7 th Grade Mathematics Lesson 1 1 “Baseball IS Math!” "Mathematics is the Alphabet with which God has written the Universe!" - Galileo "ALL Things Exist Through Mathematics." - Author unknown Reference to Tennessee Mathematics Standards: Mathematical Processes: Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely. (GLE 0606.1.6); Use technologies/manipulative appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to Create accurate and reliable models of mathematical concepts. (GLE 0606.1.8) Reference to Common Core State Standards: CCSS.Math.Content.4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Objectives: To identify two and three-dimensional shapes, line relationships, classify angles, and determine the ways that math is used in baseball. Materials: Paper and pencil Before the Game: Write the above quotes on the board. Allow students to share their thoughts regarding the quotes. Chart the responses. Use an overhead transparency of a baseball field or a picture. Have students identify perpendicular lines, parallels, angles, etc. Brainstorm a list of shapes found at a baseball park. Discuss “regular” shapes vs. “non-regular” shapes (congruent shapes, congruent sides, and congruent angles). Are there “shapes” which are symmetrical? Asymmetrical? Why does the baseball diamond need to be a regular quadrilateral? Why would it not be fair if it weren’t? At the Game and Beyond the Game: Classify objects seen at AutoZone Park into two and three-dimensional shapes. Have a scavenger hunt to find perpendicular lines, parallel lines, angles (obtuse, right and acute), and geometric shapes such as cones, spheres, etc. Find out how many lines of symmetry exist through the infield and through the entire field? Students may work in small groups to develop a list of all the different ways mathematics is used in the game of baseball (each student group should generate a list of at least 10 examples). Remind students to think about math uses before the game and after the game. Back in the classroom, compare lists. Identify: Who has the longest list? Who has the most unique response? Add to student generated lists. Create a diorama using geometric shapes
Transcript
7th Grade Mathematics Lesson 1
1
“Baseball IS Math!”
"Mathematics is the Alphabet with which God has written the Universe!" - Galileo "ALL Things Exist Through Mathematics." - Author unknown
Reference to Tennessee Mathematics Standards: Mathematical Processes: Read and interpret the language of mathematics and use written/oral communication to express
mathematical ideas precisely. (GLE 0606.1.6); Use technologies/manipulative appropriately to develop understanding of mathematical algorithms, to facilitate problem
solving, and to Create accurate and reliable models of mathematical concepts. (GLE 0606.1.8)
Reference to Common Core State Standards: CCSS.Math.Content.4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the
presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Objectives: To identify two and three-dimensional shapes, line relationships, classify angles, and determine the ways that math is used in baseball.
Materials: Paper and pencil
Before the Game: Write the above quotes on the board. Allow students to share their thoughts regarding the quotes. Chart the responses. Use an overhead transparency of a baseball field or a picture. Have students identify perpendicular lines, parallels, angles, etc. Brainstorm a list of shapes found at a baseball park. Discuss “regular” shapes vs. “non-regular” shapes (congruent shapes, congruent sides, and congruent angles). Are there “shapes” which are symmetrical? Asymmetrical? Why does the baseball diamond need to be a regular quadrilateral? Why would it not be fair if it weren’t?
At the Game and Beyond the Game: Classify objects seen at AutoZone Park into two and three-dimensional shapes. Have a scavenger hunt to find perpendicular lines, parallel lines, angles (obtuse, right and acute), and geometric shapes such as cones, spheres, etc. Find out how many lines of symmetry exist through the infield and through the entire field? Students may work in small groups to develop a list of all the different ways mathematics is used in the game of baseball (each student group should generate a list of at least 10 examples). Remind students to think about math uses before the game and after the game. Back in the classroom, compare lists. Identify: Who has the longest list? Who has the most unique response? Add to student generated lists. Create a diorama using geometric shapes
7th Grade Mathematics Lesson 2
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“Locating the Opponents”
The Memphis Redbirds play in a 16-team "AAA" baseball league known as the "Pacific Coast League." Teams are located in the Western, Midwestern and Southeastern United States.
Reference to Tennessee Mathematics Standards: Expressions & their Representation: Solve problems involving the addition, subtraction, multiplication, and division of
decimals. (GLE 0606.2.3)
Reference to Common Core State Standards: SPI 0606.2.3 Solve problems involving the addition, subtraction, multiplication, and division of
decimals.
Objectives: Interpret a map of the Pacific Coast League teams. Estimate the distance from Memphis, Tennessee to each opposing team. Students will complete the given chart and calculate the actual distances.
