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?

 

We Got A Problem #6: Useless Rulers

By the way, there’s an interesting problem kicking around Dan Meyer’s blog.  But now for something completely different…

Take a ruler or any stick.  Mark it off into three equal parts.  Then, perhaps in a different color, mark it off again into five equal parts.  This divides the ruler into how many total parts?

(The mathematician’s version: Consider a number line from 0 to 1.  Mark all multiples of 1/3 and 1/5.  How many intervals are produced?)

Start over.  On another ruler, mark it off into four equal parts, then again into ten equal parts.  How many total parts this time?

On another ruler, mark it off into twelfths and thirtieths.  (This is close to what happens with inches and centimeters, but not quite.)  How many parts now?

If you mark off the ruler into M equal parts, then again into N equal parts, how many parts are there in total?

Can you think of ways to extend either this problem or the rectangle-diagonal problem?

We’d love for readers to be able to explore these problems, so resist the urge to provide answers in the comments. Instead, we’d love helpful suggestions and ideas about different ways to think about them, successful or not. If you’d like to provide a full solution, do so with a pingback to your own blog!