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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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Tiles on a Patio

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

Square Corners

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

On each of these grids the counters lie at the four corners of a square:

Three 4 by 4 grids. Each has 4 counters positioned at the corners of a square

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Empty 4 by 4 grid

This problem is taken from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES. You can find out more about this book, including how to order it, on the Standards website here.