Progression in Subtraction – Stage 1
Children will engage in a variety of counting songs and rhymes and practical
activities.
In practical activities and through discussion they will begin to use the
vocabulary associated with subtraction.
They will find one less than a given number.
They will begin to relate subtraction to ‘taking away’ using objects to count ‘how
many are left’ after some have been taken away.
There are three people on the bus. One more gets on. How many are there now?
There are four children in the home corner. One leaves. How many are left?
How many different ways can you plant five bulbs in two bowls?
Progression in subtraction
autumn
● There are 8 grapes. I
eat one, how many are
left? I eat another. How
many are left? And if I
eat another?
● There are 10 people on
a bus, 2 get off, how
many are left?
● This tower has 6 cubes
and this one has 4 cubes.
What is the difference in
height?
spring
What is 4 take away 2?
7 subtract 3?
Subtract 2 from 11.
What is 8 less than 9?
What is the difference
between 14 and 12?
summer
● There are 5 pegs on a
coat hanger, 4 are
showing, how many are
hidden under the cloth?
What number sentences
could we write?
● What numbers go in the
boxes?
21 − 11 = ■;
21− ■ = 10;
■ − 11 = 10;
■ − ▲ = 10
‘Seven ladybirds are playing together and then three fly away. How many
ladybirds are left?’
Subtraction – Stage 2
Given a number, identify one less
Read, write and interpret mathematical statements involving subtraction (-)
and the
equals (=) sign
Subtract one- digit and two-digit numbers within 20, including zero
Solve missing number problems eg 20 - = 15
NB Ensure that children are confident with the methods outlined in the previous
stage’s guidance
before moving on.
Children will continue to practise counting back from a given number.
Initially use a number track to count back for subtraction:
Initially use a number track to count on for addition, counting on from the largest
number:
9 – 4 = 5 ‘Put your finger on number 9. Count back 4.’
Then progress to a marked number line:
9–5=4
Counting on to find a small difference:
Introduce complementary addition to find differences (only use for small differences).
The use of models is extremely important here to understand the idea of “difference”.
Count up from the smallest number to the largest to find the difference using
resources, e.g.
cubes, beads, number tracks/lines:
11 – 9 = 2
The difference between nine and eleven is two.
Progression in subtraction
autumn
spring
summer
● There are 10 grapes, ● What is 14 subtract 2? ● There are 10 pegs on a coat hanger. 6
you eat 4,how many
Subtract 30 from 70.
are showing; how many are hidden?
are left?
● What number must I
What number sentences could we write?
● There are 20 people take from 20 to leave 3? ● I think of a number. I add 10.The
on a bus, 3 get off ● Find pairs of numbers answer is 30. What is my number?
how many people are with a difference of 10.
● What numbers go in the boxes?
left?
86 − 50 = ■;
● If two towers have a
26 − ■ =16;
difference of 3 cubes,
■ − 40 = 28;
how tall might they
■ − ▲ = 40
be?
● You have 70p and spend 30p, what do
you have left? What number sentence
would you write?
Subtraction – Stage 3
Subtract numbers using concrete objects, pictorial representations, and
mentally,
including:
A two digit number and ones
A two digit number and tens
Two two-digit numbers
NB Ensure that children are confident with the methods outlined in the previous
stage’s guidance
before moving on.
Counting back using an empty number line within 100, in ones…
34 - 6 = 28
…and in tens
58 – 30 = 28
Use in conjunction with a 100 square to show jumps of tens.
Subtraction, using partitioning, on an empty number line:
-1
-1
-1
-1
-1
-10
-10
76 – 45 = 31
-10
-10
-
31
32
33
34
35
36
46
56
66
Use in conjunction with a 100 square to show jumps of tens and ones.
76
If children are confident, use more efficient jumps…
-5
31
-40
36
76
Progression in subtraction
autumn
spring
summer
● You have 57p in your
● What is 35 take
● There are 20 pegs on a coat hanger.
pocket and spend 49p, how
away 8? Take 7 from 14 are showing. How many are
much do you have left?
42.Subtract 40 from
hidden? What number sentences
● There were 24 people on a 95.
could we write?
bus. There are now only
● What must I take
● I think of a number. I add 45.The
16.How many got off? What from 14 to leave 6?
answer is 95. What is my number?
number sentence would you ● What is the
● What numbers go in the boxes?
write about this?
difference between
78 − 56 = ■;
22 and 5?
