Have you ever been to a carnival or amusement park and seen one of those people who will try to guess your weight, height, or age? If they get within a certain range of your weight, they win and keep your money. If they are wrong, you win and get a prize. I’ve occasionally wondered how they determine what their range is. This clip from Steve Martin’s The Jerk makes me wonder, instead, how they determine which prizes they can give away.
That’s the lead-in I give the students. Steve Martin can only give away that small section of prizes because he is a terrible guesser, so he often loses. If you worked for the carnival as a guesser, what can you give away?
I have the students go around and guess the weight and height of any 10 willing participants in the class. (Any student can turn down being guessed, so students had to ask first. Also, I think my students were always worried about insulting someone, because they almost always under guessed. Also, many of your students may not know how much they weigh, so doing this lesson near when they have a fitness test and get weighed in gym is a good idea.) They record their guess, the actual amount, and the difference between the two.
Then, in groups, they try to determine a metric for figuring out who is the best guesser. We talk about how being 10 pounds off for a super thin person, child, or baby is much worse than being 10 pounds off for a very large person. We also talk about how being over or under doesn’t really change how good the guess is. After I push back on their metrics, some students pick up on the proportionality of the guess to the real amount, and lead us into relative error.
I somewhat drop the conceit at that point, mostly because I’m not sure of the best way to finish it off. But I like the start, and it’s a very natural intro to relative error, and the relative size of numbers in general.
James Cleveland-Tran
The Roots of the Equation 
Comments on: "The Carnival Guesser" (2)
I’m thinking of how to adapt this for an intro on limits at infinity: in the expression x + 5, the + 5 makes less of a difference the larger x becomes. Kind of like being 5 lbs off when guessing the mass of the earth, versus being 5 lbs off guessing the mass of a gerbil.
I also just thought of another cool hook to your lesson: there is an easy way to estimate the circumference of the earth via a Fermi problem. (24 time zones * 1000 miles each) = 24000 mile circumference.
How far off are we? If we’re off by 1,000 miles is that really bad or not? What if we estimate the distance from D.C. to Seattle and we’re off by 1,000 miles? What if we estimate the distance from the earth to the Sun, and we’re off by 1,000 miles?
That’s a great idea. Really it’s all in line with things like Estimation 180 and other number sense building activities, which are so important. Relative Error just gives us a way to quantify it.