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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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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Changing Areas, Changing Perimeters

Stage: 3 Challenge Level: Challenge Level:1

Working on Area and Perimeter might give you some useful insights to help you to solve this problem. 
 
If you are having trouble making sense of the grid, have a look at this image. The robots have been arranged according to their width and height, in the same way that the cards need to be arranged according to their area and perimeter:
 
As you go from left to right, the width of the robots increases.
As you go from top to bottom, the height of the robots increases.
All the robots in the middle column have the same width.
All the robots on the middle row have the same height.