Play Ball!

Unit Summary

The first box score was printed in 1845, and ever since, people have calculated and analyzed baseball statistics. Not everyone understands the numerical joys of the sport. Therefore, your class has been hired by the Major League Baseball Commissioner to explain the mathematics of baseball so more people can appreciate the game. The class compares statistics, such as batting averages and earned run averages, and analyzes the speed of pitches, the shape of the diamond, and the distances players cover. Finally, the class develops a presentation that explains an aspect of these topics, making the national pastime more enjoyable for all.

Curriculum-Framing Questions

• Essential Question
  How can we use mathematics to help us understand daily life?
• Unit Questions
  How do numbers make our games more fun?
  How do statistics help us understand the game of baseball?
  How can we use statistics to help make decisions?
• Content Questions
  What is the difference between a player's batting average and slugging average?
  Why is information often presented in graphs instead of just in a list or table?
  How do you choose the appropriate graphical representations for certain sets of data?

Assessment Processes

View how a variety of student-centered assessments are used in the Play Ball! Unit Plan. These assessments help students and teachers set goals; monitor student progress; provide feedback; assess thinking, processes, performances, and products; and reflect on learning throughout the learning cycle.

Instructional Procedures

Introduction (1 day)
The Essential Question, How can we use mathematics to help us understand daily life? can be used as a yearlong theme. Keep referring to it as you introduce new mathematical topics. Pose the question again as you begin this unit on baseball. To tap students’ prior knowledge, conduct a class discussion about how math helps us understand our world. More than likely, students will bring up the topic of sports in relation to math. Guide the discussion by asking students the following questions:   

• How do numbers make our games more fun? 
• How do statistics help us understand the game of baseball? 
• What would baseball be like without statistics?

Starting with students' prior experiences, discuss why baseball is called “America's pastime.” Engage in vocabulary and writing activities to develop a shared interest in the topic. Tap into students’ prior knowledge about the game of baseball by having them brainstorm as many words and ideas as they can that they associate with baseball. Give students about one minute to brainstorm on their own, and then have students share concepts with the whole class. Give historical background and introduce the importance of statistics as a feature of baseball. Give students a baseball trading card to look at, and discuss what they understand about the statistics shown on the back. For a review of baseball statistics definitions and formulas, view the Baseball Almanac Web site*.

Develop the following scenario for students:
We have been hired by the Major League Baseball Commissioner to explain the mathematics of baseball so more people can appreciate the game. Your job is to analyze a variety of statistics related to baseball and then use what you have learned to publish an explanation of some aspect of baseball statistics, so people can get greater enjoyment from the game. You will use spreadsheets to make calculations using equations and visually analyze data.

Investigating Statistics (6 or 7 days)
Batting Averages: Starting with the question, Who is the greatest hitter of all time? teach the statistics of batting averages, home runs, and runs batted in (RBI). To explore batting averages, students take data from the batting averages table showing the statistics of four players and create a scatter graph in a spreadsheet program showing how the averages change over time. Have students analyze the graph, looking for strength and consistency over time, to determine the relative value of players. After this investigation is completed, have students share their thoughts about the Content Questions, Why is information often presented in graphs instead of just in a list or table? and How do you choose the appropriate graphical representations for certain sets of data?

Slugging Percentage: Discuss batting averages and how batting can be analyzed more deeply. To decide who is more important to winning baseball games, show students how to compare batting averages to slugging percentages using the slugging table worksheet and slugging answer key. Ask students to discuss what this statistic seems to calculate. Make sure students conclude that the slugging percentage tells the average number of bases a player advances for each time at bat. Have students discuss the difference between a player’s batting average and slugging percentage.

On-Base Percentage: Explain how this statistic shows the percentage of time a player can be expected to reach base safely by either a hit or walk. To calculate this number, divide the total times a player reaches base safely by their total at bats. Present the player comparison sheet to students and ask them to recommend the best player for a team they are managing. Students should back up their choice using data.

Earned Run Average (Pitching): Begin the study of pitching by comparing the number of wins a pitcher has using the all-time winning pitchers (active) sheet. Discuss the factors influencing the number of wins, and the concept and computation of the earned run average (ERA). Students pretend to be a team manager comparing pitchers, and compute the ERAs of the all-time winning pitchers. Using the statistics, have students create a bar graph, determine who is best, and defend their reasoning. Students with more knowledge of baseball may want to consider other pitching factors as well.

Physical Dimensions: Discuss the physical dimensions of baseball, such as the throwing distance from third to first base, the size of the strike zone, and pitching speed. Have students complete a baseball treasure hunt assignment to practice research and math skills needed to solve real baseball problems. Students can check their answers using the treasure hunt answer key.

Preparing and Giving the Presentation (3 or 4 days)
Have each student team begin their research and create a slideshow presentation that shows the math of baseball and helps the audience appreciate the numerical joys of the sport. Allow students to choose the type of baseball data they want to research—active or non-active players; male or female; local, national, or international leagues; and so on. A list of topics might include: 

• Compare player statistics and salaries  
• Compare the performance of two players during any year 
• Evaluate the greatest hitters of all time 
• Compare and contrast a group of players' individual statistics 
• Highlight a recent game’s statistics

Discuss the qualities of a good presentation in terms of content, organization, visual presentation, and attention to the audience. Review the baseball presentation scoring guide with students before students begin researching and developing their presentations. Check for student understanding before students get started. Teach the presentation software tools, and designate student experts to help. This phase of the project may take several extra days, depending on the experience of your students. View an example of a student presentation.

Each team’s presentation should include: 

• Introduction to how statistics helps us understand the game of baseball
• Overview of the topic—each student team poses an investigative question
• Important statistics evaluated by the team and why
• Justification of the team’s position using data and graphs
• Conclusion 
• Citation of sources

Meet with groups periodically to check for understanding and monitor progress among individuals in the group.

Have students get peer feedback to get suggestions and feedback on their presentations using the peer feedback form. After students have received feedback, have them incorporate the suggestions into their presentations before the final presentations are handed in.

Wrapping Up
Set aside a day for students to present their findings. Encourage audience members to take notes and generate questions to ask the students after each team presentation. Give students the opportunity to express relevant observations. Ask students to reflect on the Essential Question, How can we use mathematics to help us understand daily life? Have students discuss the question in relation to the Play Ball! unit and share their ideas with a partner.

Prerequisite Skills

• Experience researching on the Internet  
• Knowledge of spreadsheets, graphing tools, and presentation applications  
• Understanding of percent, decimal, and fractions

Differentiated Instruction

Resource Student

• As students work in pairs or groups, establish rules so all students participate
• Demonstrate the use of spreadsheets to perform all calculations  
• Provide step-by-step instructions  
• Reduce the number of players and calculations considered

Gifted Student

• Encourage students to consider more challenging problems, such as who is the greatest hitter of all time using a variety of statistics; the physics of the curve ball; how sabermetrics, the statistics of baseball, is used to predict who will win a game; and so on
• • Have the student present information on an interactive Web site that includes graphics and information

English Language Learner

• Ask the ELL support teacher to help students develop a glossary of terms in both English and the student’s first language  
• Enlist the help of bilingual students to help with translation and interpretation of concepts  
• Allow for visual representations to reduce the language load  
• Allow student to write in in the student’s first language for later translation

Credits

Belinda Dukes participated in the Intel® Teach Program, which resulted in this idea for a classroom project. A team of teachers expanded the plan into the example you see here.