Unit Plan 8 (Grade 8 Math): Slope as Rate of Change
8th graders explore slope as a constant rate of change, finding it from graphs, tables, and equations while connecting unit rate to steepness and meaning in context. Students explain constancy using similar triangles and write linear equations in the form y = mx + b.
Focus: Explore slope from graphs, tables, and equations; connect unit rate to steepness and context.
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 develops a deep, practical sense of slope as rate of change. Students read slope from graphs, tables, and equations, explain why slope is constant along a non-vertical line using similar triangles, and write line equations in y = mx + b. They connect unit rate to steepness and make meaning of signs, units, and intercepts in real contexts.
Essential Questions
- How do I find and interpret slope (m) from a graph, a table, or an equation?
- Why is the slope the same no matter which two points I choose on a line?
- How does y = mx + b encode slope (m), intercept (b), and real-world meaning?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Determine slope as unit rate from tables, graphs, and proportional equations (8.EE.5).
- Use similar triangles/rise-run to explain why the slope of a non-vertical line is constant; connect this to y = mx + b (8.EE.6).
- Given a line in any representation (two points, a graph, or a table), find m, interpret it with units, and write the equation y = mx + b.
- Compare slopes to decide which situation changes faster and justify the comparison.
Standards Alignment — CCSS Grade 8
- 8.EE.5: Graph proportional relationships, interpreting the unit rate as slope. Compare two proportional relationships represented in different ways (table vs graph, etc.).
- 8.EE.6: Use similar triangles to explain why the slope m is the same between any two points on a non-vertical line; derive the equation y = mx + b for a line through (0, b) with slope m, and give an equation for a line with a known slope and a point on the line.
Success Criteria (student-friendly)
- I can find m from a graph (rise/run), from a table (change in y over change in x), and from an equation (the m in y = mx + b).
- I can explain with words and a diagram why slope is constant on a line (similar triangles).
- I can write y = mx + b for a line through a given point with a given slope.
- I can compare two lines and say which one changes faster, using units to explain.