Step 2 Objective

Understand the principles of the commutative, associative and distributive laws as they apply to multiplication.

Examples of what pupils should know and be able to do

Use the commutative, associative and distributive laws in flexible approaches to calculations, e.g. (6 × 2) × 5 = 6 × (2 × 5) = 6 × 10 = 60 (example of associative law).

Probing questions

How could you use counters to show me that 3 × 8 has the same answer as 8 × 3? etc.

How could you use counters to show me that 4 × (5 + 2) has the same answer as 4 × 5 + 4 × 2? etc.

What if pupils find this a barrier?

Lay out three rows of five counters and explain that this is the same as 3 × 5 and 5 × 3.

Show by grouping of counters that (3 × 4) × 5 is the same as 3 × (4 × 5).

Use a grid method to illustrate that 3 × 24 is the same as 3 × 20 + 3 × 4.