Multiplication and division structures

The scaling structure for multiplication - part 2

The underlying mathematical principle here is what is called the commutative law of multiplication. This refers to the fact that when you are multiplying two numbers together the order in which you write them down does not make any difference. We have already seen in Chapter 4 that addition also has this property. We recognise this commutative property formally by the following generalisation, which is true whatever the numbers a and b:

b x a = a x b.

Work hard with your pupils to establish the commutative principle in multiplication and encourage them to use it in recalling results from the multiplication tables. Explicitly point out that division does not have this property.

There are two important points to note about the commutative property in relation to multiplication. First, it is important to realise that division does not have this property. For example, 10 divided by 5 is not equal to 5 divided by 10. Second, use of the commutative property enables us to simplify some calculations. For example, many of us would evaluate ‘5 lots of 14’ by changing the question to the equivalent, ’14 lots of 5’ – because fives are much easier to handle than fourteens! Grasping the principle of commutativity also cuts down significantly the numbers of different results we have to memorise from the multiplication tables: if I know seven fives, for example, then I know five sevens.