Pre-Visit Batting Average

Home , Coco Crisp, Dexter Fowler, Elvis Andrus, Hunter Pence, Joey Votto, Melky Cabrera

Statistics: Batter Up! - Level 2

Lesson 1 – Pre-Visit Batting Average

Objective : Students will be able to: • Identify the meaning of abbreviations related to player statistics on baseball cards. • Recognize statistics as whole numbers or decimals. • Set up fractions representing batting averages and other similar averages. • Practice converting fractions to decimals. • Round decimal numbers.

Time Required : 1 class period

Advance Preparation : - Set up 4 stations around the classroom as follows: o Station 1: Quarters or other small change o Station 2: A pair of dice o Station 3: A deck of playing cards o Station 4: Marbles of different colors in an opaque bag

Materials Needed : - Baseball cards – enough for each student to have one - Copies of the “Hall of Fame Hitters” worksheet (included) – 1 for each student - Prepare packets of “Day 1 Station Worksheets” (included). Make enough packet copies for students to work in pairs or in small groups. - Scrap Paper - Graph Paper - Calculators - Pencils

Vocabulary: Batting Average – A measure of a batter’s performance, calculated as the number of hits divided by the number of times at bat Statistics - A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of numerical data

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 4 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Applicable Common Core State Standards:

CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

CCSS.Math.Content.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. • CCSS.Math.Content.6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers.

CCSS.Math.Content.6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

CCSS.Math.Content.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

CCSS.Math.Content.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: • CCSS.Math.Content.6.SP.B.5a Reporting the number of observations. • CCSS.Math.Content.6.SP.B.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

CCSS.Math.Content.7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 5 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Applicable Common Core State Standards ( Continued ):

CCSS.Math.Content.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

CCSS.Math.Content.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 6 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Lesson

1. Begin by asking students to name some of their favorite sports.

2. Choose an example from the sports named by students. Ask, “In this sport, how do you know which players are the best (or the best at their position)?”

3. Discuss that in almost every sport, players are evaluated or judged using numbers and mathematics. Players compete for distance, speed, goals scored, etc. This is especially easy to see during sporting events like the Olympic Games where the smallest differences in numbers could mean winning a medal or winning nothing.

4. Ask students, “How are baseball players evaluated or judged? How do we keep track of a player’s success at the plate or on the mound?”

5. Give each student one baseball card and have students examine the information on the back of each. Ask, “What sort of information is available on a baseball card?” Information examples include: player height, player weight, dominant hand, birthday, team, special accomplishments, and statistics.

6. Point out that baseball has its own language. There are codes for different statistics listed on the back of the card. For example, BA = batting average, G = games played, AB = at bats, R = runs, H = hits, 2B = doubles, 3B = triples, HR = home runs, RBI = runs batted in, SB = stolen bases.

7. Ask students to identify which statistics are represented by whole numbers, and which are represented by decimals.

8. Discuss that all of these statistics, and others not listed on the cards, are used by team owners and managers when they are evaluating a player’s talent.

9. Explain that students will be looking more closely at one of the most common baseball statistics: batting average .

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 7 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

10. Discuss that this statistic is used to describe how successful a batter is at getting hits (singles, doubles, triples, home runs) when he or she gets a chance to bat. One complication is that many times that a batter goes up to bat, he is not given a chance to get a hit. Sometimes the player is walked or gets hit by a pitch, and sometimes the player is asked to make an out to benefit his team by helping a teammate advance around the bases (a “sacrifice bunt” or “sacrifice fly”).

11. Explain that a batting average is calculated by first counting the number of times that a batter reaches base by getting a hit. This number of hits is then divided by the number of times that he gets a chance to hit (an “At Bat”).

12. Write down the formula for batting average on the board: Hits (H)/At Bats (AB).

13. In a typical season, a good player, who plays in most of his or her team’s games, might get about 180 hits in about 600 at bats. This would give the player a batting average of 180/600 or .300.

