lesson 1 – pre-visit batting average...ccss.math.content.6.sp.a.1 recognize a statistical question...

Special Thanks to Thomas E. Campbell, 6-12 Math Teacher & Dean of Faculty at 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.

4

Statistics: Batter Up! - Level 2

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

Lesson 1 – Pre-Visit

Batting Average


5


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.


6


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.


7


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.

Lesson


8


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.


9


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.

Activity


10


• 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.


11


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.” ___________

(Day 1) Station 1: Quarters


12


Instructions:


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:______

(Day 1) Station 2: Dice


13


Instructions:


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:______

(Day 1) Station 3: Cards


14


Instructions:


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:______

(Day 1) Station 4: Marbles


15


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

Average

Fraction

Batting

Average

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


Babe Ruth


Hall of Fame Hitters


16


Hall of Fame Hitters Answer Key

Player Position At bats Hits Batting

Average

Fraction

Batting

Average

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

17



• Use multiple data sets to determine the overall success rate of a particular

activity.

• Select and create appropriate graphs representing data sets.


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 a opaque bag

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

Vocabulary:






Batting Average Ups and Downs

18











algorithm.


stand for numbers.






specified set.




such as by:






19












20


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.

Lesson

21


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 2nd

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.

Activity

22


Names: ______________________

_____________________________

_____________________________

Instructions:


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. ______________

(Day 2) Station 1: Quarters

23


Instructions:


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:______



down? _______________


(Day 2) Station 2: Dice

24


Instructions:


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:______



down? _______________


(Day 2) Station 3: Cards

25


Instructions:


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:______



down? _______________


(Day 2) Station 4: Marbles

26


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

Batting Average Boost

27


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

28



• Convert averages to percentages and vice versa.

• Use basic linear algebra to solve for an unknown variable.


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

Vocabulary:






Averages & Percentages

29











algorithm.


stand for numbers.






specified set.




such as by:






30












31


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.

Lesson

32


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

33


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.


34


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.

Activity

35


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

Performance Percentages

36


“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%

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 .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%

37


Averages & Percentages Activity Cards

Jose Reyes

181

537

Ryan Braun

187

563

Victor Martinez

178

540

Matt Kemp

195

602

Lance Berkman

147

488

Hunter Pence

190

606

Joey Votto

185

599

Carlos Beltran

156

520

Nelson Cruz

125

475

Albert Pujols

173

579

Aramis Ramirez

173

565

Derek Jeter

162

546

Melky Cabrera

201

658

Matt Holliday

132

446

Alex Avila

137

464

Austin Jackson

147

591

Jose Bautista

155

513

Michael Bourn

193

656

38

Vladimir Guerrero

163

562

Justin Upton

171

592

Jason Bay

109

444

Corey Hart

140

492

Seth Smith

135

476

Miguel Montero

139

493

Adam Jones

159

567

Elvis Andrus

164

587

Placido Polanco

130

469

Dexter Fowler

128

481

Carlos Lee

161

585

Neil Walker

163

596

39


Linear Equations Activity Cards

Jose Reyes

181 = .337

X

Ryan Braun

X = .332

563

Victor Martinez

178 = .330

X

Matt Kemp

X = .324

602

Lance Berkman

147 = .301

X

Hunter Pence

190 = .314

X

Joey Votto

X = .309

599

Carlos Beltran

X = .300

520

Nelson Cruz

125 = .263

X

Albert Pujols

173 = .299

X

Aramis Ramirez

173 = .306

X

Derek Jeter

X = .297

546

Melky Cabrera

X = .305

658

Matt Holliday

X = .296

446

Alex Avila

137 = .295

X

Austin Jackson

147 = .249

X

Jose Bautista

155 = .302

X

Michael Bourn

X = .294

656

Vladimir Guerrero

X = .290

562

Justin Upton

X = .289

592

Jason Bay

109 = .245

X

40

Corey Hart

140 = .285

X

Seth Smith

135 = .284

X

Miguel Montero

X = .282

493

Adam Jones

X = .280

567

Elvis Andrus

X = .279

587

Placido Polanco

130 = .277

X

Dexter Fowler

128 = .266

X

Carlos Lee

161 = .275

X

Neil Walker

X = .273

596

41


Activity Cards Answer Key

Jose Reyes

181 537

(.337)

Ryan Braun

187 563

(.332)

Victor Martinez

178 540

(.330)

Matt Kemp

195 602

(.324)

Lance Berkman

147 488

(.301)

Hunter Pence

190 606

(.314)

Joey Votto

185 599

(.309)

Carlos Beltran

156 520

(.300)

Nelson Cruz

125 475

(.263)

Albert Pujols

173 579

(.299)

Aramis Ramirez

173 565

(.306)

Derek Jeter

162 546

(.297)

Melky Cabrera

201 658

(.305)

Matt Holliday

132 446

(.296)

Alex Avila

137 464

(.295)

Austin Jackson

147 591

(.249)

Jose Bautista

155 513

(.302)

Michael Bourn

193 656

(.294)

42

Vladimir Guerrero

163 562

(.290)

Justin Upton

171 592

(.289)

Jason Bay

109 444

(.245)

Corey Hart

140 492

(.285)

Seth Smith

135 476

(.284)

Miguel Montero

139 493

(.282)

Adam Jones

159 567

(.280)

Elvis Andrus

164 587

(.279)

Placido Polanco

130 469

(.277)

Dexter Fowler

128 481

(.266)

Carlos Lee

161 585

(.275)

Neil Walker

163 596

(.273)


44











algorithm.


stand for numbers.






specified set.




such as by:







45













46


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.


Lesson


47


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.

Activity


48


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?

lesson 1 – pre-visit batting average...ccss.math.content.6.sp.a.1 recognize a statistical question...

Documents