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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?

Inside Seven Squares

Age 7 to 11
Challenge Level

Seven squares are set inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.

The centre square has the area of $1$ (one) square unit.

What is the total area of the four outside triangles which are outlined in red?

This problem is also available in French: Les 7 carrés

Click here for a poster of this problem.