■ − 15 = 19;
● How many more
▲ − ■ =37;
than 4 is 49?
20 − ▲ = 5
● One plant is 40 cm tall, another is
56 cm tall. What is the difference
between their heights? What number
sentence would you write?
Subtraction – Stage 4
Subtract numbers with up to three digits, using formal written method of
columnar subtraction
NB Ensure that children are confident with the methods outlined in the previous
stage’s guidance before moving on.
Further develop the use of the empty number line with calculations that bridge 100:
and with addition of a three-digit and a two -digit number:
126 – 45 = 81
Use practical equipment to support counting back in tens and bridging 100 such as
200 grid, Numicon, Cuisinaire rods etc.
Then use more efficient jumps:
-5
-40
86
81
96
106
116
126
Extend with larger numbers by counting back… 216 – 27 = 189
…and by counting on to find the difference (small difference): 231 – 198 = 33
Introduce the expanded written method with the calculation presented both
horizontally and vertically (in columns) and supported with practical activities. Use
two-digit numbers when introducing this method, initially:
78 – 23 = 55
−
70 and 8
‘Partition numbers into tens and ones
20 and 3
the ones, and then subtract the tens. Recombine to
50 and 5 = 55 give answer.’
Use practical activities (such as Dienes) to support the teaching of this method.
NB In this example decomposition (exchange) is not required.
You may replace the ‘and’ with a + symbol or give the place value column headings to
avoid confusion.
This will lead into the formal written method:
7 8 Use the language of place value to ensure understanding.
- 2 3 ‘Eight subtract three, seventy subtract twenty.’
55
NB A number line would be an appropriate method for this calculation but use two
digit numbers to illustrate the formal written method initially.
Introduce the expanded written method where exchange/decomposition is
required:
73 − 27 = 46
70 + 3
becomes 60 and13 (73 is partitioned into 60 and 13)
- 20 + 7
- 20 and 7 in order to calculate 73 - 27
40 + 6 = 46
This can be demonstrated practically and does not have to be recorded
NB children will need to practise partitioning numbers in this way. Base- ten
materials could be used to support this (such as Dienes).
When children are confident with the expanded method introduce the formal
written method, involving decomposition/exchange:
73 − 27 = 46
Use the language of place value to ensure understanding.
73
‘We can’t subtract seven from 3, so we need to exchange a ten
2 7
for ten ones to give us 60 and 13.
46
Use base ten / Dienes materials to support understanding
If children are confident, extend the use of the formal written method with numbers
over 100, returning to the expanded method first, if necessary.
235 – 127 = 108
235
- 127
Use the language of place value to ensure understanding.
In this example, it has only been necessary to exchange from
the tens column. The digit that has been ‘carried’ should be recorded under
the line in the correct column
108
Use base ten / Dienes materials to support understanding
REMEMBER: if, at any time, children are making significant errors, return to the
previous stage in calculation.
Progression in subtraction stage 4
autumn
● Understand that
subtraction is noncommutative,i.e.5 –
7 is not the same
as 7 – 5.
● Understand that
subtracting a
positive number
makes a number
less.
spring
● Understand that addition
is the inverse of subtraction
(addition reverses
subtraction and vice versa)
and use this to check
results. Check 625 − 87 =
538 with 538 + 87 = 625.
● Respond rapidly to oral or
written questions,explaining
the strategy used for 63
subtract 46. What is the
difference between 28 and
65?
What is 170 less than 250?
Find pairs of numbers with a
difference of 79.
summer
Use known number facts to
rapidly answer:
27 − 19 = ■;
43 − ■ = 4 Use a number line
or mental strategies to
answer:
136 − 78 = ■;
▲ − ■ = 54
Use jottings or a pencil and
paper method to answer:
1258 − 576 = ■
■ − ▲ = 682
.
Subtraction – Stage 5
Subtract numbers with up to 4 digits using the formal written method of columnar
subtraction where appropriate
NB Ensure that children are confident with the methods outlined in the previous stage’s guidance
before moving on.
Continue to teach the use of empty number lines with three and four digit numbers, as
appropriate.
Continue to develop the formal written method of subtraction by revisiting the expanded
method first, if necessary. Continue to use base –ten / Dienes materials to support
understanding.
258 – 73 = 185
200 and 50 and 8 100 and 150 and 8
70 and 3 becomes - 70 and 3
100 and 80 and 5 = 185
This can be demonstrated practically and does not have to be recorded
This leads to the formal written method, involving decomposition…
1 15
-
258
73
175
Use the language of place value to ensure understanding
In this example, it has been necessary to exchange from
the hundreds column.
