MULTIPLICATION
Mental strategies for multiplication include counting on in steps of a constant size,
doubling, using commutativity and multiplying by partitioning a number, multiplying each
part and then putting it back together again, e.g. double 34 by doubling 30 and doubling
4. The ‘grid’ written method builds on this partitioning of numbers, performing the
multiplication on each part and then adding the result.
These notes show the stages in building up to using an efficient method for twodigit by one-digit multiplication by the end of Year 4, two-digit by two-digit
multiplication by the end of Year 5, and three-digit by two-digit multiplication
by the end of Year 6.
To multiply successfully, children need to be able to:

count on in steps, e.g. work out 10 × 3 by counting on in 10s

understand commutativity, e.g. work out 5 × 7 by recalling seven 5s if they don’t
yet know their seven times table

recall all multiplication facts to 10 × 10 by the end of Year 4

partition number 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 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.
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Calculation policy
September 2011
Foundation Stage
Children will experience equal groups of objects.
They will count in 2s and 10s and begin to count in 5s.
They will work on practical problem solving activities involving equal sets or
groups.
Year 1
Double single-digit numbers
Double 5
Count on in steps
1
2
3
4
5
6
2, 4, 6, 8, 10…
2,
4,
6,
Double 6, two groups of 6
10
10,
+
20,
10
8
8,
+
30,
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Calculation policy
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September 2011
9
10…
10
40,
50…
10
Year 2
Count on in repeated steps
Find five 3s, six 5s, five 10s
Use commutativity
Know that 5 × 3 can be worked out as three 5s or five 3s
3×5
=
5×3
Double two-digit numbers
Double 23 is double 20 plus double 3, 40 + 6 = 46
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Calculation policy
September 2011
Year 3
Multiply single-digit numbers together
using counting on and known
multiplication facts
8 × 6: count up in 8s or 6s, or double 4 × 6
3 X 6
0
6
12
Use mental strategies
26 × 4: double 26 and double again
14 × 20: double 14 and multiply by 10
24 × 5: multiply by 10 and halve
13 × 9: 13 × 10, then subtract 13
13 × 11: 13 × 10, then add 13
18
Double two-digit numbers -Double 46
46
80
Year 4
Multiply two-digit numbers by singledigit numbers using the grid method
93 x 8 = 744
12
92
Multiply teens numbers by single-digit
numbers
17 × 3
10 × 3 = 30; 7 × 3 = 21
30 + 21 = 51
x
90
3
8
720
24
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Calculation policy
September 2011
=744
Year 5
Year 6
Continue to use mental strategies
Double 256: double 250 plus double 6
35 × 14: double 35, halve 14, 70 × 7 = 490
36 × 50: multiply by 100, then halve 360
13 × 19/21: multiply by 20, +/- 13
Continue to use mental strategies
14 × 15: 14 × 10, halve the result and then
add the two parts together, 140 + 70 = 210
39 × 25: multiply by 100, then divide by 4
13 × 49/51: multiply by 50, +/- 13
8.6 × 7: (8 × 7) + (0.6 × 7) = 56 + 4.2 = 60.2
Multiply three-digit numbers by singledigit numbers and two-digit numbers
two-digit numbers
256 x 3 = 768
x
200
50
6
3
600
150
18
Multiply four-digit numbers by singledigit numbers and three-digit numbers
two-digit numbers
4256 × 6 = 3936
=768
x
4000
200
50
6
6
2400
1200
300
36
=3936
26 x 32 = 832
256 x 23 = 5888
x
20
6
30
600
180
2
40
12
600
180
40
12
832
x
200
20
4000
3
600
50
6
1000 120
150
18
180
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Calculation policy
September 2011
4000
1000
120
600
150
18
5888
DIVISION
Children consider division as sharing (halving and quartering) and division as grouping
(how many groups in…?). The written method used for division is based on the ‘grouping’
method of division and is known as ‘chunking’.
These notes show the stages in building up to using an efficient method for twodigit by one-digit division by the end of Year 4, three-digit by one-digit division by
the end of Year 5, and three-digit by two-digit division by the end of Year 6.
To divide successfully, children need to be able to:
 count on in steps, e.g. work out 18 ÷ 3 by counting on in 3s
 understand and use multiplication and division as inverse operations;
 partition two-digit and three-digit numbers in different ways, e.g. partition 42 into
30 and 12 when dividing by 3 (dividing 30 by 3 and 12 by 3);
 recall multiplication and division facts to 10 × 10, recognise multiples of one-digit
numbers and multiply multiples of 10 or 100 by a single-digit number using their
knowledge of multiplication facts and place value;
 understand that division can leave a remainder;
 understand that division by grouping and sharing (halving/quartering) give the same
answer and choose which is most efficient for a given calculation
 use multiplication facts and place value to estimate how many times one number
divides into another – for example, how many sixes there are in 147, or how many
23s there are in 472;
 subtract numbers to find how much still needs to be divided when using chunking.
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Calculation policy
September 2011
Foundation Stage
Children will understand equal groups and share items out in play and
problem solving. They will count in 2s and 10s and later in 5s.
Year 1
Halving by Sharing
Find half of 8, by sharing 8 cubes between two people or folding a strip of 8 objects in
half.
Begin to find a quarter by halving and halving again, e.g. find a quarter of 8.
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September 2011
Year 2
Halving and quartering
Find half and a quarter of 20.
Grouping
18 ÷ 3, how many groups of 3 are in 18?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
188
Use multiplication facts to help, e.g. 60 ÷ 10: how many 10s are in 60? 20 ÷ 5: how many
5s are in 20?
Realise that division can sometimes leave some ’left over’
16 ÷ 3
Year 3
Year 4
Grouping
Using multiplication facts: 35 ÷ 5 = 7
because I know there are seven 5s in 35.
Chunking
Taking off a chunk of the divisor using a
multiple of 10: 67 ÷ 3, 100 ÷ 6
r4
Finding remainders
38 ÷ 5. Seven 5s make 35, leaving 3 left
over.
X 7
100  6
r3
100
-
60
10
x
6
6
x
6
40
Dividing giving answers just over 10
42 ÷ 3:
x10
x4
-
36
4
16
100 ÷ 6 = 16 remainder 4
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Calculation policy
September 2011
Year 5
Year 6
Chunking
Taking off larger chunks using estimation,
multiplication facts and place value:
196 ÷ 6
X30
x2
r4
Chunking
Using knowledge of multiplication facts
and place value to use chunking efficiently
to divide three-digit numbers by singledigit and begin to divide by two-digit
numbers: 556 ÷ 25
X20
x2
r6
6 × 10 = 60
6 × 20 = 120
6 × 30 = 180
6 × 40 = 240
The answer is between 30 and 40, so I’ll
subtract 30 lots of 6, leaving 16.
25 × 10 = 250
25 × 20 = 500
The answer is between 20 and 30, so I’ll
subtract 20 lots of 25, leaving 56.
196  6
196
-
180
30
x

556
6
556
16
-
12
25
2
x
-
6
500
20
x
25
2
x
25
56
4
-
32
50
6
196  6 = 32 r 4
22
556  25 = 22 remainder 6
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Calculation policy
September 2011