It’s not often I get my kids yelling and hollering about math, but if the Basketbola project was anything, it was fun.

From a math/content/standard perspective, the biggest thing the project did was visualize the result of a negative leading coefficient of a quadratic. While I hoped for a little more, I’ll take it for the first time doing the mini-project. In the future I’ll probably flesh-out some of the other properties of parabolas and address those properties a little more directly. After about 25 minutes, matching the graph to the flight of the ball was a little repetitive, though still interesting enough to hold a sixteen-year-old’s attention.

This is probably the biggest lesson/activity I’ve put together this year. Thanks to today’s snow/ice day, what was going to be spread out over 3 days will now have to be done in two. I think it’ll be doable.

First, I’ve made it a contest. There are nine total videos of people shooting a basketball. Students will watch Act 1 for each shooter and make their prediction. Does it go in, or not? Correct predictions are worth 3 points. During Act Two they’ll have the chance to change their prediction, however it will cost them 1 point. If they are wrong, they receive no points.

Act One

I’ll go through showing the nine Act Ones, as seen below. Students will make their guess. Very low entry bar. Anyone can make a guess.

Act Two

Then we’ll go into Geometer’s Sketchpad and start modeling parabolas. Here is where the competition gets interesting. Once students model their equation, they may decide their original guess was off. That’s fine, but it’ll cost them a point if they want to change. That should provide a little incentive to be as precise as possible in their modeling.

This screenshot is in Geogebra, but my students will be working with Sketchpad, which should allow things to be a little more intuitive. I’ll set them up with a standard parabola in vertex form: y = -0.5(x – 2)^2 + 2. That should be plenty to get them going and graphing.

As they progress through the shooters, they get more difficult. One picture will have a random three balls in the picture. One picture has three balls very close to each other, right after they leave the shooter’s hand. One shooter hits a bank shot which should really throw people off. I’ll have them record their equations and record whether or not they want to keep their prediction, just to keep them honest.

Act Three

The next day we’ll come back and reveal the results.

It’ll be interesting and fun to see how much they get into it, especially when the bank shot throws the entire class off. We’ll take a few minutes to discuss the investigation questions:

Why is the value of a negative? What happens if it is positive?

Describe what happened when you changed a. What happened when you made it smaller? Bigger?

Describe how h and k changed. What does the point (h, k) represent? What does the line x = h represent?

As for the contest? Whoever wins gets to add their video to the library for next year.

Sequels

There’s so many other things to do with this! I could use any other form of a quadratic as the focus of the lesson (or all of them). The sequel I like the best is this:

In fact, this is what I hope we get to if the students are able to model the first nine shots quick enough. Had I still had 3 days instead of two, I’m sure we could have. This is a pretty obvious way to show, graphically, that having only two points is not sufficient to graph a quadratic function.

You could also talk about other curves instead of parabolas, too. I’ll be very interested to see what other questions come up in class.

Since grading my exams, I’ve been thinking of ways to detach my students from their calculators. Their reaction to any kind of arithmetic is to jump, dive, kick and scream for their calculator. I thought “I’d just like them to play Monopoly for a couple hours and not use their calculators to compute the change.” Now I have another reason:

The table shows how many opponent rolls it takes, statistically, for a player to break even on their investment in a property. If you go to the site and read the comments, you’ll see many people provide anecdotal confirmation of what the statistics say. I’m starting to think that this could be a fun way to introduce probability – especially if I can join in on the fun, lay the smackdown, and say “why am I so good at Monopoly?”

The table says that your fastest way to return investment is to throw three houses on the St. James/Tennessee/New York group. This seems to be the kind of thing that students should be able to easily understand why its true:

It is not the most expensive color group

It is not the cheapest color group

It is a second color group (on a board side, meaning it earns higher rents for the same improvement costs)

It is 6-9 spaces from Jail.

The last point is the one I can see easily transitioning into probability from. What is the most often roll of two dice? Why is that important in Monopoly? The questions here are endless.

Luckily, I have plenty of versions of Monopoly sitting in a closet in my childhood bedroom. Now I just have to find a way to carve out a day to play Monopoly…

However, I got a fancy new camcorder for Christmas and decided to put it to use.

What I will try to make original is my implementation and how to really get the students into it. The video, of course, is paused when the ball is frozen in mid-air. At that point, the conversation begins at a very low entry level. Anyone can take a guess. For my algebra I students, we’ll move into Sketchpad and they’ll start playing with changing the constants to model the flight of the ball, thanks to the nicely provided picture.

For my algebra II students, we can go several routes. What I like most is that we can go tech and use sketchpad, or we can got paper, pencil, and rule and plot three points and use a system (which we’re approaching soon). That’s a nice luxury to have when time becomes a factor.

How I’ll spice up Basketbola, however, is by letting the students be the stars. A side benefit of coaching basketball is I now have a library of videos and pictures of these shots by students. So, there’ll be ten or so “problems” to solve. We’ll watch the first acts and everyone will submit their guess. At the end of the project whomever was the best prognosticator will get a chance to take a shot, kick a field goal, or try to spike a volleyball into a bucket and it’ll be added to the library. Should be fun!