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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?

Inside Seven Squares

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

You could draw it out on squared or dotty paper starting with the centre square.
Think about the scale - what size could you draw the centre square to make it easier to draw the others?
How does the second square compare in size to the centre square?