Kinesthetic intro to Pascal’s Triangle

Question in an online discussion:

I’m trying to figure out how to kinesthetically demonstrate Pascal’s triangle with my precalculus kids

My response:

I do a lot of kinesthetic activities in geometry and algebra, but haven’t yet thought about this particular topic that way.

Here’s a possibility:
– Have students stand in a triangular number arrangement
– Give the top student a penny.
– Give the top student another penny, and have him/her give the pennies, one each, to students in the next row
– Explain that this is what everyone will have to do: “when the time comes, give half of your pennies to each of the two students in the next row.”
– Now give the top student two pennies, which get passed down to the next row, and from there to the next row, which gets us to 1 2 1
– Ask that row how many pennies they have altogether. Give that many pennies to the top student. Those should trickle down to 1 3 3 1.
– Ask that row how many they have, and give that many pennies to the top student.
– etc.

You get the powers of two pattern for free.

(Disclaimer: I have not yet actually done this with students. If someone tries it, let me know how it turns out!)

–Henri