Unit Plan 29 (Grade 8 Math): Informal Lines of Best Fit
8th graders extend scatter plot analysis by drawing informal lines of best fit, writing equations from two line points, and using them to predict values. They evaluate fit visually, interpret slope and intercept in context, and explain interpolation vs. extrapolation with caution and precision.
Focus: Informally fit a line to data; assess fit visually and use the line for interpolation/extrapolation.
Grade Level: 8
Subject Area: Mathematics (Statistics & Probability • Data Analysis)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week extends scatter plot work to informal linear modeling. Students will draw a line of best fit by eye, write an equation using two points on the line, and use the line to predict values (interpolate within the data range and extrapolate beyond, cautiously). Emphasis is on clear visuals, sensible scales, qualitative judgment of fit (tight vs loose, balanced above/below), and context-aware conclusions.
Essential Questions
- What makes a hand-drawn line a reasonable fit for a scatter plot?
- How can I use two points on my line to write an equation and make predictions?
- When is extrapolation risky, and how do I communicate limits of my model?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Draw an informal line of best fit that balances points (roughly half above/below, passes near the middle of the cloud).
- Choose two points on the line (not necessarily data points) to write an equation in y = mx + b form and interpret m and b in context (qualitatively).
- Use the line to interpolate within the data range and extrapolate beyond it, stating assumptions and limits.
- Judge and compare the reasonableness of fit between two candidate lines using visual evidence (spread, balance, outliers).
Standards Alignment — CCSS Grade 8
- 8.SP.2: Informally fit a straight line to bivariate data and judge fit by the closeness of the data points to the line; use the line to solve problems in the context of the data.
Success Criteria (student-friendly)
- I can draw and label a line that reasonably fits the scatter plot and explain why it’s reasonable.
- I can write an equation using two points on my line and interpret slope and intercept in words.
- I can make predictions and explain whether they are interpolation or extrapolation and why that matters.
- I can compare two different lines and argue which is a better fit using evidence from the graph.