Sharing some ideas about math and gerrymandering with kids

Moon Duchin gave a talk about math and gerrymandering in San Diego yesterday that generated an enormous amount of excitement. One lucky bit of that excitement for me was that Francesca Bernardi shared the teaching resources from a math and gerrymandering conference in Madison, Wisconsin organized by Moon Duchin and Jordan Ellenberg:

This morning I decided to try out some of those ideas with my kids. The boys are in 6th and 8th grade and really enjoyed working through the project this morning. Overall, my impressions are that:

(i) The math all by itself is both interesting and accessible for middle school and high school kids.

(ii) Working with a larger group would produce some fascinating discussions about the tetris-like shapes involved in this project. For example, what sorts of shapes do kids consider natural and what sorts of shapes seem unnatural when dividing up a square?

(iii) The project is great for showing why gerrymandering is a difficult math problem. I think that students will see quickly that creating 6 “winning” regions out of 10 for a group that has only 40% of the population seems unfair. However, they’ll also see quickly that it isn’t as easy as they might think for the math to flush out that unfairness.

So, here’s how things went with my kids today. I started by trying to give a simple explanation of gerrymandering – a concept that they’d not heard of before:

Now I had them each work on one of the exercises from the materials that Bernardi shared yesterday. In this exercise you start with 10×10 grid that has 40 orange squares and 60 purple squares. The first challenge is to divide the large square into 10 connected regions of 10 small squares each in which exactly 4 regions have majority orange squares. The next challenge is to try for exactly 6 majority orange regions.

Here’s how the boys explained their approaches to the two exercises. You’ll see that this problem is a great way to get kids to talk and think about some basic ideas in geometry.

Now we moved on to the part of the exercise that tries to use geometric ideas to identify gerrymandering. Again, working through these different math ideas in this part of the exercise is a fantastic exercise for kids.

Before diving into this part of the project I explained three of the geometric ideas just to make sure they boys understood them prior to diving into the calculations:

The boys did their calculating work off camera. I had them pick 3 regions from each of the two shapes and work through 3 of the different metrics.

Here’s what my older son had to say after he finished:

And here’s what my younger son had to say (if you look really carefully you’ll see that he was confused on some of the calculations, but that shows, I think, why this exercise can be a great activity for kids – this could easily be a week long activity in a 6th grade math class):

Wow is this a great project for kids – and we barely scratched the surface!

One surprise for me was that the ideas of “packing and cracking” didn’t come up in the conversation with the boys. Maybe looking at the different shapes while simultaneously noting the different colors inside of those shapes is a harder exercise for kids than I guessed. Introducing the “packing and cracking” ideas would make a good follow up project.

Anyway, I think the educational project from Wisconsin’s math and gerrymandering conference is absolutely fantastic. Huge thanks to Francesca Bernardi for sharing these resources. The exercises and ideas will make a great addition to just about any middle school or high school math class – I hope they are shared widely!

If you are looking for additional resources, here a few that I’ve found to be helpful from the last year:

(1) Erica Klarreich’s article in Quanta Magazine last year

The Mathematics Behind Gerrymandering by Erica Klarreich

(2) Sam Hansen’s podcast on Gerrymandering

Relatively Prime’s “District” episode featuring Eric McGhee and Moon Duchin

(3) Jordan Ellenberg’s blog post on Alabama’s congressional districts

Are Alabama’s House seats gerrymandered?

(4) Patrick Honner’s Quanta Magazine article

The Math Behind Gerrymandering and Wasted Votes

(5) An article from January 15th, 2018 in the NY Times

A Case for Math, Not ‘Gobbledygook,’ in Judging Partisan Voting Maps

(6) An article from January 11th, 2018 about the math behind a gerrymandering ruling in North Carolina

How a Duke professor helped bring down NC’s controversial Congressional map