# Lesson 8

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 the course. 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.

Any of these tasks can stand on its own. Choose those that you have time for. It is likely that it would take more than a single day to do all of the tasks in this lesson. Make sure to leave plenty of time for discussion. Important topics of discussion should include why the quantities in question are difficult to measure and the level of precision we should use to record our estimates.

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

Teacher Notes for IM 6–8 Math Accelerated
This optional lesson can be done any time in the course. While these three activities are related, they do not need to be completed in order or during the same class period.

### Learning Goals

Teacher Facing

• Calculate a rough estimate for quantities that are difficult or impossible to measure directly and explain (orally) the reasoning.
• Choose an appropriate level of accuracy when reporting estimates of quantities.
• Make simplifying assumptions to solve problems about estimating quantities.

### Student Facing

Let’s estimate some quantities.

### Required Preparation

During the A Heart Stoppingly Large Number activity, students have the option of measuring one another’s pulse rate. If measuring pulse rate, students will need access to stopwatches.

Building On