Materials: Pacific Coast League Map, United States Map, Pacific Coast League Mileage Chart and Memphis Redbirds 2011 Schedule
Before the Game: Study Pacific Coast League Map. Use the information to complete the chart below. Estimate the distance from Memphis, Tennessee to each opposing team. Ask students to compare their measurements with classmates. Next, measure the actual distance. Teach students to use string to measure the distance from city to city on a map. Using Pacific Coast League Mileage Chart, how close were your estimates?
7th Grade Mathematics Lesson 2
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Pacific Coast League Map
7th Grade Mathematics Lesson 2
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Distance from Memphis to Opposing Teams TEAM NAME (state) LOCATION (miles) ESTIMATION MEASUREMENT
(miles) DIRECTION TRAVELLED
Albuquerque Isotopes Colorado Springs Sky So Fresno Grizzlies Iowa Cubs Las Vegas 51s Nashville Sounds New Orleans Zephyrs Oklahoma City RedHawks Omaha Storm Chasers Reno Ace Round Rock Express Sacramento River Cats Salt Lake Bees Tacoma Rainiers Tucson Padres
At the Game: Students can list things at the ballpark located, North, South, East, and West of where their seats are located.
Beyond the Game: Redbirds 2011 schedule and Pacific Coast League Mileage Chart, calculate the total number of miles the Memphis Redbirds will travel this season, in a month, or in a week. If the Redbirds were travelling by bus, at 60 miles per hour, how long would it take to travel from Memphis to the various cities?
Reference to Tennessee Mathematics Standards: Mathematical Processes: Use mathematical language, symbols, and definitions while developing mathematical reasoning
(GLE 0606.1.1); develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas. (GLE 0606.1.3)
Number and Operations: Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals. (GLE 0606.2.4)
Data, Probability and Statistics: Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions. (GLE 0606.1.5)
Reference to Common Core State Standards: SPI 0606.2.4 Solve multi‐step arithmetic problems using fractions, mixed numbers, and
decimals.
Objectives: To calculate averages with decimal points.
Materials: Memphis Redbirds Statistics with a blank total column, Key Baseball Formulas, Memphis Redbirds Box Score, notebooks/pencils, and calculators
Before the Game: Review how to find an average. Use Key Baseball Formulas to discuss the procedure for finding a batting average and to calculate the total batting average for all batters on the team. Follow the same procedures to calculate the ERA for all pitchers on the team. Instruct the students how to track the hits made at a baseball game.
At the Game: Divide team players among class members (ex. 1B, 2B, RF, etc.). With a larger class, 2-3 students could be responsible for one position/player. Assign a position as opposed to a player name as the players could change before you get to the game! Students will record statistics in notebooks for their assigned player. Be sure that students record the number of times at bat with the number of hits, etc.
Beyond the Game: Calculate each player's batting average for the game. Make Memphis Redbirds Box Score into an overhead and record all players' statistics. Then calculate the teams overall batting average for the game. From the data collected, make a worksheet similar to Memphis Redbirds Statistics leaving out one player’s average but leaving a total this time. Then have students calculate and solve for the missing number.
Discussion:
What are the lowest and highest possible batting averages?
Which batter had the best performance? Why?
What does the batting average tell you about a batter’s performance?
How often would you expect a .300 hitter to get a hit?
Have students graph their results or graph results as a class.
Batting Average - AVG The most used statistic in baseball is “batting average.” The batting average is usually a decimal correct to three decimal places. The formula for determining a hitter’s batting average is the number of hits (H) divided by the bats (AB).
AVG = H ÷ AB
Below .220 weak hitter .220 - .250 low to average hitter .250 - .300 good, solid hitter .300 & up excellent hitter
On-Base Percentage – OB% This statistic shows the percentage of time a player can be expected to reach a base safely, either by a hit (H), a walk (BB) or being hit by a pitch (HBP). The on-base percentage is represented by a decimal and carried out to three decimal places. The higher the percentage, the more likely the play is to reach a base safely.
Slugging Percentage – SLG% The slugging percentage is used to compare power hitting in a fair way. This average is represented by a decimal and carried out to three decimal places. The slugging percentage is an average found by dividing the total bases (TB) by the at bats (AB).
