Math in Basketball

EDCI 270 JONAH STEVENSON

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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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Correct!

Great work! You’re doing fantastic!

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Next

Correct!

Great work! You’re doing fantastic!

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Correct!

Great work! You’re doing fantastic!

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Correct!

Great work! You did fantastic!

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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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Sorry! Try Again!

Not quite! Try again!

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Sorry! Try Again!

Not quite! Try again!

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Sorry! Try Again!

Not quite! Try again!

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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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Teaching Math Through Basketball

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Sports Science: Basketball Shot

This video goes into more depth of the math and science behind the perfect basketball shot

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