A final score reported for a sporting event may not say much about the game itself. Pose the following question to students:
"If a final score in football is 20-14, how were the points scored?"
This question is not intended to focus on the plays used to score
but rather on the different ways that a total of 20 points (or 14
points) might be earned.
Other questions to ask the students include:
- Is it possible that the team scoring 20 points scored four touchdowns?
- Might they have scored two touchdowns?
- If so, how could their other points have been earned?
Distribute a copy of the Super Bowl Scores Activity Sheet to each student.
Super Bowl Scores Activity Sheet
Discuss with the class the fact that for a football team to have
a certain number of points, only certain combinations of scores can be
made. For example, for a team to have 5 points, they would have to
have made one field goal and one safety.
Some students may need to be told the meaning of a safety and have a brief review of the way football is scored. Here is a basic guide:
- Each touchdown is worth 6 points. After a touchdown, the scoring team can attempt to get an extra point.
- An extra point is worth 1 point. Right after a touchdown, the ball is placed at the opponent's two-yard line and kicked. If the ball goes through the goal post, the extra point is earned.
- A field goal is 3 points. If the offense can not score a touchdown, they may choose to kick a field goal. A successful kick results in the ball passing through the goal post uprights and over the crossbar.
- A safety is worth two points and is earned when the offensive ball carrier is tackled behind his own goal line.
A more comprehensive guide can be found using a search engine. Encourage the students to explore and develop as many possibilities
as they can generate. The "bar-numberline" approach suggested on the
activity sheet can be use to help them explore possibilities.
To help struggling students, you might consider using other manipulatives, such as counters, to represent points.
To conclude the activity, have students pair up and compare their answers. Make it a requirement for students to share how they got their answer, as students will have different problem solving strategies. Circulate the room and, 1- help students who have discrepancies in their answers, and 2- to note when different problem solving strategies are used. You may choose to stop the class at any point to have a pair of students share interesting ways in which they solved a problem. Finally, have a class discussion to answer the question posed at the beginning of class ("If a final score in football is 20-14, how were the points scored?"). You can either come to an answer together as a class, or have students write their answers on an index card as an exit slip.
J. David Keller, Daniel J. Brahier, and William R. Speer. The Arithmetic Teacher. January, 1993, 40(5). pp. 264‑77.