Lesson 4: 4-4 Scatter Plots and Lines of Fit
Duration of Days: 5
Lesson Objective
Investigate relationships between quantities by using points on scatter plots.
Use lines of fit to make and evaluate predictions.
When would a linear function be used to model a real-world situation?
scatter plot
line of fit
linear interpolation
S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context.
S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.
SAT questions related to writing equations: 5-4-11,4-3-8,8-4-7,1-3-12,7-3-19
functions: 8-4-4, 7-4-18, 8-4-18, 2-4-14, 3-4-20, 1-4-5, 7-4-21,
Solving Equations: 5-3-17, 6-4-32, 3-4-7, 8-3-1, 3-3-17, 6-3-17, 1-3-1, 3-3-2, 2-3-1, 7-3-16, 6-3-6,
A scatter plot consists of graphs of ordered pairs that belong to a set in which the x-coordinate represents one real-world measurement and the y-coordinate represents another. If a set of data exhibits a linear trend, a line of fit can be drawn and an equation of the line can be written to summarize the data.
See textbook page 247 for the graph showing the number ofpeople from the United States who travel to other countries. The points do not all lie on the same line, however, you may be able to draw a line that is close to all the points. That line would show a linear relationship between theyear x and the number of travelers each year y.
Remind students that predictions are only as valid as the equations used to find them. Therefore, there are as many predictions as there are equations that can be written from pairs of points.
If students need more practice making and interpreting scatter plots, then have them make a scatter plot of their height (x-values) and age (y-values) for the first 10 years of their life. Students estimate their heights as needed, but check to be sure estimates are reasonable. Ask them to draw a line of fit and write the slope-intercept form of an equation for the line. Then ask students to compare their current height with that derived from their equation.
Extension: Write (1, 10.1), (2, 9.8), (3, 10), (4, 10.5), (5, 10.4), (6, 10.8), and (7, 10.3) on the board. As a class, graph these data points on two separate graphs. Make the scale on the first graph such that the result is a scatter plot with no correlation. Make the scale on the second graph such that the result is a scatter plot with a positive correlation. Discuss how graphs can be manipulated to show different trends.
Practice: Exercises 1 -3
Exercises 18 -22
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