14. Batting average is usually rounded off to the nearest thousandth (three digits after the decimal) and most people don’t bother writing the leading zero. In fact, most baseball statisticians do not mention the decimal point. If a player has a batting average of 0.256, we would say that he or she is a “two-fifty-six hitter.” Review decimal places and how to round decimal numbers.

15. Have students locate the columns for Hits (H) and At Bats (AB) on their baseball cards.

16. Ask students to share some examples of their players’ numbers of hits and at bats. For each example, set up the numbers as a fraction. For example, a student reports that Nick Swisher had 117 hits and 422 at bats. You would set up the formula as 117/422.

17. Demonstrate how a player’s batting average is determined. Work through the examples provided by students, first setting up the problem, and then converting each fraction to a decimal rounded to the nearest thousandth.

18. Provide students with “Hall of Fame Hitters” worksheets (included) for practice OR you may assign this worksheet for homework. Have students determine each player’s batting average.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 8 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Activity

1. Introduce the activity. Explain that students will be working together to figure out their own averages for performing different activities.

2. Divide students into pairs or small groups. Provide each pair or group with a prepared worksheet packet (included).

3. Explain instructions for each station you set up in advance of this lesson: • Station 1: Quarters The goal of this station is for students to see how often they can spin a quarter or other coin and have it turn up “heads.” Have one student spin and another student record the results of each spin. Station 1 Average = Number of “heads” results/Total number of spins

• Station 2: Dice The goal of this station is for students to see how often they can roll the pair of dice and have the roll result in 2 even numbers. Have one student roll the dice and another student record the results of each roll. Station 2 Average = Number of rolls resulting in 2 even numbers/Number of total rolls.

• Station 3: Playing Cards The goal of this station is for students to see how often they can randomly draw a red card. Students should mix up the deck of cards before beginning this activity. Have one student draw a card at random and another student record the results of each draw. Station 3 Average = Number of red cards drawn/Number of total draws.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 9 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

• Station 4: Marbles The goal of this station is for students to see how often they can randomly draw a blue marble. Have one student choose a marble from the bag at random. Have another student record the color of each chosen marble. Station 4 Average = Number of blue marbles/Number of marbles chosen.

4. Students are to work through each station, documenting results and determining the average rate of success for each station. The total number of times the task is accomplished is divided by the number of times the task was attempted to get the average success rate for that particular task.

5. Remind students to round each average to the nearest thousandth.

6. Assist students with stations as necessary.

Conclusion: To complete this lesson and check for understanding, come together as a class and have students compare the results of the different stations. What were group averages for each station? Discuss meaningful comparisons from class data. Have students create graphs showing the results of each station.

*NOTE* Collect and save completed packets of “Day 1 Station Worksheets” for use in Lesson 2.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 10 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

(Day 1) Station 1: Quarters

Names: ______Instructions: 1) Choose a recorder for the group. 2) Choose one person who will spin the quarter 10 times. 3) The recorder should place a check in the box showing if each spin resulted in “heads” or “tails”.

Spin # Heads Tails 1 2 3 4 5 6 7 8 9 10

4) Count the number of times the spin turned up “heads.” ______

5) Set up a fraction showing the average number of spins that turned up “heads.” Number of “heads” results = Total number of spins

6) Calculate the average number of spins that turned up “heads.” ______

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 11 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

(Day 1) Station 2: Dice

Instructions: 1) Choose a recorder for the group. 2) Choose one person who will roll the pair of dice 9 times. 3) The recorder should place a check in the box if the roll resulted in 2 even numbers.

Roll # 2 Even Numbers 1 2 3 4 5 6 7 8 9

4) Count the number of times the roll came up as 2 even numbers. ______

5) Set up a fraction showing the average number of rolls that turned up 2 even numbers: Number of rolls with 2 even numbers = Total number of rolls

6) Calculate the average number of rolls that turned up 2 even numbers: ______

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 12 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

(Day 1) Station 3: Cards

Instructions: 1) Choose a recorder for the group. 2) Choose one person who will mix up the cards, then choose 7 cards without looking. 3) The recorder should place a check in the box showing if each card was a red card or a black card.

