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?
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
Can you work out the area of the inner square and give an
explanation of how you did it?
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.