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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Kitty in a Binary Tree

If you must translate, then here it is:

01010100 01101111 00100000 01100011 01100001 01110100 01101110 01100001 01110000 00100000 01101111 01110010 00100000 01101110 01101111 01110100 00100000 01110100 01101111 00100000 01100011 01100001 01110100 01101110 01100001 01110000 00111111 00100000 01010100 01101000 01100001 01110100 00100000 01101001 01110011 00100000 01110100 01101000 01100101 00100000 01110001 01110101 01100101 01110011 01110100 01101001 01101111 01101110 00101110