Friggatriskaidekaphile

frig·ga·tris·kai·dek·a·phile
/fɹɪɡə,triskīˌdekəˈ,fīl/

noun
a person who has an extreme love for the number thirteen.

Week 27: Patterns in the Paper Weaving

I love fiber arts and weaving. So, I have one more weaving post for this series, but this time it’s with paper. This activity is great for all ages and can be done with ribbon, bias tape or strips of paper. I like to use origami paper strips.

The idea here is to play with repeating patterns and find where you can create secondary patterns, tessellations, and other shapes. Learners can experiment with over/under weavings and see what amazing patterns emerge. Make sure to have lots of colors, and encourage experimentation (diagonal, skipping, color patterns in warp and weft, gradients, etc.)

Math is beautiful. Math is playing with patterns and abstract thoughts. This is a wonderful activity to tickle the math parts of our brains.

Weavings above are done by my family and friends. My daughter and son really made a week of weaving papers.

Some questions to ponder:

  • Can you create a matrix or array that can represent your pattern?
  • For precalc and above – what would operations on your matrices result in if you mapped colors to numbers?
  • Can you create curves or other optical illusions with weaving techniques?
  • How can weaving relate to our numbers? (number line, even/odd, etc.)
  • Can you weave a function? What is the input and output?

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:

Makings: Wave Pendulum

I have decided to start a new category on this blog for my “makings” – items and projects that I have designed/created for classroom use, art, fiber musings, or just because.

Today I decided to create an easy to store, easy to demonstrate, easy to build wave pendulum. I’ve built these in STEM classes, homeschool, and in groups with wood, broom sticks, tennis balls, and a whole bunch of nuts (hardware).

I decided to joint it with orthodontic rubber bands and I used sewing thread to hang the weights. I went with sharp triangles to hold the thread and found that I don’t have to tie it. This one is acrylic, but I am contemplating a wooden one.

I am selling the SVG file for this project here to be able to support the site and equipment.

Here are my pictures: I know the orange is a bit of an eyesore, but I love it for this sort of stuff.

And a video…

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)