A neat logarithm example for kids thanks to Chanda Prescod-Weinstein and Bruce Macintosh

A saw a really neat twitter thread last week thanks to a re-tweet from Chanda Prescod-Weinstein:

The thread explained why thinking about the (astronomical) magnitude of an object moving through a telescope’s field of view is a little difficult. It was neat to learn that something I didn’t realize was hard is actually pretty hard (though it feels like basically everything in astronomy is like that!), but another thing that jumped off the page for me in that twitter thread was that it was an excellent example to show to kids learning about logarithms.

For reference, here’s the Wikipedia page we used in the project to learn about the concept of magnitude and also get a few examples:

Wikipedia’s page on Magnitude

My younger son (in 7th grade) is just learning about logarithms now and my older son (in 9th grade) has a bit more experience with them. We started by talking about the relative magnitude formula and working through a short calculation to show why the number 2.5 shows up in the formula:

Next we looked at the Wikipedia page linked above to get some examples of magnitudes of a few objects we recognize:

Now we talked through Bruce Macintosh’s twitter thread. I wanted to go through the thread carefully to make sure the kids had a basic understanding of the concepts he was discussing (arcseconds, for example). We talked about some of the calculations, but did not do any calculating ourselves in this part. One question for the kids here was why did Macintosh use a + sign in his formula when the Wikipedia page has a – sign in the formula?

Finally, we did the calculations and found the answer to the mystery of the + and – sign from the last video. Happily, we match the answers from Macintosh’s thread:

This project was really fun. It was a really happy accident that just as my younger son was learning about logs a neat (and “new to me”) example of where logs are used showed up in my twitter feed!


Sharing ideas about the black hole picture with a 7th grader

The first ever image of a black hole was released last week, and it blew my mind! For our Family Math project this morning I decided to try to share some of the ideas relating to that image with my younger son. He’s in 7th grade and had not heard about the announcement, so it was especially fun to hear his off the cuff reactions.

I started by simply showing him the picture and asking him to describe what he saw and if it looked like what he expected a picture of a black hole to look like:

Next we watched Katie Bouman’s Ted Talk video (published in 2017) about the black hole imaging project. This video is fantastic and great to share with students because the explanation of the project, and especially why the project is so difficult, is done at a level that kids can appreciate even if they can’t understand all of the details. Here’s that video:

After we finished watching, I asked my son to tell me some things from Bouman’s talk that caught his eye:

Next I had my son read through two great twitter threads from when the announcement happened last week. Those threads are from two physics professors – Katie Mack from North Carolina State University and Chanda Prescod-Weinstein from the University of New Hampshire. Those two twitter threads are here:

Here are two of the tweets from those threads that caught my son’s eye and his explanation of why he thought those two tweets were interesting:

Now I had my son play with a on online program that Leo Stein made a few years ago that shows the amazingly beautiful paths light can take orbiting a black hole. You can find the program here:

Unfortunately our camera was having a strange fight with the computer screen at the beginning of this video, so I cut that part out. Because of that cut the video starts mid conversation, but you’ll still be able to see that Leo’s program is really great to use with kids. I love his comment at the end: “Black holes seem pretty mysterious and neat and have weird properties.”

Finally, I showed him a picture from one of the papers about the black hole image that was published last week. The link to the paper with the image is here:

Here’s our quick discussion about that image and what my son thought about it. Talking a little bit about this image can help younger students see and understand some of the statistical work that went into producing and checking the image:

It was really incredible to see the announcement of the black hole image last week. It is equally incredible that so many people in the physics community take time to share their ideas about discoveries like this with the public. I’m super grateful for the public-facing work those people do because it makes sharing new discoveries with kids possible (and fun!).

Exploring a fascinating idea from special relativity – Penrose-Terrell rotation – with kids

I saw some really neat tweets from John Carlos Baez and Greg Egan on Penrose-Terrell rotation last week:

Even though even the most basic ideas from relativity are far outside of what kids can grasp, I thought it would be fun to share these animations with my younger son. The animations in the above tweets are definitely something that kids can appreciate, and I was excited to hear what my son would have to say.

So, I started out the project today asking my son to describe anything he knew about relativity and then what he thought he’d see if a cube passed by him really fast:

Next we talked about some simple ideas from relativity and what impact those ideas might have on a cube passing by. Also, since he’s just starting to learn about square roots and quadratics in school, I showed him the Lorentz contraction formula and we did one simple calculation:

Finally, we went to the computer to look at the tweets and animations from John Carlos Baez and Greg Egan that I linked above. As always, it is really fun to hear a kid react to and describe ideas from advanced math (and physics!):

Having kids play with the Binary Black Hole explorer made by Vijay Varma, Leo Stein, and Davide Gerosa

Last night I saw an incredible tweet thanks:

Here’s the link in the tweet just in case WordPress doesn’t display everything properly:

The binary black hole explorer

The link goes to the “Binary black hole explorer” made by Vijay Varma, Leo Stein, and Davide Gerosa, and it is one of the most amazing computer visualizations I’ve ever seen!