SLG% = TB ÷ AB
Earned Run Average – ERA The earned run average is represented by a decimal and carried out to three decimal places. The formula for the earned run average is founded by multiplying a pitcher’s earned runs (ER) by nine and dividing that number by innings pitched (IP):
ERA = (ER * 9) ÷ IP
Home Run Expectancy - HR This measure shows, on the average, how often a player can be expected to hit a home run. This statistic is important because a player hitting a home run not only scores a run for the team, they hit in any other player who is on base prior to hitting the home run. The home run expectancy can be found by dividing the number of total at bats (AB and BB) by the number of home runs (HR). To simplify this as a unit ration, round to the nearest whole number.
HR: CUM AB RATIO = (AB + BB) ÷ HR
Strike Out Expectancy – SO This measure shows, on the average, how often a player can be expected to strike out. This statistic is important because not only does a strike out represent an out, runners on base cannot advance when this occurs. The strike out expectancy is found by dividing the number of cumulative at bats (AB) by the number of strike outs (SO). To simplify this as a unit ratio, round to the nearest whole number.
Oklahoma City RedHawks a-Struck out for Stoneburner in the 9th. BATTING 2B: Davis, C (1, Dickson), Garko (1, Dickson), Ramirez, M (1, Dickson), Petit, G (1, Kinney). HR: Davis, C (1, 4th inning off Dickson, 0 on, 1 out), Ramirez, M (1, 6th inning off Dickson, 1 on, 0 out). TB: Iribarren; Davis, C 7; Ramirez, M 6; Garko 3; Petit, G 2. RBI: Garko (1), Davis, C (1), Iribarren (1), Ramirez, M 2 (2). 2-out RBI: Garko; Iribarren. Runners left in scoring position, 2 out: Petit, G; Garko; Iribarren. S: Stoneburner. Team RISP: 3-for-12. Team LOB: 6. FIELDING E: Stoneburner (1, throw). PB: Ramirez, M (1). DP: 2 (Petit, G-Stoneburner-Frostad, E, Stoneburner-Petit, G-Frostad, E).
Player Pos AB R H 2B 3B HR RBI BB SO AVG
Taveras CF 5 0 0 0 0 0 0 0 0 .000
Iribarren LF 5 0 1 0 0 0 1 0 0 .200
Boggs, B RF 3 0 0 0 0 0 0 1 1 .000
Davis, C 3B 4 3 3 1 0 1 1 0 0 .750
Ramirez, M C 4 1 2 1 0 1 2 0 2 .500
Frostad, E 1B 4 0 0 0 0 0 0 0 2 .000
Garko DH 4 0 2 1 0 0 1 0 1 .500
Petit, G SS 4 1 1 1 0 0 0 0 0 .250
Stoneburner 2B 2 0 0 0 0 0 0 0 0 .000
a- Brown, M PH 1 0 0 0 0 0 0 0 1 .000
Memphis Redbirds
BATTING 2B: Cazana (1, Moscoso), Gotay (1, Moscoso). HR: Mather 2 (2, 2nd inning off Moscoso, 0 on, 0 out; 5th inning off Moscoso, 1 on, 1 out), Craig, A (1, 5th inning off Moscoso, 1 on, 1 out). TB: Rapoport 2; Descalso; Craig, A 4; Hamilton; Mather 8; Cazana 2; Gotay 3; Solano, D. RBI: Mather 3 (3), Solano, D 2 (2), Craig, A 2 (2). Runners left in scoring position, 2 out: Hamilton; Craig, A 2; Cruz, T; Gotay. GIDP: Cruz, T; Descalso. Team RISP: 1-for-10. Team LOB: 8. FIELDING E: Gotay (1, throw).
Player Pos AB R H 2B 3B HR RBI BB SO AVG
Rapoport CF 4 0 2 0 0 0 0 1 0 .500
Descalso 2B 4 1 1 0 0 0 0 1 2 .250
Craig, A LF 4 1 1 0 0 1 2 1 1 .250
Hamilton 1B 3 1 1 0 0 0 0 1 1 .333
Mather RF 4 2 2 0 0 2 3 0 0 .500
Cazana DH 4 1 1 1 0 0 0 0 1 .250
Gotay 3B 3 1 2 1 0 0 0 1 0 .667
Cruz, T C 4 0 0 0 0 0 0 0 1 .000
Solano, D SS 3 0 1 0 0 0 2 0 0 .333
Memphis Redbirds
Player IP H R ER BB SO HR ERA
Dickson (W, 1-0) 5.1 8 5 4 0 5 2 6.75
Scherer (H, 1) 0.2 0 0 0 0 0 0 0.00
Sanchez, E (H, 1) 2.0 0 0 0 1 1 0 0.00
Kinney (S, 1) 1.0 1 0 0 0 1 0 0.00 Eyre, W pitched to 2 batters in the 7th
Oklahoma City RedHawks
Player IP H R ER BB SO HR ERA
Moscoso (L, 0-1) 4.2 9 7 6 3 5 3 11.57
Eyre, W 1.1 2 0 0 1 0 0 0.00
Scheppers 2.0 0 0 0 1 1 0 0.00
WP: Dickson. HBP: Solano, D (by Scheppers). Pitches-strikes: Moscoso 102-61, Eyre, W 24-12, Scheppers 33-22, Dickson 100-65, Scherer 6-5, Sanchez, E 25-14, Kinney 12-9.Groundouts-flyouts: Moscoso 5-4, Eyre, W 3-1, Scheppers 1-3, Dickson 6-5, Scherer 1-1, Sanchez, E 4-0, Kinney 0-2. Batters faced: Moscoso 25, Eyre, W 6, Scheppers 8, Dickson 25, Scherer 2, Sanchez, E 7, Kinney 4.
