Unit 9, Lesson 1
Fermi Problems (Optional)
Grade 6
Preparation
Lesson Narrative
The activities in this optional lesson 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, make estimates, conduct research, and make 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.
The three problems in this lesson involve measurement conversion, calculation of volumes and surface areas of three-dimensional figures, or the relationship of distance, rate, and time. Each of these activities can stand on its own and teachers can select how many of the activities to complete. As students work on any of these activities, monitor for different approaches to solving the problem, and select students to share during discussion. In particular look for:
- A range of estimates.
- Different levels of precision in reporting the final estimate.
- Different representations (for example, double number line diagrams and tables).
- 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.
Let’s make some estimates.
Required Materials
Required Preparation
Internet-enabled devices are necessary only 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 needed only if you would like students to present their work in an organized way and have the option of conducting a Gallery Walk.
Internet-enabled devices are necessary only 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.
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.