag of

sweets into groups of nothing – it doesn’t make any sense to divide a number

by zero. It can’t be done. We say that dividing by 0 is undened.)

1

a 6 × 1 =

d 59 × 0 =

f 43 ÷ 1 =

h 666 × 0 =

j 999 ÷ 1 =

l 2344 × 1 =

b 9 ÷ 1 =

e 73 × 1 =

g 848 ÷ 1 =

i 424 × 1 =

k 0 × 0 =

m 74 ÷ 0 =

3 × 1 = 3

3 ÷ 1 = 3

3 × 0 = 0

3 ÷ 0 = impossible!

c 11 × 0 =

SERIES TOPIC

E 3

20

Multiplication and Division

Solve these mulplicaons:

Mental multiplication strategies – multiplying 3 numbers

There is a law in maths called the Commutave Law. This states that for certain

types of calculaon, the order of the numbers doesn’t maer. The answer will

be the same. It is true for addion.

3 + 4 = 7 4 + 3 = 7

62 + 19 = 71 19 + 62 = 71

The same is true for mulplicaon.

5 × 2 = 10 2 × 5 = 10

8 × 7 = 56 7 × 8 = 56

If you are mulplying more than two numbers, the Commutave Law sll applies.

3 × 2 × 6 = 36 6 × 2 × 3 = 36 2 × 6 × 3 = 36

2 × 3 × 6 = 36 6 × 3 × 2 = 36 3 × 6 × 2 = 36

1

a 4 × 4 × 2 =

c 7 × 3 × 2 =

e 6 × 3 × 2 =

b 3 × 10 × 5 =

d 5 × 8 × 3 =

f 10 × 8 × 10 =

a 13 × 23 × 8 = 2392 × × = 2392

× × = 2392

b 7 × 14 × 26 = 2548 × × = 2548

× × = 2548

Does the Commutave

Law work for subtracon

and division too?

2

Using the Commutave Law, create two dierent correct

mulplicaons using the same numbers:

SERIES TOPIC

21

E 3

Multiplication and Division

a b

Complete these funcon machines:

Mental multiplication strategies – doubling strategy

There are many double facts that you should know.

This includes numbers outside the mes tables we have been working on.

Here are 2 double facts that are handy to know:

double 15 is 30 double 50 is 100 Can you think of more?

1

Double

IN OUT

15 30

24

30

45

18

Double-double

IN OUT

15 60

24

30

45

50

2

Complete these doubling wheels:

7

4

911

8

15

Double

21

25

3241

12

50

Double

Can you see what

double-double is the

same as? Yes, that’s right,

it’s the same as × 4.

SERIES TOPIC

E 3

22

Multiplication and Division

Mental multiplication strategies – doubling strategy

Keep doubling to get the × 4 and × 8 facts. Here are some tables to help you. The

rst one has been done for you.

3

In this last table

choose a 2-digit

number to mulply

by 8 and double it

three mes.

We also use doubling when we mulply by 4 and by 8.

To mulply a number by 4,

double it twice.

To mulply a number by 8,

double it 3 mes.

a

12 × 4 =

Double 12 once

24

Double 12 twice

48

b

15 × 4 =

Double 15 once

Double 15 twice

c

18 × 4 =

Double 18 once

Double 18 twice

d

22 × 4 =

Double 22 once

Double 22 twice

e

16 × 8 =

Double 16 once

Double 16 twice

Double 16 three mes

f

35 × 8 =

Double 35 once

Double 35 twice

Double 35 three mes

g

× 8 =

Double once

Double

twice

Double

three mes

10 × 4 = 40

Double 10 once 20

Double 10 twice 40

11 × 8 = 88

Double 11 once 22

Double 11 twice 44

Double 11 three mes 88

48

SERIES TOPIC

23

E 3

Multiplication and Division

Use the split strategy to answer these:

Mental multiplication strategies – split strategy

The split strategy is when we mulply numbers in 2 pairs and then add the parts.

Let’s use the split strategy for 26 × 4.

•

Split 26 into 20 and 6.

•

Mulply each part.

•

Add the answers together.

26 × 4



20 × 4 + 6 × 4

80 + 24 = 104

So, 26 × 4 = 104

1

a 34 × 3



30 × 3 + 4 × 3

90 +

=

So, 34 × 3 =

b 45 × 5



× + ×

+ =

So, 45 × 5 =

c 52 × 4



× + ×

+ =

So, 52 × 4 =

SERIES TOPIC

E 3

24

Multiplication and Division

Use the compensaon strategy to answer these quesons.