Inherited runners-scored: Eyre, W 1-0, Scheppers 2-0, Scherer 1-0. Umpires: HP: Will Robinson. 1B: John Brammer. 2B: Tyler Funneman. 3B: Jason Millsap. Weather: 80 degrees, cloudy. Wind: 4 mph, In from CF. T: 3:09 Att: 3,195.
Reference to Tennessee Mathematics Standards: 5-7/Data Analysis & Probability: A. Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-
and-leaf plots, and other representations when appropriate. B. Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions. C. Collect, organize, display and interpret data for a specific purpose or need.
Mathematical Processes: D. Recognize whether an estimate or an exact solution is appropriate for a given problem situation. Number, Number Sense and Operations: E. Use a variety of strategies, including proportional reasoning, to estimate,
compute, solve and explain solutions to problems involving integers, fractions, decimals and percent’s.
Reference to Common Core State Standards: 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.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of
fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Objectives: To interpret statistics and create graphs and pie charts.
Materials: Pacific Coast League Ball Park Capacities & Dimensions, Graph paper, pencil, colored pencils or markers
Before the Game: Pacific Coast League Ball Park Capacities & Dimensions and from that information, create with the class, or have students in groups, or have students individually create graphs and pie charts that visually display these statistics. Create by hand, or on computers if available. Discuss predictions the students may have about the two league ballparks new to the 2011 season.
At the Game: Have students observe the crowd, or a specific section, to estimate attendance-using categories:
1. Male/Female 2. Age (0-2, 3-18, 19-50, 51 or older) 3. The number of innings people stay at the game 4. The number of fans wearing team apparel Jot down some notes...Document the findings on graphs? What is different between the students’ work? Discuss methods of estimation each student used.
Beyond the Game: Research the average size of lawn fertilizer sold using newspaper advertisements, estimate the amount of fertilizer needed for each ballpark.
Determine which ball park within the league is the largest, smallest, has the largest center field, etc. Research census data for each ballpark home town and develop graphs to compare park size with city population levels.
7th Grade Mathematics Lesson 4
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Pacific Coast League Capacities & Dimensions
Team Park Capacity
LF CF RF
Memphis Redbirds 14,000 319 400 322
Albuquerque Isotopes 12,700 325 400 325
Colorado Springs Sky Sox 9,000 350 400 350
Fresno Grizzlies 12,500 324 400 335
Iowa Cubs 11,000 335 400 335
Las Vegas 51s 9,334 328 433 328
Nashville Sounds 10,139 327 400 327
New Orleans Zephyrs 10,000 333 405 332
Oklahoma City RedHawks* 13,066 325 400 325
Omaha Storm Chasers 24,000 332 408 332
Reno Aces 9,000 339 410 340
Round Rock Express 11,722 330 400 325
Sacramento River Cats 14,414 330 403 325
Salt Lake Bees 15,500 345 420 315
Tacoma Rainiers* 9,600 325 425 325
Tucson Padres 11,500 340 405 340
*Team moves into new ballpark for 2011 Season. Data based on 2009 statistics.
