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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

Look at the angles of the shape and the length of its sides. The title of the problem may help!

Can you draw in the diagonals and use their lengths to help you find the area of the shape?

Have you thought about starting to tile in one of the corners?

This sheet gives two copies of the clock face to work on.