Using commutativity

3 + 8 =

Because addition is commutative, in this calculation, it is easier to begin with the 8 and add on 3, rather than starting with the 3 as presented, then adding on 8. If addition calculations are mostly presented with the larger number first, this can lead to pupils always beginning with the initial number and adding on to it, rather than using the commutative property. Pupils need to recognise that it is possible to begin with either number.

5 x 7 =

Because multiplication is commutative, in a calculation such as 5 x 7, it’s possible to use either the 5 or 7 times table to work out the answer. As the times tables can be quite a challenge for many children to learn, this is really important for them to realise, as it almost halves the number of facts that they actually have to learn! Once a pupil has learnt the 10 times table, they have actually learnt a fact from every other table as well (they now also know 10 x 3, 10 x 4 etc).

View Fixit pages for more information about the mistakes commutativity can lead to.