Stone Church of England Combined School
Division Methods in Mathematics
Mission Statement
“I can do all things through Him who strengthens me”
Philippians 4:13
We believe that our school is a special place, where children can
learn, develop and thrive in a happy, nurturing environment.
The school has high expectations of academic progress for all
children and we encourage our children to achieve academic
excellence across the curriculum so they can contribute positively to
society.
Division: Stage A
Sharing and grouping (up to 20 objects)
Level 1 and towards Level 2
Practical experiences that lead to the understanding of division as having equal
groups
Sharing
Begin to understand division as having groups of equal size
Sharing – 6 sweets are shared between 2 people. How many do they have each?
Grouping
Sorting objects into groups of 2 / 3 / 4
You have eight socks. How many pairs of socks are there?
There are 10 books. Each child is given 2 books. How many children are there?
Jo has 12 Lego wheels. How many cars can she make?
Difference between sharing and grouping
Sharing:
Number of groups is known and you are finding out the size of the groups.
Grouping:
Size of groups is known and you are finding out the number of
groups.
Pre-requisite skills
Counting skills
Counting objects in order
Understanding numerical value
Learning commentary
Sharing – 6 sweets are shared between John and Lucy. How many do they have
each?
John and Lucy:
One for John, one for Lucy, one for John, one for Lucy, one for John, one for Lucy.
How many sweets does each person have?
John has 3 sweets and Lucy has 3 sweets.
Grouping – I have 6 socks. How many pairs of socks are there? How many 2’s are
in 6?
One group / pair of 2, another group / pair of 2, another group / pair of 2.
I have 3 groups / pairs.
Vocabulary
groups of
equally
same (beginning ‘=’)
take away
share
one each
equals
add
one each
two each etc
number sentence
pair
Division: Stage B
Grouping including number lines
T U U
Towards Level 2
Grouping
6 2 can be modelled as:
There are 6 strawberries.
How many people can have 2 each?
How many 2’s go into 6?
6 2 can be modelled as:
How many 2’s are in 6? (practical: circling dots/pictures)



Key understanding: How many of (one number) goes into another?
6 2 on a number line
How many 2’s go into 6?
Answer: 3 lots of 2
Count these = 3
Also use number lines to jump in 2’s, 5’s, 10’s.
Next steps
Find one half – split total into 2 groups.
Find one quarter – split total into 4 groups.
Pre-requisite skills
Place value
Grouping objects into groups of equal size
Sharing objects into equal groups
Two more/less (linking with the number line)
Understanding of equal groups
Some use of the number line for counting in e.g. 2’s
Knowledge of the inverse (e.g. 6 2 = 3 so 3 x 2 = 6)
Learning commentary
How many …. are in ….?
How many of (one number) go into another?
Vocabulary
more
less
groups
6 2 =
less
equal
how many …
how many ….. go in to ….?
equal
more
lots of
Division: Stage C
Grouping including remainders.
Towards Level 3
C1
Understand division: No remainders
15 ÷ 3 can be modelled as:
How many 3’s go in to 15?
(5 x 3 = 15 so 15 3 = 5)
C2
Understand division: Remainders
Practical Method
How many 3’s go into 13?
Take 13 sweets and make groups of 3 sweets until you cannot make any more
groups of 3.
Can we make another group of 3 sweets? No. So there is one sweet left over.
Answer: Four 3’s with 1 left over = 4 r 1
Modeling with sweets or other objects will help to illustrate that it is not possible to
make another group of 3 which results in 1 ‘left over’
C3
Building on from Stage B : Number Line
13 3
We use our knowledge of the 3 times tables to count in 3’s
Count in 3’s
0
3
6
9
12 13
+1
4 groups of 3 make 12 and there is 1 left over which is called a remainder.
13 ÷ 3 = 4 r1
Pre-requisite skills
Link with times tables
Understand division as repeated subtraction
Learning commentary
How many …’s go into …?
Can we make another group of …?
How many are left over?
Is there a remainder?
Vocabulary
left over
remainder
lots of
division
how many …. go into ….?
can we make another group of …?
how many left over?
equal group
Division: Stage D: Chunking
Dividing 2 digit numbers by 1 digit number
TU÷U
Level 3
Sharing and grouping
30 ÷ 6 can be modeled as how many 6’s go into 30?
(Link with times tables – 5 x 6 = 30 so 30 ÷ 6 = 5)
Sharing and grouping with remainders
(i) 21 ÷ 4 = 5 r1
Link with times tables: 5 x 4 = 20 so 20 ÷ 4 = 5 and as it is 21÷ 4 not 20 ÷ 4, you have
1 left over as a remainder.
