## Misusing commutativity in written subtraction

A very common error is mistakenly using commutativity to switch individual digits instead of exchanging when necessary in subtraction calculations. This is particularly common when being faced with zero take away another number. Reinforcement of more simple facts, such as 3 – 5 is not the same as 5 – 3 may be necessary, using physical objects to illustrate this point.

Consistent use of language is also important. Pupils may switch from saying ‘3 take away 5’ or ‘3 subtract 5’ to saying ‘3 from 5’ when the smaller number is first, in order to begin with the top number.

As with addition, setting out subtraction calculations involving decimals can highlight errors in comparing decimals.

written as

Although the first example shows an understanding of place value to align the decimals correctly, neither calculation is going to give a correct answer. Pupils must realise that, when presented with a subtraction calculation, it is the first number which must be set out on top, even if it appears smaller.