What 2 numbers should be used to find 231-198 using the 10 methods for subtracting

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.