(ii) Start of chunking 21 ÷ 4
T
2
- 2
U
1
0
1
5
x
5r1 4
Answer: 5r1
Where the answer will be less than 10, method (i) is more efficient. Children will
often estimate the answer using times table knowledge before they decide which
method to use.
Pre-requisite skills
Understand division as repeated subtraction
Subtracting single multiples
Understanding chunking as making equal groups
Knowledge of column subtraction
Simple addition
Learning commentary
How many 4’s go into 21?
Take away 5 groups of 4 which is 20. Put a ring around the 5.
How much is left? 21 – 20 = 1
Can we take away any more groups of 4 without going below 0? No.
How many groups have we taken away altogether? 5
Are there any left over? 1- that is the remainder.
So the answer is 5r1.
Vocabulary
take 1 group away
how many are left?
can we make another group of …?
how many groups of …. do we have altogether?
are there any left over?
remainder (as ‘r’)
chunking
divisor
Division: Stage E:
Chunking: Becoming more efficient
T U ÷ U (dividing 2 digit numbers by 1 digit number)
Level 3
Continue with chunking and developing efficiency.
72 ÷ 6
T U
7
- 6
1
- 1
2
0
2
2
0
Answer: 12
10
x
2
12
6
x
6
Pre-requisite skills
Knowing appropriate multiplication number facts
e.g. 10 x 5
Children need to recognise key multiples to use (e.g. 10 x ….)
Subtraction (column method)
Learning commentary
How many 6’s go into 72?
Can we take away 10 x 6?
Yes, that leaves us with 12.
Can we take away any more groups of 6?
Yes, we can take away 2 x 6 from 12 which leaves us with 0 – so there is no
remainder.
So we have 10 + 2 6s, which means the answer is 12.
12 6s go into 72.
Vocabulary
groups
larger chunks
divisor
I know ….. because ….
chunk
more efficient
times tables facts
remainder
Division: Stage F
Chunking: Developing efficiency
H T U ÷ U (dividing 3 digit number by 1 digit number)
Level 4
Continue with chunking and developing efficiency (by subtracting chunks larger than
10 x …)
196 ÷ 6
H T U
1 9 6
- 1 8 0
1 6
1 2
4
( 30 x 6)
Answer: 32r4
( 2 x 6)
32 r4
Pre-requisite skills
Children need to recognise key multiples to use (e.g. 10 x …)
Children understanding the need to become more efficient and take larger chunks
(e.g. 30 x … )
Column subtraction
Learning commentary (see example)
How many 6s go into 196?
How can we make the calculation more efficient?
Take away large chunks of 6.
We can take away a group of 30 x 6 which is 180 and that leaves us with 16. Put a
ring around the 30.
Can we take away any more groups of 6?
We can take away a group of 2 x 6 which is 12 from 16 which leaves us with 4. Put
a ring around the 2.
Can we take away 6 from 4 without going below 0?
No, that is our remainder.
So we have 30 + 2 6s and a remainder of 4.
The answer is 32r4.
Vocabulary
larger chunks
multiples
multiples of ten
divisor
remainder
Division: Stage G
Chunking H T U ÷ T U (dividing 3 digit number by 2 digit number)
Level 5
Continue with chunking
e.g. 858 ÷ 16 =
H T U
8 5 8
- 8 0 0
5 8
4 8
1 0
Answer: 53r10
( 50
x
( 3
x
53 r10
16 )
16 )
Pre-requisite skills
Children need to recognise key multiples to use (e.g. 10 x …)
Children understanding the need to become more efficient and take larger chunks
(e.g. 30 x … )
Column subtraction
Learning commentary
How many ... go into ...?
How can we make the calculation more efficient?
Take away larger chunks of …..
Can we take away any more groups of ...?
How much is left?
How many groups have we taken away altogether?
Are there any left over from which … cannot be taken without going below 0?
That is your remainder.
Vocabulary
larger chunks
multiples
multiples of ten
divisor
remainder
Division: Stage H
Short division
Level 4 and 5
Start to use short division.
Start to use short division for decimals.
Th H T U
3 6 8
7
4
5
2 5 7 6
7 will not go into 2.
7 goes into 25, 3 times with 4 left over. Write your 3 above the line and write your 4
remainder small to the right of the 5.
7 will not go into 4.
7 goes into 47, 6 times with 5 left over. Write your 6 above the line and write your 5
remainder small to the right of the 7.
7 will not go into 5.
7 goes into 56, 8 times. Write your 8 above the line.
So 7 goes into 2576, 368 times.
2576 ÷ 7 = 368
Pre-requisite skills
Good knowledge of times tables, place value and subtraction.