rolling the dice

At the start of school a colleague asked me, "Can you use these?" and handed me a box of dice.  They weren't regular 6-sided dice.  They were crazy dice with 8, 10, 12, or 20 sides.  They were a dozen different colors, beautiful and unique.  I spent some time thinking about them and considering whether I could use them to help students learn something about probability.  I asked my students, "How can we figure out if any of these dice are 'loaded?'"  Together we built a project where they rolled the dice many times and attempted to determine whether the dice were loaded, whether a certain number came up more often than was statistically likely. 

Each student chose two different die and calculated the theoretical probability of each roll.  Then they rolled the pair 300 times and calculated the experimental probabilities.  Finally they commented on whether they thought any differences were significant.

In hindsight, I probably should have waited until later in the year when we study how to determine the statistical significance of differences in data, but I am pretty satisfied with how this went.  We got a chance to practice using excel, the students did something they'd never done before, and I got to take advantage of a lucky windfall. 

This is what I love about teaching, the opportunity to take a chance, try new ideas, and evaluate their effectiveness.  I encourage my fellow teachers to go ahead and roll the dice. 

Just for fun, consider a pair of dice, one with 8 sides, one with 12.  If the sides are numbered 1-8 and 1-12, what is the probability that you will roll a lucky 7 on this pair of dice? 

(The probability of rolling a lucky seven on a pair of six-sided dice is about 16.7%)