If you placed quarters end to end all along the equator and then got to keep them all, how much money would you have?
How much gasoline does your car use in a year? How does this compare to the amount of liquid (water, soda, coffee, etc.) you drink in a year?
How many revolutions will a wheel on the bus make during a trip from Aventura to Disney World?
What is the mass in kilograms of the student body in our school?
The problems above are examples of Fermi questions, named for the physicist Enrico Fermi who liked to challenge his students and colleagues with questions like these that involve measurement and reasonable estimates. These investigations can provide a lot of fun when studying measurement, or when working with large numbers, and can reinforce the concept of what constitutes a reasonable estimate.
Here’s a site with ideas to investigate more Fermi questions with your students.
Author David Schwartz offers fun ways to explore and imagine large numbers in his classic book How Much is a Million?
“If one million kids climbed onto one another’s shoulders, they would be taller than the tallest buildings, higher than the highest mountains, and farther up than airplanes can fly.
If you wanted to count from one to one million, it would take you about 23 days.
If a goldfish bowl were big enough for a million goldfish, it would be large enough to hold a whale.”
Have students conjecture about how David Schwartz came up with these claims and whether or not he is correct.
Schwartz offers some other great ideas to explore the number 1,000,000:
– What do we have a million of in this school?
– How far would a million ___________ stretch if we laid them side to side?
– Have students work together in a read-a-thon to read a million pages or for a million minutes, and create graphs to track the progress.
– Use an imaginary million dollars and try to buy everyday items until the money is all spent
– Map out a million-millimeter route and walk its entire length
Here are some more thoughts from Schwartz from the Million Mania section of his blog.