Illuminations: Mathematics and Football

# Mathematics and Football

## Super Bowl Scores

 This activity focuses on analyzing the scores for football games.  Students study combinations of numbers to produce possible scores for football games.

### Learning Objectives

 Students will: determine mathematical combinations develop the concept of multiples and combinations of multiples

### Instructional Plan

 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.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 teach 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. 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. You might consider using other manipulatives to represent points.

### Extensions

 Ask students to describe the different combinations of gains that a team can use to make a first down in four downs. For example, they can make the first down in one play, or they can make 9 yards in one play and 1 yard in the second, or they can make 8 yards in one play and 2 yards in the second, and so forth. You may want to discuss the possibility of losses, penalties, and nonintegral gains.

### NCTM Standards and Expectations

 Number & Operations 3-5Recognize equivalent representations for the same number and generate them by decomposing and composing numbers. Develop fluency in adding, subtracting, multiplying, and dividing whole numbers;

### References

 J. David Keller, Daniel J. Brahier, and William R. Speer. The Arithmetic Teacher. January, 1993, 40(5). pp. 264‑77.

1 period

### NCTM Resources

Principles and Standards for School Mathematics

 More and Better Mathematics for All Students
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