PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION
These are a selection of calculation strategies
that will be used in school from Nursery to Year 6
Counting out
9 – 3 = holds up nine fingers, folds down three and counts how many fingers are left
Counting back from
9 – 3 = counts back three numbers from nine ‘eight, seven six’
Counting back to
9 – 3 = counts back from the first number to the second, keeping a tally of the numbers that have been said
‘eight, seven, six, five, four, three’ then counts how many fingers have been used
Counting up to find a small difference
12 – 9 = counts up from the smaller number to the larger number keeping a tally of the numbers that have
been said ‘ten, eleven, twelve’ then counts how many fingers have been used
Using a known subtraction fact (instant recall)
10 – 6 = 4
17 -  = 11
20 - 17 = 3
10 -  = 2
Using a known fact to derive a new fact
20 – 5 = 15 so therefore 20 – 6 = 14
Using knowledge of place value
8 – 5 = 3 so 80 – 50 = 30 and 800 – 500 = 300
Counting on or back in repeated steps of 1, 10, 100 or 1000
86 - 52 = 34 (by counting back in tens and then in ones)
460 - 300 = 160 (by counting back in hundreds)
Subtract the nearest multiple of 10, 100 and 1000 and adjust
24 - 19 = 24 - 20 + 1 = 5
458 - 71 = 458 - 70 - 1 = 387
Use the relationship between addition and subtraction (inverse operations)
36 + 19 = 55
19 + 36 = 55
55 – 19 = 36
55 – 36 = 19
MANY MENTAL CALCULATION STRATEGIES WILL CONTINUE TO BE USED.
THEY ARE NOT REPLACED BY WRITTEN METHODS.
THE FOLLOWING ARE STANDARDS THAT WE
EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE.
Nursery
Children should be encouraged to estimate their answers prior to working them out.
Children will have the opportunity to experience a daily diet of number songs and games.
Maths experiences and connections
are threaded through structured
play activities such as the sand,
water, malleable, outdoor and role
play areas.
Through games and number rhymes the children respond to the vocabulary related to counting backwards
and subtraction.
Cheeky Monkey’s Counting Song (Number Fun 2 Song1)
5 Currant Buns in the Baker’s Shop
5 Little Ducks went
swimming one day
The children can visually recognise and say there is a difference in quantity when comparing sets of objects,
showing that they are beginning to understand the concepts of more and less.
Some children will begin to find one less
than a group of up to 5 objects.
Reception
Children should be encouraged to estimate their answers prior
to working them out.
Children are encouraged to develop a mental picture of the number
system in their heads to use for calculation.
They begin to understand number value, i.e. they are able to say that a number is more or less than another
number.
Children begin to relate
subtraction to taking
away from a group of
objects and they use
concrete materials and
structured apparatus to
calculations.
support
7 take away 1 is 6
Teachers will demonstrate how to use a numberline through songs and games.
6–3=3
-1
-1
-1
___________________________________
0 1 2 3 4 5 6 7 8 9 10
Children develop ways of recording calculations
using pictures, symbols and tally marks.
Year 1
Children should be encouraged to estimate their answers prior to working them out.
Children understand subtraction as taking away by removing a
smaller number of objects from a larger number of objects.
Children use a range of
concrete materials and
structured apparatus
such as bead strings,
numicon and base ten
to support making
connections.
13 – 5 = 8
13 –
5=8
Children use numbered lines to support their own calculations by counting back in ones.
13 – 5 = 8
0
-1 -1 -1
1
2
3
4
5
6
7
8
9
-1 -1
10 11 12 13 14 15
Children develop ways of recording their work using
numbered lines, objects or pictures.
They begin to use the symbols ‘-’ and ‘=’ to
record their number sentences.
Year 2
Children should be encouraged to estimate their answers prior to working them out.
Children use a range of
concrete materials and
structured apparatus
such as bead strings,
numicon and base ten
to support making
connections.
26 – 5 = 21
47 – 23 =
24
Children will begin to use ‘empty number lines’ themselves to count back without crossing the tens
boundary.
First in ones.
-1
26 – 5 = 21
21 22
Then in tens and ones.
-1
23 24
-1
-1
-1
25 26
-1
47 – 23 = 24
-1
-1
24 25 26 27
Next subtracting the
units in one jump by
using the known fact
7 – 3 = 4.
37
- 10
47
47 – 23 = 24
-3
24
Finally by subtracting the
tens in one jump and the
units in one jump.
- 10
-10
27
47 – 23 = 24
-3
24 27
-10
37
47
-20
47
Children will be able to use the knowledge that subtraction is the inverse of addition to make related number
sentences e.g 14 – 6 = 8, 8 + 6 = 14, 14 – 8 = 6, 6 + 8 = 14
They will also be able to use their knowledge of inverse operations to solve missing number calculations.