This is a wonderful, easily accessible, yet deceptively tricky area puzzle from Numberphile.

No prior knowledge required.

It is not easy to reach the optimal solutions for larger squares so you may wish to provide a first step to pupils.

1. The (Numberphile) introduction video explains the task (and solutions) well with clear visuals.

2. The rest of the lesson will be the pupils trying to reach optimal solutions.

*Plenty of square dotted paper (attached), or pupils could use exercise books with squared paper.