HJS multiplication – introduction.
Multiplication may be considered as repeated addition and is usually introduced as such. However,
it may also be considered as scaling up.
Repeated addition
The repeated addition of 3+3+3+3 becomes 3, 4 times (i.e 3 x 4) but as multiplication is
commutative can also be regarded as 4 x 3
Scaling
Scaling up 3 by a factor of 4 is 12. Children will experience this interpretation of multiplication in
contexts such as ‘Sam has a rope of 60cm and Jane has a rope which is 3 times as long. How long
is Jane’s rope?). https://www.ncetm.org.uk/self-evaluation/browse/strand/5302
The array is a very useful model for illustrating both the commutative and distributive laws of
multiplication and links to division
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6 x 7 =42
7 x 6 = 42
42 ÷ 6 = 7
42 ÷ 7 = 6
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(4 x 6) + (3 x 6) = 7 x 6
(3 x 6) + (4 x 6) = 7 x 6
Larger arrays should be used to model the grid method and to provide a link between the pictorial
and abstract.
10
4
24
60
6
By placing a box around the array, as in the example below, and by removing the array, the grid
method can be seen. A proportional grid should be used.
x
10
4
6
Bar models
Repeated addition
84
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Scaling
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Use the grid method for multiplication (1)
34 x 7 =
Partition
the
numbers
into tens
and units
X
7
30
210
4
28
210 + 28 = 238
Recombine the numbers back
together (probably mentally)
*This should develop from a written to a mental method during KS 2
Make sure
the numbers
stay in the
right place
in the grid
Use the grid method for multiplication (2)
136 x 7 =
Partition
the
numbers in
hundreds,
tens and
units
X 100
7 700
30 6
210 42
700 + 210 + 42 = 952
Recombine the numbers
back together.
Make sure
the numbers
stay in the
right place
in the grid
700 +
210 +
42
952
Use the grid method for multiplication (3)
Partition
the
numbers in
hundreds,
tens and
units
436 x 37 =
X 100
30
6
30 3000 900 180 = 4080
7 700
210 42 = 952
4080 + 952 = 4132
Addition methods for the part products may vary
Columnnar
Method 1 retaining partial products
Method 2 – units first
276 X 4
276 X 30
Examples from NC 2014 appendix
10s of 2nd number
multiplied first
10s of 2nd number
multiplied first
1s of 2nd number
multiplied first