© 21St Century Math Projects
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© 21st Century Math Projects Project Title: Gridiron Glory Standard Focus: Data Analysis & Probability Time Range: 3-5 Days (can be modified) Supplies: Graphing Calculators could be helpful (w/ regression functions), Paper Footballs, Long Tables (maybe borrow the cafeteria?!) Topics of Focus: - Measures of Central Tendency - Graphical Displays - Correlations - Expected Value - Data Collection Benchmarks : Interpreting Categorical 1. Represent data with plots on the real number line (dot plots, histograms, and S-ID and Quantitative Data box plots). 2. Use statistics appropriate to the shape of the data distribution to compare Interpreting Categorical S-ID center (median, mean) and spread (interquartile range, standard deviation) of two and Quantitative Data or more different data sets. Interpreting Categorical 3. Interpret differences in shape, center, and spread in the context of the data S-ID and Quantitative Data sets, accounting for possible effects of extreme data points (outliers). Interpreting Categorical 6. Represent data on two quantitative variables on a scatter plot, and describe S-ID and Quantitative Data how the variables are related. Interpreting Categorical 8. Compute (using technology) and interpret the correlation coefficient of a S-ID and Quantitative Data linear fit. Making Inferences and 2. Decide if a specified model is consistent with results from a given data- S-IC Justifying Conclusions generating process, e.g., using simulation. Using Probability to 2. (+) Calculate the expected value of a random variable; interpret it as the mean S-MD Make Decisions of the probability distribution. 3. (+) Develop a probability distribution for a random variable defined for a Using Probability to S-MD sample space in which theoretical probabilities can be calculated; find the Make Decisions expected value. Using Probability to S-MD 5b. Evaluate and compare strategies on the basis of expected values. Make Decisions © 21st Century Math Projects Procedures: A) Task 1: (p 4 – 6) Provide students with “Bragging Rights”. This assignment is designed more toward middle school students, but can be used for high school review. Students will analyze Super Bowl data to determine which divisions have historically had the most success. They will compute Winning Percentage and construct a bar graph and a pie graph. Provide students with copies of the Super Bowl Result table. B) Task 2: (p 7-8) Complete “Super Sunday LX”. This assignment is geared more toward students with algebra skills. Students will use historical television data to create lines of best to predict the future. This assignment would work best on TI graphing calculators. This also shows the limits of linear models because the Commercial Cost linear model has serious limitation. Provide students with copies of the Historical Super Bowl Television Data table. C) Task 3: (p 9-13) Complete “Super Sunday Predictions”. This is an advanced statistics assignment that will require calculations of Mean, Standard Deviation, Variance and beginning level usage of a T-Test. Students will analyze Points For and Points Against of Super Bowl Winners and Losers to see if there is a significant difference between the means (this is what the T-Test is for). If there is a significant difference, then that could be used to predict the winner of the next Super Bowl. Find out! D) Task 4: (p 14-15) Complete “Training Camp”. This is a preliminary assignment to the grand finale a Paper Football Championship Tournament! Students will measure their Paper Football skills with a variety of tasks. You will need a lot of flat table space. The cafeteria or library may be needed depending on your classroom. Students will need to work in groups of 3 or 4 to collect the data. 1 will be the player, 1 will be the aid (and goalposts) and 1 will record the data. Rules for Paper Football are provided in this PDF. With the results of the assignment, students will need to calculate their expected value. At the end they will use these four expected values to calculate their “Paper Football Rating”. Once all of the Paper Football Ratings are calculated, you should rank the students from highest to lowest. For the tournament, I would take either the top 8 or top 16 students and set up a tournament bracket (Round of 8 bracket provided). The students not playing can either be referees, coaches or they can play each other on the side. E) Task 5: (p 16 – 19) Students will participate in a Paper Football Championship Tournament. You can go as crazy with this as you’d like. If you want students to have team names and coaches, go for it. If you want a prize or a trophy, go for it. They will get into this. Each game should have two students playing the roles of referee and statisticians. These students should receive the “Drive Log” and mark attempts for further statistical analysis and keep score. The essential question with the