I’m a huge fan of Dan Meyer’s Will It Hit The Hoop lesson. Looks something like this:
Show them this video:
There’s an obvious question here, and all answers are valid. Every kid has an opinion on whether the shot will go in.
Motivating quadratics is a bit more tricky. I’m not sure what questions are most useful for getting a student to say, “hey that looks like a parabola”, but I’m not sure that’s the best use of time — we’re going to give them quadratics anyway. I think we can jump pretty quickly into the modeling.
Dan’s page has a ton of great resources — he has seven different takes, shots from different distances, some that go in, some that don’t. His takes come with a half-video, like above, a full video showing whether the shot goes in, a .png file for the image, and a Geogebra file to model. Geogebra looks like this:
Graph is interactive; students play with it to predict whether the shot will go in.
My thoughts: These were fun to make. I’m not sure how they fit into the lesson — the Geogebra files were pretty great to begin with.
Advantages with Desmos:
It’s easier to drag around two points on a quadratic — low floor to introduce students to the topic
Our Chromebooks don’t have the Geogebra app on them yet, and I’m not sure if it will ever happen
Web pages are easier to distribute to students than .ggb files
Advantages with Geogebra:
The picture is clearer — I couldn’t get the high-quality image to load in Desmos
Using sliders to adjust the vertex and a-value reinforce deeper quadratic concepts
Students can see the equation
I’m torn: I really want to use this lesson early on in quadratics to give them some meaning in context, and help students gain an intuition for what quadratics look like. To me, that suggests Desmos — vertex form is tough, and would require a lot more knowledge for students to be successful. But I can’t help thinking that the Geogebra version is hugely valuable for the parts of a quadratic, and how they relate to each other. That seems like a concrete goal for the lesson — where the Desmos version is more like “go play with quadratics and understand them better”.
I’ve got a few months to decide. Excited for it either way.