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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?

The Big Cheese

Stage: 2 Challenge Level: Challenge Level:1

You could make a note of the area of each piece as seen from above, and group them according to the cube that you started with i.e. in threes. This might help you notice some patterns to investigate. What happens if you add in these groups?
You could look at the difference in size of successive pieces.