Unit Plan 15 (Grade 8 Math): Building Linear Models from Context
8th graders learn to construct linear functions from real data and contexts, determine slope and intercept, and interpret their meanings. Students model relationships, graph equations, and evaluate predictions for reasonableness.
Focus: Construct functions to model linear relationships from data sets and real scenarios; interpret slope and intercept.
Grade Level: 8
Subject Area: Mathematics (Functions • Expressions & Equations)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week students turn real situations into linear models. They will identify appropriate input and output variables with units, decide when a constant rate of change is reasonable, and construct functions of the form y = mx + b from descriptions, tables, and graphs. Students will interpret m and b in context, graph and label models, and evaluate the reasonableness of predictions (interpolation vs extrapolation).
Essential Questions
- When is a linear model appropriate for real data, and how do I know?
- How do I determine and interpret the rate of change (m) and initial value (b) from descriptions, tables, and graphs?
- How do I communicate a model clearly with units, equation, and labeled graph, and check if it makes sense?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- From a context, define input (x) and output (y) with units, and decide whether a constant rate model is reasonable.
- Determine m and b from a description, table, two points, or a graph, then write a model y = mx + b and interpret both parameters.
- Graph the model, connect slope to unit rate, and explain why slope is constant on a line (similar triangles idea).
- Use the model to make predictions, identify a reasonable domain/range, and judge interpolation vs extrapolation.
Standards Alignment — CCSS Grade 8
- 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value from a description, table, or graph; interpret them in context.
- 8.EE.5: Graph proportional relationships, interpreting the unit rate as slope; compare proportional relationships in different forms.
- 8.EE.6: Use similar triangles to explain constant slope and derive y = mx + b; write an equation for a line given slope and a point.
Success Criteria (student-friendly)
- I can name x and y with units and decide if a linear model fits.
- I can find m and b from data or a graph and write y = mx + b.
- I can say what m and b mean (for example, “$3 per mile” and “$5 start-up fee”).
- I can make a prediction and explain if it is interpolation or extrapolation and whether it is reasonable.