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In a thrilling high school basketball championship between Bluegrass High School and Thoroughbred High School, the fate of the game rests on Kyle's shoulders as he steps up for a crucial one-and-one free throw with only one second remaining. This activity invites students to explore the probabilities of winning, tying, or losing based on Kyle’s free throw percentage. Through group discussions, simulations, and experimental designs, students will investigate different outcomes and refine their understanding of probability, culminating in a comparison between theoretical and experimental results.
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The Free Throw Problem Bluegrass High School is playing Thoroughbred High School in the state basketball championship game. The score is 72 to 73 in favor of Bluegrass High School. With 1 second left on the clock, a player from Bluegrass High School fouls Kyle, a player from Thoroughbred High School. Kyle is a 60% free throw shooter, and he goes to the line for a one-and-one foul shot situation.
Commit to an outcome Is the game more likely to end in a tie, a win, or a loss for Thoroughbred High School?
Expose beliefs • Share your answer with other members of your group. • Discuss each other’s predictions. Is there more than one answer that makes sense?
Confront beliefs • In your group, design an experiment that can be used to simulate the end of this game. • Carry out your simulation. Be prepared to share your results with the rest of the class. • How does what you found out compare to your original answer?
Accommodate the concept • Share your findings with the rest of the class. Justify your findings.
Extend the concept • Use the ProbSim APP on the TI-73 calculator to simulate the experimental probability of the outcome of the game. • Design an area model representation that can be used to justify the theoretical probability of the outcome of the game. • How do these results compare? • What is the average number of points Kyle scores per free throw situation?
Go beyond • What free throw percentage would Kyle need to have in order for Thoroughbred High School to have a 50% chance of winning this game? Justify your thinking.
Martian Basketball In Martian basketball, instead of having one-and-one free throw situations, they have one-and-one-and-one situations. That means, if a player makes both the first and the second shots, he or she can take a third hot. So the player can score 0 points, 1 point, 2 points, or 3 points. • Suppose Kyle has moved to Mars and is playing basketball there. Because of the difference on the gravity on Mars his probability of success on each shot is now 80%. • How many points is Kyle most likely to score in a one-and-one-and-one situation? Adapted from IMP Math Course 1, Key Curriculum Press