This me you need to look for more than one extra group

to subtract:

a 4 × 18



4 × =

–

So, 4 × 18 =

b 3 × 17



3 × =

–

So, 3 × 17 =

Use the compensaon strategy to answer these:

a 5 × 29



5 × =

–

So, 5 × 29 =

b 3 × 49



3 × =

–

So, 3 × 49 =

c 4 × 39



4 × =

–

So, 4 × 39 =

Mental multiplication strategies – compensation strategy

Use the compensaon strategy to make it easier to mulply 2-digit numbers

that are close to a ten.

Look at 4 × 19.

19 is close to 20, so we can mulply by the next mulple of ten which is 20.

Then we build down because we have an extra group of 4.

4 × 19



4 × 20 = 80 – 4

So, 19 × 4 = 76

1

2

We have rounded up

to 20. So instead of

4 × 18 we have 4 × 20.

This is 2 more groups

of 4. So we subtract 8.

SERIES TOPIC

25

E 3

Multiplication and Division

Roll a die to get the missing number, then use either the split or

compensaon strategy to get the answer. You can place the numbers

rolled on the die in any queson.

a 25 ×



So, 25 × =

b 36 ×



So, 36 × =

c 49 ×



So, 49 × =

d 58 ×



So, 58 × =

Mental multiplication strategies – choose a strategy

1

SERIES TOPIC

E 3

26

Multiplication and Division

Make these problems easier by using doubling and halving. Shade an array for each:

a 18 × 3

Halve Double

× =

b 14 × 4

Halve Double

× =

Mental multiplication strategies – doubling and halving

We can change the factors of a mulplicaon queson to make it easier. Look

at 16 × 3. If we halve the larger factor and double the smaller factor, we make

an array on the grid that is the same size. Both arrays have the same amount of

squares. Count the squares, are they equal to 8 × 6?

16 × 3

Halve Double

8 × 6 = 48

1

SERIES TOPIC

27

E 3

Multiplication and Division

Follow this doubling and halving trail through to the boom:

d What do you noce?

Use the doubling and halving strategy to solve these:

Mental multiplication strategies – doubling and halving

2

3

a 14 × 3

Halve Double

× =

c 16 × 5

Halve Double

× =

b 48 × 5

Halve Double

× =

d 64 × 5

Halve Double

× =

a Halve Double

8 × 56 = ?

×

So, 8 × 56 =

b Halve Double

8 × 35 = ?

×

So, 8 × 35 =

c Halve Double

8 × 45 = ?

×

So, 8 × 45 =

SERIES TOPIC

E 3

28

Multiplication and Division

Mental multiplication strategies – word problems

2

If I buy 4 packets of sweets and each packet contain 6 sweets,

how many sweets will I have altogether?

Every minute I complete one length of the swimming pool.

How many lengths will I have swum in one hour?

When you are faced by a word problem, read it carefully. Ask yourself…

What are the important numbers?

Which key words give clues to the correct operaon?

Jim makes boxes of biscuits for his 5 friends. There are 16 biscuits in each box.

How many biscuit does he make altogether?

Important numbers: 5 friends 16 biscuits in each box

Key words/operaons: ‘altogether’ suggests mulplicaon 5 × 16

Strategy: split

5 × 16 = 5 × 10 and 5 × 6

5 × 10 = 50

5 × 6 = 30

50 + 30 = 80

1

SERIES TOPIC

29

E 3

Multiplication and Division

Mental multiplication strategies – word problems

Jimmy lines up his soldiers in lines of 9. If he has 8 lines,

how many soldiers does he have?

There are 15 toys in a n. Lily has 8 ns. How many toys does

she have altogether?

Eggs come in boxes of a dozen. Our local shop has 14 boxes

on its shelves. How many eggs is this?

Mike and I are playing darts. On my rst throw

I score 3 double 15s. Mike’s score is twice mine.

How many do we score between us?

3

4

5

6

Read carefully!

What are the

important

numbers?

What are the

key words?

What operaons

do I need?

What is the best

strategy?

SERIES TOPIC

E 4

30

Multiplication and Division

Solve these sharing and grouping quesons:

a There are 9 cupcakes and 3 kids are sharing. How many are in each share?

