The mathematical purpose of this lesson is to informally assess the fit of a function by plotting and analyzing residuals. The term residual is introduced as the difference between the \(y\)value for a point in a scatter plot and the value predicted by the linear model for the associated \(x\)value. The work of this lesson connects to previous work because students analyzed bivariate data by creating scatter plots and fitting linear functions to the data. The work of this lesson connects to upcoming work because students will use the correlation coefficient to formally assess the fit 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).
Lesson overview
 6.1 Warmup: Math Talk: Differences in Expectations (5 minutes)

6.2 Activity: Oranges Return (15 minutes)
 There is a digital applet in this activity.
 Note that due to significant differences in the approach used if primarily using print or digital, the activity contains two different sets of cards to support the different versions of the task.
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 6.4 Cooldown: Deciding from Residuals (5 minutes)
Learning goals:
 Calculate and plot the residuals for a given data set and use the information to determine the goodness of fit for a linear model.
 Comprehend the connection between residuals, variability, and whether or not using a linear model is appropriate.
Learning goals (student facing):
 Let’s examine how close data is to linear models.
Learning targets (student facing):
 I can plot and calculate residuals for a data set and use the information to judge whether a linear model is a good fit.
Required materials:
 Graphing technology
 Preprinted slips, cut from copies of the blackline master
Required preparation:
 Prepare 1 copy of the blackline master for every 2 students.
 Acquire devices that can run Desmos (recommended) or other graphing technology.
 It is ideal if each student has their own device. (Desmos is available under Math Tools.)
Glossary:
 residual  The difference between the \(y\)value for a point in a scatter plot and the value predicted by a linear model. The lengths of the dashed lines in the figure are the residuals for each data point.
 Access the complete Algebra 1 Course glossary.
Standards:
 This lesson builds towards the standard: CCSS.HSSID.B.6.bMS.SID.6bMO.A1.DS.A.5a
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