Guess the Function

I substitute teach middle school. Anyone that's ever subbed (especially middle school) knows that one of the cardinal rules of subbing is to not allow any downtime. (I have a story involving downtime in a middle school classroom that ends with a student shouting, "No Brad, you're stapling your face wrong!") Because of this, I'm always prepared with a math game or activity to occupy my students.

My favorite game (and often their's too) is Guess the Function. The rules are to guess the function. Allow me to elaborate:

First I write down a function on a piece of paper. The difficulty of the function varies with the skill level of the class, but usually I start with a linear function.

Next I generate inputs (sometimes I do this by rolling dice, sometimes I ask students to shout numbers out, and sometimes I just pick numbers myself).

Then I write the number and the result of applying the function to that number on the board. Students then have the option of guessing my function, or waiting to see the result of my function on more numbers.

I give one point for right answers and penalize two points for wrong answers.

For example: suppose my function is f(x) = x + 2. I would start by writing 2 → 4 on the board (because f(2) = 4). Now bold students might start guessing, but that's a bad idea. With the available information, they might guess f(x) = 2x or f(x) = x², and they'd lose two points. After everyone has either guessed or passed, I would write another pair of numbers on the board (for example 3 → 5).

Some notes:

• I use arrow notation (3 → 5) instead of function notation (f(3) = 5) because I usually play this game with students that haven't been exposed to function notation.
• I usually have students play this in teams of four or five.
• Usually, sixth graders are much better at this game than seventh and eighth graders. Typically, seventh and eighth graders tell me that they "haven't learned this yet," whereas sixth graders don't seem to know that they don't know.
• Mathematicians will point out that for any finite collection of points, there is literally an infinite number of functions that will fit the points. This is true, but I like to think of this game as a game about psychology (what am I thinking?) as much is a game about math.
• Younger students often give English descriptions of rules (like plus two or times itself), whereas older students are comfortable with describing things algebraically (like x+2 or x²).
• I use the scoring system +1 for right answers and -2 for wrong answers because I want to discourage wild guessing. (Recall that as a sub, my goal is primarily to keep a class under control-- wild guessing descends in to chaos rather quickly.)
• When I play this game, I announce that I'm writing down a rule (not a function) because most of my students don't know what a function is.
• Examples of functions that I would use include x+1, 2x, 2x+5, x², x(x-1), 2^x, x/2, 1/x, 10 - x...

I love this game. One of my favorite things is that since it's not a part of the curriculum, the students that "aren't good at math" actually do quite well. This is because the psychological hurtles they have when facing math class aren't in place when they're just playing some dumb game the sub made up.