Draw # Red Black 1 2 3 4 5 6 7

4) Count the number of times a red card was chosen. ______

5) Set up a fraction showing the average number of times that a red card was chosen: Number of red cards = Total number of cards drawn

6) Calculate the average number of times a red card was chosen:______

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 13 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

(Day 1) Station 4: Marbles

Instructions: 1) Choose a recorder for the group. 2) Choose one person who will choose 11 marbles from the bag without looking. 3) The recorder should place a check in the box showing whether or not the marbles chosen were blue or another color.

Choice # Blue Another Color 1 2 3 4 5 6 7 8 9 10 11

4) Count the number of times a blue marble was chosen. ______

5) Set up a fraction showing the average number of times that a blue marble was chosen: Number of blue marbles chosen = Total number of marbles chosen

6) Calculate the average number of times a blue marble was chosen: ______Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 14 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Hall of Fame Hitters

Name: ______Date:______

All of the players below have been elected to the Baseball Hall of Fame. You have been given the number of at bats and hits each one had during his career. From those figures, determine each player's "lifetime" batting average.

Player Position At bats Hits Batting Batting Average Average Fraction Decimal Orlando Cepeda First Base 7927 2351

Rod Carew Second Base 9315 3053

Ty Cobb Center Field 11434 4189

Joe DiMaggio Center Field 6821 2214

Hank Aaron Right Field 12364 3771

Ozzie Smith Shortstop 9396 2460

Ted Williams Left Field 7706 2654

Brooks Robinson Third Base 10654 2848

Dave Winfield Right Field 11003 3110

Babe Ruth Right Field 8399 2873

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 15 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Hall of Fame Hitters Answer Key

Player Position At bats Hits Batting Batting Average Average Fraction Decimal Orlando Cepeda First Base 7927 2351 2351/7927 .297

Rod Carew Second Base 9315 3053 3053/9315 .328

Ty Cobb Center Field 11434 4189 4189/11434 .366

Joe DiMaggio Center Field 6821 2214 2214/6821 .325

Hank Aaron Right Field 12364 3771 3771/12364 .305

Ozzie Smith Shortstop 9396 2460 2460/9396 .262

Ted Williams Left Field 7706 2654 2654/7706 .344

Brooks Robinson Third Base 10654 2848 2848/10654 .267

Dave Winfield Right Field 11003 3110 3110/11003 .283

Babe Ruth Right Field 8399 2873 2873/8399 .342

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 16 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.

Statistics: Batter Up! - Level 2

Lesson 2 – Pre-Visit Batting Average Ups and Downs

Objective : Students will be able to: • Use multiple data sets to determine the overall success rate of a particular activity. • Select and create appropriate graphs representing data sets.

Time Required : 1 class period

Materials Needed : - Copies of the "Batting Average Boost" worksheet (included) – 1 for each student - Prepare packets of “Day 2 Station Worksheets” (included). Make enough packet copies for students to work in pairs or small groups. - Completed packets of “Day 1 Station Worksheets” from Lesson 1. - Scrap Paper - Graph Paper - Calculators - Pencils

17 Statistics: Batter Up! - Level 2

Applicable Common Core State Standards:

CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

CCSS.Math.Content.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

CCSS.Math.Content.7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

18 Statistics: Batter Up! - Level 2

Applicable Common Core State Standards ( Continued ):

CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable.

19 Statistics: Batter Up! - Level 2

Lesson

1. Review the formula for finding a batting average: Batting Average = Hits/At Bats.

2. Give students the following problem: o In one game Josh Hamilton gets 2 hits in 5 at bats. At the end of the game, what would be his new batting average?

3. Go over the problem. 2 hits/5 at bats = .400. (Remind students that batting average is always expressed to the thousandths place. In this case, zeroes must be added.)

