Fermi Questions
Introduction
Enrico Fermi is the father of "solving maths problems we will never know the exact answer to." Such as how many leaves are on all the trees in Central Park or how many chillies are in the picture on the right. Fermi questions often require you to make reasonable assumptions and estimates about the situation in order to come up with an approximate answer. You need to be able to explain and justify what you did when coming up with your solutions. Your answers may differ from each other, but if you have made sensible estimates and assumptions then the different answers should be “close” to each other.
General Steps
Generally, these are the steps you want to follow when solving Fermi Questions:
Question: State the question and clarify the interpretation.
Wild Guess: Make a wild guess involving no calculations.
Educated Guess: Make an educated guess involving a chain of reasoning and calculations based on everyday experiences and estimates.
Variables and Formulas: Define variables and create a formula to solve the Fermi question.
Gathering Information: Perform experiments, conduct surveys, make measurements, and search for information to improve estimates and to find a smallest reasonable value, a largest, reasonable value, and a most likely value for the answer to the Fermi Question.
Conclusions: Summarize the overall conclusions, possible sources of error, interesting facts learned, possible directions for future investigation.
For an example of how to apply these 6 steps, look at p4-9 of this document.
Investigations
A) Toilet Roll Investigation
"Coronavirus: Hong Kongers in panic buying of rice, toilet paper and essentials as government stays mum on impending quarantine measures" - this was the headline of SCMP on Feb 6th, 2020. People were stocking up toilet rolls and tissue papers today. Is this a need or fear?
Suppose your family has just bought two bags of toilet rolls. How long would they last?
What additional questions do you need answered to solve this question? Look at the powerpoint and the worksheet below for prompts of how you should approach this question.
Toilet roll investigation.pptmToilet roll problem.pdfB) A Lifetime of Whoppers
On December 15, 2018 a 50-year old Burger King customer, Curtis Broomer, got locked in the Burger King bathroom because of a jammed door. He said that it was the kind of bathroom where you hold your breath until you get out. He couldn't get out though. While he was trapped, he could hear the staff and customers laughing about his predicament. He was stuck in there for an entire hour until a locksmith was finally found to release him. After his escape he needed to sit in the restaurant for another hour recovering from his ordeal. The Burger King manager graciously apologized and offered him free Burger King meals for life. They in fact gave him free meals for 13 days and then they changed their minds on the offer. Curtis sued Burger King and received a settlement of $9,026.
Do you think that is fair? How did you decide? What additional questions do you need answered to solve this question? Look at the powerpoint and the worksheet below for prompts of how you should approach this question.
Burger King Bathroom.pptxBurger King Bathroom - Task Sheet.pdfC) Chicago Piano Tunners
How many piano tuners are there in Chicago? What additional questions do you need answered to solve this question? Look at the powerpoint below for prompts of how you should approach this question.
Chicago Piano Tuners.pptxFurther Practice
Some of the essential skills introduced in this lesson are "estimating" and "rounding". The relevant skills can be found on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.
Transum
Decimals Line - this is a number line showing tenths and hundredths with draggable arrows. This is designed to help you visualise how to round.
Rounding Snap - play a game of snap! If the last card put down equals the previous card to the nearest whole number then all players race to shout SNAP!
Estimation Golf - play a round of golf using your estimation skills rather than golf clubs.
Estimating - practise and improve your estimating skills.
Rounding Ten - try this self-marked exercise on rounding the numbers to the nearest whole number or the given power of ten.
Rounding DP - try this self-marked exercise on rounding numbers to a given number of decimal places.
Rounding SF - try this self-marked exercise on rounding numbers to a given number of significant figures.
Upper and Lower Bounds - try this self-marked exercise on determine the upper and lower bounds when rounding or truncating quantities used in calculations.
Rough Answers - try this self-marked exercise on rounding values in a calculation to find an approximate estimate of the answer. There are altogether 4 levels.
For more goodies on rounding and estimating on transum, click on the hyperlink.
See below or here for more Fermi Questions to investigate:
Estimation-Questions-from-News 2.docxFermi Questions - SJW.docxExtension
For more Fermi Questions by University of Maryland Physics Education Research Group click here.
If you want to read more about this, take a look at "Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin" by Lawrence Weinstein and John A. Adam
Watch Counting Crowds to find out how statisticians use density samples to estimate their statistics and Estimate Enormous Numbers to learn how to use the powers of 10 to make amazingly fast estimations of big numbers.