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This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Tiles on a Patio

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


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?

A Square in a Circle

Age 7 to 11
Challenge Level

Harry had a circle which was marked with twelve numbered dots to help him draw clock faces. The circle had a diameter of $10$ cm.

Clock Face

Harry drew lines from the $12$ to the $3$, from the $3$ to the $6$, from the $6$ to the $9$, and then back from the $9$ to the $12$.

What shape had he drawn?

Find the area of the shape.

Harry had lots of centimetre square tiles.


He covered as much of his shape as he could with whole tiles without going over the edge.

What was the largest number of whole tiles he could fit in?