Using grid paper to make drawing squares easier, start with the simplest size square and work toward larger ones. Look for an easy math pattern in the simple drawings such that it does not get complicated.


Start with the simplest grid, size 1x1. 
It can be clearly seen that there is only one square to count. 
1 square  


Now examine a 2x2 grid. 
There is one 2x2 size square. 


It is easy to see four 1x1 size squares. 



Next examine a 3x3 grid. 
There is one 3x3 size square. 


Notice there are four 2x2 size squares (one in each corner). 

It is easy to see nine 1x1 size squares. 



Look for a math pattern.
First (1), then (1+4), then (1+4+9). What comes next? (1 + 4 + 9 + __ ) 



You should see a pattern of adding square numbers and can now determine the number of squares on a checker board with (1^{2} + 2^{2} + 3^{2} + 4^{2} + ...^{}). 

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