How Many Squares on a Checker Board?
(Use cutout models to count squares)

Use grid paper. Draw a picture of the 8 x 8 checker board on the grid paper. Now outline squares of different sizes, 8x8, 7x7, 6x6 and so on. Cut them out with scissors so that they can be placed on top of the picture of the checker board.

Start with the 8x8 size cutout.				The 8x8 model can fit on the checker board in only one place.		Size 8x8 1 square
Now use the 7x7 size cutout .				The 7x7 model can fit on the checker board in four places.		Size 7x7 4 squares
Next use the 6x6 size cutout.				The 6x6 model can fit on the checker board in nine places.		Size 6x6 9 squares
This could continue until all the squares are counted, however using a math pattern will make it easier. Notice the numbers of squares are (1, 4, 9, __, __, ...). This follows the pattern of square numbers 12 = 1, 22 = 4, 32 = 9, 42 = 16, and so on.
Now this table can be easily completed using the math pattern, and the sum of all sizes of squares will be found. 8x8 size 12 = 1 7x7 size 22 = 4 6x6 size 32 = 9 5x5 size     4x4 size     3x3 size     2x2 size     1x1 size     Sum =
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