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;
Foundation Stage
Children will experience equal groups of objects.
Children will experience doubling numbers to 5. They will count in 1s, 2s,
5s and 10s
They will work on practical problem solving activities involving equal sets or
groups.
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West Coker Calculation Policy
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Year 1 (Level 1b/1a)
Double single-digit numbers to 10
Double 5
Count on in steps
1
2
3
4
5
2, 4, 6, 8, 10…
2,
Double 6, two groups of 6
10
10,
4,
+
20,
30,
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
Double 23 is double 20 plus double 3, 40 + 6 = 46
3×5
=
5×3
Double two-digit numbers
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6,
10
Year 2 (Level 2b/2a)
March 2013
6
7
8
8,
+
9
10…
10
40,
50…
10
Year 3 (Level 2a/3c)
Double two-digit numbers -Double 46
46
40
6
80
12
92
Year 4 (Level 3b)
Main Focus Grid method
Multiply any two-digit numbers by singledigit numbers
93 x 8 = 744
Multiply teens numbers by single-digit
numbers
17 × 3 =
10 x 3 =30 and 7 x 3 = 21 30+21=51
x
10
7
3
30
21
Multiply three-digit numbers by singledigit numbers and two-digit numbers
two-digit numbers
x
200
50
6
3
600
150
18
30
600
180
2
40
12
8
720
24
=744
Multiply four-digit numbers by singledigit numbers and three-digit numbers
two-digit numbers
256 x 23 = 5888
=768
26 x 32 = 832
6
3
Year 6(Level 4b/4a)
256 x 3 = 768
20
90
=51
Year 5 (Level 3a/4c)
x
x
600
180
40
12
832
x
200
20
4000
3
600
50
1000 120
150
18
Moving to long multiplication for
children who possibly struggle with
layout of grid method.
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6
4000
1000
120
600
150
18
5888
March 2013
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;
Foundation Stage
Children will understand equal groups and share items out in play and
problem solving. They will count in 1s, 2s and 10s.
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Year 1 (Level 1b/1a)
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.
Year 2 (Level 2b/2a)
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
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Year 3 (Level 2a/3c)
Year 4 (Level 3b)
Chunking
Taking off a chunk of the divisor using a
multiple of 10: 67 ÷ 3, 100 ÷ 6
Horizontal chunking on an empty number
line
Key Facts:
2 x 6 = 12, 5 x 6 = 30 and 10 x 6 = 60
Introduce the key:
2 x
5 x
10 x
100 ÷ 6
100
-
Dividing giving answers just over 10
42 ÷ 3:
x10
x4
60
(X10)
40
-
36
(X6)
4
= 16
Year 5 (Level 3a/4c)
Year 6 (Level 4b/4a)
Chunking
Chunking – 3 digit divided by 2 digit eg
long division
Using knowledge of multiplication facts
and place value to use chunk efficiently
556 ÷ 25
Key Facts 2 x 6 =12 and 5 x 6 = 30
× 10 = 60
× 20 = 120
× 30 = 180
× 40 = 240
The answer is between 30 and 40, so I’ll
subtract 30 lots of 6, leaving 16.
Key Facts
× 10 = 250
× 20 = 500
196 ÷ 6
196
-
180
(X30)
556
16
-
12
25
÷
(X2)
556
4
= 32
500 (X20)
56
196 ÷ 6 = 32 r 4
-
50
(X2)
6
=22
=
Short division or decimal answers and
money division
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West Coker Calculation Policy
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