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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?

Kissing Triangles

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

The solution is 18 square centimetres and everyone who submitted a response got it right. Of special mention was the work of Sarah at Hethersett High School and Bryony with Sarah from Maidstone Girls' Grammar, all of whom had painstakingly set out their solutions complete with annotations and diagrams.

Some people managed to spot that it there are multiple ways of drawing the shape; the point in the middle where the triangles 'kiss' can be moved left or right! Well done to those who realised that despite the variety of ways of drawing the shape, the area is always 18 cm2Brilliant!