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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?

Building with Longer Rods

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3


Why do this problem?

This activity is specially designed for the highest-attaining pupils that you ever come across. It acts as a further extension to Building with rods and  $2$ on $3$ on $4$. It's an activity that is intended to give opportunities for those pupils to explore deeply using their intuition and flair in the area of spatial awareness, also with an opportunity to create a system for solving such problems.

Possible approach

As this is designed for the highest attaining, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.

Key questions

Tell me about what you have found.
Can you describe the ways that you arrived at these shape arrangements?
How did you construct these on the computer?