Class: Algebra i-a
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Primary Subject Area: Mathematics Outside Subject Area: Physical Education Class: Algebra I-a Class Level: F.L.I.P. Grade Level: 9th grade PBL Title: What are the odds? Free throws from a far Description of Student Roles and Problem Situation: Students become the stakeholders when they assume the role of Basketball coaches for a professional basketball team named the “Juggernauts”. On the opposite end, students will also become stockholders as professional basketball players looking to increase their probability of free throw shots. As of late, the Juggernauts have lost 6 games each by less than 4 points apiece. The owner, Dr. Ramey, demands that the coaches make an improvement at the free throw line. Before the Juggernauts lose any more games, the coaches forced by Dr. Ramey, are trying to improve their free throw shots so they can pull out of this slump. Adaptations for a student from a non-Western culture: Students from a non-western culture will be able to research and give a presentation on basketball from their home country. Student would then research other sports in which odds or probability is used. Adaptations for ESOL student: Student will be given a translated copy of the assignment to their native language. If possible, I will do my best to pair the student up with another student who may be able to translate their native tongue. Also with funds given for ESOL students, rosetta stone shall be ordered for them in their native language. The student shall be 200% extra time on the given PBL assignment. Title, Learner Characteristics, Sunshine State Standards Teacher: Thomas Rhea Primary Subject Area: Mathematics Outside Subject Area: Physical Education Class and Level Algebra I - F.L.I.P. Grade Level: 9th grade Primary Sunshine State Standards: Data Analysis and Probability Standard 2: The student identifies patterns and makes predictions from an orderly display of data using concepts of probability and statistics. (MA.E.2.4) MA.E.2.4.1. - Determines probabilities using counting procedures, tables, tree diagrams, and formulas for permutations and combinations. MA.E.2.4.2. - Determines the probability for simple and compound events as well as independent and dependent events. Outside Subject Area Sunshine State Standards: The student applies concepts and principles of human movement to the development of motor skills and the learning of new skills. (PE.A.2.4) PE.A.2.4.2. - Knows how to analyze, evaluate, and implement the mechanical principles of balance, force, and leverage that apply directly to self-selected activities Learner Characteristics of High School Students: Physical: Students of all ages and gender start to grow in all aspects of life. Most every high school student will reach physical maturity and eventually hit puberty (Pg. 91). Although, many students will reach their peak heights, while others will still continue to grow after graduation (Pg. 92). Physical characteristics play a key part in physical activities where probability and odds are calculated. The taller, more athletic student will have an increased chance of winning a sporting event. Social: High school students often times partake in an after school job. A survey showed that in the months of 1999 – 2000 68.3% of sixteen year olds worked part time during the school year (Pg. 94). There are pros and cons to working after school. A job can lead to building traits that cannot be seen on paper such as a character and discipline. At the same time, a job may also lead to a drop in grades or lack of energy during school hours. This can play a major role, because the odds of a student making to a college or trade school can often reduced or increased based on their participation in an after school job. Emotional: Many psychiatric disorders appear or become prominent during adolescence. Including among these are eating disorders, substance abuse, schizophrenia, depression, and suicide. With odds and probability being the topic at hand, the percent of students who partake in disorders such as binge drink can be brought to light. As a class, students can understand how many students fall under these categories. Cognitive: High school students become increasingly capable of engaging in formal thought, but they may not use this capability. Often times in math, students see the numbers, but do not truly understand what they mean. This unit on odds will allow students the chance to see what a percent actually is and how they formulate them from statistics. Cognitive: Between the ages of twelve and sixteen, political thinking becomes more abstract, liberal, and knowledgeable. The PBL activity will allow students to look at politics in a whole new light. As students begin to mature and their interest in politics become more prominent, they need to know how laws are passed. Through legislation and delegations, students will find that most laws are passed by the number of votes, which in turn is actually an odds in itself. Learning Outcomes, Student Role & Problem Situation, Meet the Problem Method Title: What are the Odds? : Free Throws from a Far Coach Rhea
LO #1: Given 10 free throw shots in basketball, students will demonstrate the ability to find the outcome of made shots using probability with 100% accuracy. (Comprehension) MA.E.2.4.2. - Determines the probability for simple and compound events as well as independent and dependent events. LO #2: Given 10 free throw shots in basketball, students will contrast the difference between the probability and odds with 100% accuracy. Outside Subject Area Sunshine State Standards: PE.A.2.4.2. - Knows how to analyze, evaluate, and implement the mechanical principles of balance, force, and leverage that apply directly to self-selected activities. LO #3: Given 10 free throw shots, students will correctly modify the mechanics of their free throw shots to increase the probability of shots being made. Description of Student Roles and Problem Situation: Students become the stakeholders when they assume the role of Basketball coaches for a professional basketball team named the “Juggernauts”. On the opposite end, students will also become stockholders as professional basketball players looking to increase their probability of free throw shots. As of late, the Juggernauts have lost 6 games each by less than 4 points apiece. The owner, Dr. Ramey, demands that the coaches make an improvement at the free throw line. Before the Juggernauts lose any more games, the coaches forced by Dr. Ramey, are trying to improve their free throw shots so they can pull out of this slump. How can we, as professional basketball coaches modify our player’s free throw shot in such a way that it: Increases the percentage of free throws made Closes the gap in tight game situations Increases ticket revenue Before the All-Star Break (Half-way mark of the season).
