I talked about my experience in a teacher math circle in a recent post and spent some of that time describing how we played with the initial prompt: How many squares are in a 4×4 dot pattern. What are the areas? You can read that post to get a run down on what I did and where the group went with it. I wanted to present the same task to my students and see what they did.
I had a plan for Friday morning which had students revisit some work from the day before and provide justifications to each other on the rules they had written for a series of pattern questions. I knew they all had had a rough go at it the day before and I wanted a bit more time to look into original responses and plan a better way to debrief and move forward so at the last minute I decided it was the perfect time to pitch the dot pattern prompt from the Math Circle. It was Friday. They could play and hopefully I’d inspired at least one to go home and think over the weekend. Here is what went down:
I projected the 4 by 4 dot pattern on the board and and asked students how many squares they could find and what the area of those squares were. They worked alone or in pairs with either graph paper on the table white boards. Right away students started to dig in and after a bit of chatter, 14 became the it number to arrive at (with areas 1, 4, and 9 units squared). High fives all around, we were done!
Except… one student chimed in: “Mmmm… do diamonds count?” Continue reading “Students Play with Dots: Math Circle Followup”