Methods of Multiplication

Heatherside Junior School

Multiplication

lots of times groups of

repeated addition array

multiple of multiplyproduct of

doublex x x x x x x x x x x x x x x x

xxxxxxx

xxxxxxxx

x x x x x x x x x x x x x x x

Step 1 – Multiplication as arrays

2 x 3 = 6

2 + 2 + 2 = 6

3 x 2 = 63 + 3 = 6Understanding that

multiplication is repeated addition

Recognising that 3x2 gives the same answer as

2x3

x 2 3 4 5 6 7 8 9

2 4              

3 6 9            

4 8 12 16          

5 10 15 20 25        

6 12 18 24 30 36      

7 14 21 28 35 42 49    

8 16 24 32 40 48 56 64  

9 18 27 36 45 54 63 72 81

Stage 1: counting in 10s, 5s, and 2s Stage 2 (by the end of Year 2): x10, x5, x2 Stage 3 (by the end of Year 3): x3, x4, x9 Stage 4 (by the end of Year 4): x6, x7, x8

Step 2 – Knowing tables facts is key‘Learn Its’ – a progressive approach 3 facts

5 minutes3 weeks

‘Learn Its’ vocabulary

FACTS SWITCHERS FACT FAMILIES3 X 3 = 9 4 X 3 = 125 X 3 = 15

3 X 4 = 123 X 5 = 15

9 ÷ 3 = 312 ÷ 3 = 415 ÷ 3 = 5

Step 3 - Partitioning

This method helps show the value of each digit in a

number. Children develop a greater understanding of the

reasonableness of an answer and they are able to

apply known facts.

23 x 8 =

20 3

Step 4 - The Grid Method

X 20 3

8 160 24

• The number is partitioned and placed on the grid.• The total is added to calculate the final answer.

160 + 24 = 184

23 x 8 =

Step 5The Expanded Column Method

The question is…

38 x 7 =

The number is partitioned…

38 x 730 8 x 7

30 + 8 x 7 56 (7 x 8) + 210 (7 x 30) 266

Step 6 ….This is then reduced to Short Multiplication

38 x 7 =

38 x 7 = 266

We aim for children to begin to be able to use short multiplication for TU x U

by the end of Year 4.

The short method

38 x 7 266 5

Using the Grid Method for TU x TU

Remember to partition the

numbers using known facts first.

X 60 3

40 2400 120

2 120 6

63 x 42 =

2400 + 120 = 2520

120 + 6 = 126

2520 + 126 = 2646

Moving from the Grid to Column Method for TU x TU

The question is

56 x 27 =

56 x 27 42 (7x6) 350 (7x50) 120 (20x6)+ 1000 (20x50) 1512 1

The Grid Method for larger numbers

X 80 9100203

89 x 123First partition each number 89 x 123[80 9] [100 20

3]This is then shown on a grid like this…

Multiplying using the grid method

X 80 9100

20

3

Firstly, multiply each column and row and record the answer in the correct box

8000

1600

240

900

180

27

X 80 9

100 8000 900

20 1600 180

3 240 27

Completing the calculationNow total up all the yellow numbers.

= 8900

= 1780

= 267

Add all the totals to get the final answer

= 10,947

Step 7 - Long Multiplication 256 x 28 48 (8x6) 400 (8x50) 1600 (8x200) 120 (20x6) 1000 (20x50) +4000 (20x200) 7168

If children are very secure at Level 5 they may go on to usethe compact method, where 0 is used to denote the multiple of 10.

56 x 27 392 4

+ 1120 1 1512

1