### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

# Colour in the Square

### Why do this problem?

This problem is one that requires working systematically. It is a good activity for promoting discussion between learners working together and also for giving encouragement to those whose spacial ability is better than their numerical achievements.

### Key questions

Which row and which column have none of that colour in them?
Have you checked the diagonals as well as the rows and columns?

### Possible extension

Learners could try other-sized squares such as $4\times 4$ and $6\times 6$. With some squares it is possible to place one colour correctly but no more. Of which sized squares is this true?

### Possible support

You could suggest starting with just one colour, then fitting in the other colours, one at a time.