NBA Function Notation: Evaluating Game Statistics

Materials Needed

• Pencil and paper or a digital notebook
• Calculator, optional
• Timer
• NBA-themed practice problems below

Learning Target

I can evaluate functions given in function notation and interpret outputs in real-world contexts.

Objectives

By the end of the 15-minute lesson, the learner will be able to:

• Substitute an input into a function written in function notation.
• Evaluate a function accurately.
• Explain what the output means in an NBA basketball context.

Success Criteria

• I identify the input value.
• I substitute the input everywhere the variable appears.
• I simplify the expression correctly.
• I include units or a clear explanation of what the output represents.

Introduction and Bell Work: Activate Prior Knowledge — 2 Minutes

Scenario: An NBA player scores 24 points in a game. A coach wants to compare that score with the number of three-point shots made.

Complete these questions:

1. What does the variable x usually represent in a mathematical rule?
2. Evaluate: 3x + 2 when x = 4.
3. What does it mean to substitute a number into an expression?

Expected response: The learner should replace x with 4: 3(4) + 2 = 14.

Connect to today’s lesson: Just as a basketball statistic can change depending on the input, a function produces an output based on a given input.

Lesson: Function Notation in Basketball — 10 Minutes

I Do: Teacher or Adult Models — 3 Minutes

Explain:

A function is a rule that assigns exactly one output to each allowed input. Function notation uses a name such as f(x). The expression f(5) means “the output of function f when the input is 5.”

Example: Suppose an NBA player scores 2 points for every field goal made and 1 point for every free throw made. The function is:

P(x) = 2x + 4

Here, x represents the number of field goals made, and the 4 represents four free throws.

Find P(6):

1. Substitute 6 for x: P(6) = 2(6) + 4
2. Multiply: 12 + 4
3. Add: P(6) = 16
4. Interpret the output: The player scored 16 total points.

Quick check: Ask, “What does the 6 represent?” The answer is the number of field goals made, not the total number of points.

We Do: Solve Together — 4 Minutes

Work through each problem aloud. Encourage the learner to explain each substitution step.

Problem 1: Free-Throw Points

The function F(x) = x represents the number of points scored from free throws when x free throws are made.

Evaluate F(8).

Solution:

F(8) = 8

Interpretation: Making 8 free throws results in 8 free-throw points.

Problem 2: Three-Point Shooting

The function T(x) = 3x represents the points scored from three-point shots when x three-pointers are made.

Evaluate T(5).

Solution:

T(5) = 3(5) = 15

Interpretation: Making 5 three-pointers results in 15 points.

Think-Pair-Share or Explain Aloud

Answer this question:

Why is T(5) not equal to 5?

Expected response: The input is the number of three-pointers made, while the output is the number of points. Each three-pointer is worth 3 points.

You Do: Independent NBA Challenge — 3 Minutes

Choose one challenge or complete both.

Challenge A: Total Points

A player’s total points are modeled by the function:

S(x) = 2x + 3y

In this situation, x is the number of two-point field goals and y is the number of three-point field goals.

Evaluate S(7, 4).

Solution:

S(7, 4) = 2(7) + 3(4) = 14 + 12 = 26

Interpretation: The player scored 26 points by making 7 two-point field goals and 4 three-point field goals.

Challenge B: Ticket Sales

An arena earns money from ticket sales according to the function:

R(x) = 40x + 500

Here, x represents the number of additional tickets sold, and R(x) represents total revenue in dollars.

Evaluate R(20) and interpret the output.

Solution:

R(20) = 40(20) + 500 = 800 + 500 = 1,300

Interpretation: Selling 20 additional tickets produces $1,300 in total revenue.

Conclusion and Exit Ticket — 3 Minutes

Recap

Ask the learner to complete these statements:

• To evaluate a function, I first __________.
• The notation f(6) means __________.
• When interpreting an output, I should explain __________.

Exit Ticket

A basketball trainer uses the function A(x) = 4x + 2 to estimate a player’s achievement points, where x is the number of successful defensive plays.

1. Evaluate A(6).
2. Interpret the output in this context.

Answer:

A(6) = 4(6) + 2 = 26

The player earns 26 achievement points for making 6 successful defensive plays.

Assessment

Formative Assessment

• Check the bell-work substitution problem.
• Ask the learner to identify what each input represents.
• Listen for correct explanations during the We Do problems.
• Check whether the learner includes units or context when interpreting outputs.

Summative Assessment

The learner demonstrates mastery by correctly evaluating the exit-ticket function and explaining the real-world meaning of the output.

Mastery benchmark: Correctly completes at least 3 of the following 4 steps:

1. Identifies the input.
2. Substitutes correctly.
3. Calculates accurately.
4. Interprets the output in context.

Differentiation and Extensions

Support for Learners Who Need Scaffolding

• Use the sentence frame: “I substitute ___ for x, so ___.”
• Highlight the input number and the variable in the function.
• Use a calculator after the substitution step.
• Begin with functions such as f(x) = 2x before using two-variable functions.

Extension for Advanced Learners

Create an NBA-related function. Define the input and output, evaluate the function for two different inputs, and explain what each output means. Possible topics include total points, rebounds, assists, ticket revenue, or minutes played.