÷ =

b 10 lollies are shared between a group of kids so they each get 2. How many kids

are sharing?

÷ =

c There are 24 pencils and 6 pencil pots. How many pencils go into each pencil pot?

÷ =

Division – division is sharing and grouping

Division can mean sharing or grouping.

There are 12 lollies shared between 4 kids. How many are in each share?

12 ÷ 4 = 3

T

here are 16 apples and 4 go into each basket. How many baskets do I need?

16 ÷ 4 = 4

1

SERIES TOPIC

31

E 4

Multiplication and Division

Draw pictures to show these

division quesons. Then write the

division fact and decide whether it

is a sharing or a grouping queson.

Division – division is sharing and grouping

2

b From a packet of 24 pencils, each person will get 6. How many people are

sharing the pencils?

÷ =

sharing / grouping

c 48 eggs are laid by 6 hens. If they all laid the same amount, how many did

each hen lay?

÷ =

sharing / grouping

If you need to nd out

how many items there

are in each share, it’s

a sharing queson. If

you need to nd out the

number of equal shares,

it’s a grouping queson.

a Divide 16 lollies between 4 girls. How many does each girl get?

÷ =

sharing / grouping

SERIES TOPIC

E 4

32

Multiplication and Division

Show these division facts as repeated subtracon. First label the number lines and

then show the jumps.

a 36 ÷ 6 =

b 21 ÷ 3 =

Write a division fact to match these number lines. Show the jumps.

a

÷ =

b ÷ =

Division – division is repeated subtraction

1

2

Division can also be thought of as repeated subtracon.

Look at 30 ÷ 5 =

?

This queson is asking how many groups of 5 there are in 30.

Jump in 5s along the number line and then count the jumps.

So, 30 ÷ 5 = 6

0 30252015105

−5−5 −5 −5 −5 −5

56 4 3 2 1

0 36

0 282420161284

0 3224168

0 21

SERIES TOPIC

33

E 4

Multiplication and Division

Draw an array of 6 rows of 3 then describe it with mulplicaon and division facts.

× =

÷ =

Describe each of these arrays using two mulplicaon and two division facts:

Division – linking multiplication and division facts

Knowing mulplicaon facts will help with division facts. This is because they

are opposites. Look at how we can describe this array:

6 × 4 = 24 6 groups of 4 is 24.

4 × 6 = 24 4 groups of 6 is 24.

24 ÷ 4 = 6 24 divided into 4 shares is 6.

24 ÷ 6 = 4 24 divided into 6 shares is 4.

1

2

a

× =

÷ =

c

× =

÷ =

b

× =

÷ =

d

× =

÷ =

This is also called

a fact family.

SERIES TOPIC

E 4

34

Multiplication and Division

For these problems, think of a mulplicaon fact to help write the division fact:

a £25 is shared between 5 people. How much does each person get?

× =

÷ =

b 45 people get into 9 cars. How many people are in each car?

× =

÷ =

Write a fact family for each set of numbers in the triangle. The rst one has been

done for you.

a

× =

÷ =

× =

÷ =

b

× =

÷ =

× =

÷ =

c

× =

÷ =

× =

÷ =

d

× =

÷ =

× =

÷ =

Division – linking multiplication and division facts

3

4

35

7 5

27

9 3

48

6 8

40

8 5

5

7

5

35

5

7

5

SERIES TOPIC

35

E 5

Multiplication and Division

a

c

b

d

Use paerns to solve these:

a 1400 ÷ 1 =

1400 ÷ 10 = 1400 ÷ 100 =

b 5600 ÷ 1 = 5600 ÷ 10 = 5600 ÷ 100 =

c 3500 ÷ 1 = 3500 ÷ 10 = 3500 ÷ 100 =

Use a calculator to

solve these:

Use the place value tables to divide these numbers by 10 and 100.

Mental division strategies – dividing by 10 and 100

When we divide any number by 10, we move the number one place value

space to the right because the number is geng 10 mes smaller.

When we divide any

number by 100, we move

the number two place

value spaces to the right

because the number is

geng 100 mes smaller.

