At this stage, pupils will be developing fluency in the 5, 10, 2, 4 and 8 multiplication tables (3NF–2 ), so should be able to solve multiplication problems about groups of 5, 10, 2, 4 or 8. Pupils have already begun to learn that if the factors are swapped, the product remains the same (3NF–2)
“factor times factor is equal to product”.
“The order of the factors does not affect the product”.
Pupils should also learn that the commutative property allows them to use their known facts to solve problems about 5, 10, 2, 4 or 8 equal groups (for example, 2 groups of 7). An array can be used to illustrate how the commutative property relates to different grouping interpretations – the example below shows that 7 groups of 2 and 2 groups of 7 both correspond to the same total quantity (14).
This means that pupils can use their knowledge that 7 2 14× = to solve a problem about 2 groups of 7, even though they have not yet learned the 7 multiplication table. Pupils should already be solving division calculations using known division facts corresponding to the 5, 10, 2, 4 and 8 multiplication tables (3NF–2). They must also be able to use these known facts to solve both quotitive (grouping) and partitive (sharing) contextual division problems. The same array that was used to illustrate the commutative property of multiplication can also be used to show how known division facts can be applied to the two different division structures. At this stage, pupils only need to be able to apply division facts corresponding to division by 5, 10, 2, 4 and 8 to solve division problems with the two different contexts. In year 4, pupils will learn, for example, that if they know that 2 × 7 = 14, then they know both 14 ÷ 2 = 7 and 14 ÷ 7 = 2. When pupils are solving contextual problems, dividing into groups of 5, 10, 2, 4 or 8 (quotitive division) or sharing into 5, 10, 2, 4 or 8 parts (partitive division), they should calculate by recalling a known multiplication fact rather than by skip counting, as described in 3NF–2 and illustrated above.