Catriona Shearer posted another terrific geometry puzzle today and I had my son work on it today for a project. Here’s the puzzle:
Here’s how he explained his solution:
Next I had him look through the twitter thread following the problem and find a solution that he liked. He chose this beautiful solution from David Andriana:
Here’s how he explained Andriana’s soluiton:
One of the really fun things about using Catriona Shearer’s puzzles with my son is having him explain neat solutions from twitter threads. His work with Andriana’s solution today is a great example of the educational value that Catriona’s twitter threads have for kids!
We’ve been having a ton of fun for the last few weeks working through some of Catriona Shearer’s amazing puzzles. Last week I saw her share an puzzle from 2018 when she was asked for some of her favorites. Here’s that puzzle:
I thought this would be a great one for my younger son to try, and he was able to solve it.
His solution is a bit computational, so we broke his explanation into two pieces. Here he explains his approach to the problem:
With his approach drawn out now, we moved on to the computations:
Now we took a look at the twitter thread from the original problem to look for a solution that son liked. He chose the solution from Sanjay Singh
This solution was similar to how my son solved the problem, but that gave him a nice opportunity to understand the problem a bit better. Here’s his explanation of Singh’s solution:
I’m really happy that Catriona shared this problem again – it is terrific. It was also great to be reminded how long she’s been sharing these puzzles – it is going to be a long time until we get through all of them 🙂
Over the last month I’ve seen several great twitter threads on ellipses. Sort of a strange coincidence, I guess. Today I finally got around to sharing them with the boys.
We started with this tweet from Lucas Vieira. I’m having a fight with WordPress on the embedding of this one – the tweet we are looking at is the “ballistic ellipse” one at the bottom.
Here’s what the boys thought of the ideas in the animation:
Next we moved on to a post from Greg Egan that was inspired by Lucas’s post:
The kids had a tough time explaining what they were seeing here, so we talked about this picture for a little bit longer than usual:
Now we moved on to Jacopo Bertolotti’s Physics Factlet #216 on 1/r^2 orbits. This animation helped me make sense of a point about General Relativity that I’d heard, but never really understood.
The boys thought the animation was fascinating:
Finally, since Jacopo share his Mathematica code, we took a look at the program. The boys were surprised by how short it was. After looking at the code for a bit we changed some of the parameters and got a fun surprise:
I love that so many people share their amazing work on Twitter. Looking at these animations was a fun way to share a bit of math and physics with the boys this morning!
Last week I saw a terrific twitter thread from Natalie Dean, who is an assistant professor of biostatistics at the University of Florida:
Today I used the ideas in Dean’s tweets for a project with my kids. We started by taking a close look at the first example to make sure that we understood all of the concepts and calculations:
Having talked through the concepts in the first example we were now able to take a detailed look at Dean’s second example. This example is really helpful in understanding why sensitivity and specificity are such important ideas:
Now I asked the boys what they thought we could learn from these two examples. Then we looked at Dean’s conclusions:
Finally, I asked the boys to create an example that was similar to Dean’s example – so similar numbers of positives in the test, but with different percentages of the population having the disease. They spent about 10 min playing around in Mathematica and found a good one. Here they talk through what they found (sorry about the tilt in the camera – not sure what happened!):
When I saw Dean’s twitter thread, my hope was that the ideas would be accessible to kids. I think both of my kids were able to learn some important ideas from Dean’s twitter thread, so I’m extremely grateful that she’s taking the time to make these ideas accessible to the public. Definitely follow her to keep up with the latest ideas and research about the corona virus.
Catriona Shearer posted a really nice geometry puzzle today:
I thought this one would be a good challenge for my son and he was able to solve it, though he had a few false starts. He explains his thought process from start to finish here:
After he finished his explanation I had him look at the twitter thread and he liked the solution from M B Patey:
Here he explains that solution and why he liked it:
I feel like a broken record, but I love these problems. Today’s was at exactly the right level for my son and made for a great project!
Catriona Shearer shared a great puzzle this morning.
This one is a bit more difficult than others I’ve shared with my son lately, but he wanted to give it a try. He wasn’t able to solve it, but we talked about the progress me had and the ideas he had:
Next we looked at a geometric solution given by Phillip Gibbs as well as comment to Gibbs’s tweet from Dr. Rick. These tweets showed a really clever geometric solution to the problem.
Here’s what my son had to say about these solutions:
Finally, I showed my son how to see that the triangles in the picture were, indeed, 30-60-90 triangles. This is a little bit of algebra, but I thought it would be important for him to see why those triangles were there.
I really love this problem and was happy that the thread had some great geometric solutions. Even though my son wasn’t able to get this one solved all the way, I think he learned a lot working through it.
Today Catriona Shearer posted another great geometry puzzle:
My younger son was able to solve this one and he explains his solution here:
After he finished his explanation we looked at the twitter thread for a solution he liked and he chose this one from @ricardpe:
He explained that solution here:
This is our 10th project in this series. It has been really fun to have my son solve the puzzles and then explain a solution from the twitter thread. I’m really enjoying reviewing geometry with my younger son using Catriona’s ideas!
For part 9 of our series with Catriona Shearer’s geometry puzzles, we used the puzzle that she posted this morning:
My son was able to solve this problem and here’s how he explained his solution:
After he talked through his solution we went back to the twitter thread for the puzzle and he found a solution he liked:
This is actually the 2nd solution we’ve used from Amaresh G S – here’s how my son explained it:
Another great puzzle – I’m really enjoying this series!
Yesterday we played around with some introductory ideas in Stephen Wolfram’s Physics Project. Today we moved on to looking at the 3d examples in the project. We were entirely on the computer today looking at shapes, so this project was more about experiencing the ideas rather than diving into the details. Still the kids had a great time.
Here’s how the introduction to the 3d shapes went:
Now I had the boys each try to produce one of the 3d shapes using a rule they made up. This part of the project turned out to be a bit harder because of our lack of familiarity with how the underlying details work. Still, though, they produced some neat shapes and talked about them here:
Despite the difficulties today, I’m excited to play with this project a bit more. The math ideas here are something that I think the kids aren’t going to see anywhere else, and I love the lessons about building complex shapes from simple rules.
I learned about Stephen Wolfram’s Physics Project last week from a Steven Strogatz tweet:
It looked like something that would be really interesting for kids to see, so I spent a bit of time diving in. This morning I took a shot at introducing some of the basic ideas to them and they were fascinated by what they saw.
I started by talking about directed graphs – the introductory ideas are definitely accessible to kids (sorry this video is a bit out of focus – I forgot to check the focus before we started today):
Now (off camera) we constructed the next step in the sequence of graphs Wolfram is studying. My younger son explains our work below and my older son shows a slightly different way of thinking about it that he thought might be more illuminating.
Now we went to Mathematica to explore a bit. Wolfram has made his code available, so exploring his ideas at home is really easy as long as you have the latest (as of April 2020) version of Mathematica. Just to be clear, I’m using their code and don’t yet fully understand how it all works. I was able to understand it well enough to play around, though. It was fascinating to see how the graphs changed when the boys changed the rules a bit.
But the most important thing I think is in this video is just how interested the kids were in these amazing shapes.
Finally we looked at a selection of graphs made from random rules. Again the boys were fascinated by these shapes and seemed to really enjoy thinking about them.
This project was incredibly fun – hoping to find other ways to share these ideas with the boys.