Unit Plan 7 (Grade 8 Math): Proportional Relationships & Graphs
8th graders review ratios, rates, and proportional relationships by modeling with y = kx and interpreting slope as the unit rate. Students compare tables, graphs, and equations, decide when relationships are proportional, and explain how rate connects to steepness and real-world meaning.
Focus: Review ratios, rates of change, and proportional relationships; interpret and graph relationships through the origin.
Grade Level: 8
Subject Area: Mathematics (Expressions & Equations • Functions)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week strengthens students’ understanding of proportional relationships and their graphs. Learners will compute unit rates (k), decide when situations are proportional, and model with y = kx. They will interpret slope as the unit rate, and compare relationships shown as tables, equations, and graphs, including deciding which situation is “steeper” or “cheaper per unit.”
Essential Questions
- How do I recognize when a situation is proportional?
- How does the unit rate (k) connect to the slope of the line and the graph through the origin?
- How do I compare two relationships shown in different representations?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Decide whether a relationship is proportional and find the constant of proportionality k from tables, equations, and graphs.
- Graph proportional relationships that pass through the origin and interpret slope as unit rate (y increases by k for each 1 in x).
- Compare two proportional relationships presented in different ways (table vs graph, equation vs table) and justify which has greater rate.
- Communicate reasoning with precise language, units, and labeled axes.
Standards Alignment — CCSS Grade 8
- 8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways (for example, a table vs a graph).
Success Criteria (student-friendly)
- I can find k from a table (y/x), an equation (y = kx), or a graph (rise/run to the origin).
- I can graph y = kx through the origin and label axes with units.
- I can say which relationship has the greater unit rate and explain how I know.
- I can check my work by estimating and by reading points off the graph.