Problem Solving with Batting Averages

Mary Kay BacallaoColleges and Universities - Florida

Description

Students use data from an Excel document to analyze and predict trends in batting averages.

Objectives

The student uses statistical data to predict trends.

The student applies statistical data to make generalizations.

Materials

-Computers with Excel
-Orioles' Batting Averages spreadsheet (See Associated File)
-Assessment Rubric (See Associated File)
-Student computers
-Teacher computer with Excel and a projection system
-Printer and legal-size (8 ½” x 14”) paper

Preparations

1. Download the associated file and have it ready on the computers for the students to use for the activity. Note: When students print out the revised spreadsheet (See Procedures, step #19) they need legal-size paper, 8 ½” x 14.”
2. Make sure the teacher’s computer is set up with a projector so the students can see the demonstration.

Procedures

1. Begin by discussing: How many of you have played baseball or softball? Have you ever wondered how your coach determines your batting line-up? If you were the coach of your team, how would you go about creating a line-up? Does it matter to you where you are in the line-up? Do you think the batting order can cause a team to either win or lose a game?

2. Continue with the discussion: Our job today is to use a spreadsheet with formulas for batting averages to determine our own line-up. First we are going to find out how batting averages are calculated in a spreadsheet. Then we are going to analyze a sample based on some questions. We are going to use the information to create a new batting order. Keep in mind that you must have math data to support your new batting order. The players on your team are going to want to know why you changed the batting order, and you are going to have to explain it to them.

3. Review the process by which batting averages are calculated by doing some sample calculations on the board while the students use paper and pencil to calculate. You can use the following examples:
a. If Rick goes up to bat 4 times and gets a hit 2 times, what is his batting average? Solution: 2/4= .5 or in batting averages he is batting 500.
b. If Eddie goes up to bat 6 times and gets a hit 2 times, what is his batting average? Solution: 2/6= .333 or in batting averages he is batting 333. This means that in the past, he has gotten a hit 2 out of the 6 times he has been at bat. Both Rick and Eddie have gotten a hit twice, but Eddie has had more chances to bat, so his batting average is lower. Continue with more examples and applications of batting averages until the students understand how batting averages are calculated and can calculate their own.

4. Use a computer and a projector with the Orioles' Batting Averages spreadsheet (See Associated File) to teach this lesson. Open up the document and begin by explaining how the spreadsheet is set up:
a. The spreadsheet has letters across the columns at the top and numbers down the rows. One may use the letters and numbers to locate any box on the spreadsheet.
b. There is an entry for each game with the number of times the player was at bat and on base.

5. Click on a box under the title of “Average” for the first game to find the formula for the batting average.

6. Point out that if there are any “formulas” in that box, they appear in the “formula bar” above the body of the spreadsheet. The formula bar has an “=” sign and in this case there is already a formula entered with the = sign and then a letter followed by a number and then the division sign of “/” with another letter and number. You can show the students where they can find the numbers on the spreadsheet that were used in the formula. Click around on different players’ batting averages to show how all the formulas are different.

7. Pick a player’s name to follow for each game. Discuss their performance for that game based on their batting average.

8. Ask the students if the number of times the player is “at bat” has anything to do with the batting order. Why?

9. Ask the students who they think is the most consistent batter and why.

10. Have the students supply their ideas about where in the batting order the most consistent batters should be.

11. Go to the section on the total batting average summary. Compare the batting averages of the players overall.

12. Ask the students which players they think are getting better as the season goes on and which players they think are not improving. Have them discuss possible reasons for these variations such as injuries, slumps, etc.

13. Ask the students to critique the current batting order. Do they think it is the best order? Why or why not? Discuss suggestions for improvement. Remind the students to use the data to support their choices.

14. Solicit other observations about the data from the students.

15. Show the students how to enter the revised batting order and the predictions for the hits and at bats for game six. Allow the students to choose the next team name. You can change it by clicking on the title and then going to the formula bar and entering the new name.

16. Arrange the students so they have access to a computer in pairs, one per student, or in groups. Circulate and formatively assess students as they use the technology tools. Provide assistance for students who are experiencing difficulty and monitor accordingly.

17. Have students supply the new batting order and then do a “save as” and rename the original file with their name.

18. Have the students predict the game six performance by supplying the number of hits and at bats for the new batting order. The formula will calculate the batting averages automatically.

19. On a separate sheet of paper, have the students write reasons for their choices and predictions for future performance in paragraph form. Have the students print their spreadsheets on legal-size paper, attach them to the rationales and turn them in to the teacher.

20. As the students are working, assist in answering questions.

21. Ask clarifying questions to the students as they work.

Assessments

1. Use the printed spreadsheet with the revised line-up and the written rationale with supporting evidence to determine mastery. (See the Assessment Rubric located on the Excel associated file.)
2. Circulate and formatively assess students as they use the technology tools. Provide assistance for students who are experiencing difficulty and monitor accordingly.

Extensions

This lesson can be adapted to other sports. Students can create their own spreadsheets and learn how to enter formulas based on the desired result.

Attached Files

Orioles' Batting Averages and Assessment Rubric.      File Extension:  pdf