1

2

3

Th H T O

5 3 0 0

÷ 10

÷ 100

Th H T O

8 4 0 0

÷ 10

÷ 100

Th H T O

4 1 0 0

÷ 10

÷ 100

Th H T O

2 4 0 0

÷ 10

÷ 100

a 270 ÷ 100 =

b 49 ÷ 10 =

Thousands Hundreds Tens Ones

6 7 0 0

6 7 0 ÷ 10

6 7 ÷ 100

SERIES TOPIC

E 5

36

Multiplication and Division

Below is a halving-halving funcon machine. The number goes IN and is halved

and then halved again and comes OUT.

Complete the halving funcon machines. Halve the number going IN the machine

and write the answer in the OUT column:

Mental division strategies – halving strategy

When you halve numbers you are

dividing them by 2. In this funcon

machine, numbers go IN, have the rule

applied and come OUT again.

1

2

a

c

b

d

RULE:

Halve

IN

80

140

20

OUT

RULE:

Halve

IN

8

12

4

OUT

4

6

2

RULE:

Halve

IN

42

90

60

OUT

RULE:

Halve

RULE:

Halve

IN

100

36

60

OUT

RULE:

Halve

IN

70

24

36

OUT

RULE:

Halve

IN

18

50

100

OUT

SERIES TOPIC

37

E 5

Multiplication and Division

Complete the

division wheels:

Use the tables for halving-halving to divide by 4:

Mental division strategies – halving strategy

We also use halving-halving to divide by 4. Look at these diagrams:

3

4

Halve 16 once Halve 16 twice

16

8

4

a b

14

30

56

90

82

70

2042

÷ 2

36

12

60

200

84

88

4452

÷ 4

a 80 ÷ 4 =

Halve 80 once

Halve 80 twice

c 64 ÷ 4 =

Halve 64 once

Halve 64 twice

e 244 ÷ 4 =

Halve 244 once

Halve 244 twice

b 48 ÷ 4 =

Halve 48 once

Halve 48 twice

d 120 ÷ 4 =

Halve 120 once

Halve 120 twice

f 88 ÷ 4 =

Halve 88 once

Halve 88 twice

SERIES TOPIC

E 5

38

Multiplication and Division

Division problems can be much easier to solve if you

split the number.

Look at 125 ÷ 5.

Can we split the number into two mulples of 5?

Yes, we can split 125 into 100 and 25.

We divide each part by 5 and then add the two answers together.

Use the split strategy to divide these by 4:

Use the split strategy to divide these by 3:

Use the split strategy to divide these by 5:

Mental division strategies – split strategy

1

2

3

125 ÷ 5

100 25

÷ 5 ÷ 5

20 + 5 = 25

a 115 ÷ 5

÷ 5 ÷ 5

+ =

b 135 ÷ 5

÷ 5 ÷ 5

+ =

a 64 ÷ 4

÷ 4 ÷ 4

+ =

b 116 ÷ 4

÷ 4 ÷ 4

+ =

a 330 ÷ 3

÷ 3 ÷ 3

+ =

b 612 ÷ 3

÷ 3 ÷ 3

+ =

SERIES TOPIC

39

E 5

Multiplication and Division

a b

c d

Solve this riddle by matching the leer to the answer. Use a mental division

strategy for each problem.

What is it that the more you take, the more you leave behind?

68 ÷ 4 =

s

90 ÷ 6 =

p

135 ÷ 5 =

e

1200 ÷ 10 =

f

240 ÷ 4 =

o

128 ÷ 4 =

t

Use either the halving strategy or the split strategy to complete the tables. The rst

one has been done for you.

Mental division strategies – word problem

Review your division strategies.

1

2

Use the split strategy:

48 ÷ 3 =

16

48 is 30 + 18

30 ÷ 3 = 10 and 18 ÷ 3 = 6

10 + 6 = 16

Use the split strategy:

312 ÷ 3 =

Use the halving strategy:

64 ÷ 4 =

Use the halving strategy:

140 ÷ 4 =

120 60 60 32 17 32 27 15 17

SERIES TOPIC

E 5

40

Multiplication and Division

Mental division strategies – word problem

Remember the steps and quesons to ask yourself when you are trying to solve

a word problem.

Four friends have a party. They share out all the food equally. There are 164

blueberries in total. How many do they get each?

Important numbers: 4 friends 164 blueberries

Key words/operaons: ‘share’ = mulplicaon 164 ÷ 4

Strategy: halving

164 ÷ 2 = 82

82 ÷ 2 = 41

4

Tom, Milo and Xav have been trick and treang. They agree

to share their sweets out equally between them. They have

33 sweets in total. How many do they get each?

