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?
Katherine from Maidstone Girls Grammar School
made very good use of the Excel spreadsheet software to draw her
To find the ten by ten foot carpet from a twelve by nine foot
carpet with an eight by one foot hole exactly in the middle, I
started by making a lot of grids (9 by 12 with an 8 by 1 foot hole
hole exactly in the middle) so that I would be able to try
different ways to make it a 10 by 10 foot carpet.
At first, I was cutting in straight lines trying to make them
fit. Just out of interest, I counted the squares in the carpet,
there were 100. This meant that I couldn't overlap the carpet in
From this information, I thought that it would only be possible
by cutting diagonally, so I started to cut going up then across one
at a time, then I worked it out like this.
RESULT. I found the solution, but there were two. A left and a
right handed solution, here they are.