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?
How many different squares can be drawn in total by joining the dots with line segments in the part of the square lattice shown below?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.