How Many Squares on a Checker Board?
(Simplify and draw pictures)

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.
1   2x2 size
+ 4   1x1 size

5   squares
          It is easy to see
four 1x1 size squares.

Next examine
a 3x3 grid.
      There is one 3x3
size square.
1   3x3 size
4   2x2 size
+ 9   1x1 size

14   squares
          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 (12 + 22 + 32 + 42 + ...).

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