Lesson 1: Scatterplots and Lines of Best Fit
Duration of Days: 4
Lesson Objective
Students will be able to construct and interpret scatter plots for bivariate measurement data to investigate patterns of association. They will also informally fit a line of best fit to data that suggests a linear association and assess the model fit based on the closeness of data points to the line.
How are patterns used when comparing two quantities?
Why is a "line of best fit" considered an approximation rather than an exact path?
How do you identify if a scatter plot shows a linear, nonlinear, or no association?
What does the slope and y-intercept represent in the specific context of real-world bivariate data?
Scatter Plot: A graph used to display real-world bivariate data to look for trends.
Line of Best Fit / Trend Line: A line drawn through the "middle" of the data points that approximates the average trend.
Association (Linear, Nonlinear, Positive, Negative, No Association): The pattern of relationship between variables.
Outlier: A data point that lies significantly far away from the main trend of the data.
Clustering: Data points that are grouped closely together in certain areas of the plot.
Bivariate Data: Data that involves two different variables.
8.SP.A.1: Construct and interpret scatter plots to investigate patterns of association (clustering, outliers, etc.).
8.SP.A.2: Informally fit a straight line to scatter plots with linear association and assess the fit.
8.SP.A.3: Use the equation of a linear model to solve problems, interpreting slope and intercept in context.
Target J (Supporting): Interpreting patterns of association and slope/y-intercept in terms of the context.
Description: This lesson introduces students to bivariate data analysis. Students begin by constructing scatter plots and identifying associations, then progress to drawing and calculating equations for lines of best fit.
Purpose: To teach students how to use straight lines to model relationships between quantitative variables and use those models to make predictions.
DOK Level: Level 2 (Basic Application) for construction and calculation; Level 3 (Strategic Thinking) for assessing model fit and interpreting results in context.
Biology Experiments: Interpreting growth rates (e.g., sunlight vs. plant height).
Consumer Data: Analyzing the relationship between a child's age and the cost of a birthday gift.
Impact Analysis: Exploring how specific community initiatives or environmental changes affect populations
Variable Confusion: Students may mix up the x-variable and y-variable when using a trend line equation for predictions.
Over-Inclusion: Trying to make the line of best fit go through every point, including outliers, rather than the middle of the main trend.
Origin Assumption: Thinking a line of best fit must always pass through the origin (0,0).
Support: Provide structured Creating & Analyzing Scatterplots Notes and Slides to scaffold the process.
Hands on Activities
Exit Ticket
Student Work