[note: sorry for the quick write up -> only had 30 min before having to get out the door. Don’t be fooled by the short writing up – this is an amazing topic for kids to explore!]
I saw this amazing tweet from Leo Stein two weeks ago:
Some work travel prevented me from using it in a project with the boys, but I’m back from the trip now. Today was the day to dive in.
We have played with these ideas before – see the collection of project here:
One of the most enjoyable parts of that week was printing the paths the the roots of 5th degree polynomials took as we played:
Those pretty prints convinced me that playing with roots of polynomials can be a really fun project for kids.
I started the project today by simply talking about polynomials. My kids are in 6th and 8th grade and have heard about polynomials, but haven’t heard enough for us to just dive right in to Stein’s program. So, here’s the 5 min introduction to the project:
Next we dove in to Stein’s program. I used a 2nd degree polynomial as an example of how to play with the program. From the beginning, the movement of the roots as you move the coefficients was really interesting to the kids.
I had the boys play with the program off camera for about 10 minutes. Here are some of the things that they thought were interesting:
My younger son went first – simply describing what you are seeing is a good exercise in using mathematical language for a kid:
My older son went next – the movement of the roots reminds him of gravity and planets:
A long term goal of mine is to find a way to explain to kids (maybe high school students) why a 5th degree polynomial cannot be solved in general. The ideas from these “jugging roots” programs feel like the right path. The movement of the roots as the coefficients change is simply mesmerizing!
Mike's Math Page 
Have you tried reading _Abel’s Theorem in Problems and Solutions_, based on a series of lectures Arnold gave to a group of high school students? https://www.amazon.com/dp/1402021860/ https://www.mathcamp.org/2015/abel/abel.pdf
I believe your earlier root juggling experiments (and maybe this new tool as well) came about because of a chain of links that ultimately led back to that book as a source?
There definitely was a reference to a topological approach by Arnold that was explained in a YouTube video. I saw the video but missed the book. Thanks for pointing it out. Will order it today.