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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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Tiles on a Patio

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?

Making Boxes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How big is the base/bottom of this box?
How high are the sides?
So how much does it hold?

It might be useful to print out this $15 \times15$ square.