Thanks, Dan, for your thoughtful analysis of this lesson!

I wanted to mention that there are three Rosenthal prize-winning lessons chosen every year. Of these three, mine was ranked second; so in the analogy of Academy Awards, perhaps mine won Best Director. The grand prize winner (Best Film) was some kind of divisibility rule game based on Uno. I'm very keen to see that lesson. The third prize winner (Best Screenplay?) was a game based on Sumo wrestling, where players use plane transformations to push their opponent out of a given space. I haven't read that one yet, but I did talk to the author.

I'll also mention that I have the mistake of launching this lesson by rushing to the second day of it too early, assuming that the intuition about a bouncing ball in a rectangle would lead middle schoolers to draw it's path on graph paper easily after 5 or 10 minutes of thinking about it. However, the distance from an intuition about a bouncing ball and the ability to reliably draw it on graph paper takes enough students a full class to practice with that the scaffolding of the first day is critical to the success of the lesson. That was a hard-won lesson for me.

It's a great activity! I got a lot of mileage out of it in my staff development days since it's a wonderful discovery lesson which turns on many aha moments. I was inspired to create a Scratch version. The link is in my blog entry: https://dmcpress.org/2020/04/01/an-online-math-activity-pool-paths/

Thanks, Dan, for your thoughtful analysis of this lesson!

I wanted to mention that there are three Rosenthal prize-winning lessons chosen every year. Of these three, mine was ranked second; so in the analogy of Academy Awards, perhaps mine won Best Director. The grand prize winner (Best Film) was some kind of divisibility rule game based on Uno. I'm very keen to see that lesson. The third prize winner (Best Screenplay?) was a game based on Sumo wrestling, where players use plane transformations to push their opponent out of a given space. I haven't read that one yet, but I did talk to the author.

I'll also mention that I have the mistake of launching this lesson by rushing to the second day of it too early, assuming that the intuition about a bouncing ball in a rectangle would lead middle schoolers to draw it's path on graph paper easily after 5 or 10 minutes of thinking about it. However, the distance from an intuition about a bouncing ball and the ability to reliably draw it on graph paper takes enough students a full class to practice with that the scaffolding of the first day is critical to the success of the lesson. That was a hard-won lesson for me.

It's a great activity! I got a lot of mileage out of it in my staff development days since it's a wonderful discovery lesson which turns on many aha moments. I was inspired to create a Scratch version. The link is in my blog entry: https://dmcpress.org/2020/04/01/an-online-math-activity-pool-paths/

Dan, will there be a Desmos Geometry curriculum coming up soon?