4. Explain that if the 1-day average is greater than someone's overall average, the overall average will increase. If the 1-day average is lower than the overall average, the overall average will decrease.

5. Ask students, "Let's say that Josh Hamilton had an overall average of .302 before this game. What happened to his overall average after the game?" Since .400 > .302, his overall average will go up.

6. How much a player's batting average increases or decreases depends on the number of at bats the player already has. At the beginning of the season, a player's one-day average will have a greater effect on his overall average. At the end of the season, a one-day average will have a smaller effect.

7. You may choose to have students complete the "Batting Average Boost" worksheet before moving on to the activity, or you may assign it for homework.

8. Introduce the activity.

20 Statistics: Batter Up! - Level 2

Activity

1. Have students get together in the same pairs or groups they worked with during the activity in Lesson 1.

2. Pass out each group’s completed “Day 1 Station Packet,” and provide each group with a “Day 2 Station Packet.”

3. Explain that students are to work through each station again, and perform each activity five more times, documenting results and determining today’s average rate of success for each station.

4. Groups should then determine if their 2 nd day’s average would make their overall activity average go up or go down, and what the new overall activity average will become. Provide students with the following example : Let’s say Jason and Max had a .500 (5/10) average on Station 1 from Day 1. On Day 2, their average is .400 (2/5). Their overall average will go down, and the new overall average will become .467 (7/15).

5. Remind students to round each average to the nearest thousandth.

6. Assist students with stations as necessary.

Conclusion: To complete this lesson and check for understanding, come together as a class and have students compare their 2-day averages for each station. Then, total the aggregate data from each station. Discuss which type of graph would be the best fit for each station’s data set. Have students make the appropriate graphs for each station.

21 Statistics: Batter Up! - Level 2

(Day 2) Station 1: Quarters

Names: ______Instructions: 1) Choose a recorder for the group. 2) Choose one person who will spin the quarter 5 times. 3) The recorder should place a check in the box showing if each spin resulted in “heads” or “tails”.

Spin # Heads Tails 1 2 3 4 5

4) Count the number of times the spin turned up “heads.” ______

5) Set up a fraction showing the average number of spins that turned up “heads.” Number of “heads” results = Total number of spins

6) Calculate the average number of spins that turned up “heads.” ______

7) Compare your average result from today with your average result from yesterday. Will today’s average cause your overall average to go up or go down? ______

8) Calculate your overall activity average. Show your work. ______

22 Statistics: Batter Up! - Level 2

(Day 2) Station 2: Dice

Instructions: 1) Choose a recorder for the group. 2) Choose one person who will roll the pair of dice 5 times. 3) The recorder should place a check in the box if the roll resulted in 2 even numbers.

Roll # 2 Even Numbers 1 2 3 4 5

4) Count the number of times the roll came up as 2 even numbers. ______

5) Set up a fraction showing the average number of rolls that turned up 2 even numbers: Number of rolls with 2 even numbers = Total number of rolls

6) Calculate the average number of rolls that turned up 2 even numbers: ______

7) Compare your average result from today with your average result from yesterday. Will today’s average cause your overall average to go up or go down? ______

8) Calculate your overall activity average. Show your work. ______

23 Statistics: Batter Up! - Level 2

(Day 2) Station 3: Cards

Instructions: 1) Choose a recorder for the group. 2) Choose one person who will mix up the cards, then choose 5 cards without looking. 3) The recorder should place a check in the box showing if each card was a red card or a black card.

Draw # Red Black 1 2 3 4 5

4) Count the number of times a red card was chosen. ______

5) Set up a fraction showing the average number of times that a red card was chosen: Number of red cards = Total number of cards drawn

6) Calculate the average number of times a red card was chosen:______

7) Compare your average result from today with your average result from yesterday. Will today’s average cause your overall average to go up or go down? ______

8) Calculate your overall activity average. Show your work. ______

24 Statistics: Batter Up! - Level 2

(Day 2) Station 4: Marbles

Instructions: 1) Choose a recorder for the group. 2) Choose one person who will choose 5 marbles from the bag without looking. 3) The recorder should place a check in the box showing whether or not the marbles chosen were blue or another color.

