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

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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?


Stage: 2 and 3 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

What is the maximum number of pieces with the shape T which can be placed within the $5 \times 5$ grid shown, without overlapping, and with their edges along the lines of the grid?

t shape and 5x5 grid

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.