Math In Basketball Lesson Page 5
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31o The height (h) of a ball, in feet, at a given time (t) is represented by the
equation h(t) = -16t
2
+ v
t + h
where v
is the initial vertical velocity
0
0
0
and h
is the initial height.
0
o Vertex: the highest point of the parabola.
5. Distribute the “Math in Basketball: Take the challenge” handout. Let your students
know that it is now their turn to solve the challenge that Elton Brand posed to the
teams in the video. Explain that in the activity, students should use the Fast Break
Facts for information about the three key variables and Elton’s stats to figure out the
maximum height the ball reaches on its way into the basket when making a free
throw shot.
6. Ask students to work in pairs or small groups to complete the “Math in Basketball:
Take the challenge” handout. Use the “Math in Basketball: Take the challenge”
answer key as a guide to help students as they complete the activity. Note: The
handout can be used by itself or in conjunction with the “Math in Basketball: Take
the challenge” activity on the website.
• If you have access to multiple computers, ask students to work in pairs to
explore the interactive and complete the handout.
• If you only have one computer, have students work in pairs to complete the
assignment using their handouts and grid or graph paper and then ask them to
report their results to the group and input their solutions into the online
interactive for all to see the results.
7. Review the directions listed on the handout.
8. As students complete the challenge, encourage them to use the following 6-step
mathematical modeling cycle to solve the problem:
• Step 1: Understand the problem: Identify variables in the situation that
represent essential features. (For example, use the three key variables:
acceleration of gravity, Elton’s initial vertical velocity, and his release height.)
• Step 2: Formulate a model by creating and selecting multiple representations.
(For example, students may use visual representations in sketching a graph,
algebraic representations such as combining the three key variables and Elton’s
stats: 24 ft/sec and a release height of 7 feet to write an equation that models
the projectile motion, or an explanation/plan written in words.)
• Step 3: Compute by analyzing and performing operations on relationships to
draw conclusions. (For example, operations include calculating the values of t
when the ball reaches a height of 10 feet, the value of t when the ball reaches a
maximum height, and the maximum height of the basketball at this time.)
• Step 4: Interpret the results in terms of the original situation. (The results of the
first three steps should be examined in the context of the challenge to maximize
the height of the basketball during the free throw shot using Elton’s release
height and initial vertical velocity, as well as the acceleration of gravity.
• Step 5: Ask students to validate their conclusions by comparing them with the
situation, and then either improving the model or, if acceptable,
5
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