I got this idea from a teacher I marked diploma exams with a couple of years ago. I’d love to credit him, but I can’t remember who he is. This is a WCYTWT submission, or as I like to call it, WWDDWT (What Would Dan Do With This). I used it with a couple of classes last year, and they really enjoyed it, but I used it poorly. I did it at the end of a unit on Permutations and Combinations, so the students knew exactly what to do with it. It wasn’t truly a problem, because they knew exactly how to solve it when I gave it to them. I should have used it on day one of Permutations and Combinations, and let them invent the fundamental counting principle on their own.
Mozart’s Dice Game
Mozart is credited with creating a dice game, whereby you roll a pair of dice 16 times to select 16 measures to insert into a minuet section, and then a single die 16 times to select 16 measures to insert into a trio section. For example, if you roll a 6 for the first measure, you consult a chart to see what measure number to insert into the first measure of your minuet, and so on. The idea is that no matter what you roll, you always produce a minuet that fits whatever rules go along with a minuet. This site explains it in a little better detail. Mozart’s Dice Game.
You give the students the history, and then you throw this site up on the SMART board. Play Mozart’s Dice Game has a chart that looks like this:
The drop down menus let the students enter numbers that they roll on dice, so give the kids some dice, and let them enter their rolls.
Notice the link below the chart that says “Make Some Music!” Once the students have all entered their rolls, you click here and the newly created minuet will play. There’s even a “Generate Score” link below the media player that lets you generate the score for the minuet they created. My students loved this, and printed theirs off to try to play it on the piano themselves.
After the minuet plays, you tell the kids that even though this was written more than 200 years ago, you are pretty sure that nobody has heard the particular minuet the class just created ever before. Ask them to discuss this statement. They’ll say things like, “Why, did they lose the score until recently?” and dance around it until one kid finally asks, “How many minuets could be made in this game?” Then you’ve got them and you let them play around with it. They will invent the fundamental counting principal, determine that there are an incredibly large number of possible minuets, and even create their own interesting extensions.
One student even came in the next day with an iPhone app that generates minuets using Mozart’s Dice Game. The only problem with the app is that it only randomly generates minuets, and doesn’t allow you to enter your own rolls.