This lesson should begin with a review of what the students learned in Lessons Five and Six of this Unit Plan. Having them restate what they learned will help reinforce the concepts of that activity and give the teacher another
opportunity to assess students’ understanding. Today’s activity should begin with a general discussion of what students think the scatter plot of years (year of make) since 1990 vs. mileage will look like. Do they think the least squares regression line will have a positive or negative slope? How do they think the y-intercept of this line will compare to that in Lessons Five and
Six?
Students should be divided into teams of two to work at the computer. If possible the students should continue to work with the same partner they had while doing Lessons Five and Six. Each student should be given a copy of the
handout Automobile Mileage—Years Since 1990 vs. Mileage (or a similar handout of student-produced data). They should visit the Web site: http://illuminations.nctm.org/index_d.aspx?id=454
Working together, the partners can share the responsibility of making sure the data is plotted correctly. One student should plot the data, while the second reads out loud the data and makes sure it is plotted correctly.
Students should click on the applet and make the changes in the viewing window indicated on the handout. As the students begin to plot the data, walk from group to group, making sure the students are plotting the data correctly.
Encourage students to think about the data they are plotting and the resulting plots. Ask Guiding Questions such as the following as you monitor and facilitate
the group work. It would be beneficial if time allowed the class to look at data on years like 1989, 1988, etc.. How would students handle this?
- Are you beginning to notice any pattern in the shape of the plot?
- What type of function do you think will fit this data?
- Do you think the slope of the line will be positive or negative?
- What do you think the y-intercept of the regression line might be?
Allow the students to complete the plot and answer the questions on the handout. Continue to circulate and facilitate discourse between the partners while they complete this portion of the activity.
After completing the questions on the handout, students should be given the opportunity to discuss their findings as a class. The questions on the handout can be used to help guide this discussion. This will encourage students to
reflect on what they have discovered about the graphical and algebraic representations of the data and allow them to strengthen their understanding of slope as a rate of change. The teacher should pay particular attention to the
students’ understanding of the units used on both the horizontal and vertical axes.
