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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?

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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Squaring the Circle

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Bluey - green squares, white squares, transparent squares with a few odd bits of shapes around the perimeter.

Picture of a circular area tiled with squares

But, how many squares are there of each type in the complete circle?

Study the picture and make an estimate. Note the totals before embarking on a more rigorous audit of what is there.

How accurate was your estimate?

Can you give an upper and a lower bound to your estimate?

If the blue-green squares are of 1 and 1.5 units of length, the white squares of 1.5 units and the transparent squares 1.75 units of length - how "big" is the circular part of the pavement?

If the circular part was used as the design for a Roll- a- Penny stall which paid out on pennies successfully rolling fully into a transparent square: what is the probability of winning on this layout? You might like to think about the best and worst case.