This week, right before the start of another school year, one of our teachers asked me to come in and think through a different way of approaching the Integrated II restart class. First off, a big hat tip to her for recognizing the need to do something new. We spent an hour going back and forth with ideas about how to introduce the quadratics unit, the first thing the students will be doing this year.
Well, here's what we came up with, and we're all ears on more ideas:
On Day 1, students will come in and play with this model that she built in Bootstrap, then do a Notice and Wonder activity. The goal is to remove the math for as long as possible. After all, the students have already seen quadratics, so what makes you think they want to see them again? Instead, we are going to switch it up and remove the math. Nothin' to see here, kids, just a model of a rocket.
On Day 2, students will play with a similar model that gives a bit more context, taking them into space and out of it as they launch a rocket. Again, they will do a Notice and Wonder activity without a whole lot of heavy lifting in the math gym.
On Day 3, students will play Quadratipult, an activity on Desmos Activity Builder. When it gets intimidating, students will have the standard form of a quadratic written on the board so that students can easily locate where the a, h, and k values will go. Prior to the end of class, students will get time to discuss what happens when they move a, h, or k, and how they can generalize the movements. This will help for later.
On Day 4, students will receive one sheet of chart paper, some markers, and a set of instructions. In groups, they are to design a castle with targets.
- The 5 point target needs to be 20 square units
- The 10 point targets need to be 10 square units
- The 20 point target needs to be 5 square units
They will also work to calibrate a marble launcher. How far does it go? How high does it go at its highest point? How far out until it starts to fall?
With that information, groups will work in the Desmos calculator to design their calibrated path through a mathematical model (oh hey, that standard form of a quadratic comes back!)... Yes, four days until students are really doing math, but not much.
On Day 5, WE GO TO BATTLE! But really, groups will work with their models and the marble launchers to compete against other groups to get as many points as possible. They will have 5 shots, so there is not time for calibration or mistakes; having a mathematically-sound model will be a significant advantage.
For example, the 20-point target is 11 inches off the ground... where should we place the launcher so that we nail it on the first attempt? You'll need to move it closer, but how much closer? That's where the math comes in handy. On Day 5, the students are bench pressing with quadratics, but they've been engulfed by them for the four days prior.
The assessment of student progress will be how effectively they manipulate their calibrated model. The game? The game is just a fun application and a distraction from what I can only assume to be 9 years of a rocky mathematical journey.
On Day 6, we bring in a variety of other models that students would need to use their calibrated function to reach. Could you shoot a mortar over a 20 foot building, but 12 feet away? How does that look different than the need to clear a 9 foot building for a target 24 feet away?
By now, we have spent a lot of time with quadratics and, while the students know we are math-ing pretty hard, they aren't downtrodden with one problem after another. Hopefully this much time playing will make it easier to introduce the vocabulary, most of which has been introduced in previous years. Students will label their functions with Vertex, Axis of Symmetry, Roots, and Maximum/Minimum. From there, we will be able to have more relevant conversations about each.
With all that said, we are open for ideas. How have you run a repeat unit on quadratics? What questions do you have for us?
Happy "Better Intervention" Fishing