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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?

Shear Magic

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

All these triangles have a base of 1 unit and a height of 2 units. We could call them a "family" of triangles.

1 by 2 right angled triangle sheared 1 by 2 right angled triangle more sheared 1 by 2 right angled triangle very sheared 1 by 2 right angled triangle

What are their areas? What do you notice?

Can you generalise to other "families" of triangles?

You may like to use the interactivity below to investigate more triangles

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