Caitlin Clark and Sophie Cunningham: Reading Linear Function Graphs

Materials Needed

• Graph paper or a digital graphing tool
• Pencil and colored pencils or a digital drawing tool
• Calculator, optional
• Bell-work problems
• Exit ticket

Lesson Overview

Grade/Standard: MA.912.AR.2.4: Given a table, equation, or written description of a linear function, graph the function and determine and interpret its key features.

Learning Target: I can identify when graphs of functions are increasing or decreasing and when functions are positive or negative.

Time: 15 minutes

Context: Basketball scoring and game statistics featuring Caitlin Clark and Sophie Cunningham. The data in this lesson are fictional practice examples for learning purposes.

Success Criteria

By the end of the lesson, I can:

• Tell whether a linear function is increasing or decreasing.
• Identify where a function is positive or negative.
• Use a graph, table, equation, or written description to explain what the function means in a basketball context.
• Identify the x-intercept and explain its meaning when appropriate.

Introduction: Bell Work and Hook — 3 Minutes

Bell Work: Reinforce Prior Knowledge

Complete the following without assistance. Use a coordinate plane if helpful.

1. What is the slope of the line passing through (0, 2) and (2, 6)?
2. Is the line y = -3x + 5 increasing or decreasing? How do you know?
3. For the equation y = x - 4, what is the y-intercept?

Quick answers: 1. The slope is 2. 2. The function is decreasing because its slope is negative. 3. The y-intercept is 4, or the point (0, -4).

Hook

Ask: “If a graph represents a basketball player’s score difference during a game, what would it mean if the graph rises? What might it mean if the graph falls below the x-axis?”

Explain that today the learner will use graphs and equations to describe whether a basketball-related quantity is increasing, decreasing, positive, or negative.

Body: I Do, We Do, You Do — 10 Minutes

I Do: Teacher Modeling — 3 Minutes

Display the equation:

c(x) = 2x - 6

Explain that x represents the number of three-minute periods in a game and c(x) represents a fictional score difference connected to Caitlin Clark’s team.

1. Identify the slope: The slope is 2. Since the slope is positive, the graph is increasing.
2. Find the y-intercept: The y-intercept is -6, so the graph crosses the y-axis at (0, -6).
3. Find the x-intercept: Set the function equal to zero:
   0 = 2x - 6
   x = 3
   The x-intercept is (3, 0).
4. Interpret positive and negative values:
   • The function is negative when x < 3.
   • The function equals zero when x = 3.
   • The function is positive when x > 3.

Think aloud: “The line rises from left to right, so the function is increasing. It is below the x-axis before x = 3, so its values are negative there. It is above the x-axis after x = 3, so its values are positive there.”

We Do: Guided Practice — 4 Minutes

Work through the following example together:

s(x) = -x + 4

Let x represent time during a fictional basketball game and s(x) represent Sophie Cunningham’s team’s score difference.

Complete the table:

Discuss these questions:

1. Is the function increasing or decreasing? Decreasing, because the slope is -1.
2. What is the y-intercept? (0, 4).
3. What is the x-intercept? Solve 0 = -x + 4, so x = 4. The x-intercept is (4, 0).
4. When is the function positive? When x < 4.
5. When is the function negative? When x > 4.

Think-Pair-Share option: If working with another person, explain why the graph is decreasing even though it begins above the x-axis. If working independently, say or write your explanation.

You Do: Independent Application — 3 Minutes

Choose either Option A or Option B.

Option A: Equation and Graph

Graph the function:

p(x) = 3x - 9

Let p(x) represent a fictional point difference for Caitlin Clark’s team.

Then identify:

• Whether the function is increasing or decreasing
• The y-intercept
• The x-intercept
• Where the function is positive
• Where the function is negative

Option B: Written Description

A fictional basketball team begins a training game with a score difference of 8 points. The score difference decreases by 2 points every five minutes.

1. Write a linear equation for the score difference, using x for the number of five-minute periods.
2. State whether the function is increasing or decreasing.
3. Determine when the score difference is positive, zero, and negative.
4. Sketch a graph and label the intercepts.

Conclusion: Closure and Exit Ticket — 2 Minutes

Recap

Complete the following sentence aloud or in writing:

“A linear function is increasing when its slope is __________ and decreasing when its slope is __________. A function is positive when its graph is __________ the x-axis and negative when its graph is __________ the x-axis.”

Answers: positive, negative, above, below.

Exit Ticket

For f(x) = -2x + 6:

1. Is the function increasing or decreasing?
2. What is the x-intercept?
3. For what values of x is the function positive?
4. In one sentence, explain what the x-intercept could represent in a basketball score-difference situation.

Expected responses: The function is decreasing; the x-intercept is (3, 0); the function is positive when x < 3; the x-intercept represents the time when the score difference is zero, meaning the teams are tied.

Assessment

• Formative: Bell-work responses, questioning during modeling, completed table, think-pair-share explanation, and observation of graphing steps.
• Summative: Independent Option A or B and the exit ticket.
• Feedback: Check whether the learner correctly connects slope to increasing/decreasing and graph position to positive/negative. Ask the learner to correct one error using a different representation, such as a table, equation, or graph.

Differentiation and Adaptations

• Support: Provide a labeled coordinate plane, a slope reference card, a partially completed table, and the sentence frames: “The function is increasing because…” and “The function is positive when the graph is…”.
• Visual support: Shade the region above the x-axis one color and the region below it another color.
• Verbal support: Have the learner explain the graph using the phrases “rises from left to right” and “falls from left to right.”
• Extension: Ask the learner to create a new basketball-related linear function that is increasing, find its x-intercept, and write a realistic interpretation of the intercept.
• Choice: Complete the independent task on paper, using a graphing tool, or by explaining the solution orally while sketching the graph.