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HCPSS Worthwhile Math Task Who Do You Pass The Ball To? Common Core Standard Summarize, represent, and interpret data on two categorical and quantitative variables. S.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP6: Attend to precision. Common Core Algebra I, Unit 4 The Task Pe’Shon Howard is under pressure. There are 1.5 seconds left in the game against Duke University and his Maryland Terrapins team is down by 2 pts. They are in the bonus for nonshooting fouls. (If they are fouled when not shooting, they will have a 1 and 1 situation – only if they make the first do they get to shoot a second time.) He is inbounding the ball at half line and he doesn’t know which of his teammates should get the ball so he calls a time out. The players below are on the court with him. To whom should he try to pass the ball? Support the decision with statistical evidence, making sure to include why you chose the player and why you did not choose the other 3 players. The table columns with percentages were left blank in case you would like to fill them in. Maryland Terrapins Men’s Basketball Season Statistics 2011-12, Listed alphabetically: Player FGM FGA FG% FTM FTA FT% 3PM 3PA Nick 96 257 70 113 23 85 Faust Sean 100 259 91 109 36 99 Mosely James 102 198 79 140 0 0 Padgett Terrell 220 553 159 202 91 237 Stoglin KEY: FGM = Field Goals Made – 2 pts each 3P% FGA = Field Goals Attempted Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. HCPSS Worthwhile Math Task FTM = Free Throws Made – 1 pt each 3PM = 3 Point Field Goals Made FTA = Free Throws Attempted 3PA = 3 Point Field Goals Attempted Source: http://espn.go.com/mens-college-basketball/team/stats/_/id/120/maryland-terrapins Facilitator Notes 1. Not all students may be familiar with the game of basketball and a scenario like this. It may be helpful to show a quick video clip and take some time to discuss some basic terms as a class to make sure that groups feel comfortable completing the task. 2. After students are finished completing the task, have them present their results to the class. Determine overall which player students would pass the ball to and if the data supports their decision. Most likely all groups will not agree on the same player, which leads to a great discussion of how data can support different solutions. (Look for evidence of MP2, MP3, and MP6.) Follow-Up Questions 1. Are the Terrapins home or away and does that have an impact on the decision? (Look for evidence of MP2.) 2. Do certain players match up better against Duke? (Look for evidence of MP2.) 3. Are there any substitute players on the bench that might be a better pick? 4. What are the stats for the game up to the last second? Which players are shooting well today? (Look for evidence of MP6.) 5. What are recent stats for the players, i.e. the last 3 games? 6. What is the team’s record in overtime overall and against Duke? This would influence whether to concentrate on going for the win (3pt play) or the tie. (Look for evidence of MP2 and MP6.) Solutions Completed Table with sample solution: Player FGM FGA FG% FTM Nick 96 257 37.4% 70 Faust Sean 100 259 38.6% 91 Mosely James 102 198 51.5% 79 Padgett Terrell 220 553 39.8% 159 Stoglin FTA 113 FT% 61.9% 3PM 23 3PA 85 3P% 27.1% 109 83.5% 36 99 36.3% 140 56.4% 0 0 0% 202 78.7% 91 237 38.3% Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. HCPSS Worthwhile Math Task If students decide to look at the overall percentage of shots made (field goals made + free throws made + 3 points made) over shots attempted (field goals attempted + free throws attempted + 3 points attempted) these are the results: Terrell Stoglin: 470/992 = 47.4%, Sean Mosely: 227/467 = 48.6%, Nick Faust: 189/455 = 41.5%, James Padgett: 181/338 = 53.6% If students look at an overall shooter (from the data above) Padgett appears to be the best, making 53.6% of all the shots he attempts. However he is also the player who takes the least amount of shots and he has not taken a 3 point shot all season. Furthermore, if he gets the ball and gets fouled he has the worst free throw shot average at 56.4%. If the students want Maryland to win the game by giving the ball to the person who makes the most 3 point shots, then Howard should pass it to Terrell Stoglin who has the largest percent of 3 point shots made at 38.3%. Although Stoglin has the best percentage, Mosely isn’t far behind. Mosely hasn’t taken as many shots overall as Stoglin so perhaps he is more cautious with his shots and is a better choice. It would be nice if we had the stats for both players against Duke to make a better decision. Faust’s 3 point percentage is at least 10% less than Stoglin so we shouldn’t consider him unless Duke puts some of its best defenders on Stoglin and Mosely and a pass to either isn’t possible. Hopefully, it is obvious if they want to win the game, he should not pass it to Padgett who hasn’t taken any attempts at this type of shot. If the students want to tie the game for a chance to go into overtime, they might go with Padgett who has the highest field goal percentage of 51.5%. However if he is fouled, he has the lowest percentage of free throws made at 56.4%. If he misses his first free throw Maryland will lose. Knowing that Duke might know who the better players are and that we are unsure if a foul might occur, we might choose Sean Mosely. Although he doesn’t have the highest 3 point or field goal percentage of the 4 players, he does have a good percentage overall, 48.6%, and the best free throw percentage, 83.5%, in case he is fouled. Hopefully, by passing the ball to him he will shoot either a 3 pointer to win the game, a 2 pointer to tie the game, or try to get fouled so that he can get 2 free throws, make both and tie the game. Follow Up Questions: Statistics to support answers to questions 1-5 can be found by accessing the source website listed and looking at the various categories as they might apply: home and away games, previous match ups against Duke, relevant statistics for all players, individual game statistics for players in each game, the team’s record and results, including those that resulted in overtime. Although Question #6 will not have direct statistics available, since most of the game has been played (all but 1.5 seconds), the students could look at statistics for a previous game and use those – possibly they would use a previous game against Duke. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.