Page 156 - IM_Algebra1_FL Print Sample.pdf

Lesson 6: Residuals
• Make connections between residuals and variability.
• Plot and analyze residuals to assess the goodness of t.
• Understand the importance of analyzing residuals to determine whether or not using a linear model is appropriate.
Lesson Narrative
The mathematical purpose of this lesson is to informally assess the t of a function by plotting and analyzing residuals. The term residual is introduced as the di erence between the -value for a point in a scatter plot and the value predicted by the linear model for that value. The work of this lesson connects to previous work because students analyzed bivariate data by creating scatter plots and tting linear functions to the data. The work of this lesson connects to upcoming work because students will use the correlation coe cient to formally assess the t of a function.
When students take turns with a partner matching graphs of residuals to scatter plots that display linear models, students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3).
Required Materials
Pre-printed slips, cut from copies of the blackline master
Required Preparation
Prepare 1 copy of the blackline master for every 2 students
Student Learning Goals
• Let’s examine how close data is to linear models. 6.1 Why, Though?
Warm Up: 5 minutes
The mathematical purpose of this activity is for students to estimate the line of best t and justify why it is the line of best t.
Launch
Display the image for all to see. Give students 2 minutes of quiet time to work the question and then pause for a brief whole-class discussion.
Student Task Statement
Find the line of best t. Explain or show your reasoning.
Unit 3 Lesson 6: Residuals 89