Lesson 4

Linear Models

Lesson Narrative

The mathematical purpose of this lesson is to understand how a linear model is used to describe the relationship between two numerical variables, and to use a line of best fit to make predictions. The work of this lesson connects to previous work because students investigated patterns of association in bivariate data in eighth grade and in a previous lesson. The work of this lesson connects to upcoming work because students will use technology to fit a line of best fit to data and will formally assess the strength of a linear relationship.

When students articulate things they notice and things they wonder about a scatter plot and the accompanying linear model, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). Students reason abstractly by making sense of slope and intercept in context (MP2).

One of the activities in this lesson works best when each student has access to devices that can run Desmos, because students benefit from estimating the line of best fit in a dynamic way.

Learning Goals

Teacher Facing

• Fit a linear model to a scatter plot of data and informally judge its goodness of fit.
• Interpret (orally and in writing) the rate of change and vertical intercept for a linear model in everyday language.
• Predict (extrapolate) and estimate (interpolate) values not given in the data set by using an equation representing the linear model.

Student Facing

• Let’s explore relationships between two numerical variables.

Required Preparation

Devices are required for the digital version of the activity—Orange You Glad We’re Boxing Fruit. The digital version is recommended for all classes over the paper and pencil version.

Student Facing

• I can describe the rate of change and $y$-intercept for a linear model in everyday language.
• I can draw a linear model that fits the data well and use the linear model to estimate values I want to find.

Building On