Quarterback Stats: Teacher Guide
Subject: Geometry: Data & Statistics
Grade Level: High School
Last Updated: 12/18/20073
Case Summary
The Atlanta Falcons have just lost their star quarterback, Michael Vick, to legal problems. How are they going to find a new quarterback? Is the current quarterback rating statistic a valid one to use when proposing who to hire?
Credits
This case was written by Alyson Zeamer (PhD student, Psychology, Emory University, Atlanta, GA), Katheryne Mosley (teacher, The New Schools at Caver: School of Technology, Atlanta, Georgia) and Stephanie George (PhD student, Biomedical Engineering, Georgia Tech and Emory University, Atlanta, GA). Authors may be contacted at azeamer@emory.edu, kjmosley@atlanta.k12.ga.us and gtg798j@mail.gatech.edu.
This case was adapted from the reading: Multicultural Activity: Kareem AbdulJabbar (Glencoe/McGrawHill, 2001).
Learning Objectives
Students should be able to:

Become familiar with the PBL format (specifically, filling out the BIG Idea chart, sorting information, group work, and asking questions)

Describe and write a coherent summary of the data

Use critical thinking to employ math concepts in order to develop their own equation

Think creatively to present information and arguments

Work collaboratively to prepare an engaging presentation on what they learned

Strengthen oral presentation skills

Incorporate technology into a presentation

Objectively evaluate the contribution of each of their peers
Georgia Performance Standards OR Georgia Quality Core Curriculum
MA1G2. Students will understand and use the language of mathematical argument and justification.
a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.
MA1P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
MA1P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
MA1P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
MA1P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
MA1P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Assessment
Assessment included 1) responses to the Big Idea Chart for Scene: 1, 2) developing an equation for who they think is the best quarterback, 3) a group presentation to the class using available technology graded using the Rubric for Quarterback Stats Presentation to the Commissioners, 4) assignment in which they have to explain what a quarterback rating is and how it is useful, and 5) a Self/Peer Evaluation form. See student materials for these documents.
Implementation Strategy
The times listed here are only estimated because the PBL, as described below, has not been implemented in the classroom.
Day 1:

(10 min) The students are given Scene 1 and asked to individually fill out a Big Idea Chart. This is followed by a class discussion about what is needed to determine who the best quarterback actually is.

(30 min) The students are broken up into groups of 4 students and each group is given Scene 2. They must work as a group to develop their own quarterback rating equation.

(15 min) Each group is given a table specific to their group that includes statistics for 6 different NFL starting quarterbacks. They must calculate the QB rating of each of those quarterbacks based on the equation they developed.

(15 min) The students are given Scene 3 and must compare their equation to the current QB rating equation.

(Remainder of class) The students must work as a group to put together a PowerPoint presentation for the NFL Commissioners explaining their equation and how it compares to the current QB rating equation. They must include figures and graphs relevant to the data.
Day 2:

(10 min) The students finish the PowerPoint presentation they began the previous day.

(20 min) Each student must individually answer the questions on the assignment sheet about what they learned during this PBL.

(40 min) Each group is given 8 minutes to present their findings to the NFL Commissioners.

(5 min) Each student must individually fill out a Self/Peer Evaluation form for each member’s contribution to the project.
Case Notes
Our initial implementation of this PBL did not go so well, so we made several adjustments which have all been included in the teacher and student materials here. Therefore, the PBL as written here has not been implemented in the classroom to date.
Facilitator Guide (optional):

The goal of Scene 1 is to get the students thinking about what a quarterback rating is.

The goal of Scene 2 is to use current statistical data to designing a quarterback rating equation and to graphically illustrate variables

To graph the difference in equations

We will give them the tables in an excel file as well so that the students do not have to spend time entering the data

Suggest potential graphs

pass attempts/pass completions (circle)

yards gained/pass completed (bar)

The goal of Scene 3 is to get the students to:

critically examine their equation in comparison to the actual rating equation

critically examine the true measure of the equation

graph the quarterback rating differences between their equation and the actual equation for their 6 players.
Resources
Glencoe Geometry Integration Applications Connections McGrawHill Companies Inc. 2001
www.brucey.net/nflab/statistics/qb rating.html
www.nfl.org
© 2007, Alyson Zeamer, Katheryne Mosley & Stephanie George. Unauthorized use is prohibited, see Web site for Terms of Use. This material is based upon work supported by the GK12 program of the National Science Foundation, under Award #DGE0536941. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. CASES Online is brought to you by the Emory College Center for Science Education, Emory University, Atlanta, GA. This document and other resources are available from the CASES Online Web site, http://www.cse.emory.edu/cases
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