Choice # Blue Another Color 1 2 3 4 5

4) Count the number of times a blue marble was chosen. ______

5) Set up a fraction showing the average number of times that a blue marble was chosen: Number of blue marbles chosen =

Total number of marbles chosen

6) Calculate the average number of times a blue marble was chosen:______

7) Compare your average result from today with your average result from yesterday. Will today’s average cause your overall average to go up or go down? ______

8) Calculate your overall activity average. Show your work. ______

25 Statistics: Batter Up! - Level 2

Batting Average Boost

Name: ______Date:______

You have been given a player's decimal batting average for the season so far, and then given the player's hitting success in his next game. You must decide whether the game performance boosts the player's season average. Write "up" or "down" in the appropriate column.

Player Season Next Game Up or Down Chipper Jones .275 0/4

Shane Victorino .279 1/3

Justin Upton .289 2/5

Prince Fielder .342 1/4

Carlos Beltran .320 3/5

Matt Holliday .339 2/3

Joey Votto .350 2/6

Derek Jeter .365 2/4

Jose Reyes .402 0/3

Jon Jay .264 3/4

26 Statistics: Batter Up! - Level 2

Batting Average Boost Answer Key

Player Season Next Game Up or Down Chipper Jones .275 0/4 Down

Shane Victorino .279 1/3 Up

Justin Upton .289 2/5 Up

Prince Fielder .342 1/4 Down

Carlos Beltran .320 3/5 Up

Matt Holliday .339 2/3 Up

Joey Votto .350 2/6 Down

Derek Jeter .365 2/4 Up

Jose Reyes .402 0/3 Down

Jon Jay .264 3/4 Up

27 Statistics: Batter Up! - Level 2

Lesson 3 – Pre-Visit Averages & Percentages

Objective : Students will be able to: • Convert averages to percentages and vice versa. • Use basic linear algebra to solve for an unknown variable.

Time Required : 1 class period

Materials Needed : - Copies of the "Performance Percentages" worksheet (included) – 1 for each student - “Linear Equations Activity Cards” (included), printed and cut out - “Averages and Percentages Activity Cards” (included), printed and cut out

28 Statistics: Batter Up! - Level 2

Applicable Common Core State Standards:

CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

CCSS.Math.Content.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

CCSS.Math.Content.7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

29 Statistics: Batter Up! - Level 2

Applicable Common Core State Standards ( Continued ):

CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable.

30 Statistics: Batter Up! - Level 2

Lesson

Part 1

1. Review the formula for finding a batting average: Batting Average = Hits/At Bats.

2. Discuss that this statistic is used to describe how successful a batter is at getting hits (singles, doubles, triples, and home runs) when he gets a chance to bat. Although this statistic is called an “average,” it could also be called a “percentage.” The data shows us what percent of the time the batter was successful.

3. Write down the average .275 on the board. Ask students, “How would this average be converted to a percentage?”

4. Using the example of .275, demonstrate that in order to change an average to a percentage, the decimal is moved two places to the right. Thus, .275 becomes 27.5%

5. Discuss that for a major league player, a .275 average is pretty good. However this means that the batter was successful just over 25% of the time. Nearly 73% of the time, he didn’t get a hit! This demonstrates just how difficult it is to be a major league batter.

6. Now demonstrate how to turn a percentage into a decimal. Write down the percentage 32% on the board. Ask students, “If we know that a player hit successfully 32% of the time, what is his batting average?”

7. Using the example of 32%, demonstrate that in order to change a percentage to an average, the decimal is moved two places to the left. Thus, 32% becomes a .320 average.

8. Have students complete the "Performance Percentages" worksheet before moving on to the activity.

9. If your students are very comfortable with this material, move on to Part 2 of this lesson, otherwise move directly to the activity.

