Year
Foundatio
n Stage
Additional notes to support
teaching and learning
Subtraction
Children start Foundation by learning number names and the
values of each digit with lots of pictorial representation and
hands-on maths. They then learn to count backwards and
forwards using a number track.
In subtraction, the jumps go
below the line.
They learn to remove a smaller number from a larger number
and find how many are left by counting back from the larger
number using money, objects and numicon. They also
recognise how many more are needed to make a larger
number by counting on. Children learn to record their
calculations as number sentences.
9–4=
1
Year 1
2
3
4
5
6
7
8
9
In Year 1, children learn how to count forwards and
backwards, using number lines, 100 squares and cubes. They
learn how to subtract a single digit to 10 and then 20 and
understands the operation of subtraction as takeaway or
difference
10
In subtraction, the jumps go
below the line.
Encourage children to use
their rulers as number lines.
7–4=3
25 – 8 = 17
Using Dienes Cubes:
25 – 4 = 21
-
= 21
Using numicon:
Year 2
Children in Year 2 move on to counting backwards on an When subtracting on a
empty numberline. They will continue to use concrete objects number line, always subtract
and pictorial representations, including those involving the units first in preparation
numbers, quantities and measures. They learn how to subtract for column subtraction.
a two-digit number and units, a two-digit number and tens and
two two-digit numbers
It is really important that the
children understand the
equals sign as a sign of
15 – 7 = 8
equivalence, that what is on
8
10
15
one side of it has the same
value as what is on the
-2
-5
other.
For example:
24 – 12 = 12
74 – 27 = 47 worked out by counting back:
12 = 24 – 12
(using the pan balance with
47
67
70
numicon is a good way of
74
teaching this).
- 20
-3
-4
Children should understand
that unlike addition,
subtraction is not
commutative (cannot be
done in any order)
Children should understand
that difference is also
subtraction.
Year 3
In Year 3, children learn how to subtract numbers with up to 3
digits. They initially learn a more formal written method which
is the pre-cursor to vertical subtraction. In this, the numbers
are partitioned so that children can recognise the technique.
Process Steps to Success – Vertical Subtraction with
Partitioning
Estimate the answer first.
1. Write the 2 numbers vertically where the biggest number is
on the top.
2. Partition the numbers but keep them in their place value
columns.
3. Start with the units and subtract the bottom number from
the top number, putting the answer below the line. Continue
if there are hundreds.
4. Subtract the tens digits from the one above and put the
answer below the line.
75 – 32 = 43
70
30
40
5
2 3
Children move on to numbers that require decomposition
(otherwise known as ‘exchanging’ or ‘borrowing’. In this, the
golden rule is that if a number is bigger on the bottom then
Practical resources (such as
dienes or straws) should be
used alongside written
methods to support
understanding when this
method is introduced. A
useful interactive resource
that demonstrates this can
be found at:
http://www.harcourtschool.
com/activity/elab2004/gr3/3
.html
Children in year 3 should
always estimate the answer
to a calculation and use
inverse operations to check
answers
Teaching video available at:
https://www.ncetm.org.uk/r
esources/40532
Children should understand
that difference is also
you cannot take it away from a smaller number. In the first
subtraction.
example below, the 8 cannot be taken away from 5, so one ten
is exchanged for ten units making it 15-8=7.
Process Steps to Success –Subtraction with Exchange
1. Set the sum out as shown before and estimate the answer.
2. Where the units on the bottom are bigger than the top,
exchange a ten for ten units so that the number on the top is
now bigger.
3. Finish the sum as normal and check against the estimate
using the inverse operation.
400
130
537 – 251 = 286
500 30
7
200 50
1–
200 80
6
By the end of the year, children should have started to use
the vertical subtraction method (not partitioned). See below
Year 4
In Year 4, children subtract numbers with up to 4 digits using
the formal written method of column (vertical) subtraction.
Initially, teachers will show the expanded method alongside
the short method.
Process Steps to Success – Vertical Subtraction with Exchange
1. Estimate the answer first.
2. Write the 2 numbers vertically where the biggest number is
on the top.
3. Keep the digits in their HTU column.
4. Start with the units and take the bottom one away from the
top, putting the answer below the line. (If the top number is
smaller, then one ten needs to be exchanged for ten units.)
5. Take the bottom tens digit away from the top one and put
the answer below the line. (Again, if the top number is
smaller, then one hundred needs to be exchanged for ten
tens.)
Underline the answer and then check against the estimate
using the inverse operation.
5
5 6 13
4 85 1 5
Remember, if you can do the sum mentally then this is better
to do so. In the example below, this would be quite awkward
to do in the formal vertical method. In this case, it would be
much easier to count on or back using a number line:
6,003 – 1,997 = 4,006
Practical resources (such as
dienes or straws) should be
used alongside written
methods to support
understanding when this
method is introduced. A
useful interactive resource
that demonstrates this can
be found at:
http://www.harcourtschool.
com/activity/elab2004/gr3/3
.html
Children in year 4 should
always estimate the answer
to a calculation and use
inverse operations to check
answers.
Teaching video available at:
https://www.ncetm.org.uk/r
esources/40532
Subtraction should also e
taught through money and
measure.
1997
2000
-3
Year 5
6000
- 4000
6003
-3
Year 5 learn to deal with subtraction of decimals and mixed
decimals.
Process Steps to Success - Vertical Subtraction with Decimals
1. Ensure tenths and hundredths are in the appropriate
column.
2. Fix the decimal place between the units and tenths digits
and ensure they line up (like buttons on a shirt).
3. If writing numbers in squares, put the decimal place on the
line between 2 squares.
4. Complete the sum as you would for whole numbers.
3 1
£ 3. 4 5
£ 2. 2 7 £ 1. 1 8
Process Steps to Success – Vertical Subtraction with Mixed
Decimals
(As with decimals except it is essential that there is a place
holder added if the numbers do not have the same number of
decimal digits.)
1. Ensure all digits are in their place value columns.
2. Add a zero to ensure both numbers have the same number
of digits after the decimal place (to hold the place value)
3. Complete the sum as you would for normal decimals
starting with the numbers on the right hand side.
18.67 - 3.243 =
6 1
1 8. 6 7 0
3. 2 4 3 1 5. 4 2 7
YEAR 6
In Year 6, children consolidate their knowledge of subtraction.
Children in year 5 should
always estimate the answer
to a calculation and use
inverse operations to check
answers.