Open ended investigation: Mathematical sequences as musical scores

Imagine you numbered each note of a scale, and then played the mathematical sequences on the notes like they were music. What would 1, 2, 3, 4, 5, 6, 7, 8, 9,… sound like? What would it sound like if you automatically jumped back down an octave every time you passed a multiple of 7? You may find this tool useful for actually listening to the sequence of numbered notes you generate.

What would the sequence of square numbers sound like? What about prime numbers? What if you kept the tone of the notes the same, but varied the length of the notes? How long would the sequence of notes that started with a half-note, but then halved the length of each subsequent note, take to play?

What would π sound like?


Open-ended investigation: The Math of Voting

Students could look at different ways of voting, and see what impact each of these ways has on a local election in their own school. They could compare the different methods, decide on ways to check for “fairness” of the election results, and even attempt to come up with their own system of voting. This project is likely to work better and have more interest from the students if they use actual data from things they are voting on for their experiments, as well as data from other sources.