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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.

Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Square Corners

Age 7 to 11 Challenge Level:

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 without four of them lying at the corners of a square?

You might like to use this printable sheet.

This problem is taken from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES.