Working through a Bayes’ Theorem problem thanks to help from Julia Anker

My younger son is working through an introductory probability and stats book this school year. This week he came across a problem in the Bayes’ Theorem section that really gave him a lot of trouble. I was a little caught off guard by how much difficulty he was having with the problem (and how little my help was helping!) but then we got a great bit of luck when Julia Anker posted her solution to the problem:



I had my son work through Anker’s solution yesterday and today we talked about the problem. Here’s the introduction to the problem and to his thoughts about Anker’s work:

At the end of the last video I had my son pick two of the regions in Anker’s diagram to see if we could verify the calculation. Here’s the calculation for the first region:



Here’s the calculation for the second region and an overall wrap up on the problem:

I’m extremely graful to Julia Anker for sharing her solution to the problem. It is an odd problem to have spent 5 days on for sure, but thanks to the extra help my son was really able to turn the corner and understand the problem. Math twitter is the best!

Day 2 with a neat geometry puzzle that Catriona Agg shared

Yesterday we did a project on this geometry problem shared by Catriona Agg:



I also shared the problem on Facebook and a friend from college shared a solution that I’d not seen before (though looking back at Catriona’s twitter thread, it is there . . . . of course!). So, today I decided to take a 2nd day with the problem and have my son look at this new solution.

But I started by having him explain the “power of point” solution I shared with him yesterday just to get warmed up:



Next I set up my friend Raf’s solution to see if my son could solve the problem using this clever idea:

Finally, since the solution with the full inscribed circle depends on a geometry formula relating the area and perimeter of a triangle to the length of the radius of the inscribed circle, I asked my son if he could prove that formula was true. It took him a minute to find the idea, but he was able to construct the proof:



I was happy to be able to share three different solutions to the problem that Catriona shared. It definitely made for a fun little weekend geometry review!

Having my younger son work through a neat geometry problem shared by Catriona Agg

Yesterday Catriona Agg shared a nice geometry problem on Twitter:

I thought this problem would be a great one for my younger son to work through, so I asked him to give it a try this morning. Here’s how he explained his work:

Usually when I share one of Catriona’s problems I ask him to go through the twitter thread to pick out one of the cool solutions. We took a different approach today as we’d talked about “power of a point” a few weeks ago and I wanted to show him how that idea could be used to solve the problem:



I really like this problem and especially like how different solutions bring in different parts of high school geometry. Thanks (for the 1,000th time!) to Catriona for sharing a great little puzzle 🙂

Playing with “zonish polyhedra” and the icosidodecahedron

Yesterday I stumbled on George Hart’s website and found some neat ideas to play around with using our Zometool set:

https://www.georgehart.com/virtual-polyhedra/zometool.html

https://www.georgehart.com/virtual-polyhedra/zonish_polyhedra.html

After seeing these pages my younger son and I built one of the models and talked about it:

Today we explored the shape a bit more by building an icosidodecahedron and comparing it to the shape from yesterday:

Two wrap up today we looked at how spherical the icosidodecahedron is. I would have like to do the same exercise for the “zonish polyhedra” we were look at, but I’m not sure how to calculate the volume of that shape.

This was a really fun project – it is absolutely amazing how easy it is to explore 3d geometry with a Zometool set!