“Probably” Number Sense
Math Leadership Support Network ’08-’09
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.
Math Leadership Support Network ’08-’09
Commit to an outcome
Is the game more likely to end in a tie, a
win, or a loss for Thoroughbred High
School?
Math Leadership Support Network ’08-’09
Expose beliefs
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Share your answer with other
members of your group.
Discuss each other’s predictions. Is
there more than one answer that
makes sense?
Math Leadership Support Network ’08-’09
Confront beliefs
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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?
Math Leadership Support Network ’08-’09
Accommodate the
concept

Share your findings with the rest of
the class. Justify your findings.
Math Leadership Support Network ’08-’09
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?
Math Leadership Support Network ’08-’09
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.
Math Leadership Support Network ’08-’09
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
Math Leadership Support Network ’08-’09