# Project Runway and the Tower of Hanoi

I have most of a vision for my intro to math week this fall. Like last year, we’ll be practicing group norms with a task separate from the content. This year, I’m assigning four fours, which I first heard about this during Jo Boaler’s How to Teach Math course last summer. I found it really engaging, and with a low floor and high ceiling. Perfect for this! I’m also working on a set of stations that allow students to use the standards for mathematical practice. However you feel about the Common Core, this is a great list of things effective math practitioners do.

As my idea stands right now, students will rotate through untimed stations, either in pairs or individually. Each task corresponds to a different mathematical standard, although I have not decided if and when I’m going to make that clear to them. For example, for “construct viable arguments and critique the reasoning of others,” I have some examples of logical fallacies I want them to argue against. For “look for and express regularity in repeated reasoning,” I made a tower of Hanoi!

How I love being able to crochet math-related objects. I found several crochet patterns online, as well as several sets of wood-carving instructions, but nobody else seems to have done both – I blame gender roles. Admittedly, to create the platform I hammered a screw into a thin plank, twisted it enough that a hole formed, and then hammered the dowel section – that I had cut with scissors – into the barely-adequately-sized hole. The crochet part actually involved a pattern-recognition task:

I crocheted each ring from the inside out, starting with a loop of 7 stitches. The top green one has 2 rows of stitches, the light blue one has 3, the white one has 4, etc. To make flat circles rather than tiny hats or hyperbolic planes, for the second row I did two stitches every other original stitch. So around the original 7 stitches I did 2 + 1 + 2 + 1 + 2 + 1 + 2 = 11 stitches in the second row. The question is: how many stitches are there around the outside of the lime green ring?

I actually had to determine this pattern, in my real life! I had to know that after 7, there were 11 stitches, so that I knew how many stitches to do for the light blue ring. And I needed to keep the pattern going for the rest of them! It gets interesting, too, because while 7, 11, and the next number in the sequence are all odd, the next number is even, which changes the pattern a little bit. And if the pattern continued, how often would there be an even number in it?

(Not to mention that honestly, I got about 2/3’s of the way around the lime green one before I realized that it wasn’t sitting flat anymore, so I just did one stitch around for the rest of the circle)

The one I haven’t quite settled on an activity for yet is “attend to precision.” The best example I can think of for this one is on Project Runway when the fit of someone’s garment is off by probably millimeters and looks terrible. I think Project Runway has a lot to teach us about math education, really. Whenever they form them into teams there is a significant amount of eye-rolling and lack of communication that leads to poor results. All of our students could probably heed that as a warning.

What I’ll probably do for that station is ask them to cut a dowel rod or a piece of cardboard or something so that it perfectly fits in a particular space.

I’ll be back soon with some articles!