Understanding commutativity
A basic property of number that pupils often fail to recognise, or may recognise wrongly apply, is the commutative property. Addition and multiplication are both commutative operations, which simply means that the numbers in these calculations can be swapped around without changing the answer.
For example:
2 + 3 = 5 just as 3 + 2 = 5
2 x 3 = 6 just as 3 x 2 = 6
However, subtraction and division are not commutative operations.
6 - 2 = 4 This is not the same as calculating 2 - 6
6 ÷ 2 = 3 This is not the same as calculating 3 ÷ 2
Where appropriate, our worksheets allow the option to use commutativity when displaying the question, so that pupils grow accustomed to using this property.
When working with written methods, pupils can sometimes forget that addition and multiplication are commutative whilst subtraction and division are not.