Composing with Random Numbers
I happened across this game in my files. I used it with my middle school students as part of a unit about the science of sound and music. I think it would also make a great challenge for teens learning to code. This activity is based on a musical game that Mozart and his friends supposedly played.
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(If you’re already familiar with how to calculate probabilities with dice, feel free to skip to Part II)
First, let’s calculate the probability of various rolls of a pair of dice: Let’s make a chart of all the possible outcomes of rolling two dice. Each die has 6 sides, so we’ll use a 6 X 6 matrix
Die roll | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
3 | 4 | 5 | 6 | 7 | 8 | 9 |
4 | 5 | 6 | 7 | 8 | 9 | 10 |
5 | 6 | 7 | 8 | 9 | 10 | 11 |
6 | 7 | 8 | 9 | 10 | 11 | 12 |
The probability of an event is calculated by counting the number of possible ways of getting a particular outcome (such as rolling a 9 on the dice), and dividing by the total number of possibilities. Probability is expressed as either a fraction or a decimal. The probability of an event is always somewhere between 0 (impossible) and 1 (certain).
How many possible outcomes are there when you roll two dice? _______
How many different ways can you roll a 9? __________
So the probability of rolling a 9 is : __________ (express as a fraction)
Refer to the matrix above. What is the probability of each possible roll of two dice.
2: __________ 8: __________
3: __________ 9: __________
4: __________ 10: __________
6: __________ 12: __________
7: __________
Now lets create a composition: Go to Part II