Week 26: Musical Math

This piece was created using the Pisano Periods created by dividing the Fibonacci sequence by 12 and 24.

You don’t have to be a musician to play with music and math. This week, I encourage learners to experiment with sound and patterns. Below is a list of ideas to experiment with:

  1. Create a rhythm as an individual or a class that follows a sequence and build on it, (drums can be hands on tables or buckets).
    • Drum a Fibonacci set or other mathematical beats, (0, 1, 1, 2, 3, 5, repeat), with various instruments.
    • Drum a decay rhythm of holding notes, (ex: 8 beats, 4 beats, 2 beats, 1 beat, 1/2 beat, 1/4 beat, repeat).
    • Drum in a circle where learners explain the pattern of a selected drummer with math. Take turns creating and guessing patterns.
  2. Use a tuning app to study notes on an instrument in Hz. Plot the notes of an octave – what do you see? (This is better for learners that use the Cartesian coordinates.)
  3. Take a concept that is being studied and represent it with music. (Addition, subtraction, variables, exponents, etc.)
  4. Create a map from a sequence or set to a melody on an instrument. I did this with the Pisano Periods a couple of years ago and had a lot of fun with it.
    • To do this:
      • Determine the set of numbers you would like to use: {3,1,4,1,5,9,2}
      • Map the range of the set to a note: 1 = C, 2 = C#, 3= D, 4 = D#, etc.
      • Play your melody:

Week 25: Loopy Doodle Math

Doodling and math? Yes, we can play with doodles and see what patterns emerge. Finding patterns and problem-solving is a big part of math. For this week’s hands-on-math, learners are going to draw a loopy doodle where they start and end at the same point without lifting the pencil (or pen). Try to make sure that crossings are recognizable (not on top of each other). Once a doodle, or masterpiece, is created, then I encourage learners to color it in. Make lots of loopy doodles and see if any patterns or behaviours emerge. This is a great activity for discovery. Create birds, people, or city scenes with loops. Instead of coloring it in, learners can make knots by going over under, over under (erasers are good for this.)

The patterns that emerge with these doodles are fun. What do you think of the negative spaces that are created? My daughter sat down for hours last week and drew one doodle after another after another and said, “Mom, no matter how I draw these, only one color will touch the outside.” I smiled and we talked about how important discovery is. I love that we have the precious time for doodles. She was excited (and not surprised) to hear that there is a whole area of math that looks at how to shade various maps, shapes, and even doodles. My daughter’s drawings are below (with her permission – the butterflies aren’t part of the knots, but definitely needed). She gets credit for picking this week’s math activity.

Extra questions:

Do you ever need more than two colors to shade these in?

If you tangle more than one loopy doodle together, does it still work out for shading? What about knots?

Can you classify some of your knots? (count your crossings)