Expanded methods for multiplication

Expanded methods for multiplication will link with work children have already done on arrays in previous years.

Children should be familiar with the idea of partitioning numbers to make calculations easier. eg

3 x 7 could be represented as (3x5) + (3x2).

	5	2
3	15	6	15 + 6 = 21

Stage 1 (using mental method)

16 x 3 = (10 x 3) + (6 x 3)

= 30 + 18

= 48

28 x 6 = (20 x 6) + (8 x 6)

= 120 + 48

= 168

Stage 2

Children are introduced to the grid method of multiplication in order to multiply a 2-digit by a a 1-digit number.

Place value cards are used to demonstrate how 2-digit numbers are partitioned.

Children start by multiplying by the significant digit first in order to get a sense of the size of the answer.

It is important that children work with table facts they can do mentally in order to experience success.

16 x 3

	10	6
3	30	18	30 + 18 = 48

28 x 6

	20	8
6	120	48	120 + 48 = 168

By beginning with significant digit more of a sense of size of number

Key point to consider – children need to be working with table facts they feel comfortable with – otherwise they are more likely to feel failure

Stage 3

The grid layout is extended to bigger 2-digit by 2-digit numbers

56 x 27

Estimate: 1800 because 60 x 30 = 1800

56 x 27 = (50 + 6) x (20 + 7)

x	50	6
20	1000	120	1120
7	350	42	392
			1512

Stage 4

Extend to bigger numbers and decimals

23.5 x 12

Estimate: 25 x 10 = 250

23.5 x 12 = (20 + 3 + 0.5) x (10 + 2)

x	20	3	0.5
10	200	30	5	235
2	40	6	1	47
				282

Stage 5

Vertical format, expanded working

When introducing expanded methods we start with calculations that children can do mentally. It is important to show how the vertical format links with the grid method.

16
x 3		x	10	6
30	(10x3)	3	30	18	30 + 18 = 48
18	( 6x3)
48

28
x 6		x	20	8
120	(20x6)	6	120	48	120 + 48 = 168
48	( 8x6)
168

56
x 27
1000	(50x20)	x	50	6
120	( 6x20)	20	1000	120	1120
350	(50x 7)	7	350	42	392
42	(6 x 7)				1512
1512
1

23.5
x 12
200	(20 x10)	x	20	3	0.5
30	(3 x10)	10	200	30	5	235
5	(0.5x10)	2	40	6	1	47
40	(20 x2)					282
6	(3 x2)
1	(0.5x2)
282

Stage 6

Compact method

Children may need to use jottings to support the individual multiplications in this method.

16		28
x 3		x 6
48		168
1		4

56		23.5
x 27		x 12
1120	(56x20)	235	(23.5x10)
392	(56x 7)	47	(23.5x 2)
1512		282
1		1