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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?

Two Squared

Age 7 to 11
Challenge Level

If you double the sides of a square, the area becomes four times the size. It is quadrupled.

We can try the same thing with a rectangle and a rhombus.

How do the four smaller ones fit into the larger one?

We can then try with equilateral triangles:

And "L" shapes:

What has to be done to make these fit?

We could try with other shapes like hexagons.
These have to be cut and rearranged.

What is the least number of cuts needed to fit four hexagons into one larger hexagon with sides double the length?