Further develop by subtracting a three-digit number from a three-digit number:
637 – 252 = 385
600 (and) 30 (and) 7 500 (and) 130 (and) 7
-200 (and) 50 (and) 2 -200 (and) 50 (and) 2
300 (and) 80 (and) 5 = 385
Ensure that children are confident in partitioning numbers this way.
This leads to a formal written method:
5 13
-
6 3 7 Use the language of place value to ensure understanding
2 5 2 and use base-ten / Dienes materials, if necessary.
385
When children are confident, develop with four-digit numbers and decimal numbers (in context
of money and measures).
3625 – 1219 = 2406
1 15
-
3625
1219
2406
NB. If, at any time, children are making significant errors, return to the previous stage in
calculation.
Progression in subtraction
autumn
spring
summer
● Respond rapidly to oral or written
questions, explaining the strategy
used. 3754 add 30;
subtract 50 from 225 What is the sum
of 16,64 and 153? What is the
difference between 155 and 390?
Increase 190 by 37. How many more
than 952 is 1050? 570 add a number
is 620. What is the number?
Use known facts to answer:
■ + 62 = 189;
7.6 + 5.8 = ■; ■ − 62 = 189;
7.6 − 5.8 = ■
Use informal pencil and paper jottings
to answer:
■ + 756 = 924;
▲ + ■ = 1;
■ − 256 = 424;
■ − ▲ = 1.2
Use a written method to answer:
14 136 + 3258 + 487 = ■;
141.36 − 32.58
Use a calculator to: find all the
different totals you can make by
using three of these five numbers:
8, 4008, 562, 3103, 95
Find all the differences you can make
by using two of the numbers.
Subtraction – Stage 6
Subtract whole numbers with more than 4 digits, including using formal written
method (columnar subtraction)
NB Ensure that children are confident with the methods outlined in the previous stage’s guidance
before moving on.
Continue to teach the use of empty number lines with larger numbers and decimals, as
appropriate. Continue to develop the formal written method for subtraction with three and four digit
numbers returning to an expanded method and using base Ten / Dienes materials, if necessary.
This leads to the formal written method (there is potential for error in this example):
503
There are no tens in the first number (503) so we have to
-
278
exchange a hundred for 10 tens before we can exchange
225
a ten for 10 ones/units.
NB It would be appropriate to discuss the use of mental calculation methods with an example like
this one, i.e. would an empty number line be a more efficient method for these numbers?
When children are confident extend with larger numbers (and decimal numbers).
Return to an expanded method, if necessary.
When children are confident extend with larger numbers (and decimal numbers).
Return to an expanded method, if necessary.
12731 – 1367 = 11364
6
12
11
1 2 7 3 1 In this example it has been necessary to exchange from the tens
- 1 3 6 7 and the hundreds column.
11364
NB If children are making significant errors, provide calculations where only one exchange is
required. Introduce subtraction of decimals, initially in the context of money and measures.
£166.25 – £83.72 = £82.53
1 6 6 . 2 5 Ensure the decimal point lines up.
- 83.72
82.53
Continue to practise and apply the formal written method with large numbers and decimals
NB If, at any time, children are making significant errors, return to the previous stage
Progression in subtraction
1st
2nd
3rd
● Respond rapidly to oral or written
questions, explaining the strategy
used.
Take 300 from 1240.
How much less than 4.8 is 4.2?
2.8 add a number is 4.3.What is the
number?
Find pairs of numbers with a
difference of 13.5.
Use known facts to answer:
■ − 2.56 = 5.38;
7.65 − 6.85 = ■
Use informal pencil and paper jottings
to answer:
■ − 1475 = 2924;
■ − ▲ = 0.03 Use a written method to
answer:
421.3 − 82.57 = ■
Use a calculator to: Find all the
differences you can by using two of
the numbers.
1.07, 0.3, 37.03,17.73, 31.7
Subtraction – Stage 7
No objectives have been included in the programmes of study explicitly related to written methods for subtraction in Y6.
However, there is an expectation that children will continue to practice and use the formal written method for larger
numbers and decimals and use these methods when solving problems, when appropriate (see previous stage’ guidance
for methods). Our aim is that by the end of Y6 children use mental methods (with jottings) when appropriate, but
for calculations that they cannot do in their heads, they use an efficient formal written method
accurately, and with confidence.