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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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Towers

A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

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Squaring the Circle

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.

Framed

Age 11 to 14 Challenge Level:

Seven small pictures, all square or rectangular, with sides measuring a whole number of inches and each with a different area, have frames exactly one inch wide.

In each case the area of the frame is either the same as the area of the picture or a multiple of it.

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, show how they fit together to make a rectangle, and find the width of the rectangle.