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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.

Multilink Cubes

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

Colour in the Square

Age 7 to 16
Challenge Level


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 spatial 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.