## Exchanging across two or more zeroes

Pupils may make the same mistakes as when exchanging across a single zero and encouraging the use of shortcuts can again lead to further confusion, particularly in larger numbers which end in zeroes.

For example, when working out 42,000 – 18,687, if a pupil is told to go to the first non-zero digit and exchange one, turning all the zeroes to nines, this can lead to:

Here, the pupil has done as instructed, but has changed all the zeroes to nines, including the final zero where they should have put the exchanged digit.

Alternatively, they may be told to work their way left along the digits, changing each zero to a nine, until they come to a digit they can exchange from.

Now the pupil has changed the zeroes to nines and then exchanged one, but not understanding what to do with that one, has reverted to the full process of putting it in the next column. From this point the method is likely to become increasingly muddled.

To undo confusion and prevent errors and lack of confidence in dealing with zeroes, pupils need to see why zeroes become nines by working through examples systematically and recording carefully without missing out any steps.

Even when exchanging correctly, when many zeroes are involved, the repetitive nature of the process may lead them to exchange beyond the point at which they should stop. For example:

They must remember that they can’t exchange one without having somewhere left to put it!