Lesson 11 of 13
Objective: SWBAT use a system of linear equations drawn from real world data and best fit lines to make valid predictions.
To launch this lesson I pair students up and hand each pair an Entrance Task for Going Mobile. I ask that they read the slip carefully and then work together to analyze the data and corresponding graph.
Students will be drawing best fit lines (video introduction below) for both sets of data and making estimates based on the graphed lines. I expect that some of my students will extend both lines off the graph until they meet to make their estimate, which is fine (see Extended lines of best fit example).
Students will practice their equation writing skills, having to write the equations of their best fit lines in slope-intercept form. When solving the system, I remind my students to analyze the equations and decide on the better algebraic method to use. In this case, substitution is the better route. Solving the system should yield that the women's time will equal the men's time around the year 2080. Most students, if work is done with a fair amount of precision, will get between the years 2070 and 2090
It is a good idea to present the following quick video to the class before students embark in drawing best fit lines.
Source: http://www.youtube.com/watch?v=XUAu9lF6J3Y (accessed July 23 2014)
Watching for common errors: It is important that as students are drawing their lines and writing their equation, I walk around monitoring their work. I ask that they try to draw a line as close as possible to all the data points, getting more or less the same number of dots on either side of the line, and not necessarily passing the line through the first and last points of the data plot. I also keep an eye out making sure students write the correct slope. Both slopes here are negative, and too many students write a positive slope for these lines.
The coolest part of this lesson is the Application Section. Each pair of students gets to graph data comparing users of desktops and laptops in the world. Students have no problem plotting data at this point, but it is helpful to remind them that they are dealing in millions here and that 1000 on the graph represents a billion, and so forth.
I make sure that my students use the x-axis to represent the years and the y-axis to represent the number of users. Each pair of students gets a copy of the Data Table Going Mobile on personal computer users in the world. They should have graph paper, pencil, and rulers at hand in order to do the activity. Once students graph the data and draw their best fit lines, they should complete each question below the table. I walk through the class monitoring student work and helping out with the graphing, making sure students make large enough graphs to be able to present clear data and make better use of these to answer the questions.
If computers for each group and a printer are available, students can create their own graph at the following site:
Graphs can be printed to draw their best fit lines. There is a link to a tutorial for using Create-A-Graph on the lower left hand side.
To end the lesson, I choose a group that has done a good job with their graphs and ask that they go up and place their graph on the document camera for the whole class to see. With their graph projected, I ask that this group answer the questions (2 through 5) out loud to the class. It's a good idea to pause between questions and ask the class about their answers in comparison to the group presenting. Most students should have designed graphs predicting that the number of mobile pc users will equal and surpass desktop users around 2015. The algebraic solution to their system should have yielded similar results.
If a group's graphic and system solutions are very different, I ask that they first speculate why this could have happened, and then determine why. When this happens, I present the situation to the class. If no group has this problem, I make sure I ask the class the questions, "What if a group's work yielded far different results?" What could have gone wrong?
To conclude, I ask that someone make a concluding statement on the purpose of today's lesson. I expect something along the lines of "Systems of best fit lines can be used to make predictions" or "Systems drawn from real data can be used to find information that we don't know"