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 model can fit on the checker board in only one place. 
Size 8x8 1 square 



Now use the 
The 7x7 model can fit on the checker board in four places. 
Size 7x7 4 squares 



Next use the 
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 1^{2} = 1, 2^{2} = 4, 3^{2} = 9, 4^{2} = 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.


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