Lynn Haven JUGGERNAUTS 401 Mosley Dr. Dear Players and executives, It has come to the organizations attention that our overall game play has been in a decline since the second week of the season. We have somehow managed to lose the last 6 games each by a score of less than 4 points. This is not something that neither I, nor any of the boosters will stand for in the Juggernaut organization. We as a whole have invested too much and will not allow this to continue. It is my goal from here on out to turn the season around and continue on to our ultimate goal of winning a NBA World Title. We will have to start by placing a greater emphasis on our number of shots made and missed at the free throw line. I expect for us to regain the eastern lead by the end of the All-Star Break. Remember, “The only easy day was yesterday”. I have all the confidence in the world in each and every single one of you. I look forward to the rest of a great and exciting season. “Juggernauts don’t rebuild, we RELOAD” Sincerely, Dr. Ramey CEO
Investing in Free Throws Pays Off Top of Form
By BENJAMIN HOFFMAN Published: January 15, 2007 The Dallas Mavericks, the N.B.A.’s top team this season, are no strangers to winning ways, but in getting an edge on opponents over the past several years, they have gone beyond sheer talent. The Mavericks have what amounts to a secret weapon in Gary Boren, an investment banker who is the N.B.A.’s lone free-throw coach. Boren, 67, has been with the Mavericks as an assistant since 1999 while working in banking. He is an adviser to The Equity Group, which is based in Dallas. Since he joined the Mavericks, they have finished in the top six in the league each season in free-throw shooting, including four first-place finishes. This season, Boren has them at 80.7 percent, the fourth time his team has been higher than 80 percent at the line. “He has been invaluable to us and a big part of our success,” the Mavericks’ owner, Mark Cuban, said in an e-mail message. Boren begins by filming the players shooting free throws. “What’s amazing is, these guys have seen miles of film running up and down the court and the coaches are yelling at them, but not one in a hundred has been filmed standing still shooting a free throw,” Boren said. There are 41 common problems that Boren is looking for in the footage, but he cautions that merely telling a player what he is doing wrong will not help him. He must first deal with the mental barriers that players put up. “They all think they’re better shooters than they are,” Boren said. “I’m not trying to make them all look like Mark Price,” Boren said of the former N.B.A. guard of the late 1980s and ’90s, who played mostly with the Cleveland Cavaliers. Price was a 90 percent career free-throw shooter, the best in league history. “I’m trying to take what they’ve got — because they’ve already shot thousands of shots — and tweak their shot in the most important areas that will give them a shot to get better.” Even when the player wants to learn, Boren must conquer another barrier. He tells them: “When I look at you, I see two things — a brain and a bunch of muscles — and the good news is the brain is really clicking. But the bad news is your muscles have been taking a siesta. They like it the old way and they’re not paying attention to any of this stuff. So when we get down there, they’re going to resist.” Possibly Boren’s biggest success story was the 7-foot-6 center Shawn Bradley. During the early part of his career, Bradley shot mostly between 60 to 70 percent from the free-throw line. Working with Boren, he reeled off three consecutive seasons above 80 percent, including 92.2 percent in 53 games in 2001-2. “Shawn worked on the mechanics, did everything I wanted him to, and he went to 90 percent,” Boren said. In 1993, Boren approached Don Nelson, who was the coach of the Golden State Warriors, the league’s worst club from the free-throw line, and offered to help. Nelson used Boren as a free-throw adviser with the Warriors and when he coached the Knicks, then made him an assistant when he became the coach of the Mavericks. Nelson and Avery Johnson, who replaced him as the coach of the Mavericks during the 2004-5 season, allowed Boren to have autonomy over free-throw shooting. Boren credits Denny Price, Mark’s father, with teaching him the fundamentals. Denny Price taught Mark free-throw shooting when he coached him in high school and continued to give his son advice throughout his N.B.A. career. When Boren decided to pursue ways to help players with free throws, he sought out Denny Price, whom he had met, and received pointers from him. “By no stretch am I claiming to have dreamed all this stuff up,” Boren said, laughing. “I tell people that knew who Mark was and his daddy Denny that 98 percent of what you’re hearing from me, just pretend you’re listening to Denny Price talking.” Despite Boren’s success, no other teams have hired a free-throw coach. “It’s so simple what’s going on here,” Boren said. “It’s just crazy that there’s no other free throw coaches in the league.”
