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dashed line does not seem to take into account the cluster of points that have a range greater than 4.
4. Sample response: The solid line is the better t for the data since it goes through the middle of the data with approximately equal number of data points on either side of the line. The dashed line t 4 points extremely well but is below the majority of the data.
Activity Synthesis
The purpose of this discussion is to understand bad t, good t, and best t. In each scatter plot, the solid line represents the line of best t.
Ask a student who uses the term slope while working the questions, “Can you explain the relationship between the two lines in question 1 using the concept of slope?” (The slope of the dashed line is positive and the slope of the solid line is negative.)
Ask a student who uses the term -intercept, “Can you explain the signi cance of the -intercept in question 4?” (The dashed line intersects the -axis approximately 0.5 units below the solid line. Because the two lines have approximately the same slope, they appear parallel in the scatter plot.)
If time permits, discuss questions such as,
• “Is the dashed line in question 1 a bad t, good t, or best t?” (The line is a bad t because it does not show the correct relationship between the variables. It shows that the value of increases as the value of increases, rather than the value of decreases as the value of increases.)
• “Is the dashed line in question 2 a bad t, good t, or best t?” (It is a good t because it is close to going through the middle of the data and follows the same trend as the data.)
• “Why might the solid line be the line of best t?” (It is the line of best t because it goes through the middle of the data, follows the same trend as the data, and has about the same number of points above the line as it does below the line.)
5.2 Card Sort: Data Patterns
15 minutes
The mathematical purpose of this activity is for students to:
• distinguish between linear and nonlinear relationships in bivariate, numerical data • informally assess the t of a linear model
• compare the slope and the vertical intercepts of di erent linear models
• describe the relationship between two variables.
A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).
Unit 3 Lesson 5: Fitting Lines 69