SWBAT fit a quadratic function to an image of projectile motion and use the model to make predictions.

Objects launched into the air follow a curve that can be described with a quadratic function. Modeling with a quadratic function allows us to predict the path of the object.

20 minutes

To begin the discussion of quadratic modeling, we watch this video about projectile motion in football. Its a little bit dated, but its a good visual introduction to projectile motion that gets the attention of the athletes in the room [MP4].

I also have a Warm-up worksheet for the students to complete.

50 minutes

I have used Dan Meyer's Will it Hit the Hoop? series as a modeling activity many times in my classroom and find that it is always very engaging for students. This lesson follows Dan Meyer's "3-Act" format, which includes an introductory video, a modeling activity, and a "reveal" video that lets students know if the model they selected was effective in determining the outcome.

In the past, I have used the Nspire calculators as the modeling platform, importing the image into a graphing page and instructing students to fit a function to it. However I recently found a blog post by Karl Fisch, who remade the activity as a Google Doc that links to Desmos, a beautiful, free graphing utility that is web-based. I now use this Desmos version of the activity because students can access it even if they do not have NSpire calculators.

For this modeling activity, students need the following:

- internet access through a tablet or laptop so that they can access the Google document Basketball Quadratic Activity from my Edmodo site.
- a Basketball Activity Record Sheet sheet for recording their predictions and parameter values

There are seven different basketball shots to work with. For each shot, student follow the Three-Act format. We work through the first shot together, as outlined below.

**Act 1**: show the video, halftake1 of the partial shot, which cuts off before the ball reaches the basket. Ask student what questions they have about the scenario.

**Act 2**: model the shot using an image embedded in the graphing utility, Desmos [MP5].

**Act 3**: show the "reveal" video, fulltake1, and let students see if they correctly determined whether the ball would go in the basket or not.

After pausing for questions, students get their laptops or tablets and choose a partner if they wish. If they work with a partner I insist that they take turns with the modeling part of the activity, with one person completing the even numbered shots and the other person completing the odd numbered shots. At the end of the period, I collect the record sheet from students.

Some students will need assistance with the technology aspect of this assignment because they are working with multiple applications, some of which are new to them. For this reason I use the 3-Cup System to make sure students are getting the support they need to move forward.

The primary goal of this activity is help students understand the power of using a mathematical function to predict future events [MP4]. This is also a great activity for mathematical communication because students naturally want to talk about their predictions based on the model [MP3].

10 minutes

When 10 minutes of class time remain, I ask students to return laptops and return to their desks. We recap the activity, with students sharing challenges they ran into and whether they enjoyed the activity. The homework for the evening, Projectile Motion Worksheet, asks students to summarize how the parameters in the algebraic form of a parabola must be altered to make the parabola change shape/position in specified ways. This worksheet also includes two projectile motion problems.