guesstimation and fermi problems

Guesstimation and Fermi Problems

Thursday, May 20, 2010

When it’s safe to cross the street?

Which line will be fastest at the movies?

How many pizzas you need to buy to feed your friends?

How do you decide...


Estimation!!!


Fermi Problems

AKA Fermi estimates or “back-of-envelope” problems

Solved using “best guess” or justified approximations

Useful for finding reasonable answers (close enough)

A great way to work on out-of-the-box thinking!


Enrico Fermi

Famous Italian physicist

Well known for solving difficult problems in his head

Used a combination of common sense, intuition and data


Understand the problem

Think of a plan

Carry out the plan

Look back, is your answer reasonable?

How do you solve them?


How many ping pong balls would it take to fill

this classroom?

The Problem:


What are you asked to find?

What information are you given?

What information do you need to find, measure or approximate?

Understand the Problem


Think of a Plan

This is a volume problem

How many small things can fit into a large thing?

# small things = (large thing Volume) ÷ (small thing Volume)

What assumptions or approximations are you going to make?


Carry Out the Plan

What is the volume of this classroom? V = H x W x L

What is the volume of a ping pong ball? V = H x W x L OR V=4/3πr3

# ping pong balls= (room V) ÷ (ball V)


Look Back

Does the answer seem reasonable?

Is there a way to improve your estimate?

Look at each assumption you made


Now you try some!!!


Name _________________________________________________ Date ______________________

Figure Out Fermi

Enrico Fermi was a famous Italian physicist well known for solving difficult problems in his head, using a combination of common sense, intuition and data.

Directions: Following is a list of common Fermi problems. Your challenge is to work in pairs or table groups to figure out the answers. Hint: You will need to collect some basic information for each question before you can solve the problem.

1. What is the total weight of all the students in our school?

2. How many hours of TV will the students in our class watch this year?

3. How many minutes will all the students in our school spend on their cell phones this school year?

4. How many times does a personʼs heart beat in a lifetime?

5. Now, create one of your own Fermi-style problems below.


guesstimation and fermi problems

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