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Classroom Stories: More Ruminations on a Theme: Fermi Warm-Ups

By Stacy Palen & John Armstrong

This week, we have a guest post from a colleague at Weber State University. John Armstrong is also teaching in the inadequate classroom. He is experimenting with a way to fill the time while he figures out what’s changed about the A/V situation since the last class two days ago… 

Thanks to some intermittent multimedia issues in my new “temporary” classroom, I’m forced to get creative with the first ten minutes of class every day. So, I start by giving a Fermi problem to my students. I ask the question and they can work on the answer while I jiggle cables and try turning things off and on again.

Physicist Enrico Fermi was famous for posing seemingly unsolvable questions that he would then proceed to solve with a few back-of-the-envelope calculations. The most famous of these—how many piano tuners are there in the city of Chicago—requires some educated guesses about population, the popularity of pianos, and the diligence of their owners, but you get surprisingly close to the “correct” answer without knowing much of anything.

In astronomy, this tool has been leveraged in the Drake Equation to estimate the number of civilizations in our galaxy, proving that even when you can’t know some of the parameters you need to measure, you at least have a framework for study. The first three terms of this equation—the number of new stars formed in the galaxy, the number of these stars that form planets, and the number of Earth-like planets in each system—were largely unknown when I started my studies in the mid-nineties. They now have pretty good estimates. We are now on the verge of an estimate of how many planets can evolve life, which is something that could happen in the next decade or so.

But when I reached this point in my class, going from a simple Fermi problem to the Drake Equation seemed like a heavy lift.

I’ve always started the semester with a formal activity on estimating the number of pebbles in a jar. We measure the volume of the jar, remove a few pebbles and systematically measure their volumes, and then divide the two. The amount of agreement between the groups is surprising.

But thanks to my A/V woes, I’ve started asking a question every day. How much does the mass of humans increase each year? How far does a bumblebee travel in a day? How much food energy do you consume in a year? And each day, more and more students seem to dive in. Better yet, some of them have come in after doing some of their own estimations. How many bricks are in their house? How much electricity do they consume every year? 

The answer to the last question turns out to be surprising: It’s about ten times the amount of energy that you eat in food.

While I’ve always seen the value in Fermi problems, their routine application is giving my students extra practice and increasing their numeracy. And they also seem to be sparking my students' interest in their own questions.

I can’t wait to get to the Drake Equation!

—John Armstrong

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