If you asked me to name something that'd trigger a teenager's passion, I wouldn't leap at "Correctly Guessing a Has-Been Celebrity's Age" straight away. But there they were, hollering, competing, and rallying over near misses like frat boys over fantasy football.
- You have your students make three columns: Name, Guess, and Actual.
- You project twenty-or-so celebrities (a broad range of ages) onto the wall. You have 'em guess the age out loud.
- As they toss out guesses you say, "It's probably a bad idea to toss out your guess. We're all competing for the title of Best Age Guesser. Keep 'em close."
- You keep projecting, they keep guessing. Maybe you ask 'em, "twenties or thirties or forties?" to keep 'em participating together.
- Then you go back through and give the ages. They write those under the "Actual" column. Watch 'em get crazy here, freaking out 'cause they were only three years off Natalie Portman's age. Watch some of 'em blow Nelson Mandela by decades.
Enter the mathematics here:
- You ask, "how do we decide who guessed the best?" Expect intial suggestions like, "Whoever guessed the most right." and "Whoever got closest to each age."
- Take care of that first suggestion by asking who got the most right (Vicki, let's say) and then ask the class, "Can we stop searching for the best guesser now? Is Vicki guaranteed? Why not?"
- Ask for clarification on the second suggestion. Get to a place where they're subtracting the actual answer from the guess, getting negative numbers for underguesses and positive number for overguesses.
Make the math as hard or as easy as you want here.
Algebra and Below:
- Someone will suggest you add the new column of numbers up. You ask, "What number do we want there?"
- Someone'll suggest "Zero." You talk about the girl who overguesses Tiger Woods by 30 years and underguesses Oprah by 30 years.
Girl has a zero but couldn't guess your age if you handed her your driver's license.
- "So what do we do?"
- Drop the negatives. It doesn't matter if you guess over or under, only that you're off.
- Have them find the mean of their new column, full of positives. What does it mean? (The average number of years they were off per guess.)
- Ask if it means they guessed over or under on average. (Can't tell, we dropped the negatives.)
- Have them find the average including the negatives. ("Who guessed under on average? Who guessed over?")
- Connect this to absolute value.
- Talk about why the square of the differences is preferable to their absolute values. (x2 is differentiable where absolute value isn't.)
Give the winner a fun-sized candy bar. Let her select a celebrity for inclusion in next year's lineup.
Credit Where It's Due:
Got this idea from my ed-school mentor several years back. Yo, AB, I still use your stuff, man.
[Update: Matt has some pretty priceless extensions to this lab.]
How does the Mean and Median of all student guess do in this competition?
Creating a histogram of the guesses.
Looking at the standard deviation of the student guess. Do standard deviations vary with the age of the person.
And I reply:
Oh yeah, that’s great. It’s so clear now. I need to feature as many or more celebrities as there are students in the class. After the main event then I assign a celebrity to each student, they collect the guesses from around the class and perform a statistical analysis. Maybe I have Keynote slides set up so they punch in their data and present it real quick.
For Your Consideration: