Math In Basketball Lesson Page 4
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31out the height of the basketball at any given time; he uses statistics to maximize the
height of the basketball so it has the best chance of going into the basket.)
6. Ask students to describe the challenge that Elton Brand posed to the teens in the
video segment. (The challenge is to use the three key variables and his stats to
figure out the maximum height the ball reaches on its way into the basket in order
to make a free throw shot.)
LEARNING ACTIVITY 1
1. Explain that the students will now have an opportunity to solve the problem, which
involves using the Fast Break Stats for information about the three key variables
(acceleration of gravity, initial vertical velocity, release height) and Elton’s stats.
2. Ask students to think of situations in their daily life where they may need to apply
the concept of maximizing. (Sample response: finding the best price to charge for
the school play to get the most people to attend while still making a profit.)
3. Discuss why you would need to maximize the height of the basketball trajectory.
(Sample responses: to make sure it reaches the hoop; the higher the shot, the
further from the basket it peaks or reaches maximum height, increasing the
likelihood the player will make the shot; higher arcs require a player to have more
strength and use the proper mechanics.)
4. Review the following terminology with your students:
o Coordinates: an ordered pair of numbers that identify a point on a coordinate
plane.
o Function: a relation in which every input (x-value) has a unique output (y-
value).
o Acceleration of Gravity: causes a ball to speed up, or accelerate, when falling
at a rate of -32 ft/sec
2
. Use only downward pull or half of -32 ft/sec
2
, which is -
16 t
2
.
o Initial Vertical Velocity: the angle and speed when the ball leaves the
player’s hand. Multiply by time to get the vertical distance traveled.
o Release Height: the starting position of the ball when it leaves the player’s
hand.
o Trajectory: the path that a basketball follows through space as a function of
time.
o Maximum Height: the value in the data set where the basketball reaches its
greatest vertical distance at a given time on its way into the basket.
o Parabola: the graph of a function in the family of functions with parent
function y = x
2
.
o The path of the ball when thrown is a trajectory represented by a
parabola which can be modeled mathematically with a quadratic
equation. This equation represents the position of the path over time.
4
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