Lesson 1

Fermi Problems

Lesson Narrative

This lesson is optional. The activities in this lesson plan are sometimes called “Fermi problems” after the famous physicist Enrico Fermi. A Fermi problem requires students to make a rough estimate for quantities that are difficult or impossible to measure directly. Often, they use rates and require several calculations with fractions and decimals, making them well-aligned to grade 6 work. Fermi problems are examples of mathematical modeling (MP4), because one must make simplifying assumptions, estimates, research, and decisions about which quantities are important and what mathematics to use. They also encourage students to attend to precision (MP6), because one must think carefully about how to appropriately report estimates and choose words carefully to describe the quantities.

Each of these activities can stand on its own. If students do the first before the second, the second will take less time. It is very likely that it would take more than a single day to do all of the activities in this lesson. One option is to let students choose an activity that interests them. If you choose to conduct the lesson in this manner, begin by posing these scenarios, one for each activity in this lesson, to students:

  1. “Imagine that an ant ran from Los Angeles to New York City.”
  2. “Imagine a warehouse that has a rectangular floor and contains all of the boxes of breakfast cereal bought in the United States every year.”
  3. “Imagine that the entire Washington Monument had to be completely retiled.”

Then ask:

  1. “Which one interests you the most? Why?”
  2. “What questions could we ask about each situation?”
  3. “What information would you want to know in order to investigate that particular situation?”

Each student or group can explore the problem that interests them the most and share their findings.

As with all lessons in this unit, all related standards have been addressed in prior units; this lesson provides an optional opportunity to go more deeply and make connections between domains.

Learning Goals

Teacher Facing

  • Estimate quantities in a real-world situation and explain (orally and in writing) the estimation strategy.
  • Justify (orally) why it is unreasonable to have an exact answer for a situation that involves estimation, and critique (orally) different estimates.
  • Make simplifying assumptions and determine what information is needed to solve a Fermi problem about distance, volume, or surface area.

Student Facing

Let’s make some estimates.

Required Preparation

Internet-enabled devices are only necessary if students will conduct research to find quantities that they need to know. As an alternative, you can supply the information when they ask for it.

Tools for creating a visual display are only needed if you would like students to present their work in an organized way and have the option of conducting a gallery walk.

CCSS Standards