How Many Squares on a Chessboard?

Age Range: 7 - 11

How Many Squares on a Chessboard?

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 2x2 squares!)...

There are many more different-sized squares on the chessboard.
The complete list of answers is shown below:

1, 8x8 square
4, 7x7 squares
9, 6x6 squares
16, 5x5 squares
25, 4x4 squares
36, 3x3 squares
49, 2x2 squares
64, 1x1 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).

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Connorsplanet

the answers!?

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Doreen

thanks.. it was clearly and simply explained :))

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bob

i dont understand the explanation btw the answers 204 connorsplanet

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sgfsgsdg

so basically what they are trying to show is that these squares can overlap (well actually they weren't showing this, but regardless). If they didn't then that's when the number 16 with the 2x2 squares would come into play, but if you look for all the squares whether they overlap or not there is 204P.S the 7x7 squares completely overlap each other yet within the whole chessboard there is still space for 4 of them

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lucy

BRILLIANT! Thanks for helping me with my maths homework cause I needed the working out as well. LOL!

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Kaitlyn

I do not know that how many squares on a chessboard because I don't play before but I want to learn to play this game. So please can you share the whole information about how to play this game with me here?

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Peter O'Kelly

How many rectangles are there on a chess board?

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rukmagoud

u can use the formula 1square+2 square+3 square+................+8 square as n(n+1) (2n+1)/6 to get the answer

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Sparsh Gupta

1296

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Dory

Great! Thanks for solving my college homework! Well explained

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Someone answer ...

what about for a checkerboard that isn't 8x8? how do you figure it out for any other number; nxn checkerboard??

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Jeff

What is the rule for finding how many squares are in any size chessboard?

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