Page 162 - IM_Algebra1_FL Print Sample.pdf

Student Task Statement
1. Match the scatter plots and given linear models to the graph of the residuals.
2. Turn the scatter plots over so that only the residuals are visible. Based on the residuals, which line would produce the most accurate estimates? Which line ts its data worst?
Student Response
1. ◦ A matches with K ◦ B matches with G
◦ C matches with L ◦ D matches with H ◦ E matches with J ◦ F matches with I
2. B ts its data the best. J or L ts its data the worst.
Activity Synthesis
The goal is to make sure students understand the connections between a scatter plot displaying a linear model and a graph of the residuals.
Much discussion takes place between partners. Invite students to share how they made the matches.
• “What were some ways you handled nding the matches for B and C? Recall that B and C used the same data but di erent linear models.” (The line in C was not as good of a t as line B, so I knew the graph of the residuals would be further away from the horizontal axis.)
• “Look at the matches for E and J. How can you tell from the graph of the residuals that the linear model is not a line of best t?” (The rst half of the residuals are positive and the second half are negative. This lets me know that the line does not pass through the middle of the data.)
• “What do you notice about the residuals in graph K? Explain what you notice in the context of scatter plot A.” (The residuals go in a u-shaped pattern. The data in the scatter plot does not appear linear and is curved, so when you plot a line through it, you would expect the residuals to show the curvature.)
• “Describe any di culties you experienced and how you resolved them.” (It was tough guring out how to decide where to begin when nding matches. I used my partner’s strategy of looking at the values on the -axis to help narrow down the choices.)
Unit 3
Lesson 6: Residuals
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