Fermi Problems

20 min

Teacher Prep
Setup
Students in groups of 4. Access to calculators. 10 minutes of group work followed by whole-class discussion.

Narrative

Students attempt to calculate their exact age. Because this is a constantly changing quantity, they attend to precision when they think carefully about how accurately to report the answer (MP6). The mathematics involved is multiple unit conversions in the context of time. In addition to the fact that age is always growing, precise times of birth may not be known.

Launch

Arrange students into groups of 4. Ask them to order themselves according to their age: who is the youngest? Who is the oldest? What information do you need to know to decide?

Tell students that they will be finding their exact age. 

Provide access to calculators. Give students 10 minutes of group work time, followed by whole-class discussion.

Student Task

What is your exact age at this moment?

Sample Response

Sample response: I was born on April 4, 2011 at 12:09 p.m. Today is December 17, 2024, and right now it is 10:55 a.m. So I am 13 years, 256 days, 22 hours, and 46 minutes old right now. I can’t get any more exact because I don’t know the second I was born. Plus, I’m not sure if I should answer the question for when I begin to write my solution, or for when I will be done writing my solution, because I keep getting older.

Activity Synthesis (Teacher Notes)

Invite students to share answers and discuss difficulties in answering the question. The discussion should include the following points:

  • We can give an estimate, but the question cannot be answered because we probably do not know the exact time when we were born and “at this moment” keeps moving forward.
  • How we express our answer depends on what we know about the time we were born. We probably know the day, but do we know the time? Should we answer to the nearest hour? Minute? Second?
  • Did you take into account leap years?

Ask students how they usually answer the question, “How old are you?” (This will probably be in whole number of years lived.) Why? (Because this whole number communicates enough information for most purposes.) After more than six months have passed since someone’s last birthday, the person still doesn’t normally round up when they report their age, even though this is customary for reporting many other types of measurements.

MLR8 Discussion Supports. For each response or observation that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Anticipated Misconceptions

If students struggle with what is meant by “at this moment” in the prompt, consider asking:

  • “Tell me about your age.”

  • “What does ‘at this moment’ mean to you?”

Standards
Building On
  • 4.MD.2·Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
  • 4.MD.A.2·Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Addressing
  • 7.NS.3·Solve real-world and mathematical problems involving the four operations with rational numbers.
  • 7.NS.A.3·Solve real-world and mathematical problems involving the four operations with rational numbers.<span>Computations with rational numbers extend the rules for manipulating fractions to complex fractions.</span>
  • 7.RP.A·Analyze proportional relationships and use them to solve real-world and mathematical problems.
  • 7.RP.A·Analyze proportional relationships and use them to solve real-world and mathematical problems.

15 min

20 min