Lillies are sold in bunches of 7. A orist has

42 lillies. How many bunches can she make?

3

Read carefully!

What are the

important

numbers?

What are the

key words?

What operaons

do I need?

What is the best

strategy?

SERIES TOPIC

41

E 5

Multiplication and Division

Jon needs to buy some les. They cost £9 each. He has £72.

How many les can he buy?

Andy loves astronomy. He’s worked out that he can see about

32 000 stars with his new telescope. If there are about 100

stars visible in any one galaxy. How many galaxies can he see?

Kate has been planng trees. She has planted a total of 155

trees in rows of 5. How many rows has she planted?

Charles is saving up to buy a new bike. The bike costs £170.

He gets £74 for his birthday, and £4 pocket money a week.

How many weeks will he have to save unl he can get the bike?

5

6

7

8

Mental division strategies – word problem

SERIES TOPIC

E 6

42

Multiplication and Division

Pracse these problems:

Written methods – short multiplication

1

Start with the ones. 4 × 3 = 12 ones.

Rename this as 1 ten and 2 ones. Put the 2 in the ones

column and regroup the 1 to the tens column.

3 × 5 plus the regrouped 1 is 16 tens.

Rename this as 1 hundred and 6 tens.

H T O

5 4

×

3

1 6 2

1

a

H T O

b

H T O

c

H T O

4 2 3 8 2 5

×

9

×

7

×

4

d

H T O

e

H T O

f

H T O

2 6 5 5 6 2

×

4

×

8

×

7

g

H T O

h

H T O

i

H T O

8 6 9 3 7 7

×

6

×

5

×

9

SERIES TOPIC

43

E 6

Multiplication and Division

Solve these mulplicaons:

Written methods – short multiplication

2

a

Th H T O

b

Th H T O

c

Th H T O

1 2 3 2 5 6 1 8 7

×

4

×

6

×

8

d

Th H T O

e

Th H T O

f

Th H T O

3 4 2 4 6 5 6 7 8

×

7

×

5

×

9

Use short mulplicaon to solve these word problems:

3

a On a farm, 6 lambs were born

every day over 25 days. How

many lambs were born in total?

b For my school fete day, I baked

9 trays of cupcakes. If there are

14 cupcakes on each tray, how

many did I bake in total?

H T O

×

H T O

×

SERIES TOPIC

E 6

44

Multiplication and Division

Use the division symbol to solve each problem:

a 42 cupcakes were iced by 7 kids. If they each iced the same

amount, how many did they ice each?

b How many pots were used if 6 seeds were planted in each

pot from a packet of 54?

c I run the same distance each day. Over 9 days the total

distance is 72 km. How far did I run each day?

a

d

g

b

e

h

c

f

i

Solve these division problems using the division symbol:

Written methods – short division

1

2

Another way to represent division is with the division symbol.

This is the same as 36 ÷ 6 = 6

If the answer is a single digit, it should go in the

ones column.

T O

6

3 6

5

3 5

4

2 8

9

1 8

6

5 4

2

1 4

4

1 6

5

2 5

7

4 9

8

4 8

SERIES TOPIC

45

E 6

Multiplication and Division

Now put these split numbers back together:

Solve these division problems with 3-digit numbers:

Pracse spling these:

Written methods – short division with 3-digit numbers

In short division with 3-digit numbers we split the number:

468 is 400 + 60 + 8

400 divided by 2 is 200, so we put a 2 in the hundreds place.

60 divided by 2 is 30, so we put a 3 in the tens place.

8 is divided by 2 is 4, so we put a 4 in the ones place.

1

2

3

4

a 368 is ______ + ______ + ______

c 567 is ______ + ______ + ______

b 445 is ______ + ______ + ______

d 235 is ______ + ______ + ______

a 500 + 70 + 8 is ____________

c 200 + 40 + 6 is ____________

b 700 + 90 + 4 is ____________

d 800 + 50 + 5 is ____________

a b

H T O

2 3 4

2

4 6 8

Here are two division problems with missing numbers in the quesons. Find out

the missing numbers by using the numbers that are part of the answer as clues.

a

c

b

d

4

8 4 4

3

6 9 3

2

8 4 2

1 2

4 4

3

6

2

4 8 8

SERIES TOPIC

E 6

46

Multiplication and Division

Pracse these problems. We have put the zero in to remind you:

Written methods – short division with 3-digit numbers

Somemes we need to split the number a dierent way,

for example: 515 = 500 + 15

500 divided by 5 is 100, so we put a 1 in the hundreds place.

