Progression Through Calculations - Subtraction
THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO
ACHIEVE.
1st Stage
Children begin to count backwards in number
rhymes or stories.
Continue to count back in ones from 20.
Begin to relate subtraction (the term given to
what the pupils are doing) to taking away (one method for subtraction).
Objects are to be placed in lines to prepare pupils for the Bar Method.
Find a number one less than – numbers to 10.
2nd Stage
Children are encouraged to develop a mental picture
of the number system in their heads to use for
calculation. They develop ways of recording
calculations using pictures or practical representations.
My shepherd looks after 8
sheep. He has lost 5 and he
has 3 left.
 Teachers demonstrate the use of the number line and children begin to use it with
support. They use a 100 square to count back.
Children will also use other practical resources to subtract.
These examples show 6 – 3 = 3
 The number line should also be used to show that 6 - 3 means the ‘difference between
6 and 3’ or ‘the difference between 3 and 6’ and how many jumps they are apart.
-1 -1
-1
0
1
2
3
4
5
6
7
8
9
10
 Children then begin to use number lines to support their own calculations - using a
number line to count back in ones. This can also be shown on a bead string.
13 – 5 = 8
The Bar Method approach should be used alongside using the string of beads
13-5
Pupils will also investigate and solve missing number problems which include addition to
show the relationship between subtraction and addition
2 + □ = 10
□ + 4 = 12
12 – 4 = □
Children begin to use the words associated with subtraction.
3rd Stage
Children will begin to use number lines and partitioning to support calculations.
Counting back

First counting back in tens and ones.
47 – 23 = 24
20
3
-1
24

-1
25
-1
26
- 10
27
- 10
37
47
Subtracting the tens in one jump and the units in one jump. THIS METHOD
MUST BE SHOWN ALONGSIDE THE PREVIOUS METHOD
47 – 23 = 24
20 3
-20
-3
24

27
47
Bridging through ten can help children become more efficient. THE WARM UP
ACTIVITY MUST BE PARTITIONING NUMBERS IN A VARIETY OF WAYS.
42 – 25 = 17
-3
17
20
-2
22
-20
42
Counting on
If the numbers involved in the calculation are close together or near to multiples of 10,
100 etc, it can be more efficient to count on. The Bar Method should also be used
alongside this for problem solving.
 Count up from 47 to 82 in jumps of 10 and jumps of 1.
THIS METHOD REFERS TO FINDING THE DIFFERENCE.
82 – 47
Help children to become more efficient with counting on by:



Counting on the units in one jump;
Counting on the tens in one jump and the units in one jump;
Bridging through ten.
4th Stage
Children will continue to use empty number lines with increasingly large numbers. They will
begin to use informal pencil and paper methods (jottings) to support, record and explain
partial mental methods building on existing mental strategies. The bar Method should be
shown and used alongside this during problem solving.
 Where the numbers involved in the calculation are close together or near to
multiples of 10, 100 etc, counting on using a number line should be used. THIS
METHOD REFERS TO TAKING AWAY.
102 – 89 = 13
5th Stage
Partitioning and decomposition – A TAKING AWAY METHOD
This process should be demonstrated using arrow cards to show the partitioning and base
10 materials to show the decomposition of the number. Partitioning warm ups are useful
prior to this lesson
A NUMBER LINE SHOULD BE SHOWN ALONGSIDE THE FIRST METHOD.
89
=
80 and 9
- 57
50 and 7
30 and 2 = 32
Initially, the children will be taught using examples that do not need the children to
exchange.
From this the children will begin to exchange.
71
- 46
=
Step 1
70 and
- 40 and
1
6
=
Step 2
60 and
- 40 and
20 and
11
6
5
= 25
The calculation should be
read as e.g. take 6 from 1.
This is then recorded by the children as
60
70 and 11
- 40 and 6
20 and 5 = 25
PLACE VALUE COUNTERS/ DIEN’S
EQUIPMENT SHOULD BE USED WHILST TEACHING THIS METHOD.
Children should know that units line up under units, tens under tens, and so on.
The children then work with larger numbers where more than one exchange needs to take
place. This method should not be used beyond the addition of 4 digit numbers as it can
become cumbersome and confusing.
The teacher will demonstrate this using:
754
- 86
Step 1
=
700
+ 50 + 4
80 + 6
Step 2
700
-
+ 40
80
Step 3
600
+ 140 + 14
(adjust from H to T)
80 + 6
+ 60 + 8 = 668
-
-
600
+ 14
+ 6
(adjust from T to U)
This is then recorded by the children as
600
140
700
600
+ 50 + 14
80 + 6
+ 60 +
8 = 668
6th Stage - decomposition
Once secure, the decomposition is refined to
614 1
//
754
- 86
668
Children should:

be able to subtract numbers with different numbers of digits;

using this method, children should also begin to find the difference between two
three-digit sums of money, with or without ‘adjustment’ from the pence to the
pounds;

know that decimal points should line up under each other. When moving onto decimal
subtraction, it is good practice to go back to the expanded method so that pupils can
see what is happening. Place value counters can help too.
£8.95
=
8 and 0.90 and 0.05
leading to 8.85
-4.38
4 and 0.30 and 0.08
-4.38
-
=
8 and
4 and
4
0.80 and
0.30 and
0.50
0.15
0.08
0.07 = £4.57
7th Stage
Children will continue to use the methods but should also:



be able to subtract numbers with different numbers of digits;
begin to find the difference between two decimal fractions with up to three digits
and the same number of decimal places;
know that decimal points should line up under each other.
The decomposition of larger numbers will continue like this:
5 13 1
6467
- 2684
3783
By the end of Year 6 Children should:

be able to subtract numbers with different numbers of digits;

be able to subtract two or more decimal fractions with up to three digits and either
one or two decimal places;

know that decimal points should line up under each other.
Children will be taught 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:
1) they are not ready.
2) they are not confident.
Once children have moved onto a more concise method in year 5 and 6 they will not
go back to using the expanded methods.
Children should be encouraged to approximate their answers before calculating.
Children should be encouraged to check their answers after calculation using an
appropriate strategy.
Children should be encouraged to consider if a mental calculation would be appropriate
before using written methods.
Policy Updated October 2015 – D. Swallow