Unit Plan 30 (Grade 8 Math): Using Slope & Intercept for Prediction
8th graders interpret slope and intercept in real-world contexts, using linear models to predict and compare data. They decide when proportional or non-proportional models fit best, explain units and meaning clearly, and assess prediction reasonableness with evidence.
Focus: Interpret slope/intercept of a fitted line in context; use the equation to model and predict.
Grade Level: 8
Subject Area: Mathematics (Statistics & Probability • Functions • Algebra Connections)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Building on hand-drawn lines of best fit, students now use and interpret the linear model. They connect slope to a real-world rate of change and intercept to a meaningful starting value (or explain when it isn’t meaningful). Students use the model to make predictions, compare predicted vs actual values (informal prediction error), and explain when a proportional model (through the origin) is or is not appropriate.
Essential Questions
- What do slope and intercept tell us in a real context?
- When is a proportional model reasonable, and when do we need y = mx + b with a nonzero intercept?
- How should we use a line to predict responsibly, and how can we judge whether our prediction is reasonable?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Interpret slope (m) as a rate of change with correct units and interpret intercept (b) as a baseline/starting value (or explain when x = 0 is outside the situation).
- Decide whether a proportional relationship (passes through the origin) fits a context (connection to 8.EE.5) or whether a linear function with intercept is more appropriate (connection to 8.F.4).
- Use a fitted line (equation from a by-eye line or given) to predict y for a given x and label predictions as interpolation or extrapolation with cautions.
- Compare predicted vs actual values and describe prediction error (actual − predicted) qualitatively to assess reasonableness.
Standards Alignment — CCSS Grade 8
- 8.SP.3: Use the equation of a straight line fitted to data to solve problems in the context of the data; interpret slope and intercept.
- 8.EE.5 (connection): Graph proportional relationships, interpret unit rate as the slope; compare proportional relationships.
- 8.F.4 (connection): Construct a function (linear) to model a relationship and interpret rate of change and initial value.
Success Criteria (student-friendly)
- I can explain what 1 unit of x does to y using the slope and give units.
- I can explain what the intercept means (or why it doesn’t make sense here).
- I can use y = mx + b to make predictions and label them as interpolation or extrapolation.
- I can compare two models (through origin vs with intercept) and justify which fits the situation.