15 divided by 5 is 3, so we put a 3 in the ones place.

What goes in the tens place?

A zero does. The zero has the very important job of

keeping the other numbers in their place!

5

6

Pracse these problems. This me, you need to remember the zero!

a

c

b

d

a

c

b

d

H T O

1 0 3

5

5 1 5

0

4

8 1 2

3

9 1 8

0

3

9 1 2

4

8 3 2

0

3

9 2 4

6

6 1 2

0

4

8 2 4

4

8 1 6

SERIES TOPIC

47

E 7

Multiplication and Division

Colour the counng paern on each 100 square:

Patterns and algebra – skip counting

Using a 100 square can help us to idenfy skip counng paerns.

1

a Count in 6s.

c Count in 9s.

b Count in 7s.

d Count in 3s and 6s. Shade the 3s and

circle the 6s.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

e Look at the completed number square in queson d. Describe the paern that you

see. What is the relaonship between counng in 3s and 6s? Explain your answer.

__________________________________________________________________

SERIES TOPIC

E 7

48

Multiplication and Division

Complete these number paerns by looking for skip counng paerns.

a

b

c

2

6 24 30

9 18 36 54

32 20 8

Only 3 numbers are shaded in each of the skip counng paerns below. Work out

the paern and complete the shading:

Patterns and algebra – skip counting

3

4

Colour the skip counng paern for 3s up to 30. If you kept going on a complete

hundred grid, would 52 be coloured in?

How can you tell without using a whole hundred grid?

_____________________________________________________________________

a

This shows a skip

counng paern of:

b

This shows a skip

counng paern of:

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

SERIES TOPIC

49

E 7

Multiplication and Division

Roll a die to make the starng number. Connue the sequence by following the rule:

a

b

c

Complete these number paerns, by following the rules wrien in the diamond

shapes. Describe the rule underneath.

The rule is ___________________________________________________________

1

2

3

Patterns and algebra – completing and describing patterns

Figure out the missing numbers in each paern and write the rule.

a

Rule: _________________________

b

Rule: _________________________

7 21 45 36 208 104 52

Some number paerns can be formed with two operaons each me.

For example:

The rule is to mulply by 2 and add 3 each me.

2 7 17 37

× 2 + 3 × 2 + 3 × 2 + 3

Rule: + 4 × 2

Rule: + 1 × 3

Rule: + 3 × 2

3

+ 5 x 2 + 5 x 2 + 5 x 2

This is a paern involving mulplicaon.

The paern begins at 2.

The rule is: mulply by 5.

2 10 50 250 1,250

× 5 × 5 × 5 × 5

SERIES TOPIC

E 7

50

Multiplication and Division

Complete the table for each problem:

a Tom receives £5 a week pocket money as long as he does all his chores. How

much pocket money does Tom get aer 10 weeks?

b A ower has 7 petals. How many petals are there in a bunch of 10 owers?

c A ag has 6 stars. How many stars are there on 10 ags?

d At a pizza party, each person eats 3 pieces of pizza. How many pieces of pizza do

10 people eat?

Patterns and algebra – predicting repeating patterns

When we use number paerns in tables, it can help us to predict what comes

next. Look at the table below and how we can use it to predict the total number

of sweets needed for any number of children at a party.

This table shows us that 1 sweet bag contains 8 sweets and 2 bags contain 16

sweets. We can see that the rule for the paern is to mulply the top row by 8

to get the boom row each me.

Number of sweet bags 1 2 3 4 5 10

Number of sweets 8 16 24 32 40 80

To nd out how many sweets are in 10 bags, we don’t need to extend the table,

we can just apply the rule.

10 × 8 = 80. So, 10 bags contain 80 sweets. This helps us plan how many

sweets are needed for a party.

1

× 8

Weeks 1 2 3 4 5 10

Pocket money 5 10

Flowers 1 2 3 4 5 10

Number of petals 7 14

Flags 1 2 3 4 5 10

Number of stars 6 12

Guests 1 2 3 4 5 10

Pizza pieces 9 12

SERIES TOPIC

51

E 7

Multiplication and Division

Look at each paern of shapes and complete the table below:

Show what this enre sequence would look like with 10 repeat secons:

Each of these kids wrote the rst 3 numbers of a skip counng paern of 6,

starng at dierent numbers. Each kid’s sequence goes down the column.

