A classic question.

Pupils investigate the number of smaller (1 by 1) cubes within larger cubes which have 0 of their faces painted/1 of their faces painted...

Pupils first consider numerical cases and then generalise.

Expanding double brackets, collecting like terms, knowledge of cube and square numbers.

*Ideally distribute a very small number of multi-link cubes. If too many are distributed then pupils may get distracted!

1. Print off one copy of pupil sheet for each pupil.

2. Explain that a larger cube is being dunked into a vat of paint which will cover the exterior faces of the large cube in paint. Then perhaps through whole class questioning ask pupils how many faces of one of the smaller cubes will be painted, and then another cube with a different number of faces painted.

3. Pupils get on with investigating the problem.