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
year’s guidance before moving on.
Further develop the use of the empty number line with calculations that bridge 100:
126 – 45 = 81
-5 -10 -10 -10 -10
81 86 96 106 116 126
Use a 200 grid to support counting back in tens and bridging 100
Then use more efficient jumps:
81 86 126
Extend with larger numbers by counting back…
216 – 27 = 189
-1 -6 -20
189 190 196 216
21
…and by counting on to find the difference (small difference):
231 – 198 = 33
+2 +30 +1
198 200 230 231
‘The difference between 198 and 231 is 33.’
Introduce the expanded written method with the calculation presented both
horizontally and vertically (in columns). Use two-digit numbers when introducing this
method, initially:
78 – 23 = 55
70 + 8
−20 + 3
50 + 5 = 55
You might replace the + sign with the word ‘and’ to avoid confusion.
This will lead into the formal written method:
7 8
-2 3
5 5
‘We can’t subtract seven from three, so we need to
exchange a ten for ten ones to give us 60 + 13.’
Use base ten materials to support understanding.
73 is partitioned into 60+13 in
order to calculate 73-27
6 13
7 3
- 2 7
4 6
Use the language of place value to ensure
understanding.
In this example it has only been necessary to
exchange from the tens column.
Use base ten materials to support understanding. 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
year’s guidance before moving on.
Further develop the use of the empty number line with calculations that bridge 100:
126 – 45 = 81
-5 -10 -10 -10 -10
81 86 96 106 116 126
Use a 200 grid to support counting back in tens and bridging 100
Then use more efficient jumps:
81 86 126
Extend with larger numbers by counting back…
216 – 27 = 189
-1 -6 -20
189 190 196 216
21
…and by counting on to find the difference (small difference):
231 – 198 = 33
+2 +30 +1
198 200 230 231
‘The difference between 198 and 231 is 33.’
Introduce the expanded written method with the calculation presented both
horizontally and vertically (in columns). Use two-digit numbers when introducing this
method, initially:
78 – 23 = 55
70 + 8
−20 + 3
50 + 5 = 55
You might replace the + sign with the word ‘and’ to avoid confusion.
This will lead into the formal written method:
7 8
-2 3
5 5
NB A number line would be an appropriate method for this calculation but use twodigit
numbers to illustrate the formal written method initially.
‘Partition numbers into tens and ones/units.
Subtract the ones, and then subtract the tens.
Recombine to give the answer.’
NB In this example decomposition (exchange) is
not required.
Use the language of place value to
ensure understanding:
‘Eight subtract three, seventy
subtract twenty.’
22
Introduce the expanded written method where exchange/decomposition is
required:
73 − 27 = 46
70 + 3 becomes 60 +13
- 20 + 7 - 20 + 7
40 + 6 = 46
NB children will need to practise partitioning numbers in this way. Base- ten
materials could be used to support this.
When children are confident with the expanded method introduce the formal
written method, involving decomposition/exchange:
73 − 27 = 46
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
2 15
2 3 5
- 1 2 7
1 0 8
NB If, at any time, children are making significant errors, return to the previous stage
in calculation.
Use the language of place value to ensure
understanding.
‘We can’t subtract seven from three, so we need to
exchange a ten for ten ones to give us 60 + 13.’
Use base ten materials to support understanding.
73 is partitioned into 60+13 in
order to calculate 73-27
6 13
7 3
- 2 7
4 6
Use the language of place value to ensure
understanding.
In this example it has only been necessary to
exchange from the tens column.
Use base ten materials to support understanding.