Paper Football Championship is does the Expected Value “Paper Football Ratings” predict who the winner of the tournament will be. This is ultimately theoretical versus experimental probability. Nonetheless, it will be fun. © 21st Century Math Projects Every NFL team has a rivalry. Many of these rivalries stem from being in the same division and playing each other more often than any other teams. Some of these rivalries go back 50 years (Bears vs. Packers) and others are relatively new (Ravens vs. Steelers), but nonetheless they are all competing for the ultimate prize -- a Super Bowl Championship. Every team may feel their division is difficult, but which one has had the most historical success in the Big Game? Use the Super Bowl Results table to tabulate the correct data below. Then, use the Super Bowl Win data and total appearances to calculate a team’s Winning Percentage. You will use these results to answer follow-up questions (Hint: There have been 47 Super Bowls. If you total the wins and losses, these should add to 47 each.) Super Super Super Super Winning Winning Bowl Bowl Bowl Bowl AFC Pct. NFC Pct Wins Losses Wins Losses East East Buffalo Bills Dallas Cowboys Miami Dolphins New York Giants New England Patriots Philadelphia Eagles New York Jets Washington Redskins Total Total North North Baltimore Ravens Chicago Bears Cincinnati Bengals Detroit Lions Cleveland Browns Green Bay Packers Pittsburgh Steelers Minnesota Vikings Total Total South South Houston Texans Atlanta Falcons Indianapolis Colts* Carolina Panthers Jacksonville Jaguars New Orleans Saints Tennessee Titans Tampa Bay Buccaneers Total Total West West Denver Broncos Arizona Cardinals Kansas City Chiefs San Francisco 49ers Oakland Raiders** Seattle Seahawks San Diego Chargers St. Louis Rams*** Total Total Footnotes: *Formerly the Baltimore Colts **Also the Los Angeles Raiders ***Formerly the St. Louis Rams © 21st Century Math Projects Use the data create graphs and determine answers to the following questions. 1. Construct a Double Bar Graph to display the Wins & Super Bowl Appearances of the eight divisions. 2. Construct a Pie Graph for Super Bowl Wins by division. 3. Which division has the most Super Bowl Wins? Which has the least? 4. Which division boasts the highest winning percentage in the Super Bowl? 5. In your opinion, which division has achieved the most success in the Super Bowl? Use evidence from the data to support your claim. © 21st Century Math Projects Super Bowl Results Super Bowl Winning Team Score Losing Team I Green Bay Packers 35 – 10 Kansas City Chiefs II Green Bay Packers 33 – 14 Oakland Raiders III New York Jets 16 – 7 Baltimore Colts IV Kansas City Chiefs 23 – 7 Minnesota Vikings V Baltimore Colts 16 – 13 Dallas Cowboys VI Dallas Cowboys 24 – 3 Miami Dolphins VII Miami Dolphins 14 – 7 Washington Redskins VIII Miami Dolphins 24 – 7 Minnesota Vikings IX Pittsburgh Steelers 16 – 6 Minnesota Vikings X Pittsburgh Steelers 21 – 17 Dallas Cowboys XI Oakland Raiders 32 – 14 Minnesota Vikings XII Dallas Cowboys 27 – 10 Denver Broncos XIII Pittsburgh Steelers 35 – 31 Dallas Cowboys XIV Pittsburgh Steelers 31 – 19 Los Angeles Rams XV Oakland Raiders 27 – 10 Philadelphia Eagles XVI San Francisco 49ers 26 – 21 Cincinnati Bengals XVII Washington Redskins 27 – 17 Miami Dolphins XVIII Los Angeles Raiders 38 – 9 Washington Redskins XIX San Francisco 49ers 38 – 16 Miami Dolphins XX Chicago Bears 46 – 10 New England Patriots XXI New York Giants 39 – 20 Denver Broncos XXII Washington Redskins 42 – 10 Denver Broncos XXIII San Francisco 49ers 20 – 16 Cincinnati Bengals XXIV San Francisco 49ers 55 – 10 Denver Broncos XXV New York Giants 20 – 19 Buffalo Bills XXVI Washington Redskins 37 – 24 Buffalo Bills XXVII Dallas Cowboys 52 – 17 Buffalo Bills XXVIII Dallas Cowboys 30 – 13 Buffalo Bills XXIX San Francisco 49ers 49 – 26 San Diego Chargers XXX Dallas Cowboys 27 – 17 Pittsburgh Steelers XXXI Green Bay Packers 35 – 21 New England Patriots XXXII Denver Broncos 31 – 24 Green Bay Packers XXXIII Denver Broncos 34 – 19 Atlanta Falcons XXXIV St. Louis Rams 23 – 16 Tennessee Titans XXXV Baltimore Ravens 34 – 7 New York Giants XXXVI New England Patriots 20 – 17 St. Louis Rams XXXVII Tampa Bay Buccaneers 48 – 21 Oakland Raiders XXXVIII New England Patriots 32 – 29 Carolina Panthers XXXIX New England Patriots 24 – 21 Philadelphia Eagles XL Pittsburgh Steelers 21 – 10 Seattle Seahawks XLI Indianapolis Colts 29 – 17 Chicago Bears XLII New York Giants 17 – 14 New England Patriots XLIII Pittsburgh Steelers 27 -23 Arizona Cardinals XLIV New Orleans Saints 31 – 17 Indianapolis Colts XLV Green Bay Packers 31 – 25 Pittsburgh Steelers XLVI New York Giants 21 – 17 New England Patriots XLVII Baltimore Ravens 34 – 31 San Francisco 49ers © 21st Century Math Projects Every year the Super Bowl typically tops the highest rated television events and it is usually by a wide margin. Just like everything else, this has been the product of years of growth and increased interest.