A Fermi Problem

5 min

Narrative

This Warm-up allows students to preview examples of Fermi problems, two of which they will explore further in the next activity. The questions are presented with a series of open-ended questions. As they identify questions that they find the most and the least intriguing, students are likely to notice that answering the questions requires finding some missing information and making some assumptions.

Launch

Arrange students in groups of 2–4. Give students a minute of quiet think time and another minute to share their responses with their group. 

Student Task

Here are some questions.

  • How many times does your heart beat in a month?
  • How many hours of television do you watch in a year?
  • How many tubes of toothpaste would you need in a lifetime?
  • Is one month enough time to read the dictionary out loud?
  • Is one gallon of hand sanitizer enough to sanitize the hands of everyone in the school over a school day?
  • How long would it take to paddle across the Pacific Ocean?
  • How long would it take to give every dog in America a bath?

Which question do you find most interesting? Which question do you find the least interesting? Be prepared to explain your reasoning.

Sample Response

Answers vary.
Activity Synthesis (Teacher Notes)

Invite 1–2 students to share the questions they find most interesting and why. For each question shared, ask if others in the class also selected that question and whether they did so for a different reason. Repeat the steps with the questions that students find the least interesting. 

Explain that these questions are called “Fermi problems,” named after Enrico Fermi, an Italian physicist. Fermi loved to think up and discuss problems that are impossible to measure directly but can be roughly estimated using known facts and calculations. Tell students that they will now explore a Fermi problem together.

Standards
Building On
  • 4.MD.A·Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
  • 4.MD.A·Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
  • 5.MD.A·Convert like measurement units within a given measurement system.
  • 5.MD.A·Convert like measurement units within a given measurement system.

40 min