An investigation from Jenny Murray:

If you double the sides of a square, the area becomes 4 times the size. It is quadrupled.

We can try the same thing with rectangles and diamonds.

How do the 4 smaller ones fit into the larger one?

We can then try with equilateral triangles:

And "L" shapes:

What has to be done to make these fit?

We could try with other shapes like hexagons.
These have to be cut and rearranged.

What is the least number of cuts needed to fit 4 hexagons into one larger hexagon with sides double the length?

Explore all sorts of straight-sided shapes.

They do not need to be regular shapes as long as you can draw them twice the size.

You could try with a trapezium, a star and a parallelogram, and other letter shapes such as "T", "E"? and "H".

You could go on to making the bigger shapes three times the size.

How many little shapes will you need to fit into the larger one now? Draw a record to show how they fit.