I attended a gerrymandering conference last summer. It was thought-provoking, eye-opening, and overall the best conference I've ever been to. Created by Tufts professors, the Geometry of Redistricting workshop invited hundreds of educators, computer scientists, lawyers, and other professionals from around the country to learn about and brainstorm solutions to the complicated issue of gerrymandering. According to Merriam-Webster, to gerrymander is "to divide (a territorial unit) into election districts to give one political party an electoral majority in a large number of districts while concentrating the voting strength of the opposition in as few districts as possible." In short, the way you divide land can determine the winner of an election. Because the gerrymander-er is working with dividing pieces of maps, they are working with math, and as an educator at the gerrymandering conference I was encouraged to bring what I had learned back to my classroom.
At some point during the last two days of the conference, facilitators asked me and other participants to gerrymander a ten-by-ten grid as a sort of warm-up exercise. Using something similar with my students seemed like a no-brainer - it was simple, fun, and enlightening. Below is the activity I eventually used with one of my classes (on the last period of a Friday!)
1. Before diving into a ten-by-ten grid, I started with a simpler one. I gave each student a sheet with three ten-by-five grids with the first two columns filled with x's (as pictured below). I asked students to divide the first grid into five equal sections so that 3/5 of the sections are dominated by blank blocks while the other 2/5 of the sections are dominated by x blocks. If these were voting districts, it would seem that dividing the blocks up in this way would be "fair" (the majority of districts are dominated by the majority group with perfect proportionality).
2. For the second grid, I asked my students to divide the fifty blocks into five equal sections in which all of the sections have more blank blocks than x blocks. This sounds a bit confusing at first (to mostly anyone, I think) and I had to repeat the direction a few different times in slightly different ways. After a minute or two, though, most students were able to figure out that simply dividing the sections in their horizontal rows two at a time does the job. This can be seen in the second grid of the picture above: Each section is now dominated by blank blocks. If these were voting districts, the blanks would have control of all the districts. As you might expect, students believed this set up to be very unfair.
3. For the third grid, I asked students to divide the fifty blocks into five equal sections so that a majority of sections have a majority x blocks. In the third grid of the picture above, you can see that 3/5 of the sections are dominated by x blocks. Now, the minority controlled the majority of the districts. Students thought this was unfair but also "cool." There's something fun about helping the underdog win.
4. I expanded on the third grid at this point in class. When, if ever, should the minority control most of the districts? Who actually does this with maps? (Answer: both major political parties in the United States have gerrymandered.) Which real districts are gerrymandered? What do they look like? How do people feel about it? What, if anything, is being done about it?
5. After a lively discussion and looking at real gerrymandered districts with the help of the internet, I gave students another sheet. This time the sheet had two ten-by-ten grids with x's in 40 of the 100 blocks. This exact arrangement of x's was taken from the activity facilitated at the Tufts conference. I asked my students to divide the 100 blocks into ten equal sections so that (1) on one grid the majority of sections were dominated by blank blocks and (2) on the other grid the majority of sections were dominated by the x blocks. Pictured below is one work in progress, mistakes included.
6. Once some of the mistakes were cleared up, students were very excited to show off their gerrymandered maps. I shared different arrangements from student volunteers using my document camera and we talked about strategy in performing the act of gerrymandering. For example, students shared how they were able to concentrate a large number of the dominant group in fewer sections by packing them together. This gives the minority group a chance to spread themselves across over more districts, a gerrymandering technique that's called "cracking and packing."
7. I closed the lesson with a reminder that because real districts don't exist in perfect square blocks, the math and computer science behind redistricting is immensely complicated. I also reminded my students that this is an ongoing issue, and one to which we will return as more and more articles come out about gerrymandering.
(Update: the issue of gerrymandering came up in the recent Alabama senate race between Doug Jones and Roy Moore. Although Doug Jones won the majority of votes, had the race been decided by districts Moore would have won 6 to 1!)
If you teach, I hope you'll considering facilitating a similar lesson soon!