Transcript The teaching of division at WBJS-A parents` guide.

The Teaching of Division at
West Byfleet Junior School
March 2016
1. Children need to understand that
division can be sharing
or grouping (repeated subtraction)
6÷2
What is 6 shared by 2?
How many groups of 2 can be
made from 6?
Division as Sharing
In the first stages children naturally start their
learning of division as division by sharing,
e.g. 6 ÷2.
Division as Grouping (Repeated Subtraction)
To become more efficient, children need to
develop the understanding of division as grouping,
e.g. 6 ÷2.
Division as Grouping (Repeated Subtraction)
24 ÷ 2 =
or
There are 24 cupcakes, how many people can have 2 cupcakes each?
This should also be modelled alongside a number line to emphasise that grouping is
repeated subtraction.
0
2
4
6
8
10
12
14
16
18
20
22
24
2. Children need to have Mental Strategies
Counting in steps
Halving
Doubling
Multiplication tables facts up to 12x12
Relate division to multiplication –
that division is the inverse of multiplication
X and ÷ by 10, 100, 1000
3. Children are taught mental
strategies and informal jottings
before moving to formal written
methods
53÷4= 13r1
Don’t forget the
remainder!
-4
-4
-4
-4
-4
48 ÷ 4 = 12
2 groups
-4
-4
-4
-4
-4
-4
-4
10 groups
Before starting the more formal written
method of ‘chunking’, children should first
use the repeated subtraction on a vertical
number line.
48 ÷ 4 = 12 (groups of 4)
leading to
48 ÷ 4 = 10 (groups of 4)
+ 2 (groups of 4)
= 12 (groups of 4)
4. Formal written methods
Repeated Subtraction (Chunking)
Short Division
Long Division
Division by Repeated Subtraction (Chunking)
TU ÷ U
Children will develop their use of grouping (repeated subtraction) to be able to subtract
multiples of the divisor, developing the use of the 'chunking' method.
72 ÷ 3
3)
-
24
72
30
42
30
12
6
6
6
0
Answer :
10x
10x
2x
2x
1x
3
2x
6
5x 15
10x 30
Children should write
key facts in a menu
box. This will help
them in identifying
the largest group
they can subtract in
one chunk.
24
Children should write their answer above the calculation to make it easy for them and the
teacher to distinguish.
Any remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2.
Division by Repeated Subtraction (Chunking)
HTU ÷ U
Children can start to subtract larger
e.g. 196 ÷ 6
multiples of the divisor (e.g. 20x 30x).
Any remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2.
Children need to be able to decide what to do after division and round up or down
accordingly. They should make sensible decisions about rounding up or down after
division. For example 240 ÷ 52 is 4 remainder 32, but whether the answer should be
rounded up to 5 or rounded down to 4 depends on the context.
Division Repeated Subtraction (Chunking)
HTU ÷ TU
972 ÷ 36
27
36 ) 972
- 720
252
- 252
0
Answer :
20x
7x
27
1x36=36
2x36=72
3x36=108
4x36=144
5x36=180
6x36=216
7x36=252
8x36=288
9x36=324
10x36=360
Children may still use the menu box if required, but would also be expected to use
larger multiples of the divisor (e.g. 20x, 30x, 40x).
Children are taught to show remainders as fractions, i.e. if the children were dividing
32 by 10, the answer should be shown as 3 2/10 which could then be written as 3 1/5
in its lowest terms.
196÷6 (Repeated Subtraction/Chunking)
1x6=6
2x6=12
3x6=18
4x6=24
5x6=30
6x6=36
7x6=42
8x6=48
9x6=54
10x6=60
20x6=120
30x6=180
972÷36 (Repeated Subtraction/Chunking)
1x36=36
2x36=72
3x36=108
4x36=144
5x36=180
6x36=216
7x36=252
8x36=288
9x36=324
10x36=360
Short Division (Bus stop!!)
Is a quick trick method to be used when children are
secure in division and formal chunking methods
Short Division
5674÷4 (Short Division)
748÷51 (Short Division)
Key Facts
1x51=51
2x51=102
3x51=153
4x51=204
5x51=255
6x51=306
7x51=357
8x51=408
9x51=459
Long Division
Key Facts;
1x14=14
2x14=28
3x14=42
4x14=56
5x14=70
6x14=84
7x14=98
8x14=112
9x14=126
10x14=140
748÷51 (Long Division)
Key Facts
1x51=51
2x51=102
3x51=153
4x51=204
5x51=255
6x51=306
7x51=357
8x51=408
9x51=459
Children are encouraged to approximate
before calculating and check whether
their answer is reasonable.
By the end of year 6, children will have a range of
calculation methods, mental and written. Selection will
depend upon the numbers involved.
Children should not be made to go onto the next stage
if:
they are not ready.
they are not confident.
Children should be encouraged to consider if a mental
calculation would be appropriate before using written
methods.

Children need to know number and multiplication facts by heart and be
tested regularly.

Children should always estimate first.

Thought should be given as to whether a mental method would be more
appropriate.

Attention should be paid to language – referring to the actual value of the
digits.

Answers should always be checked, preferably using a different method, e.g.
the inverse operation.

Errors need to be discussed; problems should be diagnosed and then
worked through – do not simply re-teach the method.

Children who make persistent mistakes should return to the method that they
can use accurately until they are ready to move on.

When extending to harder numbers, refer back to expanded methods. This
helps reinforce understanding and reminds children that they have an
alternative to fall back on if they are having difficulties.