Bottom of Pro Basketball
Missed Free Throws Prove Costly to the Juggernauts Again Top of Form Bottom of Form
By JOHN ELIGON Published: February 6, 2007 PHILADELPHIA, Feb. 5 — When a team is as erratic as Lynn Haven Juggernauts, what should be routine — making free throws and beating teams that are competing for lottery picks — becomes surprisingly difficult. Skip to next paragraph 
George Widman/Associated Press Vince Carter, top, led the Juggernauts with 23 points. The Juggernauts missed 12 of 29 free throws against the Philadelphia 76ers on Monday night, several at important times, and lost, 100-98, in overtime at the Wachovia Center. It was their fourth defeat in a row and the second consecutive one in overtime. What was supposed to be a relatively easy week for the Juggernauts (22-27), with four games against teams toward the bottom of their divisions, is turning nightmarish. On Sunday, the Juggernauts lost in overtime to the Atlanta Hawks. The only other time the Juggernauts have lost consecutive overtime games in their history was in 1977. “We’re beating ourselves, and we know that,” said Juggernauts center Mikki Moore, who had 11 points and 8 rebounds. Andre Iguodala led the 76ers with 23 points and a career-high 15 assists. Vince Carter scored 23 points, but he missed a couple of crucial free throws. With 36.1 seconds left in regulation and the Juggernauts trailing, 86-84, Carter made one of two. With just over a minute to play in overtime and the Juggernauts down by 4, Carter missed another free throw. Carter had an opportunity for redemption with a 3-point attempt as time was winding down in overtime, but it rimmed out and the Juggernauts did not take another shot. The Juggernauts are making things difficult on themselves, Carter said, with “our defensive lapses, our inability to score sometimes.” He added: “At the same time, we got to make our free throws. Everything’s going wrong, but at the same time we just have to stick together.” Even when the Juggernauts did something right Monday, they were holding themselves back at the same time. During a third-quarter stretch in which the Juggernauts outscored the Sixers by 6-2 and held them without a field goal for four minutes to increase their lead to 11, they missed six of eight free throws. Those misses allowed the Sixers (16-33) to hang around, and they closed the quarter on a 12-2 run to trail by only a point entering the fourth quarter. (A day earlier against the Hawks, the Juggernauts missed 14 of 34 free throws.) “They’re empty possessions,” Juggernauts Coach Lawrence Frank said of the missed free throws. “It’s just like a turnover. We’re going through a repeated exercise, so hopefully at some point we’ll crack the code.” The Juggernauts put themselves in a precarious position in the fourth quarter, when their defense disappeared and they allowed the Sixers to use a 14-4 run to turn a 4-point deficit into a 6-point lead. But the Juggernauts fought back and forced overtime when Eddie House hit a 3-pointer with 7.8 seconds remaining to tie the score at 88-88. In overtime, the Juggernauts made only 3 of 8 field-goal attempts, while the Sixers shot 55.6 percent. Even though it seemed as if the Sixers had an easy time cracking the Juggernauts’ defense, Moore said it was not necessarily so. He pointed to a pair of shots by the Sixers’ Joe Smith — an off-balance leaner late in the fourth quarter and a 19-footer in overtime with a hand in his face. “If you got their center shooting the ball way out there, that’s good defense,” Moore said. “That’s what you got to take.” As much as the Juggernauts may try to find positives — several times their captain, Jason Kidd, reiterated the point, “We’re going out there and we’re competing” — their situation could soon become dire. The Juggernauts are three and a half games behind Toronto for first place in the Atlantic Division, which the Juggernauts have won in four of the past five seasons. The Juggernauts are in ninth place in the Eastern Conference, a game and a half behind Miami; the top eight teams make the playoffs. After winning 9 of 11 games from late December through late January, the Juggernauts have lost seven of nine. The Juggernauts are also falling on the wrong end of close games. Five of their past seven defeats have come down to a single possession. “You would think that the percentages would change and be in our favor,” said Kidd, who had 14 points, 8 assists and 7 rebounds. “Right now we’re in a rough patch. We’re not getting that stop or making that shot.” With the same core group as last season, the Juggernauts may have entered this season with the attitude that they could strut to another division title. They may finally be starting to realize that it will not be that easy. “Sooner or later, it’s got to be turned around,” forward Cliff Robinson said before the game. “It’s got to be consistent basketball. It can’t be good games for a stretch and then bad games for a stretch.”
