Appendix
Subtraction at Key Stage 2
These are the different stages that boys in the Prep School will go
through in order to understand and use subtraction. They will be
taught the method in class that best suits their understanding at the
time.
Number Bonds
Boys should know by heart their number bonds to 10 and 20 and use their
fact families to find the inverse:
Eg: 7 + 3 = 10
10 – 7 = 3
14 + 6 = 20
20 – 14 = 6
From these facts, they use their number bonds to 100 to find the
inverse:
Eg: 55 + 45 = 100; therefore 100 – 45 = 55 and 100 – 55 = 45
67 + 33 = 100: therefore 100 – 67 = 33 and 100 – 33 = 67
Subtracting Single Digit Numbers:
Boys should also learn to subtract quickly any pair of one digit numbers.
However, they may need to use counters initially.
Eg: 8 – 5 = 3
9–7=2
Decimal Number Bonds:
Eg: 0.3 + 0.7 = 1
1 – 0.3 = 0.7
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Mental Strategies
Subtracting thousands, hundreds, tens and units:
Eg: 46 – 20 = 26
346 – 100 = 246
6756 – 3000 = 3756
Counting backwards in multiples of 10, 100, 1000 from a given number:
Subtract near multiples of 10 and adjust:
Eg: 146 – 49 = 146 – 50 + 1
146 – 50 = 96
96 + 1 = 97
Subtract near multiples of 100 and 1000 and adjust. This strategy is
particularly useful when solving problems:
Eg: A CD costs £8.99. How much change do you get from a £20 note?
£20 - £9 + 1p
£20 - £9 = £11
£11 + 1p = £11.01
Partitioning:
Eg: 79 – 36
70 – 30 = 40
9–6=3
Therefore 79 – 36 = 43
Eg: 67 – 28
67 – 20 = 47
47 – 8 = 39
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Number Lines
These methods are still predominantly mental strategies, but they can be
used to record a written answer.
Counting on using a number line
Eg: 46 – 23 = 23
+7
+16
23
30
46
Find the difference between 157 and 48 = 109
+52
+57
48
100
157
This method is of course similar to how a shopkeeper might give change in
a shop.
This strategy is also useful when solving time problems:
Eg: Tim arrived at school at 7.45am. The school day started at 8.55am.
How long did he have to wait?
+ 15 mins
7.45am
8am
+ 55mins
8.55am
The difference is 70 minutes or 1 hour 10 minutes.
Boys are encouraged to use this method using only 2 or 3 “jumps” on the
number line.
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Formal Written Methods
Boys will then develop an efficient standard written method of
subtraction. At first, this will not involve any decomposition.
Eg: 8 7 4
- 523
351
At this stage, it is important to keep reinforcing the place value.
Eg: 800 – 500; 70 – 20; 4 – 3
Following on from this, decomposition is introduced.
Eg: 8 9 123 12
- 4
5 7
4 7 5
It is important to stress at this stage that we exchange the 1 ten for 10
units. We then exchange the 1 hundred for 10 tens.
Decimals are then introduced.
Eg: 1 4 . 4 – 8 . 2 5
-
0114 .3410
8.25
6.1 5
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