A WRITTEN METHOD FOR MULTIPLICATION FOUNDATION STAGE AND YEAR 1 Count in steps of 10, 5 and 2.

YEAR 2 Children record pictorially as they develop their understanding of repeated addition, e.g. counting in sets of two, e.g. sets of two pence coins; five, e.g. tally bundles; tens, e.g. sets of 10 pennies. Use of arrays to illustrate repeated addition. 4 + 4 + 4 = 12

3 + 3 + 3 + 3 = 12 Record repeated addition on a number line e.g. for the array above,

4 + 4 + 4 = 12 leading to four, three times or 4 x 3 0

0

0

0

4

8

0

12 3 + 3 + 3 + 3 = 12 leading to three, four times or 3 x 4

0

0

0

0

0

3

6

9

0

12

Using such models will help develop children’s understanding of the commutativity of multiplication, i.e. 4 x 3 = 3 x 4

Before the introduction of written methods for multiplication, children should be able to: recall multiplication facts for the tables used; partition numbers into multiples of one hundred, ten and one; work out products such as 70 × 5, 70 × 50, 700 × 5 or 700 × 50 using the related fact 7 × 5 and their knowledge of place value; add two or more single-digit numbers mentally; add multiples of 10 (such as 60 + 70) or of 100 (such as 600 + 700) using the related addition fact, 6 + 7, and their knowledge of place value; add combinations of whole numbers.

YEAR 3 (Also Year 2 for children working within L3)

Remember – it is stage of learning that is crucial, not age.

Mental method using partitioning: Use of arrays to make the link between arrays and the grid method, e.g 13 x 3 Partition into 10 x 3 and 3 x 3 10 x 3 = 30

Indicate

3x3=9

on array

13 x 3 = 39 This may be a demonstration stage only, depending on children’s understanding. Multiplication of ‘teens’ numbers, e.g. 16 x 3 Multiplication of multiples of 10, e.g. 54 x 3 Setting out e.g. 47 x 3 40 x 3 = 120 7 x 3 = 21 47 x 3 = 120 + 21 = 141

YEAR 4 The grid layout Lower achieving children will continue to use this layout even when compact methods are introduced to higher achievers. ‘Teens’ number x U, e.g. 14 x 6 TU x U, e.g. 87 x 6 Setting out Demonstrate alongside the mental method. Children then practise the grid layout. e.g. 14 x 6

x

10

4

10x6=60

6

60

24

= 84

4x6=24 14x6=60+24 =84

The traditional layout requires children to use adequate spacing. Although in this example, the addition can be done mentally, with a more complex calculation, children may need the extra step of writing out the partial products in a separate vertical calculation.

Remember – it is stage of learning that is crucial, not age.

Short multiplication TU x U, e.g. 37 x 6 Setting out Demonstrate alongside grid layout, making links where possible. Note that in the grid method the most significant digits are multiplied first, whereas in short multiplication the working starts with the least significant digit. Comparisons should be made with the compact methods for addition and with decomposition or equal addition, if they are used. Children then practise short multiplication. If after some time, they continue to experience difficulty, they should return to the grid method. HTU x

6

30

180

7

42

37 4

x

6

222

222 Figures need to be carried on the doorstep HTU x U, e.g. 4 7 6 x 7 £·p x U, e.g. £3·64. x 8

Note: Children who are continuing to use the grid layout should, when working with money or measures, convert to the smaller measure e.g. convert £.p to pence, and then back to the original units if required.

YEAR 5 Progression to long multiplication Grid layout ‘Teens’ number x ‘teens’ number, e.g. 18 x 14 TU x ‘teens’ number, e.g. 56 x 17 TU x TU, e.g. 56 x 27 HTU x TU, e.g. 375 x 83 (L5) Setting out Following on from the vertical layout used for TU x U, the first number would be partitioned down the lefthand side. However, if children’s understanding of the commutativity of multiplication is secure, they will see that the second number could equally well be partitioned at the top.

e.g. 56 x 27 Estimate first: 60 x 30 = 1800 x

20

7

50

1000

350

6

120

42

or

x

50

6

1350

20

1000

120

1120

162

7

350

42

392

= 1512

Children should add the partial products in the way they find easiest, adding mentally where they are able, and using written method when Remember – it is astage of learning that isneeded crucial, not age. They can check by adding in a different order.

= 1512

Most children will continue to develop their use of the grid method. Those who are on track to achieve secure L4 or L5 at the end of Y6, and are confident with the grid method, should be introduced to the following stages.

YEAR 6 Expanded vertical layout for long multiplication (Y5 for more able children) It is possible to omit this stage of the progression. If the school thinks that children will be able to make the links between both short multiplication and the grid method, they may decide to go straight to the compact layout for long multiplication. TU x TU, e.g. 78 x 34 HTU x TU, e.g. 274 x 78 (L5)

Compact method for long multiplication TU x TU, e.g. 76 x 58 HTU x TU, e.g. 274 x 78 (L5) Setting out Reduce the recording further. e.g. 274 x 78 Estimate first. 300 × 80 = 24 000 274 x

78

19180 2192

Carry figures on doorstep Not shown here to avoid confusion Multiply by the tens digit first

21372

Setting out (following on from short multiplication and the grid method) e.g. 567 x 58 Estimate first. 600 x 60 = 36 000 Demonstrate alongside the grid method and refer to short multiplication. Children then practise the compact layout. If after some time, they continue to experience difficulty, they should return the grid method. 567

x

500

60

7

50

25000

3000

350

28350

8

4000

480

56

4536

29000

3480

406

32886

x

58

28350 4536 32886

Add vertically to check. .

Remember – it is stage of learning that is crucial, not age.

Remember – it is stage of learning that is crucial, not age.