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

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

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Multilink Cubes

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

Possible Pieces

Age 5 to 11 Challenge Level:
Yvonne from Kügeliloo School in Zurich Switzerland wrote to say they found eight solutions to challenge 1 and 32 solutions to challenge 3. It would have been good to see pictures of them.

Millie from Nene Valley Primary sent in her work with a picture:

First I tried to make one puzzle that worked, and then I realised that there was a pattern of pegs and holes. The pegs went round in a circle and so did the holes, so only the middle peg or hole could change, or the circle could go round the other way. 
A larger more legible version is available here.pdf 

Well done Millie, and thanks to Yvonne for her two answers. If you have a go at this challenge, let us know what you find out.