How Many Squares are There?

I posed the following problem to my 7th hour Algebra 2 class yesterday as a warm up:

How many squares are there?

Most students were interested in the problem and stared at the board for a while trying to figure it out. I gave them some time to work on it and then asked for answers. Many said 10 or 11. I asked for a student to come up and show the squares he counted. He got them all but one, and the class pointed it out. (Answer is at the end of the post.)

This problem was still on the board when I came into Pre-Calc today. The students were instantly fascinated. I didn't even direct them to the problem. A few students at their desks were considering it and as other students trickled in they noticed and stopped to look at the problem before sitting down. By the time the bell rang, there was a semi-circle of students all looking at the board and working on the problem. I wish I could have gotten a picture! If only all math classes were this engaging for students!!

I was surprised with how intensely students were engaged in this problem. I have seen other cases where students are fascinated with puzzles, especially students who aren't very into math class. (In Algebra 1, I supply puzzles for when students are finished with work, but students have started working on them during class, distracting them from notes.) The challenge that I see in this experience is: How do I make math class more like a puzzle? I believe that most people are naturally engaged by puzzles or by challenges that are just within their reach. How do I harness this interest and use it to teach math?

(Answer to puzzle: 11 squares)