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 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 14: Guess the rule – math game

One of my hobbies is to take completely non-math related games and modify them for classes. I don’t know what to call this game, it is probably a variation of “psychiatrist” or something, but here is how it goes:

  • In a group of at least 4 players, ask one player to leave the room and go out of earshot.
    • Tell this person that when they come back they can ask as many questions as they would like to figure out the rule.
  • Next, the remaining group creates a rule that answers must follow.
    • This can be a logical rule
      • always lie
      • truth then lie then truth
      • always tell the truth
    • This can be a number of words rule
      • always answer in two words,
      • anwer in one, then two, then three words
    • This can be a sequence rule
      • include the next number of the fibonacci sequence in your answer (A1- I had one good fish, A2 – One reason I don’t like questions, A3 – Two of a kind, A4 – I really only like tricycles in threes, etc.)
    • This can be a sound pattern rule (like syllables, rhymes, etc)
    • Or whatever crazy rule your class/group comes up with.
  • once the rule is guessed or the player gives up, play again!