Week 16: Geometric Sketching – Hummingbird

I love to incorporate drawing skills into math education. This week I encourage learners to start seeing birds (or other animals/people) as shapes. Heads are circles, torsos are ellipses, beaks are triangles, wings are long ellipses…

Sketching is a skill. A skill is something that you can master in time (think growth mindset). This week I challenge learners to start a daily doodle routine. Just doodle something (anything) for 1-2 minutes a day.

Here is an example of the activity. I will use a hummingbird as guidance, but please feel free to pick any object/bird/animal. I tried to do this as a quick sketch example:

Some of the concepts and discussions around sketching can include proportions, ratios, what shapes fit best, etc. I encourage learners to research and dive deeper into sketching skills and drills. I truly believe that art and spatial awareness can be beautifully integrated into learning math.

Additional activity: For high school students in Algebra 2 or higher, they can use Geogebra to sketch the shapes for an animal. How do you plot a circle? an ellipse? triangles? etc. Desmos can be used at a precalculus and calculus level.

https://www.geogebra.org/graphing/x6k9wnag

Week 15: String Art

This is a classic, yet fun activity with math:

  • Start with a compass or protractor and create a circle with evenly spaced points around it. Students can figure out how many degrees need to be between points (example: if you want 10 points, then there are 36 degrees between each point, for 9 points : 40 degrees, etc.)
  • Draw your circle and points on a board
  • Place pins or nails in your board
  • Wrap string in various patterns and see what emerges.
    • Students can study remainders (mod functions), multiplication, and sequences.
    • Star patterns, secondary polyhedra, and cardioids may emerge.
  • If you don’t have wood and nails, then this can be done on paper with a pencil and ruler or sewing with string on paper.
  • Encourage students to look at other shapes, axese, or lines and create works of art. (boards can be painted, multiple colors and thicknesses of string can be used, and students can contemplate 3-dimensional approaches for this art (like with dowels).

Week 13: Clay Möbius Strips

There are lots of amazing paper Möbius strips that are fun. You can cut down the middle, twist multiple times, make a Möbius paper chain, and try it with various materials. For a basic paper tutorial, I found a good one here.

Rather than creating the classic paper strips, this week learners will be creating Möbius strips with clay. Using a polymer or air-dry clay, encourage the creation of these wonderful mathematical shapes with a sculpting medium. A clay extruder can come in handy, but isn’t necessary.

I have had students make pendants, infinity signs, and amazing patterns with their projects. For advanced sculpting, learners can create a paper strip first, and then sculpt the same curves.

Matt Parker with Standupmaths also has a great video on these fun strips and how they can make linked hearts:

Week 9: Dragon Curve

The Dragon Curve is a fractal that is well explained in this numberphile video. This week learners can create a dragon curve with a strip of paper, Lux Blox, Python programing, Legos or toothpicks.

Paper:

For paper, I would suggest using a strip of thin paper. Thicker paper doesn’t produce as many folds as thinner paper. You fold the paper in half, and just make sure you fold from left to right. You can tape, glue or pin your dragon curve down when you are down. One question I like to ask students is: “does the length of paper change how many folds you can get? If so, how?” It is a fun experiment to run.

Lux Blox:

I put together a pdf on this project here.

Python:

If you have never used Python, then I recommend going here. For kids there is a great DK book here.

With python, I would encourage learners to think about how the algorithm would look to create the Dragon Curve. There needs to be a loop for each iteration, but what does that look like? Here is my code (copy and paste it into a py file), but I encourage learners to try first. If you notice that I have an input for angle, it’s because I liked playing with the angles of the dragon curve to create different patterns and variations of the curve. You can hardcode it to 90 degrees if you wish. Play and you never know what you will find.

Week 8: Density Through Pointillism

This week we are going to look at density in a two-dimensional sense. The idea is to create two dimensional images using various densities of points. The medium and approach can vary for the classroom. Some ideas are:

  • Sand art on a stick surface using different densities of sand (try light colored sand and a dark surface or vice-versa)
  • Pointillism with pens, pencils or markers to create a peice
    • play with shading and contrast
    • practice drawing shapes and objects first
  • Pea gravel on asphalt to create images
  • Moving densities with people to create a moving scene or mandala (this takes some choreography)
  • Paint with round pencil erasers as the point/dot maker
  • Round stickers on a contrasting surface
  • For larger grains or objects learners can measure the density of different areas by calculating how many grains/objects are in a given area (ex: grains of sand per square inch)

Students can calculate the density for various areas of their projects and note observations. Classrooms can discuss and play with density functions, look at density maps (ex: population density), look at pointillism art, and/or use apps that change photos into pointillism sketches (pointillist is the one I use).

me with the pointillist app

Week 6: Randomness using pi

Pi with Lux Blox

This week learners will create a work of art using pi. The goal here is not to understand pi, but to play with randomness. We will dive into the ratio of circumference and diameter on another week. Pi’s decimals go on forever and without pattern. Here are some ideas to play with that randomness:

  • Build a skyline with your favorite building toy using the digits of pi
  • Use graph paper and shade a skyline of pi
  • Assign a note from 0-9 on instruments or bells and have the learners play the digits in order to hear the randomness
    • Example: C = 0, D = 1, E = 2, F = 3, G =4, A = 5, B = 6, C = 7, D = 8, E = 9 (where you use more than an octave. You can also use sharps, flats, or skip notes)
    • You can also assign chords to each digit rather than notes
  • String or circle art with pi (you can do a circle with 10 points)
Pi using a circle with a point every 36 degrees
Students’ pieces