When I build activities, I often look for patterns in things we talk about outside of class. Here are three of our favorites from this school year.
Early P.S. Don’t skip the final section of this post. It’s where I explain why they’re our favorites. Spoiler: It’s not about the content.
Linear: Buying the Win
Among the strongest college football teams, it turns out there’s a reasonably steady relationship between how much you pay your coach and how well your team does. This activity is grounded in a scatter plot with data from the top college teams. Students analyze the data, estimate a line of best fit, and make predictions based on the function they’ve created. They also take a close look at how well a linear model really represents the data, especially at the extremes.
Find the activity here: Buying the Win.
Exponential: Maxing Cards
Students love to outsmart adults. Here, they learn how credit cards work… then learn how much credit card debt the average U.S. adult typically carries. They’re stunned by the impact of compounding debt and are all about explaining what steps they’ll take to be sure they’ll never be at the wrong end of a collections call.
Find the activity here: Maxing Cards.
Quadratic: The Case of Aaron Rogers
Like anyone else, athletes usually get better over time. However, at some point, they peak, and their performance drops. Quadratic function, meet Aaron Rogers. This activity analyzes the touchdown passes per season of Aaron Rogers over time. Students begin by analyzing the raw data, then make predictions using a model of his data, and then dig deeper to analyze the model itself.
Tip: One of the goals of this lesson–and many of my lessons–is for students to question whether this data is rigged. It’s real data… but I ran this model for a number of athletes before finding one that so nicely fit a quadratic model. In reality, athletes may peak, but the peaks are rarely this clear and they rarely stay in the game long enough to come down so far.
Extension: Have your students validate the hypothesis that athletes’ performance can be modeled by a quadratic function by analyzing data for other athletes using Excel, Google Sheets, Desmos, etc.
Find the activity here: The Case of Aaron Rogers.
Why these are favorites
Before you dash away, I need to clarify why they’re favorites. It’s not because they’re about football or colleges or credit cards. They’re favorites because they lead to unexpected insights in a challenging, yet accessible, way. Bottom line, it’s about the questions, not the content.
In Buying the Win and The Case of Aaron Rogers, the insights arise when the model conflicts with our intuition. For example: What winning percentage would you expect if you paid your coach $4 million? What about $10 million? 344 percent! Wait… [Cue debate about the model]
In Maxing Cards, the biggest insights come from subsequent discussion. For example: Let’s take it one step further. How much more would you end up paying if you only paid the minimum amount each month? Will you ever do that? Will you ever have as much debt as the average American does today? Ok, now take a guess: What percent of the people in this class will have as much debt as the average American today? What makes 90% of us sure we personally won’t have that much debt, even though we think about 60% of the rest of the class will?
Let me know if you have any questions, suggestions, or requests!