Solution: Seeing Squares
Seeing Squares asked students to find out how many squares were in the figure below:
The easiest way to make sure you count all the squares is to approach this problem systematically. One such approach is to list the various sizes and orientations of squares and then carefully count the number of each. The following list shows this approach.
Normally-oriented squares:
- one large (3x3)
- four medium (2x2)
- nine small (1x1)
Squares rotated 45 degrees:
- 12 small
- 5 medium (don't forget the one in the middle!)
Total number of squares: 31.