## Zero in written subtraction

Pupils may seem confident when adding or subtracting zero to a number, until the written method for subtraction is introduced.

In this calculation, we may begin by saying, "0 - 6, we can’t do that." This, particularly when coupled with the knowledge that, in subtraction, ‘the bigger number goes on top’, can result in pupils automatically switching the digits and saying 6 – 0 = 6. If corrected and asked what is 0 - 6, confusion can then result in an answer of 0. This is particularly true if this is phrased in more concrete terms such as, "You have zero sweets and I want to take away 6." In a pupil’s eyes, if they have zero sweets and you want to take 6 away, you can’t do so… and they still have zero left! To overcome this, the need to actually take 6 away must be reinforced and that to do this, they need to get sweets from somewhere for you to take away from, which links to the concept of exchanging .

As well as confusion when zero appears in the calculation, pupils can also be confused about zero in the answer.

A pupil may view the zero in the top number as an unwanted or invalid digit, and in this calculation may say ‘0 – 3, can’t do that’. This can result in them saying ‘Can’t do that’ when zero is the result of a calculation. So when working out 7 – 7 in the tens column, they can say ‘7 – 7 = 0, can you do that?’ Zero needs to be confirmed as a valid digit. In this case, it is just telling us that there will be no tens in the final answer.

Some reinforcement of the effect of zero in calculations may be beneficial.