First, you’ll watch a video to learn about Elton Brand, an accomplished NBA player, and how he uses math in his work. At the end of the video Elton sets up a basketball-related algebra challenge. You will work with a partner to solve the challenge.

Before you get started, record your name(s) in the space below.

After you’ve finished this activity, you will be able to:

• Describe some of the ways athletes use mathematics and algebraic reasoning in sports;
• Identify a strategy and create a model for problem solving;
• Recognize, describe, and represent quadratic relationships using words, tables, numerical patterns, graphs, and/or equations;
• Understand the concept of a function and use function notation;
• Learn to recognize and interpret quadratic functions that arise in applications in terms of a context, such as projectile motion;
• Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.

Vocabulary

Read these words and their definitions. When you see them, you may click on them to read the definition again.

• Coordinates
• Function
• Acceleration of Gravity
• Initial Vertical Velocity
• Release Height
• Trajectory
• Maximum Height
• Parabola
• Vertex

Most of us have played basketball at one time or another—whether it’s on a local team, at the neighborhood court, or in the driveway. As with any sport, there is a certain amount of skill involved that only comes with practice, but there is also strategy—and strategy takes the player to the next level. Have you ever thought about how mathematics can help your game?

Discuss these questions with your partner, then record your answers in the box below. Don’t forget to save your work!

• What sports do you like to watch and how do you keep track of your favorite team’s progress?
• How do you think a basketball player might use mathematics to help them improve their game?

This video features Elton Brand, an NBA player who describes how he uses mathematics to help make his free throw shot more accurate. Click “View” on the left to watch the video. You may want to watch the video multiple times before answering the questions below.

• As you watch the video, write down a few of the ways Elton Brand uses math in his game.
• Think about situations in your daily life where you may need to apply the concept of maximizing (e.g., finding the best price to charge for the school play to get the most people to attend while still making a profit.) Why do you need to maximize the height of the basketball trajectory?

In the video you just watched you met Elton Brand, learned about his basketball career and heard about some of the strategies he uses to improve his performance in the game. Elton talked about how the math behind his free throw shot has helped him develop as a player.

You will solve the challenge on the next screen, but before you do, describe the challenge that Elton posed to the teams in the video—what is he asking them to do? If you want, you can use the Back button below to review the video.

Now it’s your turn to solve the challenge. First, click “View” on the left to open the Math in Basketball: Take the Challenge handout. Print out the handout.

Next, click “View” on the left to explore the Take the Challenge interactive. Work with your partner to develop a strategy and complete the handout as you work through the activity.

It’s time to see how the teams in the video solved the challenge. Click “View” on the left to watch the video. Be sure to carefully observe the strategies the teams used. If it will help you, watch the video multiple times.

• How do the teams' strategies compare to the one you used? Be sure to use evidence from your work and the video to explain your answer.
• What difficulties did you face (if any) when completing the challenge and how did you overcome those obstacles?

Now that you have developed a strategy that works for you, it’s time to try another challenge. First, click “View” on the left to open the Math in Basketball: Try Other Challenges handout. Print out the handout. In this activity, you’ll choose from a new set of statistics, and use them to figure out the maximum height the ball reaches during a different player’s free throw shot.

Choices include:

• Initial Vertical Velocity of 5 feet, 6 feet, or 8 feet
• Release Height of 20 feet, 22 feet, or 24 feet

Note: Use the 3 key variables and the stats to calculate the ball’s height, h, at a given time , t, by setting up an equation to be started.

Next, click “View” on the left to explore the Math in Basketball: Try Other Challenges interactive. Work with your partner to develop a strategy and complete the handout as you work through the activity.

Reflection: Now take the time to reflect on this activity and record your thoughts. Click “View” on the left to download the Reflection handout. Print out the handout.

Instructions

Discuss the questions on the handout with your partner. Then, answer the questions on your own. Be ready to present your conclusions for a classroom discussion.

When you're finished, print out your notes from this lesson and hand them in to your teacher along with both handouts and your reflection.