This is fun…but is it math?

A few months ago, I got an email from one of the art teachers in the school.  She was offering her classroom, a makerspace of sorts, and her creative expertise to any teacher that wanted to bring their class down.

I jumped at the opportunity.  After all, what have I been enjoying most about math lately? Making and appreciating #mathart.

So. We brainstormed and ultimately settled on doing a project that would lead into our upcoming similarity unit.  It would have the kids constructing equilateral triangles descending in size, alternating colors, each triangle with a side length the same as the height of the previous triangle.

The students had never done constructions before, so it was a good introduction to using a compass, and it was also a chance for the students to play with the artistic concepts of structure, contrasting color choice, and composition.  The kids had fun, and the results were stunning!

This whole project took about two 50 minute class periods.  Toward the end of the second day, one of the students said: “Mrs. von Oy. This is fun and all, but it doesn’t seem like we’re really doing much math.”

Well. Turns out we are. Lots of it.

And also? Maybe math just is fun, and we teachers need to bring the fun out a little more often.

So here’s the plan for the “triangle art” debrief discussion:

1. Why did that particular compass construction create an equilateral triangle? (and did it matter if your compass was too loose to keep its radius the same?)
2. Did it matter what size triangle you started with?
3. How many triangles could you make if you were to keep going? (Most students made about 10 triangles. This is a great time to begin getting kids to think about asymptotic behavior, even to think about limits)
4. What is the difference between how many triangles you could make out of paper, and how many you could imagine mathematically? (a question to provoke conversation about the nature of mathematical abstraction. Perhaps I will have students read this blog post by Ben Orlin in class or for homework: There’s No Such Thing as Triangles)
5. If you made the spiral pattern (like the one below), could you ever get all the way around, and how do you know? (A student conjectured today that it would be impossible because the triangles were getting smaller. That led to a great discussion of side lengths getting shorter vs. angles getting smaller…or do they stay the same measure? Would love to have the whole class in on this conversation)
6. If the side length of the first triangle was 10 cm, what would the side length of the second triangle be?  (Let the students struggle with this one. They know the Pythagorean Theorem, but haven’t spent much time using it for interesting problems yet. I want to see them figure this out on their own.)

What are some questions you would ask your students? Send some comments my way…I’d love to facilitate an even more robust discussion.