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Lesson 4: Linear Models
• Activate prior knowledge by informally tting a line to a scatter plot and informally judging its goodness of t.
• Interpret the rate of change and the vertical intercept of a linear model in the context of the data.
• Use an equation representing a linear model for a relationship between two variables to make predictions.
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 t 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 connect to upcoming work because students will use technology to t a line of best t to data and 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 bene t from estimating the line of best t in a dynamic way.
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 Learning Goals
• Let’s explore relationships between two numerical variables. 4.1 Notice and Wonder: Crowd Noise
Warm Up: 5 minutes
The purpose of this warm-up is to help students recall information about scatter plots, which will be useful when students expand their understanding in a later activity.
While students may notice and wonder many things about these images, the relationship between the number of people and the maximum noise level, interpreting the line of best t, and a general understanding of a scatter plot are the important discussion points.
Unit 3 Lesson 4: Linear Models 47