Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

## Super Bowl Scores

3-5
1

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

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 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.

### Reference

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

Assessment Options

1. Use student's activity sheet as a form of assessment.
2. Choose to have students answer the question at the beginning of class on an index card. Use their answers to determine whether or not they are comfortable with mathematical combinations.
3. Circulate the room while students compare their activity sheet answers and take note of students who have difficulty verbalizing how they got their answers vs. students who are proficient with this.

Extensions

1. Ask students to describe the different combinations of gains that a team can use to make a first down in four downs.
2. 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.
3. You may want to discuss the possibility of losses, penalties, and non-integral gains.

Questions for Students

1. What other sports can you think of where combinations could be used?

2. Does the sequence of points matter?

[The scoring sequence at the end doesn't matter as long as the number of field goals, touchdowns, and extra points is the same. However, it is important that an extra point is always paired with a touchdown.]

Teacher Reflection

• How could you modify this lesson so that is more engaging?
• How could you differentiate this lesson to meet the needs to proficient and struggling students?
• What sorts of extensions can you use to help students diversify their problem solving strategies?

### Get the Picture—Get the Story

3-5
In the following lesson, students act as reporters at the Super Bowl. Students study four pictures of things that they would typically find at a football game: players, a scoreboard, a crowd, and a concession stand. Students are asked to create problem situations that correspond to their interpretation of each of the pictures.

### Super Bowl Scavenger Hunt

3-5
In many homes, the Super Bowl is an event of some significance. This activity is designed to have students examine some enjoyable (and, sometimes, obscure) questions using mathematics during the game. The questions on the activity sheet require that the students make observations about the game.

### Learning Objectives

Students will:

• Determine mathematical combinations.
• Develop the concept of multiples and combinations of multiples.

### NCTM Standards and Expectations

• Recognize equivalent representations for the same number and generate them by decomposing and composing numbers.
• Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.