Progression in Subtraction National Curriculum 2014
What will subtraction look like?
EY
FS
Y1
Teacher modelling, pictorial representation
Practical demonstrations of subtraction relating to
‘take away’.
E.g. 10 – 1?
Use of number tracks.
Vocabulary of subtraction in practical activities
Read, write and interpret addition (+), subtraction(-)
and equals (=) signs.
Subtract 1 digit and 2 digit numbers to 20 including
zero.
Number tracks leading to number lines introduced
for recording ‘jumps’ back. (note children will need
to be taught the difference between a track and
a line)
1
2
3
4
5
6
7
8
Can you count back 5? Take away 5.
Difference introduced practically and then on
number tracks and lines, e.g. 12 - 7
Can you make a rod 12 blocks long? My block is 7
blocks long. What’s the difference?
difference
0 1 2 3 4 5 6 7
Key Points
Notes
Teach through story telling and real life
situations
Use songs and rhymes, etc e.g. Sing ten
green bottles
Pupils memorise and reason with number
bonds to 20 (from year 2) in several
forms (e.g. 9 + 7 = 16; 16 - 7 = 9; 7 = 16 9).
They should realise the effect of adding
or subtracting zero. This establishes
addition and subtraction as related
operations.
Pupils combine and increase numbers,
counting forwards and backwards.
They discuss and solve one step problems
in familiar practical contexts, including
using quantities. Problems should include
the terms put together, add, altogether,
total, take away, distance between, more
than and less than, so that pupils develop
the concept of addition and subtraction
and are enabled to use these operations
flexibly.
Use concrete objects and visual
representations and missing number
problems such as 7 = ? - 9
Mostly mental calculations with children
making informal jottings leading to
introduction of number sentence.
Understanding subtraction as “take away” and
find a small “difference “by counting up.
Use informal written methods to support the
subtraction of a 1-digit number from a 1digit number or a 2 –digit number and a
multiple of 10 from a 2-digit number
Teach through real life situations, songs
and rhymes
When using number lines, ensure the children
recognise the difference between an empty
number line and one that is labelled.
0 1 2 3 4 5 6 7 8 9 10 11 12
Pupils use concrete apparatus to experience take
away and difference in practical activities.
Count out 16 straws. If you give your friend 7, how
many will you have left?
Y2
(a) Pupils practice finding the difference by counting
on using a number line. They are able to choose
when to take away and when to find the difference
when answering a subtraction problem.
0
27
difference
0
+3
27
+20
30
55
+5
50
so 55 – 27 = 28
55
55 – 27 = 28 27 + ? = 55
55 - ? =27 ? + 26 = 55
(b) Pupils use concrete apparatus to explore
exchange in practical activities. E.g. Subtract 18p
from 33p
(c) Pupils begin to organise their subtractions
using expanded columnar methods
87 – 54
80
-50
30
7
4
3
Pupils extend their understanding of the
language of addition and subtraction to
include sum and difference .
Teach through real life situations and use
concrete objects and visual representations
including number quantities and measures.
Pupils practise addition and subtraction
to 20 to become increasingly fluent in
deriving related facts such as using 3 + 7
= 10, 10 - 7 = 3 and 7 = 10 - 3 to calculate
30 + 70 = 100, 100 - 70 = 30 and 70 =
100 - 30.
Use Base Ten/Dienes to show exchange
Pupils will solve subtraction problems in a
real life context.
Use the inverse relationship between
addition and subtraction. To understand
that subtraction cannot be done in any
order. They will check their calculations.
Pupils should partition numbers in
different ways for example 23 = 20 +3
and 23 =10 + 13 to support subtraction.
Recording addition and subtraction in
columns supports place value and
prepares for formal written methods
with larger numbers.
Teach children to look for special cases i.e.
take away a small amount (55-2=53) and by
counting back -9 by compensation
34 – 9 = 34 –10 and then add one back
Subtract using concrete objects, pictorial
representations and mental skills
TU - U
TU - multiples of 10
TU - TU
All children still need story telling to solve
subtraction problems – put them into
context.
81-57=difference
+3
+20
57
Y3
60
+1
80
=24
81
From Year 2 (no exchanging)
187 – 54
Progressing to:
(b) 81
– 57 =
100 80
50
100 30
7
4
3 = 133
= 80
- 50
take away
1
7
Pupils practise solving varied addition
and subtraction questions.
“1 take away 7 is tricky
so exchange”
80
- 50
20
1
7
4 = 24
Pupils add and subtract mentally
HTU – U
HTU – multiple of ten
HTU – multiple of hundred
They practise using columnar addition
and subtraction with increasingly large
numbers up to three digits to become
fluent (from year 4).
Pupils progress to subtract numbers with up to 3
digits
30
300
-100
200
or
341- 123
Base Ten/Dienes to show exchange
Coins/counters on a place value chart,
number lines.
11
Estimate the answer to a calculation.
Check answers with the inverse operation.
341- 123
It is important to continue to use concrete
materials to aid understanding.
For mental calculations with two-digit
numbers, the answers could exceed 100.
70
81
- 57
Pupils secure, apply and develop their
understanding of place value and
partitioning. They begin to record in
columns.
11
40
20
10
1
3
8
30
11
300
40 1
-100
20 3
200
10 8
Solve problems including missing numbers
and using number facts,
Hundreds
Tens
Units / Ones
Y4
(a) Pupils continue to calculate difference
mentally using a number line
(b) Pupils progress to using the compact columnar
method for subtraction.
70
784 = 700
- 56 700
80
50
20
1
4
6
8
7 1
adjust from T to U
= 728
784
- 56
728
Progressing to 4 digit numbers
Pupils continue to practise both mental
methods and columnar spacing for
addition and subtraction with
increasingly large numbers to aid fluency.
Subtract numbers with up to 4 digits,
including up to 2 d.p. in the context of
money
Continue to support understanding with a
range of concrete materials, including Base
Ten to show exchange
Coins/counters on a place value chart,
number lines.
Thousands
Hundreds
Tens
Units/Ones
Estimate and check answers to
calculations.
Understand subtraction as the inverse
of addition.
Solve two-step problems in contexts,
deciding which operations to use and
why.
Y5
Pupils continue to calculate difference mentally,
supported with a number line.
(a) Pupils use the column method to solve increasingly
more complex calculations involving many
exchanges, and solve subtractions with more than
4 digits
(b)
Pupils practise using the formal written
methods of columnar addition and
subtraction with increasingly large
numbers to aid fluency.
They practise mental calculations with
increasingly large numbers to aid fluency.
e.g. 12 462 – 2300 = 10 162
Solve multi step problems in context.
Pupils subtract decimals with more than one decimal
place and with differing numbers of digits.
0 1 12 1
123.04
- 85.60
37.44
Use rounding to check for accuracy in
both calculations and problem solving.
Continue to support understanding with a
range of concrete materials, including Base
Ten to show exchange
Coins/counters on a place value chart,
number lines.
Pupils continue to find the difference using the
number line with increasingly large numbers.
Y6
(b) 6467 – 2684
5
-
13
1
6467
2684
3783
3783
+ 2684
and check answer
6467
1 1
then 324.9 – 7.2
1
1
8 1
3 2 4.9 0
7.2 5
3 1 7.6 5
and continue to use inverse to check
.
Pupils practise addition and subtraction
for larger numbers, using the formal
written methods of columnar addition
and subtraction.
They undertake mental calculations with
increasingly large numbers and more
complex calculations.
Use rounding and estimation to check for
accuracy in both calculations and
problem solving.
Consolidate skills from year 5