Subtraction
Year Group: Key Objectives
Year 1:
 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
7 =__ - 9.
Written Strategies
Activities/recording
Practical Apparatus, coins, Numicon etc.
Number lines – what is the difference between 5 and 9?
Representations/Vocabulary
Use a number line to count back
-1
-1
-1
-1
-1
_____________________________________________________________
4
5
6
7
8
9
Use a number line to count on
+1
+1
+1
Number line, Number track,
100 square, Deines apparatus,
Numicon, Coins and notes,
Practical apparatus e.g.
counters, Number mobiles,
Pictorial representations of
problems, Dominoes,
Calculation, subtraction, take,
take away, distance between,
equals, is equal to, is the
same as, difference, count
back, how many more/less
+1
_________________________________________________
5
6
7
8
9
Year 2:
 Solve problems with subtraction:
- Using concrete objects and
pictorial representations,
including those involving
numbers, quantities and
measures
- Applying their increasing
knowledge of mental and
written methods
 Recall and use subtraction facts to
20 fluently, and derive and use
related facts up to 100
 Subtract numbers using concrete
objects, pictorial representations,
Activities/Recording
Continue to develop understanding using practical apparatus.
Children need to be secure with their knowledge of number bonds and
place value before moving on to the next stage. They also need to be
secure at partitioning and recombining numbers.
They would use a number line to count on and back more efficiently than in
Year 1.
e.g. 26 – 12 =
Counting back
-2
As above plus:
Arrow Cards (TU), Column
representations of Tens and
Units, Models of written and
mental strategies used for
calculation,
Numbers partitioned in
different ways e.g. 23 = 20 +3
= 10 + 13, meanings of < > =,
-10
___________________________________________
14
16
26
As above plus:
tens, ones, change, columns,
place value, boundary,
partition, method, strategy,
and mentally, including:
- a two-digit number and ones
- a two-digit number and tens
- two two-digit numbers
- adding three one-digit
numbers
Counting on
+8
+6
8 + 6 = 14
________________________________________
12
20
26
Use a number line to count on and back using larger two-digit numbers.
Children need a lot of practice in counting forwards and back in different
steps before they will be able to cope with this stage.
e.g. 76 – 48 =
Counting back
-8
-10
-10
-10
-10
____________________________________________________
28
36
46
56
66
76
This would be refined to larger jumps as appropriate to the child’s ability,
e.g. -40 in one go.
Counting on
+2
+20
+6
______________________________________________________
48
50
70
76
Children may also partition easy numbers and record them in an informal
way e.g.
76 – 28 = 76 – 20 – 8
or
76 – 28 = 70 – 22
= 56 – 8
= 50 – 2
= 50 – 2
= 48
= 48
or
76 – 28 = 76 – 30 + 2
= 46 + 2
= 48
inverse, inverse operation,
calculate
Year 3:
 Subtract numbers with up to three
digits, using formal written
methods of columnar subtraction
 Subtract numbers mentally,
including:
- A three digit number and
ones
- A three digit number and
tens
- A three digit number and
hundreds
Recording
Moving to decomposition – Number lines are an effective and useful
strategy to use to subtract/find the difference. Children should move
towards decomposition methods if they are secure with using number lines
and can return to that strategy if they do not understand decomposition.
Children should begin by partitioning numbers as this will support the
development of the decomposition compact method of subtraction.
e.g. 88 – 56 =
–
80
50
30
8
6
2
As above plus:
Arrow Cards (HTU), models of
column subtraction strategies,
Number lines marked in
tenths,
As above plus:
Hundreds, tenths, decimal,
decimal point, decimal place,
Increase, decrease, plus,
minus, adjust
= 32
Children also need to be able to partition numbers in different ways to be
able to cope with different calculations.
e.g.
54 = 50 + 4 = 40 + 14 = 30 + 24 = 20 + 34 etc.
540 = 500 + 40 = 400 + 140 = 300 + 240 etc.
This will enable the children to ‘exchange’ tens for units, hundreds for tens
etc. more easily. This should be modelled using practical equipment (deines,
Numicon) and visual representations
e.g. 88 – 49 =
–
80
40
8
9

–
70
40
30
18
9
9 = 39
 -
600
200
400
140
60
80
e.g. 754 – 268 =
-
Year 4:
 Subtract numbers with up to 4
digits using the formal written
methods of columnar subtraction
where appropriate
700
200
50
60
4
8
14
8
6 = 486
Recording
Partitioning may continue for children who still need reinforcement of place
value and who may still be very reliant on other resources e.g. arrow cards,
deines etc.):
As above plus:
Arrow Cards (ThHTU), models
of column subtraction
strategies, Number lines
This can then be refined to the compact method of subtraction by marked in hundredths
decomposition. When numbers are exchanged, the digits are placed
to the left of the digit in the next column.
As above plus:
e.g.
Year 5:
 Subtract whole numbers with
more than four digits, including
using formal written methods
(columnar subtraction)
 Subtract numbers mentally with
increasingly large numbers
8 18
4 9
3 9
7 145 14
2 6 8
4 8 6
7
–
6
–
Recording
Children should continue to develop their fluency with numbers and
efficiency of working. They should also look at examples containing
decimals and different amounts of digits after the decimal points or where
more than two numbers are subtracted. They should be taught to ensure
numbers are lined up by using decimal points and should be encouraged to
put a 0 in as a place holder if they need to e.g. 19.7 – 6.76
1. Two-digits – no adjustment
47 – 23 6.5 – 4.2
2. Two-digits adjustment – one adjustment
43 – 27 7.2 – 4.8
3. Three-digits – no adjustment
469 – 246 85.6 – 51.2
4. Three-digits – one adjustment
452 – 138 537 – 163
5. Three/four-digits with two or more adjustments
413 – 275
2134 – 1519
316.4 – 79.8
2004 – 968
Place value charts to
Millions/thousandths, models
of column subtraction
strategies, Number lines
marked in thousandths
Tens/hundreds of thousands,
Millions
Recording
Children should continue to use the compact method to undertake addition
calculations. The examples below show the increased grading of difficulty
and we aim for children in Year 6 to be able to subtract numbers with
different amounts of digits after the decimal point.
6. Numbers with zeros
470 – 142
As above plus:
As above plus:
1 89. 167 10
- 6. 7 6
1 2. 9 4
Year 6:
 Solve problems involving
subtraction
 Perform mental calculations,
including with mixed operations
and large numbers.
Thousands, hundredths,
negative number, round
60.4 – 34.7
7. Decimals with different numbers of decimal places
32.6 – 8.48
23.83 – 7.9
100.3 – 8.756
As above plus:
Place value charts up to Tens
of millions, models of column
subtraction strategies,
pictorial representations of
subtraction of decimals,
As above plus:
tens of millions