Unit Plan 16 (Grade 8 Math): Qualitative Graphs & Stories of Change
8th graders analyze and sketch graphs to describe how quantities increase, decrease, or remain constant. They interpret steepness, key features, and domains to connect visual patterns with real-world stories.
Focus: Sketch and interpret graphs that describe increasing/decreasing intervals, steepness changes, and key features.
Grade Level: 8
Subject Area: Mathematics (Functions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week strengthens students’ ability to tell the story of a function without crunching numbers. Learners read and sketch graphs that show increasing, decreasing, and constant intervals; notice steepness (faster/slower change); and identify key features such as intercepts, peaks/valleys, plateaus, and meaningful domain/range restrictions. Emphasis is on clear input–output language, units, and matching a verbal description to a qualitative graph.
Essential Questions
- How do I describe a function’s behavior (increasing, decreasing, constant) from a graph or story?
- What does steeper vs flatter mean in context (faster/slower rate of change)?
- How do I sketch a reasonable graph from a real-world description, including key features and domain/range?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Describe a function’s behavior from a graph: intervals where it increases, decreases, or stays constant; identify key features (intercepts, peaks/valleys, plateaus, jumps).
- Sketch a graph that matches a verbal story, including reasonable domain/range, units, and labels.
- Use qualitative rate-of-change language to compare intervals (faster/slower, more/less steep) without calculating exact values.
- Distinguish whether a situation suggests a continuous or discrete graph and justify the choice.
Standards Alignment — CCSS Grade 8
- 8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Success Criteria (student-friendly)
- I can point to intervals on a graph and say where the function goes up, goes down, or is flat, and what that means in the story.
- I can sketch a graph from a description, label axes with units, and include key features.
- I can compare parts of a graph as faster or slower change using steepness words.
- I can choose whether the graph should be discrete (points) or continuous (connected line/curve) and explain why.