Math In Basketball Lesson Page 8
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31• How did you determine an effective strategy for solving the challenges in this
lesson? What are your conclusions and the reasoning behind them? (Sample
answer: First you could find the total flight time of the ball. Since the height of
the ball is a function of the time the basketball is in the air, and the path is a
trajectory or parabola, it has an axis of symmetry that passes through the
vertex or highest point. Students may use this fact to make a table of values,
and since it is U-shaped between the two points it is at 10 feet, students may use
the symmetry to include values to the left and right of the vertex. A trace
function or key in a graphing calculator, as well as a sketch of the graph, may
be used to solve the problem.)
• Compare and contrast the various algebraic and graphical representations
possible for the problem. How does the approach used to solve the challenge
affect the choice of representations? (Sample answers: If you decide to graph the
points and then think of the basketball as an object that is traveling on a
parabolic path, or trajectory, you would use this information to find the
maximum height by finding the average between the two points it is at 10 feet; if
you decide to write the equation of the function by combining the three key
variables: acceleration of gravity, initial vertical velocity, and release height for
Elton Brand or a given player, you could use transformations to write it in
Standard Form for a quadratic equation, then find the times by using the
quadratic formula or completing the square as algebraic strategies.)
• Why is it useful to represent real-life situations algebraically? (Sample
responses: Using symbols, graphs, and equations can help visualize solutions
when there are situations that require using data sets or statistics to maximum
performance of an athlete.)
• What are some ways to represent, describe, and analyze patterns that occur in
our world? (Sample responses: patterns can be represented with graphs,
expressions, and equations to show and understand optimization.)
2. After students have written their reflections, lead a group discussion where students
can discuss their responses. During the discussion, ask students to share their
thoughts about how algebra can be applied to the world of sports. Ask students to
brainstorm other real-world situations which involve the type of math and problem
solving that they used in this lesson. (Sample responses: sports-related problems
might include “catching air” in snowboarding, throwing a baseball or football,
hitting a golf ball, and shooting a model rocket to maximize the height of the ball or
rocket; maximizing the area of a garden/farm given specific fencing options;
modeling relationships between revenue and cost.)
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