31 Statistics: Batter Up! - Level 2 Part 2

10. Part 2 of this lesson places the information addressed earlier in the form of a linear equation. Students will use basic algebra to solve for a particular variable.

11. Ask students, “Let’s say we know that Derek Jeter went to bat 8 times during a double header. He hit successfully 62.5% of the time. How many hits did he get?”

12. Explain the process of solving the problem: o First, convert the percentage to a decimal. 62.5% becomes .625 o Now, place that information in the formula for batting average. H/AB = Average H/AB = .625 o The problem also tells us how many times Jeter went to bat. Place that information in the equation as well. H/8=.625 o To solve a linear equation, you have to add, subtract, multiply, or divide both sides of the equation by numbers and variables, so that you end up with a single variable on one side and a single number on the other. Any operation done on one side must be done on the other. o In this case, in order to get H by itself, multiply each side by 8. H/8 x 8 = .625 x 8 o We now have the answer: H = 5

13. Try a similar problem, this time solving for at bats. “Let’s say we know that Prince Fielder got 7 hits during a 3-game series. He hit successfully 63.6% of the time. How many times did Prince Fielder bat?” o Again, start by converting the percentage to a decimal. 63.6% becomes .636 o Place that information in the formula for batting average. H/AB = Average H/AB = .636 o Place Fielder’s number of hits into the equation. 7/AB = .636 o This time, in order to solve for AB, we need to first multiply by AB. 7/AB x AB = .636 x AB 7 = .636AB o Now we need to get AB by itself, so we divide by .636 on each side. 7/.636 = .636AB/.636 o We now have the answer: 11 = AB

32 Statistics: Batter Up! - Level 2

14. Remind students that when solving for hits or at bats, the answer must be a whole number. No one gets 6.5 hits in a game. Therefore the answer must be rounded to the nearest whole.

15. Introduce the activity.

33 Statistics: Batter Up! - Level 2

Activity

Option 1 – Averages & Percentages Only

1. Pass out “Averages and Percentages Activity Cards” (included), one to each student in the class.

2. Have the students convert the fractions into batting averages, then into percentages.

3. Once every student has finished, have students put themselves in order from the highest batting percentage to the lowest.

4. Finally, add the fractions to compute a collective batting average and batting percentage for the entire class.

Option 2 – Linear Equations

1. Pass out “Linear Equations Activity Cards” (included), one to each student in the class. Some students will solve for number of hits, some students will solve for number of at bats.

2. Have students solve their equations, then convert the player’s batting average to a percentage.

3. Once every student has finished, have students put themselves in order from the highest batting percentage to the lowest.

4. Finally, using the data determined from their equations, have students calculate a collective batting average and batting percentage for the entire class.

Conclusion: To complete this lesson and check for understanding, for homework, have students research the statistics for two baseball players of their choice. Compare their performances and determine which of the two had a better year statistically. Students should write an analysis that justifies their position.

34 Statistics: Batter Up! - Level 2

Performance Percentages

Name: ______Date:______

Part 1: You have been given players’ decimal batting averages, and players’ batting percentages. Convert each decimal to a percentage, and each percentage to a decimal.

Player Average Percentage Alex Rios .227 Mark Teixeira 24.8% Carl Crawford .255 Torii Hunter .262 Brett Gardner 25.9% Adrian Gonzalez 33.8% Juan Pierre .279 Casey Kotchman 30.6% Michael Young .338

Part 2: You have been given each player’s number of hits and number of at bats. Determine each player’s batting average, then convert the average into a percentage. The first problem has been done for you.

Player Hits At Bats Average Percentage Miguel Cabrera 197 572 .344 34.4% Jacoby Ellsbury 212 660 David Ortiz 162 525 Alex Gordon 185 611 Billy Butler 174 597 Robinson Cano 188 623 Ichiro Suzuki 184 677 Coco Crisp 140 531 Kevin Youkilis 111 431 B.J. Upton 136 560 Evan Longoria 118 483

35 Statistics: Batter Up! - Level 2

“Performance Percentages Answer Key”

Part 1: You have been given players’ decimal batting averages, and players’ batting percentages. Convert each decimal to a percentage, and each percentage to a decimal.

