Materials needed for this lesson:
1. Student family portfolios.
2. Graphing 2-Variable Equations worksheet (see Lesson 6 Resources folder).
3. Graph paper, colored pencils, rulers.
4. TI-83+ calculators for students, and the ability to project the teacher’s calculator screen onto a television or whiteboard.
This section does not contain a suggested script.
Review students' Writing 2-variable Equations worksheet together. Answer any lingering questions students may have and ensure that all students are proficient at symbolizing these two-variable situations. Inform them that today they will be learning how to give graphical representations of their two-variable equations.
Give the students each a copy of the Graphing 2-Variable Equations worksheet. Have them get into student pairs. Go through the first question as a class, having each student pair generate a table of ordered pairs that would make the equation work. Have student pairs graph their ordered pairs and "connect the dots". Then, have student pairs exchange their work with a different student pair to see that although everyone had slightly different ordered pairs, they all got exactly the same line. Lead a discussion as to why it is possible to find different combinations that make the equation true, and why they all "line up" (i.e. that the line represents precisely that infinite set of ordered pairs where the combination of x and y values make the equation true).
Next, have the student pairs work through question 2 together. Once the majority of student pairs are done, lead a discussion comparing answers and answering lingering questions. Then, have student pairs work on question 3 together. This question is tricky, as it requires students to choose an appropriate scale for their graph (units of 1 will not be feasible). If necessary, lead a brief discussion/lesson explaining the use of scales in graphing (how you can go up by 5's, 20's, even 1000's on either axis, and that the two axes do not have to have the same scale). Allow sufficient time to discuss the differences in graphs that different student groups get (having used slightly different scales). If time allows, graph the equation y = 125x + 50 on your teacher-model TI-83+ and project the graph using different scales on the x- and y-axes. It might even be instructive to show the "ZStandard" window, on which the graph wouldn't even appear!
Enrichment: This lesson provides an excellent opportunity to provide an introduction to the graphing functionalities of the TI-82/83 series calculators. Once students have derived equations and graphed them on their own, you can quickly demonstrate how to graph the same equations on the TI graphing calculators (as all examples of equations in this lesson are already in slope-intercept form).
If time permits, students can work on question 4 together. Otherwise, it makes an excellent homework assignment.