Friday, November 24, 2023 # How Many Squares On A Chessboard?

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Although this investigation seems quite simple, it requires a methodical approach if the correct answer is to be attained.

As the title suggests, the investigation involves children finding out how squares there are on a chessboard. You might think that there are only 64, but you would be wrong…

The diagram below shows that there are indeed 64 squares, you there are also some more… Don’t forget the one large square (shown in red here)… And, also the 16 two-by-two squares shown below (although these aren’t the only 2×2 squares!)… There are many more different-sized squares on the chessboard.
The complete list of answers is shown below:

• 1, 8×8 square
• 4, 7×7 squares
• 9, 6×6 squares
• 16, 5×5 squares
• 25, 4×4 squares
• 36, 3×3 squares
• 49, 2×2 squares
• 64, 1×1 squares

Therefore, there are actually 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 squares on a chessboard! (in total, 204).

A worksheet with a large chessboard which children can use to investigate this problem can be found below.

If the children manage to find all of them, ask them if they can see a pattern in the results (i.e. the square numbers in the table).