Wednesday, February 19, 2020

Take a Guess!

Image by Jondolar Schnurr from Pixabay
Remember those contests from your elementary school carnival where you would guess how many jelly beans or gumballs were in the giant jar (and if your guess was best, you won the jar!)? I've always loved those contests, but I haven't had much luck winning them. I'm sure there are great strategies of estimation, but I usually just went with winging it.

In my high school physics course, my teacher implemented a variation on the theme with Fermi Questions on the first day of class. A Fermi question asks participants to make a quick estimate as an answer to a math problem, often about something very big or very small. Perhaps it was equal parts jelly beans and physics class that inspired a guessing game I use in chemistry class.

I teach the mole relationship early on in class and circle back to it in every unit. I like how each time we return to the mole, the students' understanding of the concept, and the bigness of the mole, deepens. With each revisiting, I pose a question for them to guess. How many atoms of iron make up this nail? How many molecules of sugar are in this sugar packet? How many molecules of carbon dioxide can I liberate from a bottle of Diet Coke? And my most recent question: What is the weight in pounds of the oxygen in our classroom?

I asked my students this question a week or so ago in class. They write their names and their guesses on a small strip of paper (and the winner gets the oxygen!). A picture of the guesses of one class is below:

Notice the difference in the sizes of the guesses, from 0.000000001 lbs to 120 lbs. Of course, they immediately want to know who has the best guess, so then I provide them with time and space, but not too much in terms of directions, to figure it out. 

There are several reasons why I love doing these guessing games. First, it heightens their desire to complete the task (that I was always going to make them do anyway). Sure, I could just pass out a worksheet and tell them to calculate it, but asking them to guess first - and making it a contest - makes them invest and makes them want to win. Second, it is a great way to formatively see how they are thinking about the mole, how their understanding of a huge number is progressing. When I first ask about the atoms in a nail, many of the answers are numbers like 100 or 1000 and very few are in scientific notation. It's very hard to comprehend how small the atom is. Would they be able to see atoms if they were 1/100 of a nail? They aren't so sure because, at that point, they struggle to differentiate between a small number and a really really small number. Finally, it gives them a frame of reference for whether or not their answers are correct at the end. When they have first made a guess, they wonder if their answer is correct. They compare it to the guess. They think about what they calculated.

As to who had the best guess in the photo above, I don't want to say and spoil it for you or for my future classes, but I highly recommend completing the investigation and the calculation to find out!