Title: What are the Odds? : Free Throws from a Far Coach Rhea
LO #1: Given 10 free throw shots in basketball, students will demonstrate the ability to find the outcome of made shots using probability with 100% accuracy. (Comprehension) MA.E.2.4.2. - Determines the probability for simple and compound events as well as independent and dependent events. LO #2: Given 10 free throw shots in basketball, students will contrast the difference between the probability and odds with 100% accuracy. Outside Subject Area Sunshine State Standards: PE.A.2.4.2. - Knows how to analyze, evaluate, and implement the mechanical principles of balance, force, and leverage that apply directly to self-selected activities. LO #3: Given 10 free throw shots, students will correctly modify the mechanics of their free throw shots to increase the probability of shots being made. Description of Student Roles and Problem Situation: Students become the stakeholders when they assume the role of Basketball coaches for a professional basketball team named the “Juggernauts”. On the opposite end, students will also become stockholders as professional basketball players looking to increase their probability of free throw shots. As of late, the Juggernauts have lost 6 games each by less than 4 points apiece. The owner, Dr. Ramey, demands that the coaches make an improvement at the free throw line. Before the Juggernauts lose any more games, the coaches forced by Dr. Ramey, are trying to improve their free throw shots so they can pull out of this slump. Problem Statement:
Meet the Problem Documents: Internet Sources: http://www.82games.com/random20.htm http://www.swish22.com/article2.html http://www.mrbasketball.net/instuff/30tips/e5art2FreeThrowShot.html http://ezinearticles.com/?Shooting-The-Perfect-Free-Throw&id=287838 News Paper Sources: See attached: Know/Need to Know Board What We Know:
What We Need to Know:
Capstone Description What are the Odds: Free throws from afar Primary Sunshine State Standards: MA.E.2.4.1. - Determines probabilities using counting procedures, tables, tree diagrams, and formulas for permutations and combinations. LO #1: Given 10 free throw shots in basketball, students will demonstrate the ability to find the outcome of made shots using probability with 100% accuracy. (Comprehension) MA.E.2.4.2. - Determines the probability for simple and compound events as well as independent and dependent events. LO #2: Given 10 free throw shots in basketball, students will contrast the difference between the probability and odds with 100% accuracy. Outside Subject Area Sunshine State Standards: PE.A.2.4.2. - Knows how to analyze, evaluate, and implement the mechanical principles of balance, force, and leverage that apply directly to self-selected activities. LO #3: Given 10 free throw shots, students will correctly modify the mechanics of their free throw shots to increase the probability of shots being made.\ Description of Student Roles and Problem Situation: Students become the stakeholders when they assume the role of Basketball coaches for a professional basketball team named the “Juggernauts”. On the opposite end, students will also become stockholders as professional basketball players looking to increase their probability of free throw shots. As of late, the Juggernauts have lost 6 games each by less than 4 points apiece. The owner, Dr. Ramey, demands that the coaches make an improvement at the free throw line. Before the Juggernauts lose any more games, the coaches forced by Dr. Ramey, are trying to improve their free throw shots so they can pull out of this slump. Problem Statement:
Capstone Performance: As professional basketball players, students will participate in a real-life assessment that will test their ability to calculate probability and odds. Each student will be assessed on an individual basis. The students will be taken out of the classroom environment and brought down the gym. Students will take part in a free throw competition to see who can have the highest free throw average. Students will be separated into two groups; one group of boys and one group of girls. Each student will first shoot 10 free throws and then record the number of free throws made and the number of free throws missed. After every student has had his or her turn, the head boys’ basketball coach will give instructions on how to modify his or her shots. The students will then get a practice round of free throw shots to determine the 2 best coaching tips that helped increase their free average. After the practice round, the students will get a final 10 free throws using their modified techniques. Each student will record the new number of made free throw and the number of missed shots. Once all students record their free throws, the students will then be moved back to the classroom to finish the capstone performance. Each student will be given a Free Throw conversion chart to accurately determine the number of free throws made and missed. Each student will then determine the probability and odds of their first round of free throw shots. Then each student will determine the probability and odds of the round of free throws after being coached to modify and improve their shots. After finding the probability and odds of both rounds, students will then find the change of percent and state whether it was an increase or decrease in free throws made. The final portion of the capstone performance will be to list the best over coaching solution that led to an increase in free throw shots. Finally, students will identify at least 4 reasons why they chose one of Coach Martello’s tips as their best coaching solution.
