The Roots of the Equation

Vimes’ Theory of Socioeconomic Injustice

As I was planning my linear functions unit, I noticed a problem about someone choosing between two electric companies, with the standard idea of one having a larger start-up cost but a lower monthly rate. I realized these problems are very common, and they reminded me of of a quotation from my favorite author, Terry Pratchett:

The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money.

Take boots, for example. He earned thirty-eight dollars a month plus allowances. A really good pair of leather boots cost fifty dollars. But an affordable pair of boots, which were sort of OK for a season or two and then leaked like hell when the cardboard gave out, cost about ten dollars. Those were the kind of boots Vimes always bought, and wore until the soles were so thin that he could tell where he was in Ankh-Morpork on a foggy night by the feel of the cobbles.

But the thing was that good boots lasted for years and years. A man who could afford fifty dollars had a pair of boots that’d still be keeping his feet dry in ten years’ time, while the poor man who could only afford cheap boots would have spent a hundred dollars on boots in the same time and would still have wet feet.

This was the Captain Samuel Vimes ‘Boots’ theory of socioeconomic unfairness.

– Men at Arms

I wanted to share this concept with my class, so I looked for problems. One thing I realized, though, was that many of these problems involved one person choosing between two things. This makes it so there is one clearly correct answer.

But oftentimes, in the real world, people don’t have a choice. One person can afford the upfront cost to pay less in the long run, but another person can’t, and winds up paying more overall, as in the Pratchett quote above. So I decided to reframe the problems as comparisons between two people, to highlight that injustice.

The lesson started with a model problem, then I gave each group a different problem from the set below.

(I went through this page of unisex names to make all of the problems gender-neutral.)

Each table worked on a different problem (with some differentiation on which group worked on which), then they jigsawed and, in their new groups, they shared out their problems and how they solved them. Then, most importantly, they looked for similarities and differences between the problems.

We then read the Pratchett quote and discussed its meaning, and students had to agree or disagree (making a claim and warrant for each). We had a good discussion on whether it really applied to today’s world or not.