Similar to the painted cube problem, this time pupils investigate the number of hidden faces of single lines of cubes, then 2D grids, then 3D cuboids.

Expanding double brackets, but because pupils do not need to equate their final answers to $n^{3}$ as in the painted cube investigation, pupils do not need to know how to expand triple brackets.

The (A3) pupil sheet should do the heavy lifting!

1. Just make sure pupils have access to some mini-cubes to manipulate as they work through tasks, and they should be able to work through at their own pace.

2. Distribute one copy per pupil, or pair (if preferred) and make sure you have a copy of the teacher sheet for reference.