Tuesday Patterns

Tuesdays look a lot like Mondays, except instead of puzzles we have patterns. We get all of our patterns from VisualPatterns.org.

By the end of three minutes students have counted the first three figures and thought about the pattern. Many have an idea for fifty but only a couple kids think using equations.

I start by asking the whole class to choral respond how many in figures one, two and three. To help students generalize the pattern, I ask for a volunteer to explain how they counted figure three. Then I have two other students apply the same method of counting to figures two and one. Once we've counted all three, students are eager to share their solution. Most students want to go directly to 50 without generalizing first. I'm happy to let them, then we check to see if their pattern for 50 matches the pattern for the other numbers. We frequently run into the assumption that figure 50 will have 50 rows (or columns or ducks) and I spend a lot of time directing them back to the first three examples. We always talk about how to describe the pattern. Depending on time or the recursiveness of the pattern we don't always write an equation. You can see that one of my classes got there and the other didn't and that's okay. Both classes generalized even though only one did so formally.

One day as I was about to begin this process, one student said, “I feel like such a little kid when you ask us how to count.” I offered that if they could write the equation already we could skip that step. They tried a few equations but couldn’t get it. So then one of them said, “Okay! Can we count now?” I smiled, and said, “Of course!” And they quickly found an equation. I was so happy that they realized how helpful the strategy was and were willing to admit it!