PROGRESSION THROUGH CALCULATIONS FOR SUBTRACTION
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:
1) they are not ready.
2) they are not confident.
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.
MENTAL CALCULATIONS (ongoing)
These are a selection of mental calculation strategies:
Mental recall of addition and subtraction facts
10 – 6 = 4
20 - 17 = 3
17 - _ = 11
10 - _ = 2
Find a small difference by counting up from the smaller number
82 – 79 = 3
Counting on or back in repeated steps of 1, 10, 100, 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
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.
Subtraction Methods
KEY VOCABULARY FOR SUBTRACTION: subtract, take away, minus, less, fewer, difference & decrease.
Foundation
Year 1
Year 2
 Say the number that is one less than a
number from 1 to 10.
 In practice activities and discussions,
beginning to use the vocabulary involved in
subtraction when taking away objects /
groups.
Children are encouraged to develop a mental picture
of the number system in their heads to use for
calculation. They develop ways of recording
calculation using pictures etc.
Language used with children includes: Take (away),
leave, how many are left/left over?, How many have
gone? One less, two less, ten less, how many fewer
is..? difference between, is the same as
Oral and practical work
Songs and rhymes
Dice and number games, counting back
 Read, write and interpret mathematical
statements involving addition (+),
subtraction (-) and (=) signs.
 Represent and use number bonds and
related subtraction facts within 20.
 Subtract one digit and two digit numbers to
20, including zero.
 Solve one step problems that involve
subtraction using concrete objects and
pictorial representations, and missing
number problems such as 8 – [] = 5
Children are encouraged to develop a mental
picture of the number system in their heads to use
for calculation. They develop ways of recording
calculation using pictures ect.
They use number lines, numicon, 100 squares and
bead strings to support calculations.
Children then begin to use numbered lines to
support their own calculations - using a
numbered line to count back in ones.
e.g subtract a two digit number and ones
15 – 7 = 8
13 – 5 = 8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Number stories using objects
 Solve subtraction problems using concrete
objects and pictorial representations,
including: *a two digit number and ones. *a two
digit number and tens. *two two-digit numbers.
 Recall and use subtraction facts to 20 fluently,
and derive and use related facts up to 100.
 Show that the subtraction of one number from
another cannot be done in any order.
 Use the inverse relationship between addition
and subtraction to check calculations and solve
missing number problems.
 Start to record subtraction in columns.
Children will continue to use concrete objects and
pictorial representations including numbers, quantities
and measures to solve problems.
Bead strings can be used to illustrate subtraction
including bridging through ten by counting back 3
then counting back 2
Counting back in 10s and ones
37-12=25
-2
25
Numicon can be used to show the difference
between the size of two numbers:
-10
27
37
How many are there? How many now? (after some
have been removed) Teacher modelling number
sentences, 8 take away 3 is 5
Physical and practical work on number tracks and
semi structures numberlines
Jumping backwards
Finding the difference between 2 towers of cubes
leading to using the ENL for numbers that are close
together ‘Count on’
42 – 39 =
+1
+2
39
Number stories, 15 people on a bus 3 get off, how
many are left on?
7–3=
7-
=4
-3=4
Counting back in 10s from multiples of 10s
Giving change to 20p
Number lines 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.
6–3=3
________________________________
0 1 2 3 4 5 6 7 8 9 10
40
42
Help children to become more efficient with counting
on by:
-Subtracting the units in one jump;
- Subtracting the tens in one jump and the units in
one jump;
- Bridging through ten.
Use addition as the inverse operation to check an
empty box problems e.g.
– 8 = 12
To know that subtraction is not commutative
Teachers beware of 4-8 can’t do it
(you can when you start doing
negative numbers)
Start to record subtraction in
columns, using expanded methods:
Year 3
 Subtract a range of numbers
mentally including: * A three
digit number and ones.
*Three digit number and
tens. *A three digit number
and hundreds.
 Subtract numbers with up to
three digits, using formal
methods of columnar
subtraction.
 Estimate the answer to a
calculation and use inverse
operations to check answers.
 Solve problems, including
missing number problems,
using number facts, place
value and more complex
subtraction.
 Subtract fractions with the
same denominator within one
whole (for example – 5/7 –
1/7 = 4/7).
Children will continue to use concrete
materials eg Numicon and other
representations with increasingly large
numbers.
Children will begin to use informal
pencil and paper methods (jottings) to
support, record and explain partial
mental methods building on existing
mental strategies.
Year 4
 Subtract numbers with up to
four digits, using formal
methods of columnar
subtraction where
appropriate.
 Estimate and use inverse
operations to check answers to
a calculation.
 Solve addition and subtraction
two step problems in contexts,
deciding which operations and
methods to use and why.
 Subtract fractions with the
same denominator.
 Solve simple measures and
money problems involving
fractions and decimals to two
decimal places.
Using ENL to both count back and find
the difference between two numbers
by counting on (up to four digits).
Extend to decimals to two decimal
places.
Year 5
 Subtract whole numbers with
more than four digits,
including using formal
written methods (columnar
subtraction).
 Subtract numbers mentally
with increasingly large
numbers (eg. 10,462 - 2,300
= 8,162).
 Use rounding to check
answers to calculations and
determine, in the context of
a problem, levels of
accuracy.
 Solve addition and
subtraction multistep
problems in contexts,
including to three decimal
places, deciding which
operations and methods to
use and why.
 Add and subtract fractions
with the same denominator
and denominators that are
multiples of the same
number.
Using ENL to both count on and back,
including finding the difference
between two numbers.
Complimentary addition:
6467 – 2648 =
Year 6
 Subtract whole numbers with
more than four digits,
including using formal
written methods (columnar
subtraction).
 Perform mental calculations,
including with mixed
operations and large
numbers.
 Solve addition and
subtraction multi-step
problems in contexts,
deciding which operations
and methods to use and why.
 Add and subtract fractions
with different denominators
and mixed numbers, using
the concept of equivalent
fractions.
Use an ENL to count on and back.
26467 – 12684 =
Use formal method of compact
decomposition.
Support by re-assigning new values to
Move towards compact
decomposition, including
Partitioning and decomposition
This process will initially be
demonstrated using arrow cards to
show the partitioning and
base 10 materials to show the
decomposition of the number for
numbers up to three
digits. Links will be made to concrete
materials such as Numicon and Deines.
89
- 57
= 80 + 9
- 50 + 7
30 + 2 = 32
Initially, the children will be taught
using examples that do not need the
children to exchange.
Expand method of decomposition for
numbers too large to do mentally.
572 – 158 =
Decomposition – IF they are ready,
some children will move onto the
concise method, where the above
method is refined as follows.
6 14 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
Numicon:
decimals.
Expanded method of decomposition,
leading to more compact recording.
Subtract fractions with the same
denominator and multiples of a same
number. Model this with different
representations (e.g. physical objects,
diagrams etc).
Decomposition
6 14 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.
Extend to decimals.
NB If your children have reached the
‘concise’ stage they will then continue
this
method through into year 6. They will
not go back to using the expanded
methods.
Apply to problem solving contexts such
as money and measures.
Subtract fractions with different
denominators and mixed numbers,
using the concept of equivalent
fractions. Model this with different
representations (e.g. physical objects,
diagrams etc).
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.