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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?

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Framed

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

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Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Towers

Age 11 to 14 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...