“Everyone” knows that 3×3 + 4×4 = 5×5. This little factoid, and other Pythagorean triplets, can be the basis of a nice set of puzzles. Here’s the first. If you draw a 5×5 square on graph paper, how can you cut it up (following the lines on the graph paper) so that the pieces can be rearranged to form a 3×3 square and a 4×4 square?
This is not so hard to do. Here’s one possible solution :
How long and wide must a rectangle be, for its area to equal its perimeter? Assume the width and length are whole numbers.
This is a nice little puzzle to let younger kids explore – if they find the puzzle as interesting or frustrating as I expect, they’ll remember the formulae for perimeter and area for the rest of their lives. For older kids, a bit of algebra gives the answer quickly.
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