math in basketball edci 270jonah stevenson click anywhere to continue
TRANSCRIPT
Teacher’s Material
Objectives:
Students will be able to understand how mathematics can apply to basketball situations by viewing a video and reading material while also answering follow-up questions
Students will understand the applications of certain basketball techniques and understand how they apply to the real world, e.g. projectile motion, by having a mini-quiz on different forms of projectile motion
Students will understand how to use the quadratic formula and other mathematical tools to solve problems to appropriate understanding with a final quiz.
Teacher’s Material Continued
Target Audience/Learning Environment:
Algebra 1 or Algebra 2 students
Middle School students/High School students
Computer lab or own computers
Headphones for videos
Scratch paper as well as pen/pencil would be ideal for practice problems
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What are we doing today?
In this module, we will learn about the point of maximizing in basketball and in the real world.
You will watch a video by NBA All Star Elton Brand to see how to properly maximize the basketball shot.
There are videos to watch as well that go into more depth of how math is very important in basketball.
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Home page:
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Lesson: This is the main lesson area where the activity takes place
Video Section: This is where some additional videos for reference can be found
Math Formulas/Definitions: This is where definitions of certain terms can found
Quiz Button: This is where, if you are ready, you can go on to the quiz section
Video
Math
Quiz
Lesson
Math
Introduction:
• In this section, I will go over the key concepts of what we are learning that weren’t described in the lesson but are equally important.
• If the information is too hard to understand, there will be a link to Khan’s Academy that may benefit the learning process. Try to only use it if you really have no clue what is going on.
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Coordinates & Function:
Coordinates: Set of values that show an exact position
Ex. (0,1) , (0.5,2) , (3,6)
Function: A relationship where you input one set of data (x) to get another (y)
Ex. F(x) = x^2, F(1) = 1, F(2) = 4, F(3) = 9
https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/coordinate-plane/v/the-coordinate-plane
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Acceleration of Gravity
Acceleration of Gravity: The speed of the object speeding up or slowing down when the ball is falling down
Initial Vertical Velocity: The speed when the ball is first released or when the object is first moving
Release Height: The initial height that the ball or object is released at
Trajectory: The path as an object travels through a space over time
https://www.khanacademy.org/science/physics/newton-gravitation/gravity-newtonian/v/introduction-to-gravity
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Maximum Height
Maximum Height: Largest vertical distance that the ball reaches as it travels
Parabola: The shape of the graph with the set of y = x^2, most used with quadratic formulas
Vertex: Highest or lowest point on the vertex (depends on which way the parabola opens)
http://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic_formulas/v/projectile-height-given-time
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Math Formulas
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These formulas may be found useful when trying to figure out the problems in the quiz or on other problems.
Quiz!
There will be 3 questions to see if you understand what is going on in this lesson.
Try your best to work out the problems as much as possible without receiving help.
Feel free to hit the review button to go over some of the practice problems or to understand a concept better.
Best of luck!
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Quiz Problem #1
If the release height is initially 5 ft. and the initial velocity is 20 ft./sec., what is the time when the ball reaches a height 10 ft.?
0.450.85
0.650.35
a
b
c
d
Quiz Problem #2
If the release height is initially 5 ft. and the initial velocity is 20 ft./sec., at what time does the ball reach it’s maximum height?
0.63 seconds0.54 seconds
0.82 seconds0.55 seconds
a
b
c
d
Quiz Problem #3
If the release height is initially 5 ft. and the initial velocity is 20 ft./sec., what is the maximum height?
15.1212.44
11.2519.43
a
b
c
d
Lesson-Math in Basketball
Introduction:
• How do you think math could relate to sports?
• Brainstorm a couple of ideas about how math could relate to anything in basketball
(e.g. Shooting, Passing)
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Submit
Fill out box and hit submit to go on.
Brainstorm
Different ways that math can be found in basketball:
• Statistics of a player’s performance
• Length of quarters
• Time of shot clock, overtime, time-outs
• Dimensions of the basketball court
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Video Introduction
Lesson plan introduction: Elton Brand, former NBA player
What kinds of tools will you need for this project to be done?
What sorts of things was Elton Brand talking about in this video?
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Fast Break
Lesson
In this lesson, we are going to learn about the basic free-throw shot and certain math formulas that apply to the basketball shot.
The first thing we should begin to think about is the idea of maximizing.
Why would we need to need to maximize the shot? Where else do we want to see the maximum of an item or a statistic?
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Maximizing-PowToon
This mini-presentation goes into more depth of why maximizing anything is important and why it is important in basketball.
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PowToon
Algebraic Terms
Let’s review some terms used in this lesson that you may or may not know:
Acceleration of Gravity- Speed of item falling is usually around -32ft/s
Trajectory- The path that objects take over a certain amount of time
Maximum Height-In this case, the largest vertical distance the ball traveled
More terms can be found in the Algebra/Formula Section of this lesson
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Can You Tell What You’re Doing?
Before you get a chance to try a couple of questions, first take a look at this interactive tool to see if you can correctly form an equation that focuses on maximizing the height.
Fast Break Facts given by Elton Brand:
• This exercise helps to understand the concepts that we have just learned about and apply the concepts.
Fast Break Facts
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Practice Problem #1
Using the Fast Break Facts and Elton Brand’s given info, what is the acceleration of gravity, initial velocity, initial height given?
Acceleration = -16t^2, Vi = 24ft/sec., Height = 7 ft.
Acceleration = -20t^2, Vi = 27ft/sec., Height = 9 ft.
Acceleration = -32^2, Vi = 48ft/sec., Height = 14 ft.
Acceleration = -20t^2, Vi = 26ft/sec., Height = 18 ft.
a
b
d
c
Correct!
Great work! You’re doing fantastic! What should the equation look like after you have figured out the variables?
h(t) =
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Sorry! Try Again!
Not quite! Try reviewing the Fast Break Facts if it is confusing at this point.
Fast Break Facts
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Sorry! Try Again!
Not quite! Try reviewing the Fast Break Facts if it is confusing at this point.
Fast Break Facts
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Practice Problem #2
Using the equation from the Fast Facts sheet, what time does the ball reach 10 feet?
0.24 sec. and 1.42 sec.
0.14 sec. and 1.36 sec.
0.16 sec. and 1.50 sec.
0.5 sec. and 1.2 sec.
a
b
c
d
Hint: Use Quadratic Formula
𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎
#2 Solution
First understand what the equation looks like:
24 = Initial Velocity, 7 = Initial Height
Since we know 10 is the height, we can plug it in as h to get
Using what we know about algebra, we can subtract 10 from either side and we get:
We can’t immediately factor this equation, so we’ll use the quadratic formula
10=−16 𝑡 2+24 𝑡+7
0=−16 𝑡2+24 𝑡−3
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#2 Solution Continued
Using the quadratic formula we plug in the numbers using a = -16, b = 24, and c = -3
Plugging in we see the equation looks like
We get two answers from this equation: x = 0.14 and 1.36 seconds
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Follow-Up
Other high school students have tried to do exactly what you just did. Watch to see if they did anything differently as they explain their work.
A final quiz is coming up to see if you truly understand what the equation represents. Feel free to review past problems and other formulas that could be used.
Follow-Up
NextBack Review Quiz
Review
Fast Break Facts:
Practice Problem #1:
Practice Problem #2:
Math Explanations:
1
2
Fast Break Facts
Math
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Video Section
Here are some videos that can help you on your path to understanding the math behind some basketball techniques.
Video Introduction:
TED Talk: Teaching Math Through Basketball
SportScience: Basketball Shot:
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