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