Having the boys work through another fantastic puzzle from Catriona Agg

Catriona Agg posted this geometry puzzle on Twitter this morning:

I had the boys work on the problem on their own and then talk through their progress.

My older son went first – his solution is along the same lines as most of the solutions in Catriona’s twitter thread, though is reasoning is pretty interesting to hear:

My younger son went next. He wasn’t able to find the solution on his own, but was able to get there while we talked about his work. I’m sorry that I forgot the camera was zoomed in on the paper here. I do zoom out a little over half way through. Hopefully the words are clear even if some of the work is off screen:

At the end of the last video my son had worked through the main idea of the problem. Here he finishes the solution and talks about what he liked about the problem:

As usual, having the boys work through one of Catriona’s puzzles made for a great project. I really liked the algebra / geometry combo that this problem had as I think that was great practice for my younger son. I also think the more intuitive solution my older son had shows how mathematical intuition develops as kids get older.

Talking through Chapter 2 of Jordan Ellenberg’s How not to be Wrong with my younger son

For a math project this month I’m having my younger son (in 9th grade) read a chapter of Jordan Ellenberg’s How not to be Wrong each day. The book is terrific if you’ve not read it.

Yesterday my son read chapter 2 and today I asked him to pick three things that he thought were interesting or just caught his eye.

The first was the way the Greeks thought about pi:

The next thing he found interesting was Zeno’s paradox:

Finally, we talked about some of the really neat ideas about infinite series in the chapter:

I doubt that we’ll do a project on every chapter, but there are so many neat ideas in the book so I bet we’ll get to have at least 5 fun discussions. The book isn’t really aimed directly at kids, but I think most of the ideas are accessible. It’ll be fun to see what he thinks the interesting ideas are!