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)

Week 24: Pastel Diagrams and Plots

Hyperbolic Paraboloid

Sometimes math diagrams, plots, and examples can be a little dry in our books and on the board. This week learners will be taking a diagram or plot that they want to improve upon and sketch it up with pastels, paints, or other media. Color, composition, and artistic embellishments can be added while, keeping the overall concept in tact. Ask them what a math textbook would look like if they created it. Would you have a cheshire kitty in the mix? Would you turn each chapter in to a different land or island?

These sketches don’t have to be fancy, I recommend small pieces of paper and having fun with it (most of these are around 3×5 inches and took a few minutes.) Most of all – have fun!

Pyramid
Binary, powers of two, exponential…
D6, cube, hexahedron, volume, probability…

Week 23: Fibonacci Weaving

If I am not playing with math, then I am tangled in yarn and thinking about math. This week I combined the two and wove A small fibonacci washcloth. Fiber arts are so versatile and an insanely fun way to express mathematics. In future weeks we will look at collage (wool applique), Cantor art, etc.

Fibonacci is a sequence where you start with 0 and 1. You then add those to get 1: {0,1,1}, and then you add 1 and 1 to get 2: {0,1,1,2}, and then you keep adding the last two numbers to get the next number. Here is a comic I created for Marie’s Atlas on Fibonacci:

For weaving, you need a piece of cardboard, small loom or even a notebook card (for thread weaving). The idea here is to create any form of Fibonacci patterns in your work. For mine I did 8 for a lower border, then 1 blue, 1 white, 1 blue, 1 white, 2 blue, 2 white, 3 blue, 3 white, and so on. Below is a sample. There are tons of ways to weave this sequence. You can use different sized looms, patchwork squares with areas that equal the sequence, etc. Have fun!

Week 22: Tessellations – Paper Method

This week we will do tessellations that fit together through translation (moving without rotation). We will look at reflection and rotation in other weeks. There are a few different ways to do this, but we will use the paper method today. I always start the class by talking about what different kinds of shapes can tessellate (triangles, trapezoids, hexagons, rectangles, etc.). We look at the tessellations around us (bricks, floor tiles, fabrics, etc.)

If you have never made a tessellation before, the easiest way is to use a rectangle sheet of paper, with a pencil, scissors and tape. Here are the instructions:

  • Step 1: Sketch a curve that stretches from the bottom left to the bottom right corner of your rectangle
  • Step 2: Cut out your curve and move it to the opposite side of your rectangle. Tape it together as perfectly as you can.
  • Step 3: Sketch a curve from the top left of your rectangle to the bottom left.
  • Step 4: Cut out the curve on the left and then tape it to the opposite side (again as perfectly as you can).
  • Step 5: Trace your shape on a sheet of paper and add some fun details: