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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