Week 46: Half-Square Triangles (Truchet Tiles)

If you are a quilter, then you will be a pro with this week’s activity. For the last six months my quilting mother lived with us through chemo and we watched her quilt her heart out. Now that she moved back to her home, I had to laugh because she would have been so much fun making these tiles this week – I should have done this sooner! So many traditional and historical quilts use these squares (a great segue into history – Underground Railroad, folk art, stories, family histories, etc.).

This week I encourage learners to actually sew some tiles, specifically half-square triangles. Another name for these squares is Truchet Tiles. These are tiles that are not rotationally symmetric. The tiles can create a variety of patterns and tessellations. Make some tiles and then play. (The reason I encourage sewing is that the problem-solving, process, and mistakes lead to so much learning.)

If sewing isn’t your thing, then I have a JPG file below you can print and play with. There are also tons of maker ideas for these tiles (Paint squares of cardboard, wood, felt, etc.). A piece of graph paper will also work (shade in half of the squares diagonally).

How to sew:

  • Iron the fabric that you wish to use.
  • First cut out 25 squares of Color-1 and 50 squares of a Color-2. (You may want to do 2×2″ squares for small tiles or 10×10″ for larger tiles.) You can also do 36 squares of Color-1 and 72 of Color-2. Do you see the ratio? NOTE: Cut these squares carefully (millimeters matter).
  • Next cut down the diagonals of 25 of Color-1 and 25 of Color-2 (The same amount of each color if you are doing more than 25 tiles).
  • Now, take one triangle of each color and place them face to face and sew them with a quarter inch seam (make sure your seam width is consistent for all of this work).
  • Iron the square you just made so that the seam is folded flat to one side and then place it on one of the squares of Color-2. Sew around the border to attach the half-square triangle to the square bottom.

  • Now cut the extra fabric, while squaring the tile (make sure you use a grid or corner to make sure it is square as you cut).
  • Repeat this for the other 24 tiles (or more if you so chose).

We also made draftboard versions of these tiles to play even more:

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Week 45: The Quincunx

This week learners can dive into probability through a quincunx (also known as a Bean Machine). Learners can make bean machines with building toys (Legos), pins and a cork board, or nails and wood (or other methods they devise (3d-printing, sculpture, etc)). Here is a template to use.(It’s a png and is also at the bottom of this page.) Make sure to size the printable to the size ball that you are using before you nail or pin.

What is fun about Quincunxes is that they show how possibilities play out. The idea is that every time a ball reaches a pin it has two possibilities: Left or Right. Learners can draw the possibility trees as an exercise to see how the distribution works. The middle columns have far more paths than the outer columns. The number of possible paths to a column is related to Pascal’s Triangle (or the Jia Xian triangle that was discovered much earlier).

Math is Fun has a tool to play with possibilities here.

One of my kids decided to continue to play with the pins:

Template:

Side note: I chose not to call it a Galton Board here because of the history of its inventor being a racist and coining the term for eugenics.

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Week 44: Conics, Orbits, and Projectile Motion

You don’t have to be in high school math to play with conics, orbits, and projectile motion. This week (or month) learners can play with projectile motion, orbits, and conics sections with the activities below:

1.) Slicing cones

  • Learners can mold cones with clay and slice to see the possible shapes. This will give circles, ellipses, parabolas, and hyperbolas.
  • Create a cone sculpture with an intersecting plane using paper, string, pipe cleaners, or other mediums.
  • Try John Sharp’s sliceform template.
  • Check out this Conics Geogebra tool by Irina Boyadzhiev.

2.) Observe parabolas through projectiles

  • Create a straw rocket (don’t aim it at someone) and take slow motion videos of their flight and observe the curve that is created. For a template and activity, go to NASA’s website here. Look at various launch angles and analyze the differences and similarities in curves.
  • Create a water balloon launcher with PVC pipes (or other parent/teacher approved apparatuses). Record their launches and analyze. (Water rockets are also fun.)
  • Play with a garden hose and the curves created by shooting water up into the air.
  • Play with the PhET simulator.
Rocket Launch

3.) Play with ellipses and circles through gravity

  • Use tacks and string to create ellipses (2 tacks) and circles (1 tack or compass). Create an abstract work of art with these tools.
  • Play with this gravity simulator by the NSTMF (really fun!)
  • Universe Sandbox is a program that costs money, but is excellent for playing with orbits and answering a lot of learners’ “what-if’s.” I love, love, love this tool!
  • JPL learning activities are here.
  • Use a large piece of elastic cloth and place weights in it. See if you can create orbits with marbles. We have found that a hula hoop works with swimsuit material. Here is a video as well.
  • Take time to get outside and observe the planets, comets, and astronomy that is with us every day.

There are so many other ways to play with these curves, so experiment, draw/paint, and enjoy.

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Week 43: Circles and Art

Circles are so much fun! This week I encourage learners to get out their compasses or a circle to trace and start making patterns on paper. Patterns with circles can start simple, but can also get really complex. You can combine your compass with a straight edge and get amazing patterns and tiles. Try intersecting circles and then placing your compass at intersections and adding more circles. Shading with markers, ink, or colored pencils can make beautiful stained glass-like mosaics.

Here are some ideas to play with circles and art:

  • The Metropolitan Museum of art has a great activity here to take a look at Islamic art and geometry.
  • Cut out some of your patterns to make a puzzle.
  • Use tissue paper and make a see-through design on wax paper.
  • Go big with string and chalk outside for your designs!
  • Dip the top of a can or cup in paint and use it to create circle patterns on boards or fabric.
  • Try playing with the negative space within the art – see how it changes the tiles and overall appearance.
  • Use a digital drawing or design app and play with color pallets and design.
  • Try adding details and embellish.
  • Play with the Girih app (costs money) from the Apple app store.
  • Play with an app: https://girihdesigner.com/.

I made tiles for my kids to play with and we’ve been having a blast:

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