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In a fourth down situation in football, most coaches in the NFL decide to punt the ball to the other team. But is giving the ball away with such regularity really a good idea, and should teams punt as often as they do?

In this lesson, students use quadratic functions to develop a model of expected points, which measure how many points a team can expect to score from different field positions. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

Students will

  • Read graphs to estimate the probability of scoring a touchdown or field goal from different field positions
  • Add quadratic functions to develop a model of a team’s expected points at different field positions
  • Evaluate a quadratic function to model the probability that a team will convert on fourth down
  • Calculate a team’s total expected points if they go for it on fourth and if they punt
  • Develop strategies for when to punt on fourth down

Before you begin

Students should be able to evaluate quadratic functions and add two quadratic functions together. Some previous experience with piecewise functions will also be helpful. This lesson also makes use of expected value; students should feel comfortable with the idea that, for example, if a team has a 50% probability of successfully kicking a 3-point field goal, then the expected value of attempting the kick is 0.50 × 3 = 1.50 points.

Common Core Standards

Content Standards
Mathematical Practices


NFL, Grantland, Pulaski Academy