Player Average Percentage Alex Rios .227 22.7% Mark Teixeira .248 24.8% Carl Crawford .255 25.5% Torii Hunter .262 26.2% Brett Gardner .259 25.9% Adrian Gonzalez .338 33.8% Juan Pierre .279 27.9% Casey Kotchman .306 30.6% Michael Young .338 33.8%

Player Hits At Bats Average Percentage Miguel Cabrera 197 572 .344 34.4% Jacoby Ellsbury 212 660 .321 32.1% David Ortiz 162 525 .309 30.9% Alex Gordon 185 611 .303 30.3% Billy Butler 174 597 .291 29.1% Robinson Cano 188 623 .302 30.2% Ichiro Suzuki 184 677 .272 27.2% Coco Crisp 140 531 .264 26.4% Kevin Youkilis 111 431 .258 25.8% B.J. Upton 136 560 .243 24.3% Evan Longoria 118 483 .244 24.4%

36 Statistics: Batter Up! - Level 2

Averages & Percentages Activity Cards

Jose Reyes Ryan Braun Victor Martinez

181 187 178 537 563 540

Matt Kemp Lance Berkman Hunter Pence

195 147 190 602 488 606

Joey Votto Carlos Beltran Nelson Cruz

185 156 125 599 520 475

Albert Pujols Aramis Ramirez Derek Jeter

173 173 162 579 565 546

Melky Cabrera Matt Holliday Alex Avila

201 132 137 658 446 464

Austin Jackson Jose Bautista Michael Bourn

147 155 193 591 513 656

37 Vladimir Guerrero Justin Upton Jason Bay

163 171 109 562 592 444

Corey Hart Seth Smith Miguel Montero

140 135 139 492 476 493

Adam Jones Elvis Andrus Placido Polanco

159 164 130 567 587 469

Dexter Fowler Carlos Lee Neil Walker

128 161 163 481 585 596

38 Statistics: Batter Up! - Level 2

Linear Equations Activity Cards

Jose Reyes Ryan Braun Victor Martinez

181 = .337 X = .332 178 = .330 X 563 X

Matt Kemp Lance Berkman Hunter Pence

X = .324 147 = .301 190 = .314 602 X X

Joey Votto Carlos Beltran Nelson Cruz

X = .309 X = .300 125 = .263 599 520 X

Albert Pujols Aramis Ramirez Derek Jeter

173 = .299 173 = .306 X = .297 X X 546

Melky Cabrera Matt Holliday Alex Avila

X = .305 X = .296 137 = .295 658 446 X

Austin Jackson Jose Bautista Michael Bourn

147 = .249 155 = .302 X = .294 X X 656

Vladimir Guerrero Justin Upton Jason Bay

X = .290 X = .289 109 = .245 562 592 X

39 Corey Hart Seth Smith Miguel Montero

140 = .285 135 = .284 X = .282 X X 493

Adam Jones Elvis Andrus Placido Polanco

X = .280 X = .279 130 = .277 567 587 X

Dexter Fowler Carlos Lee Neil Walker

128 = .266 161 = .275 X = .273 X X 596

40 Statistics: Batter Up! - Level 2

Activity Cards Answer Key

Jose Reyes Ryan Braun Victor Martinez

181 187 178 537 563 540

(.337) (.332) (.330) Matt Kemp Lance Berkman Hunter Pence

195 147 190 602 488 606

(.324) (.301) (.314) Joey Votto Carlos Beltran Nelson Cruz

185 156 125 599 520 475

(.309) (.300) (.263) Albert Pujols Aramis Ramirez Derek Jeter

173 173 162 579 565 546

(.299) (.306) (.297) Melky Cabrera Matt Holliday Alex Avila

201 132 137 658 446 464

(.305) (.296) (.295) Austin Jackson Jose Bautista Michael Bourn

147 155 193 591 513 656

(.249) (.302) (.294)

