How Many Squares?

Directions: Find all the squares in this figure.

4 x 4 squares








Hint: There are more than 16 squares. Some squares overlap.




Most people will count the squares in a haphazard way. Encourage them them to think of a systematic way to count and verify all squares have been considered. One way people do this is to verify the number of squares from the smallest squares to the largest. The smallest being 1 x 1 and the largest being 4 x 4. Between these two sizes are squares 2 x 2 and squares 3 x 3. The harder part is identifing the squares that overlap. Once the overlapping squares are noticed, they can be systematically counted by finding them in order from say starting at the top, moving right, and down. Then repeating for the next size.


Mind boggler: How many squares in this figure.



Dr. Robert Sweetland's notes
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