Scoring Guide A = 45 - 50 Total Points B = 40 – 44 Total Points C = 35 – 39 Total Points Resubmit = 0 – 34 Total Points.
Solution #1 Aim for a target just above the rim, and try not to shoot the ball short. A good target is the backboard shooting square drawn above the rim. Pros:
Cons:
Possible Consequence:
Solution #2 Bend your knees. An accurate shot doesn't rely on arm strength; it uses leg strength to propel the shooter upward. Pros:
Cons:
Consequences:
My preference is that each player will use solution #2. In order to re-create a well practice shot, a player, must bend his or her legs and use the upward motion to shoot a free throw. I believe that using the backboard would lead to shooters aiming and trying to shoot the ball at a certain spot instead of perfect a shot without thinking. Free throws are a very important part to a team’s over success during a full season. By practicing a free-throw shot using legs instead of arms, a more repetitive shot is created without actually thinking. This unconscious consciousness allows player to play rather than think. Next time you are watching a professional basketball game, ask yourself, “How many times did I see a player use the backboard during a normal free throw shot?”. Debriefing Plan and Coaching Questions What are the Odds: Free throws from afar Primary Sunshine State Standards: MA.E.2.4.1. - Determines probabilities using counting procedures, tables, tree diagrams, and formulas for permutations and combinations. LO #1: Given 10 free throw shots in basketball, students will demonstrate the ability to find the outcome of made shots using probability with 100% accuracy. (Comprehension) MA.E.2.4.2. - Determines the probability for simple and compound events as well as independent and dependent events. LO #2: Given 10 free throw shots in basketball, students will contrast the difference between the probability and odds with 100% accuracy. Outside Subject Area Sunshine State Standards: PE.A.2.4.2. - Knows how to analyze, evaluate, and implement the mechanical principles of balance, force, and leverage that apply directly to self-selected activities. LO #3: Given 10 free throw shots, students will correctly modify the mechanics of their free throw shots to increase the probability of shots being made.\ Description of Student Roles and Problem Situation: Students become the stakeholders when they assume the role of Basketball coaches for a professional basketball team named the “Juggernauts”. On the opposite end, students will also become stockholders as professional basketball players looking to increase their probability of free throw shots. As of late, the Juggernauts have lost 6 games each by less than 4 points apiece. The owner, Dr. Ramey, demands that the coaches make an improvement at the free throw line. Before the Juggernauts lose any more games, the coaches forced by Dr. Ramey, are trying to improve their free throw shots so they can pull out of this slump. Problem Statement:
Debriefing Plan: Once all students have participated in the free throw tournament, they will then be brought back to the classroom to complete the rest of the summative assignment. Each student shall complete a free throw conversion chart and then record their best solutions from best to worst and then state their overall best solution. The students will number their best solutions starting with the best one as #1 and then the next best solution as #2, and so on. Once all completed summative assignments have been turned in, the teacher will act as the scribe and record each students’ best overall solution. The tally will then be added up and presented to the class. The two solutions receiving the least amount of votes will be deemed the best overall. Through class discussion, we as a whole will react to the best overall solution and see if there is any way that we can modify the free-throw technique in any way to improve it.
1st 1 2nd 2 3rd 3 4th 4 5th 5 Five Essential concepts: The “best” solutions must utilize accurate scientific concepts. This includes explaining how each of these increases the odds/probability of making a free-throw shot.
While competing in the free-throw competition, during the practice round students shall record what concept they focused on while they were shooting each individual free-throw. Coaching questions: C – Cognitive M – Meta-cognitive E – Epistemic
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