41 Vladimir Guerrero Justin Upton Jason Bay

163 171 109 562 592 444

(.290) (.289) (.245) Corey Hart Seth Smith Miguel Montero

140 135 139 492 476 493

(.285) (.284) (.282) Adam Jones Elvis Andrus Placido Polanco

159 164 130 567 587 469

(.280) (.279) (.277) Dexter Fowler Carlos Lee Neil Walker

128 161 163 481 585 596

(.266) (.275) (.273)

Statistics: Batter Up! - Level 2

Applicable Common Core State Standards:

CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

CCSS.Math.Content.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

CCSS.Math.Content.7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 44 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson. Statistics: Batter Up! - Level 2

Applicable Common Core State Standards ( Continued ):

CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 45 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson. Statistics: Batter Up! - Level 2

Lesson

1. To begin this lesson, review the formulas for determining batting average and slugging percentage. *Note* If your students did not cover slugging percentage as part of their learning experience with the Baseball Hall of Fame and Museum, simply review batting average.

2. Ask students to brainstorm ways that statistics might relate to other baseball skills. Ask, “What are some activities that baseball players are expected to perform on the field at which they might not be successful every time.” Possible answers include: pitching a winning game, pitching many strikes, successfully stealing a base, etc.

3. Discuss that there could be (and there are) many different types of statistics for all sorts of activities that take place on the field. Students will now take a closer look at batting and pitching statistics from different eras.

4. Introduce the activity.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 46 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson. Statistics: Batter Up! - Level 2

Activity

1. Assign each student 2 weeks of game logs: one for a pitcher and one for a batter from the 1950s era, and one for a pitcher and one for a batter from the current year. Students will ultimately have 2 weeks of logs for 4 players. Game logs are available at http://baseball-reference.com .

2. Each game log should have Games, At Bats, Runs, Hits, 2B, 3B, HR, RBI, Put Outs, Assists, Errors for a batter. For a pitcher the log should have Games, Innings, Wins, Losses, Hits, Runs, Earned Runs, Strike Outs, and Walks.

3. Have students calculate the total for each category for each of their players.

4. Once students have finished, ask students questions to encourage them to interpret their players’ data. For example, “Based on your data, can you determine which skills your players were particularly good at?” “How did you reach that conclusion?”

5. As a class, create four master lists as follows: • 1950s Batters • 1950s Pitchers • Modern Pitchers • Modern Batters

6. Have all students report their data for each category. Calculate totals for each.

7. Look at the data compiled on the class master lists. Determine averages for each category.

8. Discuss what graphical representation would be the best fit for each data set. Have students make the selected graphs.

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 47 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson. Statistics: Batter Up! - Level 2

A Note about ERA: Measuring a pitcher's earned run average, or ERA, is a way of determining how effective the pitcher is without taking other players' errors into account. ERA represents how many runs a pitcher gives up during an entire game pitched, so the lower the number the better. ERA standards have varied throughout the years. Today, ERAs in the low 2.00s are considered excellent, with the average typically running over 4.00. (www.livestrong.com)

For this exercise, students don’t need to calculate ERAs. That information should already be on each pitcher’s game log. To determine the ERA of the aggregate data, students can simply average the ERAs already calculated.

Conclusion: To complete this lesson and check for understanding, have students compare the data from the 1950s with the data from the current year. Discuss the similarities and differences between the statistics of each era. What might account for the changes in statistics from the different eras?

For homework, have students write journal entries in which they address the importance of statistics. Do statistics tell a manager or an owner everything he or she needs to know about a player? What are some skills that can’t be revealed through statistics?

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 48 Waynflete School in Portland, ME – and – Daniel T. Crocker Math Teacher at Hall- Dale Middle School in Farmingdale, ME for their contributions to this lesson.