Imagine the sequence connues.

Mel Brianna Brad Gen Jo Kate

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

a Who had the number 42 in their column? _______________________________

b Who had the number 50 in their column? _______________________________

2

3

Patterns and algebra – predicting repeating patterns

Repeat secon 1 2 3 4 5 10

Number of circles 2 4 6 8 10 20

Number of triangles 1 2 3 4 5 10

Look for the secon that

repeats. What is it made

up of? This is the rule.

SERIES TOPIC

E 7

52

Multiplication and Division

Complete the table for each sequence of matchsck shapes and nd the number

of matchscks needed for the 10th shape.

a Shape 1 Shape 2 Shape 3

Shape number 1 2 3 4 5 10

Number of matchscks 4

b Shape 1 Shape 2 Shape 3

Shape number 1 2 3 4 5 10

Number of matchscks 6

c Shape 1 Shape 2 Shape 3

Shape number 1 2 3 4 5 10

Number of matchscks 7

Patterns and algebra – predicting growing patterns

Number paerns in tables can help us with problems like this. Mia is making

this sequence of shapes with matchscks and wants to know how many she

will need for 10 shapes.

Shape number 1 2 3 4 5 10

Number of matchscks 3 6 9 12 15 30

To nd out how many matchscks are needed for 10 triangles, we don’t need

to extend the table, we can just apply the funcon rule:

Number of matchscks = Shape number × 3

1

× 3

Shape 1 Shape 3Shape 2

SERIES TOPIC

53

E 7

Multiplication and Division

2

Patterns and algebra – predicting growing patterns

Look at these growing paerns. Complete the table and follow the rule to draw

Picture 5:

Picture number 1 2 3 4 5

Number of dots 1 3 5 7

Rule Picture number × 2 – 1 = Number of dots

a Picture 1 Picture 2 Picture 3 Picture 4 Picture 5

l

l l l l

l

l l l

l

l ll

b Picture 1 Picture 2 Picture 3 Picture 4 Picture 5

Picture

number

1 2 3 4 5

Number of

squares

4 6 8 10

Rule Picture number × 2 + 2 = Number of squares

How many squares will Picture 8 have?

SERIES TOPIC

E 7

54

Multiplication and Division

What numbers go in to these number funcon machines?

a b

What numbers will come out of these funcon machines?

a b

Look carefully at the numbers going in these funcon machines and the numbers

coming out. What is the rule?

a b

This is a funcon machine.

Numbers go in, have the rule

applied, and come out again.

Patterns and algebra – function machines

RULE:

7

3

8

IN

42

18

48

OUT

RULE:

÷ 9

45

108

81

IN OUT

RULE:

× 9

IN

36

63

90

OUT

RULE:

63

70

28

IN

9

10

4

OUT

RULE:

× 7

12

5

8

IN OUT

RULE:

÷ 6

IN

9

6

12

OUT

1

2

3

RULE:

× 4

9

2

6

IN

36

8

24

OUT

SERIES TOPIC

55

E 7

Multiplication and Division

Balance each set of scales by wring a number in the box. Then write the

matching equaon.

a

b

Balance each set of scales by wring a number in the box that is equivalent to the

total number of shapes. Then write the matching equaon.

a

b

Patterns and algebra – understanding equivalence

Look at these balanced scales.

On one side there is the sum 4 × 3 and

on the other side there is a total of

12 triangles. This makes sense because it

shows the equaon 4 × 3 = 12.

Equaon is another word for a sum. With

equaons, both sides must be equal.

1

2

6 ×

× 7

56

6 ×

54

× =

4 × 3 = 12

4 × 3

4 ×

SERIES TOPIC

E 7

56

Multiplication and Division

Work out the values of the symbols in each problem:

a

5

×

9

=

b

6

× =

c

7

× =

63

d

6

× =

42

Patterns and algebra – balanced equations using + and ×

There are 2 dierent equaons we could write for one set of balanced scales.

1

8

+

8

+

8

=

24

3

×

8

=

24

888 24

9 9

9

7 7 7

63

42

SERIES TOPIC

57

E 7

Multiplication and Division

Find the values of both symbols from the clues:

a If both sides are equal to 36, what is the value of each symbol?

