Download KS2 Maths - Multiplication and Division

The following guide explains how multiplication and
division are taught within the school, from entering
Year 3 to completing Year 6.
It follows on from the information about Maths in the
Early Years and KS1 phases of the school.
The following guide explains how multiplication and
division are taught within the school, from entering
Year 3 to completing Year 6.
By the end of KS1, the children will have learnt to
count in steps of 2s, 5s and 10s. They will also be
learning to count in 3s.
0 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Your child will have learnt to double numbers up to
100, eg double 35 is 70.
By the end of Year 3, the children should know:
x2
x3
x4
x5
x8
x 10
By the end of Year 4, they should know all their times
tables, up to 12 x 12.
Doubling is used to help students multiply by:
2:- x 2 (double then number)
4:- x 2 x 2 (double it, then double again)
8:- x 2 x 2 x 2 (double it three times)
20:- x 2 x 10 (double the number, then multiply by 10)
Partitioning helps children in all year groups to
calculate multiplication mentally:
eg. 18 x 2 (or double 18)
10 x 2 = 20
8 x 2 = 16
20 + 16 = 36
This method can be used for larger numbers too.
In Y5 and 6, children will be doubling as a mental
strategy. They may also combine this with partitioning:
eg. double €6.73
€12
€1.46
€13.46
The calculations become harder by increasing the size
of the numbers, but the strategies stay the same.
In Year 6, children will be encouraged to 'round'
numbers to help them multiply mentally.
eg. 4.3 x 19
They should calculate 4.3 x 20 first and then 'adjust' by
taking away 1 'lot' of 4.3.
eg 4.3 x 20 - 4.3
86
- 4.3 = 81.7
As they enter Year 3, children will be able to record
multiplication in this way:
2 x 5 or
5x2
5
+
5
or
2+2+2+2+2
5
+
5
2+2+2+2+2
This is called an array.
In Years 3 and 4, children learn to multiply using the
'grid' method. This is 'foolproof'! By partitioning the
numbers and recording them in a grid, it ensures every
part of each number is multiplied by every part of the
other number.
x 20 3
4 x 23
20
4 80 12
3
80 + 12 = 92
In Year 4, children extend this method for use with two
2-digit numbers. And in later years, the numbers
continue to grow!
x
18 x 46
8 40 6
6
10 400 60
8
10
40
320 48
720 + 108 = 828
But they also begin to learn to multiply vertically...
Vertical Multiplication
253
x 6
1200
300
18
Slightly trickier!
(200 x 6)
(50 x 6)
(3 x 6)
1518
As with vertical addition and subtraction, when
working with your children at home, please
remind them to keep all the Th H T and U
neatly aligned in their correct columns.
Squared Maths books help with this.
253
x 16
2000
500
30
1200
300
18
4048
1
Have a go at this calculation, first using the grid method
and then vertically:
63 x 31
x
63
x 31
By the start of Year 3, most children will know division
as 'sharing', ,'grouping' or 'halving'.
eg. How many towers of 5 cubes can I make from 20?
0 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
During Year 3, children continue sharing, grouping and
halving.
They also begin using partitioning to help divide.
eg. What is half of 96?
96
80
16
48
NB note how 96 has been
partitioned.
In Years 3 and 4, children learn that division is the
inverse of multiplication. They should be able to show
related facts,
eg. 8 x 4 = 32
32
32
4=8
8=4
In Years 4, 5 and 6 children learn to calculate division
problems using a method known as 'repeated subtraction'. This
requires them to repeatedly subtract the number they are
dividing by until they cannot take any more away.
eg. 15 3
3
15
3 (1 x 3)
12
3 (1 x 3)
9
3 (1 x 3)
6
3 (1 x 3)
3
3 (1 x 3)
0
But sometimes the numbers are too big and the
calculation would take too long. To speed it up, children
learn to subtract larger chunks.
eg. Instead of subtracting 3 each time, they subtract 30
or an even bigger chunk.
3
95 3
95
30 (10 x 3)
65
30 (10 x 3)
35
30 (10 x 3)
5
3
(1 x 3)
2
or
3
95
90 (30 x 3)
5
3
(1 x 3)
2
Finally, in Years 5 and 6, the children learn to use 'short
division'. Work from left to right and 'carry' in the next
column.
7584
6
We set it out like this:-
6 7584
6 7584
Another example
Long division
Short division
2 1 2 r5
12 2549
2 4 0 0 (200)
149
120
29
24
5
(10)
(2)
2 1 2 r5
1 2 2 5 1429
The examples given in this guide have generally used
numbers of 1, 2 or 3 digits. This is to keep it simple, for
us to clearly see the method used. As your children
become older and more proficient, they will work with
bigger numbers.
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