### Pebbles

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?

### Great Squares

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

### Square Areas

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

# Towers

##### Stage: 3 Challenge Level:

We build an imaginary tower of squares inside a right angled isosceles triangle. The largest square stands on the hypotenuse of the right angled triangle. Each square has two vertices touching the other sides of the triangle. Only three squares are drawn in the diagram but imagine that there are infinitely many getting smaller and smaller and smaller...

What fraction of the area of the triangle is covered by the squares?

You can do this without a lot of calculation and without any advanced mathematics. If you wish to extend this project you can ask: What if the triangle was equilateral? Or what if the tower was made up of rectangles? Or...