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.

Aliens, Planets and Nebulae Update:

Mission 5 is now posted to the Math RPG page. I know I say Math RPG, but we all know that this is a total STEAM game. I can’t believe some of the absolutely creative and innovative ideas students come up with. Music blasters, laser cutters, lego models of carnivorous sunflowers, pages of comics about the crew, and so on.

I hope to have all 10 missions up and posted in the next few weeks. I feel that once 10 missions are posted, facilitators will be comfortable enough to create their own for the topics they would like to cover. Please send any feedback and if you haven’t checked out the game yet – here is a link.

Do we want to create a mission folder where facilitator can share missions? Let me know. I would love to see this project based learning while in character grow.

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!