Part 5 of sharing Catriona Shearer’s geometry problems with my younger son

Yesterday we looked at this interesting geometry puzzle from Catriona Shearer:

My son took a pretty computational approach to the problem and the calculations gave him a little difficulty. Today my main idea was to share Ian Agol’s neat solution, but I wanted to review one piece of yesterday’s calculation with him as an arithmetic review:

Now we moved on to looking at Ian Agol’s solution (using the picture made by Greg Egan):

My son studied this solution and picture for about 10 min before we started the project. Here’s how he explained it:

I liked following up yesterday’s computational solution with this terrific non-computational one.

Part 4 of Sharing Catriona Shearer’s geometry puzzles with my younger son

I’ve been sharing some of Catriona Shearer’s geometry puzzles with my younger son lately. The idea is for him to try to solve the problem and then explain a solution from the twitter thread about the problem.

The puzzle we looked at today was posted by Shearer on April 10th:

Watching him work through the solution is a great example of what a kid learning math looks like. His approach is very computational – sometimes the calculations can sort of overwhelm the geometry ideas for kids and that’s sort of what happens here:

The solution from the twitter thread that he liked was from Brenda Meshejian

He does a nice job of explaining this solution:

Part 3 of sharing Catriona Shearer’s geometry puzzles with my younger son.

This is third in what I hope will be a long series of projects taken from Catriona Shearer’s geometry puzzles. You can find the other projects by searching for her name on the blog.

Today’s puzzle is from February:

My son was able to solve this one and he walks through his solution below:

After he solved the problem I had him find a solution in the problem’s twitter thread. He picked the solution from Rich Holmes:

He presents this solution below and explains why he thought it was interesting.

We also got two phone calls (updates on the corona virus from our local government) during the filming – sorry about that distraction.

I’m really enjoying these “present your solution / present a second neat solution” projects. Catriona’s puzzles and twitter threads are fantastic for exploring geometry with kids.

Using Catriona Shearer’s geometry puzzles with my younger son day 2

I’m going to spend a few – and hopefully many – days reviewing geometry with my younger son with the help of Catriona Shearer’s amazing geometry puzzles. You can follow along with our progress by using the Catriona Shearer tag in the blog or just searching for her name.

Today’s puzzle was from December:

My son was able to solve this puzzle and his solution is in the video below. I’m always really happy to see how careful he is with the details as he works through problems – this trait did not come from me!

After he solved the problem we went to the twitter thread to find a solution (hopefully different from his) that he thought was interesting. As with our first project from last night, he chose the solution from Nèstor Abad:

Here’s his presentation of Abad’s solution. Again, I’m happy that he was make to make (and understand) the details of the arguments with similarity and congruence:

I’m really happy with how this project went today – looking forward to another one tomorrow!

Using Catriona Shearer’s puzzles with my younger son

Catriona Shearer has been publishing amazing geometry puzzles for years now. We’ve used a few of them for projects in the past, but I thought that using the puzzles and some of the clever solutions presented in the twitter threads would make for a nice geometry review for my younger son. Although these puzzles can be pretty challenging for kids, I’m hoping that the combination of thinking about them and seeing clever solutions will make for a great series of math activities.

We started with the puzzle from Feb 29th:

This puzzle gave him some trouble, so instead of presenting a solution I asked him to talk about it and some of the ideas he tried:

Next I asked him to find a solution in the twitter thread for the problem that he liked and thought he could explain. He picked the solution from Nèstor Abad:

Here he explains that solution:

Catriona’s puzzles are so great. I’m definitely interested to try out a few more of these puzzles with my son and see how the combination of trying to solve them on his own plus explaining a neat solution goes.