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?
In the examples below identical squares of side one unit contain some circles shaded blue.
In which of the four examples is the shaded area greatest?