Connecting yesterday’s probability project with a few old 3d geometry projects

In yesterday’s project we were studying a fun probability question posed by Alexander Bogomolny:

That project is here:

Working through an Alexander Bogomolny probability problem with kids

While writing up the project, I noticed that I had misunderstood one of the
geometry ideas that my older son had mentioned. That was a shame because his idea was actually much better than the one I heard, and it connected to several projects that we’ve done in the past:

Paula

 

Learning 3d geometry with Paula Beardell Krieg’s Pyrmaids

Revisiting an old James Tanton / James Key Pyramid project

Overnight I printed the pieces we needed to explore my son’s approach to solving the problem and we revisited the problem again this morning. You’ll need to go to yesterday’s project to see what leads up to the point where we start, but the short story is that we are trying to find the volume of one piece of a shape that looks like a cube with a hole in it (I briefly show the two relevant shapes at the end of the video below):

Next we used my son’s division of the shape to find the volume. The calculation is easier (and more natural geometrically, I think) than what we did yesterday.

It is always really fun to have prior projects connect with a current one. It is also pretty amazing to find yet another project where these little pyramids show up!

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