Monday, March 7, 2016

Mathematical Dominoes: A fun and incentivizing classroom problem solving game

I've been thinking lately about fun and incentivizing ways to structure small group problem solving in a math circle.  Last week, I posted about an activity where students solve math problems to find a secret code and unlock a password protected document.  Here's something else I found: Mathematical Dominoes. Each team of 1 - 3 players works on problems at their own pace, selecting them one-by-one from a pool of available problems.

The problems are written on the back of two-sided cards, and the front of the cards look like dominos.  The numbers on the domino indicate the difficulty level of the problem and the number of points to be won or lost by working on it.  Students choose based on the domino side and can only flip it over afterwards.

How does scoring work for an [x:y] domino?
1. If you correctly solve the problem on the first try, you get x + y points.  So [3:4] gains 7 points.
2. If you correctly solve the problem on the second try, you get max(x, y) points.  So [3:4] gains 4 points.
3. If the second answer is incorrect, you lose min(x, y) points.  So [3: 4] loses 3 points.
4. A [0:0] domino is special - you only have one try.  A correct answers gets 10 points, and an incorrect answer has no penalty.

When the students finish with a problem, they return it to the pool and pick a new one.  There are judges who check answers and keep track of points, but they don't need to know a lot of math. The competition ends after a set amount of time, and the team with the highest score wins.

There's a lot of strategy towards choosing your domino - [1:6], [3:4], [1:4], [3:6] all have slightly different reward/penalty structures, and should therefore indicate different levels of difficulty and riskiness.  Because of this, choosing problems to put on the dominos seems like it would be very challenging.  Luckily, Prime Factor Math Circle has some up on their website to get you started.

They also list some of the reasons why this game has worked so well:
• It’s rules and format are as interesting and exciting for a 3rd-grader as for a 9th-grader
• It engages each and every student in active problem solving
• It can be played for as long as it is needed and can be stopped at any moment
• It requires very few helpers
• It allows all students to work at their pace and their level 

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