This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
On each of these grids the counters lie at the four corners of a square:
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
This problem is taken from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES.