Lesson 4: Interpreting a Graph

What is the Input Variable?
What is the Output Variable?
What are the Units for Each Variable?
How does the Output Variable Change as the Input Variable Increases/Decreases?

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Lesson Description: In this lesson, students engage in graphical analysis. Rather than plotting points, they are presented with completed graphs and tasked with extracting meaningful information. Key skills include: Reading Coordinates in Context: Determining what an (x, y) point represents (e.g., at 3 hours, the distance traveled was 150 miles).Domain and Range Awareness: Identifying the practical boundaries of a graph (e.g., why a graph of "height vs. time" doesn't go below the x-axis).Rate of Change (Intuitive): Observing how a change in the horizontal variable affects the vertical variable (e.g., "For every year that passes, the value of the car drops by 2,000").Interpolation and Extrapolation: Estimating values between known points and predicting future trends based on the current direction of the line.
Purpose: The purpose of Section 5.4 is to foster quantitative reasoning. In most professional settings, workers are not asked to build a coordinate plane from scratch; they are asked to look at a report or a dashboard and make a decision. By learning to interpret slopes as "rates" and intercepts as "starting costs," students bridge the gap between abstract math and professional utility. This section is especially critical for students entering health careers (reading patient charts) or business (analyzing sales trends).
Depth of Knowledge (DOK) Level
DOK Level 2 & 3
Level 2 (Skill/Concept): Extracting specific values from a graph and performing basic calculations based on those values (e.g., "Based on the graph, how much did the temperature rise between 2:00 PM and 4:00 PM?").
Level 3 (Strategic Thinking): Interpreting the "story" of the graph. Students must explain the meaning of a flat line versus a steep line in a specific context. They may be asked to compare two different graphs (e.g., two different cell phone plans) and determine which is more cost-effective based on where the lines intersect.

Class and Online Work

Section 5.4 You Try Page 124

Practice Problems

Textbook with guided class notes and videos