Profile Sheet
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:
Primary Subject Area:
Outside Subject Area:
Class and Level
Grade Level:
Thomas Rhea
Mathematics
Physical Education
Algebra I - F.L.I.P.
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
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.
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).
Meet the Problem Documents:
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
Internet Sources:
http://www.82games.com/random20.htm
http://www.swish22.com/article2.html
News Paper Sources:
Investing in Free Throws Pays Off
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 freethrow 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.”
Pro Basketball
76ERS 100, JUGGERNAUTS 98 (O.T.)
Missed Free Throws Prove Costly to
the Juggernauts Again
Missed Free Thro
nytimes.com
By JOHN ELIGON
By JOHN ELIGON
http://w w w .nytim default
FEB 06 2007
The New York Tim
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.
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 fieldgoal 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.”
Problem Statement, Know/Need to Know Boards, and Possible Resources
Title: What are the Odds? : Free Throws from a Far
Coach Rhea
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:

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).
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:
1.) In over 5% of NBA games, the losing team would have won had if it would have
made 78% of its free throws.
2.) Free throw will be the difference in 1 out of 50 games. (Probability)
3.) For the 05-06 season to March 23rd it turns out that 38% of losing teams in a game
would have tied or won if they had sunk all their free.
4.) The distance of a free throw shot is 13’9”.
5.) A player has a relaxed 10 seconds to shoot the free throw.
6.) The Dallas Mavericks have the only free throw coach in the NBA.
7.) The Dallas Mavericks are shooting 80.7% at the free throw line.
8.) The Lynn Haven Juggernauts have a 22 – 27 Win/ Loss Record.
9.) The Juggernauts missed 12 out of 29 free throws against the Philadelphia 76ers.
10.) The Juggernauts missed 14 out of 34 free throws in the previous game.
What We Need to Know:
1.) How can we improve our free throw shots?
2.) Is there one perfect free throw shot?
3.) How can we find the probability of the number of free throws made?
4.) How can we find the odds of the number of free throws made?
5.) Why are we shooting poorly?
6.) Are legs or arms more important when shooting free throws?
7.) What are the mental problems when shooting free throws?
8.) What are some ways we can practice free throw shots?
9.) What is the difference between odds and probability?
10.) Do girls or boys shoot better free throws?
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:

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).
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.
Rubric for Assessing the Capstone Performance
Free Throws From afar
Scoring Rubric
Summative Assessment
Criteria
Free Throw
Competition
Records all
information
Probability
and Odds
Best
Solutions
Percent of
Change
Superior
Adequate
5 Pts.
1 Pts.
Participates in all 3
Participates in all
rounds of the free throw rounds except the
competition.
practice round.
10 Pts.
Student records the
number of free throws
made and missed in all
3 rounds.
6 Pts.
Student records
the number of
free throws made
and missed in the
first and final
round.
20 Pts.
Student determines the
probability and odds of
the number of free
throws made with
100% accuracy.
10 Pts.
Student
determines either
probability or
odds of the
number of free
throws made with
100% accuracy,
but not both.
10 Pts.
5 Points.
Student states their 2
Student states the
best solutions, and then 2 best solutions,
identifies their overall
but fails to identify
best solution.
their overall best
solution.
5 Pts.
Student determines the
percent of change in
the number of free
throws made between
the first and second
round, and also states
whether it is an
3 Pts.
Student
determines the
percent of change
in the number of
free throws made
between the first
and second
Unacceptable
0 Pts.
Fails to
participate in
the 1st or last
free throw
round.
0 Pts.
Student fails
to record the
number of free
throws made
and missed in
the first or last
rounds
0 Pts.
Student does
not determine
either
probability or
odds with
100%
accuracy.
0 Pts.
Student fails
to identify
neither their
two best
solutions nor
their over best
solution.
0 Pts
Student fails
to determine
the percent of
change in the
number of free
throws made
between the
increase or decrease.
Scoring Guide
A = 45 - 50 Total Points
B = 40 – 44 Total Points
C = 35 – 39 Total Points
Resubmit = 0 – 34 Total Points.
round, but fails to
state whether it
was an increase
or decrease.
first and
second round.
Two alternative Solutions and “Best” Solution Analysis
What are the odds: Free throws from a far
Problem Statement:

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).
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:
1.)
2.)
3.)
4.)
Cons:
A safe way to shoot free throws
Target will never move
Less athleticisms is required
All regulation basketball goals will have this square
1.) Most professionals do not use the backboard
2.) Relies on the backboard, instead of a perfect stroke while shooting
3.) Depends on strength rather than skill
4.) Increased chance of a rebound going to the defense
Possible Consequence:
1.) Players will rely on the backboard which may foster bad habits during regular field goal
shots.
2.) Players will be ridiculed for using the backboard instead of learning the proper shooting
technique.
Solution #2
Bend your knees. An accurate shot doesn't rely on arm strength;
it uses leg strength to propel the shooter upward.
Pros:
1.)
2.)
3.)
4.)
Gives the ability to emulate other professional basketball players
Shot focuses on repetition rather than strength
Allows player to focus on legs strength
Easier for girls to use
Cons:
1.) Takes more time to master
2.) No one correct shot
3.) Players who have stronger legs will have an advantage
4.) Hard to correct once player has determined their own shooting style
Consequences:
1.) Another period for free throws must be added to the practice schedule
2.) Players might lose confidence in their abilities having to learn a new shooting style
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:

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).
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.
Place
Points Awarded
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.
1.) Odds – What you want divided by everything
2.) Probability – What you want, divided by what you don’t want
3.) Motion
4.) Arch
5.) Bending of the knees.
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
Type of
Question
C
M
E
C
M
E
C
M
E
C
M
E
C
M
E
Question
Meet the Problem
What is the student role in this problem?
What do you already know about basketball?
How realistic is this problem?
Know/Need to Know Board
How can a player increase their free throw percentage?
How will you modify your own free-throw shot?
Is it necessary to find the answers to all the “need to know”
questions to improve your own individual free-throw shot?
Problem Statement
How can improving free-throw shots increase the Juggernauts ticket
revenue?
Are you comfortable with the problem statement your group has
written? Would you add anything?
Can you name some “conditions” that would be common to all
problems?
Research
Where can you find information on basketball camps?
What basketball terms can you think of that might be helpful in
doing a “Google” search for this problem?
Will you ever find the one perfect free-throw shot?
Generating Possible Solutions
What does your percent of change in free throws made tell you about
your best overall solution?
Why do you feel that Solution 1 is better than Solution 2? Explain
your reasoning.
What free-throw technique is used most in the NBA?