Six years ago, I released a lesson called Will It Hit The Hoop? that broke the math education Internet. (Not a big brag. It was a much smaller Internet back then.)
I think the core concept still works. First, students predict whether or not a shot goes in the hoop based on an image and intuition alone. Then they analyze the shot using quadratic modeling and update their prediction. Then they see the answer. For most students, quadratic modeling beats their intuition.
The technology was a chore, though. Teachers had to juggle two dozen different files and distribute some of them to students. I remember loading seven Geogebra files onto student laptops using a thumb drive. That was 2010, a more innocent time.
So here’s a version I made for the Desmos Activity Builder which you’re welcome to use. It preserves the core concept and streamlines the technology. All students need is a browser and a class code.
Six year older and maybe a couple of years wiser, I decided to add a new element. I wanted students to understand that linears are a powerful model but that power has limits. I wanted students to understand that the context dictates the model.
So I now ask students to model this data with a linear equation.
Then I show students where the data came from and ask them to describe the implications of their linear model. (A: Their linear ball goes onwards and upwards forever.)
And then we introduce parabolas.