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Reference to Tennessee Mathematics Standards: Mathematical Processes: use mathematical language, symbols, and definitions while developing mathematical reasoning
(GLE 0606.1.1); apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. (GLE 0606.1.2); Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas (GLE 0606.1.3); Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies. (GLE 0606.1.4); Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions (GLE 0606.1.5); Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely (GLE 0606.1.6); Recognize the historical development of mathematics, mathematics in context and the connections between mathematics and the real world (GLE 0606.1.7); Use technologies/manipulative appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts (GLE 0606.1.8)
Reference to Common Core State Standards: 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.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. CCSS.Math.Content.6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Calculating a Pitcher’s Earned Run Average ERA stands for Earned Run Average, which is the average number of times batters earn a run against a pitcher. The lower a pitcher’s ERA, the better. Use Key Baseball Formulas to view the calculation for ERA. 1. Calculate the average ERA of the Memphis Redbirds pitching staff using Memphis Redbird Statistics. 2. Using the statistics from the daily box score from “Education Day,” find the ERA for each starting pitcher. 3. Write a paragraph explaining why you think an ERA becomes more accurate with more innings pitched.
Calculating Batting Average Using Redbirds team statistics compute batting averages and graphically compare from one game to the next. Use www.memphisredbirds.com to locate Redbirds game day box scores and daily statistics. 1. Did the student correctly compute the averages? 2. Did the student display the results correctly? 3. At “Education Day,” calculate the Redbirds batting average for one inning.
Basic Math Skills Use paper and pencil or the calculator to find the answers to these problems. 1. I had 40 total hits for the season. I had 22 singles and 10 doubles. I had the same number of triples as home runs. How many
home runs did I have? 2. For the season, Joe had 47 total hits. He had 12 doubles, 3 triples, and 5 home runs. How many singles did he have? 3. I had 3 triples for the season. I had twice as many home runs as triples. I also had twice as many doubles as home runs. How
many extra base hits did I have?
Using Formulas to Calculate Statistics about Batting and Pitching Using paper, pencil and a stopwatch
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1. Estimate/calculate how fast a pitcher throws for either one inning or ten pitches. Students could use stopwatches to time how long it takes a pitch to get from the pitcher’s hand to the catcher’s glove. In class, use the formula “Distance = Rate x Time” to calculate the speed of the pitches. Students could create a spreadsheet of the information to compare speeds. In addition, compare speeds of students within the class or compare against Redbirds pitchers at “Education Day.”
2. Record the pitches thrown for an inning at “Education Day” and calculate the ratio of balls versus strikes thrown by the pitcher.
3. Keep blank scorecards available in the classroom. Students can take home cards and watch games on television using the same concepts as lesson #5
Use the Students’ Experience and Activities from “Education Day” to Estimate Totals for an Entire Game or Season Using AutoZone Costs, pencil, and paper 1. Use the announced attendance for “Education Day” to create calculations.
a. If the Redbirds averaged the same attendance as “Education Day,” what would their total attendance be for the season (based on a 71-game home season)?
b. If everyone paid $2 per ticket, how much money was collected for admission for the day? c. Create a chart comparing how much money each student spent for the day. Calculate the average amount of
money spent per student on food and souvenirs. Using that average, calculate how much the entire crowd spent.
2. Have students keep track of how they spent their time at the game. What percentage of their time was spent where?
Comparison of Student/Player Information Using Redbirds 2011 Roster, calculate the average height, weight, and age for the Redbirds players. Have students select a player and compare their height, weight, and age with those of that player. Students can calculate differences and find percent differences, etc.
Using Maps 1. Using Redbirds 2011 Roster, have students calculate the distance each Redbirds player is from their hometown to Memphis.
Convert miles to yards to feet to inches or into metric units. Which players are the farthest from home or the closest to home?
2. Using Pacific Coast League Mileage Chart, determine how far the opposing team travels to get to the game. 3. Using an average speed, calculate how long it will take the visiting team to get to the game. 4. Use the same calculations to compare how long it will take your class to get to the game. Estimate the distance prior to the
trip and compare the estimations to actual data. Compare this to the travels of the visiting team.
Mock Draft Using Memphis Redbirds Statistics and Redbirds 2011 Roster, divide students into teams and hold a mock draft of Redbirds players. 1. Why were some players taken before others? Ask students to support their selections with the statistics given. 2. Did students use the statistical information to make 3. Sound decisions as to who to draft? 4. Discuss how this process is similar to real drafts. 5. How was it determined who received the 1st pick? What were the chances that your team was going to receive the first pick
in the draft?
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Calculating Baseball Using Memphis Redbirds Statistics and Key Baseball Formulas, duplicate Memphis Redbirds Statistics with blank columns such as AVG, ERA, HR, and SO. Have students perform calculations to fill in the missing statistics.
Statistics Predictions Have students make predictions on number of pitchers thrown by starting pitcher, number of hits, runs, errors, etc. Count numbers at game and graph predictions and actual numbers at school
