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Take a square of paper.
Put a mark half way along each side (ABCD). (You can do this easily by folding.)
Join two midpoints (DC), as shown, then mark half way along the
new line (E).
Now join this new midpoint to the other two. (EA, EB).
Cut along these lines.
Now use the four shapes to make a triangle.
Make a cube out of straws and have a go at this practical challenge.
Reasoning about the number of matches needed to build squares that share their sides.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?