1.4 Understanding that addition and subtraction are inverses of each other

Children first learn to apply inverse relationships to quantities before they can apply them to numbers.

For example, five-year old children understand that if you have 6 biscuits and you add 3 more biscuits and then take those same 3 biscuits away, then you have the same number of biscuits that you started with.

However, if you were to take away 3 different biscuits, the child may not realise that the result is the same number of biscuits that you started with. This suggests that the child is thinking in a very concrete way about the biscuits themselves, rather than abstractly thinking about numbers.

When children eventually understand that addition and subtraction are inverses of each other, this is a big step towards them developing number sense.

Multiplying using additive reasoning

Children learn how to multiply in the first instance by using repeated addition. For example, if there are 3 flowers in each of 4 vases, children can work out the total by counting 3 for each vase using a one-to-one correspondence. This underpins the concept of multiplication and paves the way for developing secure methods of multiplication calculations later on.

If children do not understand the concept of multiplication as repeated addition then learning their multiplication tables will not really help later in their school career. The basic foundational concept is important.

Laying the foundations for future mathematics learning

If children are able to understand that addition and subtraction are inverses of each other, and if they can use one-to-one correspondence to solve early multiplication problems, this gives them a secure foundation for later learning of mathematics, not just in arithmetic. It is important that children who struggle with this in the early school years are given extra support to make these developmental strides.