SUBTRACTION
YR
Subtraction as ‘taking
away’ from a group
Practical or
recorded
using ICT (eg
digital photos /
pictures on
IWB)
Main methods used at Level 1: Practical
or recorded using ICT. Pictures /
Symbols (see above)
L1
Pictures / Objects
Symbols
I have five cakes. I eat two of them. How many do I have left?
Mum baked 9 biscuits. I ate 5. How many were left?
Might be
recorded as:
5–2=3
Taking away – jumps of 1
(modelled using bead strings)
Criteria for Level 1
1a. Take 1 away from any number up to
10 and know what the answer is
Know whether to subtract by
recognising the word
that is used in a problem
1b. Know all the names associated with
adding or subtracting
Take 1 away from any number and
record the operation
Take the smaller number from the
larger when subtracting two unit
numbers
1a. Work out whether to add or
subtract when faced with a simple
problem
Know all subtraction bonds to 10
Counting on – jumps of 1
(modelled using bead strings)
13 – 5 = 8
11 – 8 = 3
-2
8
-1
-1
-1
-1
-1
-3
10
13
Criteria for level 2:
2c. Set out a subtraction on paper and take
the larger number
away from the smaller number
Solve simple problems by working out which
operation is needed
Know addition and subtraction bonds to 10
2b. Subtract a 2 digit number from another 2
digit number using
apparatus
Use key words in problems to decide whether
to subtract and then solve
2a. Subtract a 2 digit number from another 2
digit number without apparatus
Use key words associated with numerical
problems to help work out which operation to
use
9
10
11
12
1 less
(nos up to 10 )
(see recording)
Counting on
(efficient jumps)
Subtraction facts to 10
TU – multiple of 10
Number line / no
number line
1 / 10 less than
a number
8 + 2 = 10
10 + 1 = 11
+1 +1 +1
No number line:
0 1
13 – 3 = 10
10 – 2 = 8
8
Mental Calculation
[Might be recorded as: 9 – 5 = 4]
Taking away (efficient jumps)
13 – 5 =8
Main methods used at Level 2: practical
methods and expanded methods such as the
use of the empty number line. Applying bods
to 20 and 100.
Level 2
Rapid Recall
Recording
AGE-RELATED
EXPECTATIONS
2 3 4 5 6 7 8 9 10 11
13
Pictures / Symbols
Partitioning
Number lines – counting on
45 – 22 = 23
74 - 27
74 -27 = 47
+40
+3
74 – 20 = 54
54 – 4 = 50
50 – 3 = 47
Or
326 - 78
Number lines - taking away
74 -27 = 47
326 256 250 -
70 = 256
6 = 250
2 = 248
Subtraction facts to at
least 10
0
27 30
[Also jumps can be in 10s and 1s]
70
Subtraction facts
to 20
74
Differences of
multiples of 10
Number line – counting on
141 - 89 = 52
+41
+11
[Also jumps can be in 10s and 1s]
89
Difference by
counting up
+4
100
141
Note the use of number bonds to 10/100 in
order to use empty number line.
TU – U / multiple of
10
Main methods used at level 3: empty number line,
expanded decomposition and compact decomposition
L3
Criteria for level 3:
3c. Confidently subtract 2 digit numbers from each
other with no exchange
Know the key words associated with subtraction and
use them when solving problems
3b. Subtract any 2 digit number from another using
decomposition when necessary
Use rounding skills to estimate and check answers
3a. Subtract HTU/TU from HTU using
decomposition
Solve addition and subtraction problems requiring 2
steps
Check if answer is reasonable
Main methods used at level 4: compact decomposition
(although strong mental strategies will ensure that
children can make judgements about the best
strategy)
L4
L5
Criteria for L4
4c Subtract with thousands to 2 decimal places
Use estimation to work out whether a calculation is
likely to be correct
Use subtraction to solve multi step problems involving
whole numbers and decimals
4b Use a pencil and paper method confidently and
accurately to
solve ThHTU- ThHTU
Find the difference between 2 decimal fractions with
up to 3 digits and the same number of decimal places
Solve multi step problems involving numbers in real
life
4a Use a pencil and paper method confidently and
accurately to solve subtraction problems involving any
number of digits
Check answers using the inverse operation
Use subtraction to solve word problems involving
numbers in real life
Subtract 2 or more decimal fractions with up to 3
digits and either 1 or 2 decimal places
5c Consolidate efficient written methods of
subtraction for whole numbers and decimal fractions
Use checking procedures to check results
Explain verbally how an answer is calculated
Solve subtraction problems in a variety of contexts
5b subtract negative numbers in context
appropriately use brackets in subtraction
complete calculator and non calculator subtraction
use approximate estimates subtraction using numbers
to 100,000
Number lines – counting on
Partitioning
754 – 186 = 568
+ 500
Decomposition
(compact method)
754 - 186
+ 54
Derive differences of
pairs of multiples of 10
/ 100 / 1000
754 – 100 = 654
654 – 80 = 574
574 – 6 = 568
+14
754
TU – TU
Decomposition (expanded)
723 – 458 = 265 [Red Alert]
700
400
20
50
Subtract pairs of
multiples of 10 / 100 /
1000
3
8
(Th)HTU – (Th)HTU
(small difference)
600 110 13
400 50 8
200 60 5
Number lines – counting on
Partitioning
72.5 – 45.7 = 26.8
+ 4.3
72.5 – 45.7
+ 20
+ 2.5
72.5 – 40 = 32.5
32.5 – 5 = 27.5
27.5 – 0.7 = 26.8
Decomposition
2362 – 548 = 1814 [Red Alert]
2000
300
500
60
40
1000
1300
500
800
50 12
40 8
10 4
1000
45.7
50
70
72.5
Note: this could primarily be used as a model
for how decimals could be subtracted.
Decomposition
(compact method)
2
8
Use number facts for
mental subtraction
9–2=7
0.9 – 0.2 = 0.7
0.09 – 0.02 = 0.07
Near multiple of 1000
– Near multiple of
1000 (eg 6070 –
4097)
Decimal – Decimal
(eg 9.5 – 3.7)
Note: this is essentially a
number line without the
number line.
Recognise when one method is more efficient. (See Y5 methods of recording) i.e when 8002 – 7998 = would not be best served by doing a formal
decomposition


HTU – HTU
(by finding the
difference)
TU – near multiple of
10 (positive answers)
Leads to
186
200
700
Vertical number line may be used to record calculation
TU – U / TU
There was 2.5 litres in the jug. Stuart drank 385 ml. How much was left?
18.07 km – 3.243 km
(as above)
Integer / decimal
(1dp) – Integer /
decimal (1dp)
(In Y1: Subtraction as ‘taking away’ and ‘difference’ (by counting on)
U–U
TU – U
(bridging 10)
Y2 Subtraction as inverse of addition TU – TU
(bridging 10s)
Y4 HTU – TU
HTU – HTU
Decimals: money
(£7.85 - £3.49)
Y5 ThHTU – HTU
Decimals up to 2dp
(72.5 – 45.7)
Y6 Consolidate / extend Y5 including:
Decimal to 3 dp relating to measures