Big League Decisions
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Authentic Assessment in Algebra NCCTM 2009 Big League Decisions Brian Smith Wake Forest University [email protected] Introduction: Using statistical data to make decisions is a common and well-known everyday use of mathematics. Companies and corporations rely heavily on bright mathematical minds to make key choices using their skills in statistics. Major League Baseball is one business in which this type of analysis occurs every day, most specifically in the acquisitions of players. This project uses statistics from different players found in a baseball almanac to try and find a particular statistic that best predicts a player’s future success. In this case, at-bats define future success and batting average, hits, homeruns, on-base percentage and slugging percentage will be tested for their ability to predict success. Batting average represent the percent of a player’s at- bat where the player records a hit, on-base percentage is the percent of a player’s at-bat where the player reaches base, and slugging percentage is a weighted batting average, in which extra- base hits take on additional value. NCTM Standards: Algebra, Data Analysis & Probability, Communication, Connections, Representation, Problem Solving NCSCOS Objectives: Algebra II 2.04 Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data. a. Interpret the constants, coefficients, and bases in the context of the data. b. Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. Goals: Students will collect data from the internet and organize it in tables. They will then graph and analyze their data and make conclusions on what they observe. Activities: Working in small groups, students will select seven former rookies of the year to research Using http://www.baseball-almanac.com/, they will record the batting average, hits, home runs, on-base percentage and slugging percentage of the season in which the player won rookie of the year. They will also record the player’s lifetime at-bats. Students will record the data in a spreadsheet and construct a scatter plot for each statistical category. From this plot they will find a linear regression and a correlation coefficient for each set of data Each group will discuss their data and decide which category best predicts future success Assessment: Group work will be assessed informally, through observation and informal questioning. Each individual student will be given a list of five fictional baseball players, and will have to write a hypothetical, business letter to the general manager of their favorite baseball team about what player should be chosen and why they know he should be chosen by what they did with their groups in class. Students should attach their graphs and tables Authentic Assessment in Algebra NCCTM 2009 Directions 1. Go to http://www.baseball-almanac.com 2. Scroll over “History” and click on “Awards.” 3. Click on “Rookie of the Year” and then your player’s name. 4. Record data in your spreadsheet. Authentic Assessment in Algebra NCCTM 2009 Big League Decisions See http://www.baseball-almanac.com Player Career At- Batting Hits Home Runs On-base Slugging Bats Average (H) (HR) Percentage Percentage (AB) (AVG) (OBP) (SLG) Notes: All statistical categories with the exception of at-bats should only be taken from the year in which that particular player won the rookie of the year. The abbreviations in the parentheses are how each statistic is represented in the table on the website. Authentic Assessment in Algebra NCCTM 2009 Sample Student Work Player Career At- Batting Hits Home Runs On-base Slugging Bats Average (H) (HR) Percentage Percentage (AB) (AVG) (OBP) (SLG) Alvin Davis 4240 0.284 161 27 0.391 0.497 Ron Kittle 2708 0.254 132 35 0.314 0.504 Ozzie Guillen 6686 0.273 134 1 0.291 0.358 Walt Weiss 4686 0.25 113 3 0.312 0.321 Chuck Knoblauch 6366 0.281 159 1 0.351 0.35 Derek Jeter 8025 0.314 183 10 0.37 0.43 Nomar Garciaparra 5426 0.306 209 30 0.342 0.534 9000 8000 7000 6000 5000 Bats ‐ 4000 At 3000 2000 y = 48530x ‐ 8154.1 1000 0 R² = 0.4407 0.24 0.26 0.28 0.3 0.32 0.34 Batting Average *students will make a scatter plot and linear regression for all five statistics vs. at-bats Authentic Assessment in Algebra NCCTM 2009 Big League Decisions – Scoring Rubric Major League Minor League Little League 5 4 3 2 1 0 Internet Research Students effectively Students navigated website Students required navigated website and and gathered information assistance to navigate easily gathered from online almanac website and gather information from online information from online almanac almanac Data Table Data is presented Data is presented mostly Data table contains several accurately and neatly in accurately and neatly in inaccuracies and/or is not the table table neat Scatterplot/Regression Scatter plot is appropriate Scatter plot is appropriate Scatter plot may not and accurately represents and mostly accurate. appropriately represent data. Linear regression is Linear regression is data and has inaccuracies. graphed with points, graphed and includes title, Linear regression is includes title, labels and labels and correlation missing important correlation coefficient coefficient information Analysis and Students carefully Student’s conclusions Student’s conclusions Conclusions analyzed the information could be supported by simply involved restating collected and drew stronger evidence. Level information. Conclusions appropriate conclusions of analysis could have were not supported by supported by evidence. been deeper. Mathematical evidence. Mathematical Mathematical reasoning reasoning was mostly reasoning was not evident was evident evident Business Letter The letter looks The letter looks The letter is poorly professional and is clearly professional and is mostly organized and is unclear. written. It has no clear. It contains few It contains many grammatical errors and errors and does a good job grammatical errors and effectively portrays the of portraying the student’s does not portray the student’s conclusions conclusions students’ conclusions Total: Comments .