I’m planning my first unit of the year. We’ll explore radicals, exponents, and their relationship with the real number system. I enjoy planning this unit because it’s full of fascinating puzzles, deep structure, and a variety of representations. However, it’s pretty lacking in real-world applications. You can only ask so many questions about finding the side length of a square given its area — and how often does that actually happen?
But I just remembered a fun application that I’m excited to teach when I introduce cube roots:
This was an installation at Bowdoin College, where I went to school. The artist, Madelyn Sullivan, designed it to represent one ton of carbon dioxide — the approximate emissions of one US citizen over two weeks. This article summarizes the installation.
Some information will have to be withheld — the article gives away the dimensions of the cube, but starting with one ton of carbon dioxide gives plenty of information. I went through the math and was surprised at how hard the conversions were — I’ll need to scaffold the conversions and give students key information, though it would’ve been fun to have them do the research.
I’m not sure how well this all fits together — it seems like it may be a leap to go from “hey, let’s talk about climate change” to “I wonder how big a ton of CO2 is”, and then “what if we want to put that in a cube? How long would one side be?” It’s not perfect, but I’m in need of some application, and a personal story is always a good hook for my students.