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Find-The-Squares

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					Find The Squares
How many squares are there in this square?

Make a list of the different sizes of squares. Use colour on your diagram to show the different sizes of squares that you can get from each big square. Can you predict the number of squares in a 8 by 8 square? Using your answer for an 8 by 8 board, how many squares are there in a 10 by 10 board?

Solution 2 by 2 square size of squares 1 x 1 2 x 2 total 3 by 3 square size of squares 1 x 1 2 x 2 3 x 3 total 4 by 4 square size of squares 1 2 3 4
x x x x

number 4 1 5 number 9 4 1 14 number 16 9 4 1 30

1 2 3 4

total The number pattern is:4 by 4 square 16 ¦ ¦ ¦ ¦ 4x4

9 4 1 ¦ ¦ ¦ ¦ ¦ 1x1 ¦ 2x2 3x3

In an 8 by 8 square, the total number of squares is:82 + 72 + 62 + 52 + 42 + 32 + 22 + 12 = = 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 204 squares

A 10 by 10 board is an 8 by 8 board plus 92 plus 102 = = 204 + 81 + 100 385 squares


				
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posted:11/27/2009
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