When children multiply and divide from Year 3, they are thinking mathematically. If children think that multiplying by 2 means making 2 groups, they are thinking additively. If children think that multiplying by 2 means making a number 2 times larger, they are thinking multiplicatively. Similarly, if children think that dividing by 2 means dividing into 2 groups or groups of 2, they are thinking additively. If children think that dividing by 2 means making a number 2 times smaller – half the size, they are thinking multiplicatively.

To multiply and divide, children use the distributive property – a natural property of multiplication that can be used to multiply numbers of any size. Division, although not technically distributive. is distributive when it is seen as multiplication by a fraction.

These concepts are explicitly investigated in the Multiplication and Division Concept Levels 10 (multiply and divide by 2), 11 (multiply and divide by 4), 12 (multiply and divide by 3), 13 (multiply and divide by 5), 14 (multiply and divide by 9), 15 (multiply and divide by 6), 16 (multiply and divide by 8), and 18 (multiply and divide by 7).