Understand and apply the distributive property of multiplication (2)

The first place that pupils will have encountered the distributive law is within the multiplication tables themselves. Pupils have seen, for example, that adjacent multiples in the 6 times table have a difference of 6. Number lines and arrays can be used to illustrate this. Pupils should be able to represent such relationships using mixed operation equations, for example: 5 × 6 = 4 × 6 + 6 or 5 × 6 = 4 × 6 + 1 × 6 4 × 6 = 5 × 6 – 6 or 4 × 6 = 5 × 6 – 1 ×6 Pupils should learn that multiplication takes precedence over addition. They should then extend this understanding beyond the multiplication tables, for example, if they are given the equation 20 × 6 = 120, they should be able to determine that 21 × 6 = 126, or vice versa. Pupils also need to be able to apply the distributive property to non-adjacent multiples. The array chart used to show the connection between 4 × 6 and 5 × 6 can be adapted to show the connection between 5 × 6, 3 × 6 and 2 × 6. As for adjacent multiples, pupils should be able to use mixed operation equations to represent the relationships: 5 × 6 = 3 × 6 + 2 × 6 3 × 6 = 5 × 6 – 2 × 6 2 × 6 = 5 × 6 – 3 × 6 Again, pupils should understand that multiplication takes precedence: the multiplications are calculated first, and then the products are added or subtracted. Pupils can use language patterns to support their reasoning. Language focus “5 is equal to 3 plus 2, so 5 times 6 is equal to 3 times 6 plus 2 times 6.”