How many Squares?

In my bag of tricks when I was substituting was the drawing of a similar box as seen below. I liked how the students had to think critically to see all the possible squares.

Recently on Facebook I have repeatedly seen this adaptation which adds up to MORE squares.

How many squares are there?

 To show you how I visualize it in my head, I've drawn progressively smaller squares.
1

 +4 (see the four overlapping 3x3 squares?)

 +9 (Nine overlapping 2x2 squares?)

 +16 (sixteen base 1x1 squares)

 +2 (two additional overlapping 1x1 squares)
+8 (the smaller squares formed by the previous two's addition to the grid)

=40

Now, some people will not be able to visualize this many squares, while others will insist they see more, but they are mistaken. They are counting rectangles as squares, but rectangles are not squares even though squares can be counted as rectangles.

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