Division Policy
Division is closely related to multiplication and children need to be very secure
in counting in sets of 2,5,10,etc before they will be able to complete the
associated division.
Teachers need to be aware that the division symbol has two meanings. One
being “ sharing equally between” (which will lead on to fraction work) and the
other being “grouping” (which is the inverse of multiplication).
There is a close relationship between halving and dividing and although they are
grouped into stages here, they might be taught in a different order depending
on the maturity of the child.
Stage 1 – Pre division skills
Sharing out- “Can you give everyone a nursery a…..?”
“Can you share the porridge between the three bears- how can you make sure it is fair?”
Stage 2- Group and share small quantities
Using objects, diagrams and pictorial representations to solve problems
involving both grouping and sharing
Children will need to regularly practise counting in 2’s, 5s and 10s, so that they know them by
rote, by heart.
Step 1- Counting with Concrete objects
Children should be taught to understand the difference between “grouping” objects (How
many groups of 2 can you make?) and “sharing equally between” (share these sweets between
2 people).
Given a set of objects - children experience counting them
in equal groups of 2s, 5s and 10s.
2.4.6.8
How many groups of 4 can be made with 12 stars? = 3
GROUPING
SHARING
There are 15 sweets in 1 bag. How many sweets will 5 children get each?
Children need to use lots of practical apparatus, arrays and picture representations.
Children can also be encouraged to use pencil and paper jottings to share amounts equally,
This will lay the foundations of fraction work.
Can you divide this bar in to 2, 3, 5?
A progression of this is to use this bar method for simple sharing of amounts .
So 12 shared in to 3
Step 2 – Halving up to 12
Halving numbers up to 5 – using fingers
½ of 6 = 3
Matching numicon- replacing a larger numicon with 2 smaller
numicon of equal value.
Dominoes ------ Which are divided into halves?
Find half
of a group of objects by sharing into 2 equal groups.
Key Vocabulary: share, share equally, one each, two each…, group, groups of,
lots of, array :
Stage 3 – Linking counting in 2s , 5s and 10s for
division
Making connections between arrays, number patterns, and counting in twos, fives and tens.
Step 1 – Halving or dividing by 2 - numbers within 20
Children should understand that halving is the opposite of doubling. They should also be
introduced to the mathematical symbol for division.
Using fingers to count in 2s – Each finger is 2
How many 2s in 16? Count
How
your fingers. Yes, there are 8
lots of 2s in 16. 16÷2= 8
Dropping 2p’s in to a tin- , 2p, 4p, 6p, 8p
Using simple arrays
How many 2s in 14 ?
There are seven 2s in 14
14 ÷ 2= 7
How many coins did I
drop in the tin? Yes four
2p’s is 8p. 8 ÷2 = 4
Step 2 – As above but with fives and tens.
How many 10ps in 50p.
50 ÷10 = 5
Count to 40 in 5’s. How many
fingers are you holding up? Yes, 8
lots of 5 are 40
40 ÷ 5 = 8
This stage needs to be completed in many practical ways, lots of rote counting and
emphasis on language. Concrete apparatus such as, tens apparatus, coins and numicon,
and making arrays will need to be used to reinforce that it is “ how many sets of?,”
“ how many groups of?” or “ how many lots of?”, or to reinforce the sharing in to equal
groups.
Arrays will help to show children the reversibility of division.
How many 5s in 15?
15 ÷5 = 3
5
15 shared in to 3 groups is 5
5
3 groups of 5 is 15
5
15 ÷3 = 5
Once the children have got this they will be able to apply it to other divisions, for example
12 ÷ 3 =
How many 3s in 12?
This represents 12 ÷ 3, posed as
how many groups of 3 are in 12?
Pupils should be able to show that the
same array can represent 12 ÷ 4 = 3 if grouped
horizontally.
This will also show the children the relationship
between multiplication and division.
Step 3- Use mental recall, investigation and jottings
Children should begin to use their knowledge of the multiplication facts for 2, 5 and 10
times tables to help them with the division calculation.
Use 100 square to find multiples of a number and then work out the related division .
20 ÷ 5 = 4
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Group from zero in equal jumps of the divisor to find out ‟how many groups of _ in _?‟.
Pupils could use a bead string or practical apparatus to work out problems like “A CD
costs £3. How many CDs can I buy with £12?‟ This is an important method to
develop understanding of division as grouping.
By learning to count by rote in 3s, 4s and so on,
children will be able to use their fingers to
quickly work out the answers to more tricky
division facts.
Rough drawings or jottings should also be encouraged to help children develop their mental
maths skills. When working out 20 ÷ 4= children should ask “ how many 4’s in 20? They could
record this by building up squares to make a bar.
18 ÷ 3 =
1
2
3
4
5
6
_________________________________________________________
3
6
9
12
15
18
Key Vocabulary: share, share equally, one each, two each…, group, equal groups of, lots of, array, divide, divided by,
divided into, division, grouping, number line, left, left over
Stage 4 – Using partitioning to halve numbers
Step 1 – Halving 10,20, 40, 60, 80, 100
Using fingers, 10p’s, tens apparatus or numicon as before. Relate to doubling numbers to 5.
Half of 60 = 30
60 ÷ 2=30
Step 2 - Halving “ easy even ” numbers to 100 e.g. 24, 32,44
Half of 24
24÷ 2
24
20
10
4
+
2 = 12
Always show the links.
Step 3- Halving 30 , 50, 70, 90 and 100
These are tricky and have to be learnt. Coins, numicon, tens apparatus and lengths of
paper can be used.
There is a pattern to this – but numbers can be split half of 30 is the same as –
½ of 20 + ½ of 10.
Step 4- Halving “ tricky even “ numbers to 100 , such as 76 , 92 , 38
Half of 76
76÷2
76
70
35
6
+
3=
38
Stage 5 - Divide 2 digit numbers by a single digit
Leaving a remainder
Step 1- using the previous practical methods –
15÷4
=
1 group
2 groups
3 groups
3 remaining
Step 2 Grouping on a number line or as an array:
Children continue to work out unknown division facts by
grouping on a number line from zero. They are also now
taught the concept of remainders, as in the example. This
should be introduced practically and with arrays, as well as
being translated to a number line. Children should work
towards calculating some basic division facts with remainders
mentally for the 2s, 3s, 4s, 5s, 8s and 10s, ready for
“carrying‟ remainders across within the short division method
3
3
3
3
And 1 more
Key Vocabulary: share, share equally, one each, two each…, group, equal groups of, lots of, array,
divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short
division,carry‘, remainder, multiple