### Free Throw Problem

```“Probably” Number Sense
The Free Throw Problem
Bluegrass High School is playing
Thoroughbred High School in the state
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
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Discuss each other’s predictions. Is
there more than one answer that
makes sense?
Confront beliefs
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In your group, design an experiment
that can be used to simulate the end
of this game.
prepared to share your results with
the rest of the class.
How does what you found out
Accommodate the
concept

Share your findings with the rest of
Extend the concept
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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?
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