## Misusing commutativity in subtraction

When using subtraction to find the difference between two numbers, pupils need to take the smaller number away from the larger one, regardless of the order in which they are presented.

What is the difference between 2 and 6?

So to answer this question, a pupil must work out 6 - 2 to find that the difference is 4. This may lead to the misconception that the larger number must always come first.

The fact that subtraction is not commutative and that numbers in a written calculation cannot be switched, needs to be reinforced. Otherwise, pupils may work out a calculation such as

2 - 6 = as 6 - 2 =

Pupils must understand that when they begin with a number which is smaller than the amount they need to subtract, they will get an answer that is less than zero. Reinforcement using physical objects to illustrate this point may be necessary.

Where pupils aren’t secure in this understanding, similar digit switches are likely to occur when using a written method .