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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?

Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

This question is about isosceles triangles with an area of 9 cm$^2$.

One of the vertices must be at the point (20, 20).
Each vertex of the triangle must be at a grid point of a square grid,
so all the vertices will have whole number coordinates.
How many different triangles satisfy these four conditions?

Try to find them all. You may wish to use the GeoGebra applet below.

Can you explain how you know that you have found them all?

Click here for a poster of this problem.