Home Numeracy – The Fermi Math Game

Semi-truck We hear so much about literacy in the home – reading to your child, having periodicals in the house, having family reading time. But we rarely talk about numeracy in the home, especially after the basics of having your child count things. That's a shame because as students become more sophisticated math thinkers, math can become a very enjoyable family game.

When I was in college my friends and I played a game we called "Guesses by Crackpots" in which we would use estimation to figure out possible solutions to outrageous questions – How many cars are on I-80 right now? How many bags of grass seed would it take to re-seed the median strip of I-95? How many marshmallows would fit in the dome in the cathedral in Florence? When I became a teacher, I learned that this game was played by others and is often called "Fermi" math in honor of Enrico Fermi.

During foundation math (as a reminder, that's the 15 minutes of math in which students work primarily on computation and computational fluency) a group of students recently tried to figure out how many semi-trucks would be filled by the candy collected by U.S. kids on Halloween.

You begin with questions:

How many people are in the U.S?
How many kids are in the U.S.?
How many of those kids trick or treat?
How big is a semi truck?
What is the volume of a semi-truck?
How many pieces of candy does the average kid get?
How much volume of candy does the average kid collect?

From there you begin to make estimates (some of your questions may remain unanswered as you discover a different path to a solution). We allowed ourselves one "Google" question for which we could get an answer.

The rule is as long as you share a good reason, you can make an estimate or assumption. Sometimes kids began to argue the details "My brother collected a garbage bag of candy!" "My baby sister didn't collect more than 3 pieces." Often the counter examples cancel each other out and solidify our understanding of the average.

We think there are about 300,000,000 people in the U.S. (assumption – there are actually 316,000,000 but 300 million is a lot easier to work with.)
About 20% of the population is under 20 (that's the fact we chose to look up.)
That means that 60,000,000 people are under 20 (20% of 100,000,000 is 20,000,000 so you multiply that by 3)
We figure about 80% of those people Trick or Treat (which I considered a high estimate but was over-ruled by the Halloween-centric audience.)
8,000,000 is 80% of 10,000,000 so 48,000,000 kids trick or treated (8,000,000 x 6 groups of 10,000,000)
We used my son Hal's half eaten Halloween candy to determine that he collected about 1/3 of a cubic foot of candy.
So 48,000,000/3 = 16,000,000 cubic feet of candy collected.

The next step was to figure out the volume of a semi which the kids did by sitting 3 across and measuring the width of the average car then multiplying that by 10 feet for the height and _____ feet for the length (they were still arguing when it was time to leave.)

We haven't quite yet gotten to an answer but I wanted you to see the process.

This game is fun to play as a family and is a great way to pass time on car trips. It's fine for you to take the lead in some of the figuring – you are doing great modeling. You are demonstrating having fun with math, making estimates, and thinking through problems logically. You are also demonstrating that most math "problems" don't have a single right answer. Most math is pretty messy.

Your own family Fermi math problems may start a lot more simply:

How many dozen eggs does our family eat in a year?
If no snow melted (or compressed) all winter, how high would the snow usually get? What if it didn't melt over the summer – how high would it be in your lifetime?
How long would it take a hamster to roll in its Hamster ball to Faribault?
Would it be possible for someone to collect a garbage bag of candy while Trick or Treating?

I hope you'll make Fermi math a part of your family's math fun. Share great questions with us and we'll gather them together to share with others.