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:

Week 21: Hexagon Tessellations

I love tessellating! This week we are playing with hexagons. Learners can either draw or cut various hexagonal designs with various colors. It is fun to see what secondary patterns can occur. Do other polygons tessellate?

This is a wonderful activity to practice mindfulness and presence as you play with these shapes. It is an opportune project for students to learn single pointed mindedness.

Use lots of colors – tissue paper is also fun. I didn’t post many pictures, because I don’t like to give all the patterns away – I really love the discovery that happens with this project. A paper cutter can come in handy here if you have a large class.

Here is a template to cut from. It is also a good time to break out protractors and comapasses and play with 120 degrees (the outer angle of a regular hexagon).

In our home, we have been playing with laser cut hexagons this week; and if you are a hobbyist with a laser and interested in a set, then I have SVG files here.

Week 20: Angles within a circle

This week learners can play with angles with both grand projects and smaller art projects. There are 360 degrees in a circle or 2pi radians. Learners can draw a circle and then mark every 20 degrees (or every 30 or any factor of 360).

tick marks every 20 degrees

Factors: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 60, 72, 90, 120, 180, 360

Once the circle and tick marks are made, learners can start connecting points by skipping a set amount (skip every 5 marks). The key here is to be consistent – make sure they skip the same number of marks with each line. The lengths of the lines should be the same, so they can use that to check each line. I like to use circular protractors, but it’s not necessary.

After creating a star, or mix of polygons, learners can color them in, create a template for sewing applique, laser cut, combine them into a mobile, and more.

Week 19: Math Haiku

Poetry forms are like a puzzles. You have to take the words you want to say and rearrange them, find synonyms, and reformulate them until they can fit in a form. This problem solving is so similar in math.

One of the first forms to play with is the Haiku. It is a three line poem with no rhyming scheme that fits a syllable pattern of 5/7/5. Traditionally there is a season mentioned (Kigo) and a cutting word to compare two ideas (Kiru). Learners can try to do a traditional Haiku, or they can just work with the syllable pattern to start. This can be done in any classroom to contemplate the concepts that are being learned in a different way. When we relate these abstract ideas to our inner beings, we remember.

Once poems are complete, maybe a work of art can complement it.

Here are some that I wrote. Please share yours!