In this activity, students explore a professional athlete’s performance time. They’ll explore this question through real data for one athlete—Aaron Rogers, the quarterback for the Green Bay Packers. Is he getting better and better? Did he get better and level off? Or did he hit a peak and start heading downhill?
In this activity, students calculate key features of quadratic functions (axis of symmetry, vertex, y-intercept, x-intercepts), graph parabolas, and analyze their model in the context of a real world scenario. Students can solve the equations with factoring, so knowing the quadratic formula or completing the square isn’t required.
Good to know
*This is a Word document
, so you’ll have the power to adjust, add, or delete any questions to meet the needs of your class. If you need it as a PDF, just e-mail me at firstname.lastname@example.org.
*It includes pre-work
(at the bottom), so your warm up is covered and you can scaffold your way into this activity! Just print and go!
*If you take time to explore and discuss, this will take a full period
. If needed, you can have students finish the analysis questions at home and discuss further the following day.
How it works
There are three phases to this activity:
Phase I: The Basics.
Students see a table showing how many touchdown passes he threw each season. They’re asked to explain trends they see in the data, to identify the independent / dependent variables, and to consider possible restrictions on domain and range.
Phase II: Getting Dirty.
Students receive an equation modeling the data. Using that equation, they answer questions about the data. For example: How many touchdown passes does it predict he’ll throw in his second season? How many touchdown passes does the model predict he’ll throw in his best season? Using their answers to each question, they’re expected to plot a graph of the function.
Phase III: Getting Clever.
Queue up the debate… students answer bigger picture questions. Here, they consider questions like: If you were a recruiter for another team, would you offer to pay him more, less, or the same next season? If Aaron Rogers threw 40 touchdown passes next season, would you have more or less faith in the model? Is a quadratic model the right way to model an athlete’s performance over time? And as always… Why? (This phase is designed to make the math matter, exploring what it can tell us, how we could leverage the insight mathematical models offer, and how we can improve those models.)
When you download this, you can use, share, and modify it freely so long as you don't do so for commercial purposes and always cite Steve Walker at Marauders' Math as your source! See more details at CC BY-NC 4.0 license