# Semi-Mathy Games

Here are some silly semi-mathy things I’ve done with my students either as bonus problems or fillers.  I cannot vouch for their pedagogical value.

• +1 or +3.  A bonus question appeared at the end of a test.  ”Write Free +1 and you’ll get a bonus point on the test, no questions asked.  Or write Go For +3 and if two-thirds of the class does it, all who do will get 3 bonus points.  Saying anything out loud voids the bonus for everyone.”  I was pretty surprised that in most classes, not enough students went for the +3.  One student wrote Free +3 and got nothing…
• Choose A or B.  In class, students were given this choice: “Write A and you’ll get a point for everyone in the class who writes A.  Write B and you’ll get twice as much as anyone who writes A.”  After a long debate, most students picked B.  Far fewer students picked B when the choices were revealed publicly instead of privately.  (Social commentary followed…)
• The probability you’ll get this question right.  Still one of my favorite bonus problems of all time, this came from my wife: “If train A leaves Denver at 50 miles per hour, and train B leaves Chicago at 60 miles per hour, what is the probability that you’ll get this question right?”  Students who wrote 1 or 100% were right, students who wrote 0 were wrong, and anything in between was resolved with a coin or random number generator.  (There’s a fun discussion over whether a student who writes 0 can be right by being wrong… but if they’re right then they’re wrong…)
• The dollar auction.  This one is evil.  See http://en.wikipedia.org/wiki/Dollar_auction for a full description.  In one class, a student successfully “escaped” by outbidding the other player significantly.   In another class, a third student jumped into the auction midstream allowing another to escape.  If I were still teaching, I would repeat the process using the bidding systems by Beezid and other “penny auction” sites (http://en.wikipedia.org/wiki/Penny_auction).  Hopefully by exploring these auction styles with students they will avoid being scammed for real money later in life.

What else?

Bowen is one of the lead authors of CME Project, a high school mathematics curriculum focused on mathematical habits of mind. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won \$1,000 for knowing the number of degrees in a right angle.

### 4 Responses to Semi-Mathy Games

1. Mimi says:

Fun! Thanks for sharing!

2. Nathan says:

I sometimes use a prisoner’s dilemma type game that I stole from a Yale game theory course:

“At the bottom of your test, write the letter α or β. Extra credit will be determined as follows: I will randomly pair your test with one other person from the class and

1) Give you both 1 point if both tests are marked with a α.
or
2) Give you both 2 points if both tests are marked with a β
3) Give the person who marked β 0 points and the person who marked α 3 points if the tests are marked differently.”

By the way, are you planning on attending ICME in Korea this year?

• Bowen Kerins says:

This seems a little unfair, since your random pairing causes a lot of the variance. I guess I’d have to mark alpha if I didn’t know what I was being compared to, because I’m guaranteed at least 1 point and an “average” of 2 (if I assume everyone else splits 50/50). Meanwhile if I mark beta, my maximum possible is 2 and my “average” is 1.

Another way to do this that doesn’t involve randomness is to compare your test to the majority of the class:

0) You get 0 points if you mark beta and the majority of the class marks alpha
1) You get 1 point if you mark alpha and the majority of the class also marks alpha
2) You get 2 points if you mark beta and the majority of the class also marks beta
3) You get 3 points if you mark alpha and the majority of the class marks beta

This makes the “beta is cooperative” very clear: by marking beta you can give the entire class at least 2 points (if enough people join in).

Never been to ICME, someday perhaps. I’ll be at the AMS/MAA Joint Meetings in Boston this week.

3. Fawn Nguyen says:

These are fun! For the second game, you wrote, “Far fewer students picked B when the choices were revealed publicly instead of privately.” Not sure I understand how the game would work if choices were made known to everyone.
I agree, I would definitely mark alpha in the Yale game since it has, for reasons you stated, better odds.