Even though the math and physics going in in the background is way way way too advanced for kids, I thought it would be fun to hear them describe what they were seeing. Imagine having the opportunity to see simulations of rotating black holes when you were in 7th and 9th grade!!

My younger son went first:

My older son went next – we’ve just finished up the section in his calculus book on parametric equations and polar coordinates, so I thought he’d find these simulations to be especially interesting:

I loved showing these simulations to the boys. Even if they can’t totally understand what’s going on, it sure is a nice peek at what can come down the road if they find physics to be interesting.

And, as always, it is so fantastic to see scientists sharing amazing work like this on twitter!

Using an idea from one of Katherine Johnson’s NASA technical papers to introduce polar coordinates

Yesterday we did a fun project on parametric equations and touched on the motion of planets at the end:

Playing with parametric equations in Desmos

Even though the discussion of planetary motion in the last project wasn’t even close to a complete picture, the kids seemed pretty interested in it, so I continued with that idea today. The goal for today was to show them why the ideas we talked about yesterday weren’t quite right and how we could use polar coordinates to study the same ideas.

The main idea I drew on for today’s project came from one of Katherine Johnson’s technical notes on NASA website:

Screen Shot 2018-11-11 at 12.01.17 PM

The link to that paper is here:

NASA Technical Note D-233 by T. H. Skopinski and Katherine G. Johnson

and the specific equation I’ll be using from that paper is equation 1a which gives an equation for an ellipse in polar coordinates:

Screen Shot 2018-11-11 at 12.01.37 PM

I’ll also be drawing from some lecture notes on planetary motion I found via a google search:

Richard Fitzpatrick’s lecture notes on planetary motion on the University of Texas website

I started the project by introducing polar coordinates – sort of a high level conceptual introduction for my younger son and a few more details for my older son:

Next I showed the them the polar coordinate description of an ellipse from the Katherine Johnson paper and how if we applied the velocity and acceleration ideas from yesterday that we’d see the acceleration wasn’t always directed at the same point:

Next we looked more carefully at the movement around the ellipse and (after a while) saw that the line from the ellipse back to the origin was moving with a constant angular velocity.

The boys were able to explain that the movement of planets in an elliptical orbit probably wouldn’t have a constant angular speed:

Finally, we used the paper from the University of Texas to explore the ellipses corresponding to the orbits of various planets.

Definitely some neat ideas to share with kids and also a fun way to bring some important pieces of math history to life!

An amazing visual / math project for kids I learned from Jessica Rosenkrantz

Last week I learned about an incredible fluid flow project from Jessica Rosenkrantz. I don’t want to give away the delightful surprise, so I’m not going to share the original tweets, but here is RosenKrantz’s pinned tweet – check her timeline for tweets on June 24, 2018 to see the inspiration for this project (and to see the idea we explore in today’s project executed to perfection):

Also, here are two other projects we’ve done with her work at Nervous System:

The puzzles and everything else from Nervous System will blow your mind!

Using the Infinite Galaxy Puzzle from Nervous System to talk topology with kids

For today’s project you need a little bit of paint (or s similar liquid), and two sheets of glass. Be careful doing this project with young kids – my kids are 12 and 14 and I thought they’d be able to handle the sharp glass themselves with gloves.

You spread out a bit of paint on one pane of glass, put the second pane on top, and then pull the two panes apart. What shapes do you expect to see in the paint after the panes are separated?

My younger son tried it out first:

My older son went second:

I think this is an amazing project to try with kids. Hearing what they think will happen and then hearing how they react to and describe what happens is really fun!

Struggling through an AMC 8 problem

My younger son has been practicing for the AMC 8. This week we’ll be going over a few problems here and there that give him trouble. The problem from the practice test today was #16 from the 2016 AMC 8:

Problem 16

This problem really gave him some trouble – as you’ll see from his 5 min struggle below:

I was caught a bit by surprise over the difficulty he was having. It wouldn’t surprise me if the mistakes he was making were quite common mistakes for a problem like this, but I was stuck on what to do. So, I decided to show him one path that leads to the solution to the problem:

So, having shown him one way to solve the problem, I challenged him to find a different solution. Initially he struggled, but then he did something pretty clever:

I definitely struggle to see a good way forward when a problem is giving one of my kids as much trouble as this one was. Hopefully my son was able to see some of the important ideas in the problem after we talked through it in the second video. I really do like the solution he came up with in the third video, though, especially since it is more geometric and less reliant on calculation.