2

× =

3

×

=

b If both sides are equal to 10, what is the value of each symbol?

2

×

5

=

5

×

=

Find the values of these symbols:

a If

is 5, what is the value of

?

2

×

5

=

5

×

=

b If

is 8, what is the value of

?

3

×

8

=

6

×

=

2

3

Patterns and algebra – balanced equations using + and ×

SERIES TOPIC

E 7

58

Multiplication and Division

Patterns and algebra – using symbols for unknowns

1

2

Write an equaon for these word problems. Write an equaon using a

s

for the

unknown number.

a Bec collects sckers. She has 48 bumper sckers, 12 glier sckers and 15 smiley

face sckers. How many sckers does Bec have in her collecon?

b Charlie saved £5 a week of his pocket money over 8 weeks but then spent £15.

How much did Charlie have at the end of 8 weeks?

c 5,000 people are spectators at a football match. 2,700 are there to support Team A

while the rest are there to support Team B. How many spectators support Team B?

s

=

48

+

12

+

15

=

s

=

In this triangle, the numbers on the sides are the totals.

So

10

+ =

30

Work out the value of the other symbols:

=

20



=

25 30

15

10

s

=

SERIES TOPIC

59

E 8

Multiplication and Division

What

to do

Triple product apply

Geng

ready

This is a game for 2 players. You will need a copy of

this page, 6 counters each and 3 dice.

20 15 12 2 8

6 12 6 16 6

36 20 18 8 10

12 10 6 12 4

10 12 15 24 25

Player 1 rolls all 3 dice and chooses 2 of the numbers to mulply.

If the player can see the answer in the grid, they claim this number

by placing a counter over the number. Then Player 2 has a turn.

The winner is the rst to place all 6 counters on the grid.

copy

SERIES TOPIC

E 8

60

Multiplication and Division

Factor bingo apply

Geng

ready

What

to do

This is a game for three players. Each player needs a

copy of this page. The caller needs a pile of the numbers

from 1 to 9.

Each mulplicaon grid contains all the answers, while the factors

are missing. Remember factors are the numbers that you mulply

to get the answer.

The aim of the game is to be the rst player to ll their grid with

the factors. One hint is provided in each grid to start you o.

Choose one person to be the caller and the other two play the

round. The caller picks a number without looking and reads it out

to the players. The players write it on the grids, if it ts as a factor.

The rst to ll in one of the grids completely is the winner.

copy

1 6

2 7

3 8

4 9

5



×

6 42 24 18

63 36 27

35 20 15

×

3

12 20 28

18 30 42

27 45 63

×

8 40 64

3 3 15 24

9 45 72

×

9

4 14 18

2 7 9

12 42 54

SERIES TOPIC

61

E 8

Multiplication and Division

Geng

ready

What

to do

Doubling strategy to 20 apply

This is a game for two players. You will need a copy of

page 63, a die and a pencil to write down your scores. You

may like to make extra copies of page 63 to play again later.

Strategy 1 Strategy 2 Strategy 3

Double

Player 1

Die Strategy Score

6

1

2

3

12

2

1

2

3

16

4

1

2

3

16

6

1

2

3

24

3

1

2

3

12

Total 56

Player 2

Die Strategy Score

5

1

2

3

40

3

1

2

3

12

1

2

3

8

4

1

2

3

16

2

1

2

3

16

Total 52

The aim of this game is to score the highest number of points each

me without going over 20. Roll the dice and choose which strategy

you will use. From the Strategy column, circle 1 for double, 2 for

double-double or 3 for double-double-double. For example, Player 2

has rolled a 5 and has chosen strategy 3 double-double-double. This

makes a score of 40 but because it is over 20 it doesn’t count. Look

at the rest of the sample game to see how the game turned out.

copy

Sample game

SERIES TOPIC

E 8

62

Multiplication and Division

Doubling strategy to 20 apply

Strategy 1 Strategy 2 Strategy 3

Double

Player 1

Die Strategy Score

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

Total

Player 2

Die Strategy Score

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

Total

SERIES TOPIC

63

E 8

Multiplication and Division

Symbols solve

What

to do

Can you work out the value of each symbol?

The values are 2, 3, 4, 6, 8, 9 and 12. Remember, the same symbol

means that it’s the same number.

=

× × =

× =

× × =

× =