Intent In this activity, students create and read graphs using the graphing calculator, in particular the Y=, Graph, Window, and Trace keys.

Mathematics Students employ technology to graph linear and nonlinear functions and use the graphs to answer questions. The trace feature of the calculator allows students to find In-Out pairs. The ability to use this technology is required for later investigations in the unit and throughout the IMP curriculum.

Progression The teacher briefly introduces the basic steps for graphing a function on a graphing calculator before students work on the three parts of this activity in their groups.

Approximate Time 30 minutes

Classroom Organization Groups, followed by whole-class discussion

Materials Graphing calculators Calculator manuals or guidebooks

Doing the Activity The main goal of this activity is to acquaint students with the basic functions of their graphing calculators (or equivalent technology), including the following operations. Enter and edit functions and have the calculator draw their graphs. Adjust the viewing rectangle, either directly or by using the zoom feature, to see a particular portion of the graph and to get more precise information about the graph. Use the trace feature to get the coordinates of a point on a graph. Some students may have discovered these operations on their own, but you should probably assume that most have had little experience with the graphing capabilities of their calculators. Begin by illustrating these operations with one or two simple examples, starting with a linear function, such as an example from a recent activity. Then let students explore on their own for a while. One point to emphasize is that the calculator will only graph an equation entered in the Y= form—that is, the form that expresses the output, which the calculator calls Y, directly in terms of the input, which the calculator calls X. When students seem comfortable with these simple mechanics, have them begin the activity. While students work, they are likely to struggle with several ideas. Encourage group members to work together to answer any questions. If an entire group has a question, limit what you show them to the Y=, window (and zoom), graph, and trace menus on the TI-84 plus. Although the calculator provides several mechanisms for solving equations (such as the Calc:Intersect and Table), do not demonstrate these at this time. The focus on the trace feature is intentional, as it will to continue to develop the connection between the visual location of, and meaning for, points on a graph in a coordinate system. One of the mathematical challenges of this activity is understanding the need to adjust the viewing rectangle in order to get the right part of the graph on the screen, as well as the steps for doing so. Finding a good viewing window is an essential skill for working with graphing calculators. Encourage students to play with the window limits and to develop their own strategies. If a group is struggling to find a window they are satisfied with, help them to focus on the meaning of what they see in the graphing screen. One question you might pose is, What scales have you assigned to the calculator’s display? What do you want to see? Or, What sort of numbers do you want to see that aren’t in your viewing window?Are these in the x- or the y-direction?Once students make this decision, you can remind them how to adjust these settings in the window menu. Another frustration students may encounter is being able to get better approximations than what the trace feature initially provides, especially for Question 3. Remind them that they can use the zoom feature or one of the options in the zoom menu. Often just this reminder is enough for students to figure out where to go next.

Discussing and Debriefing the Activity Focus the discussion on how to read information from the graphs to answer the questions in the activity. This will likely entail some sharing of calculator-use methods and discussion of the zoom and trace features. Over time, students will grow more comfortable with manipulating viewing rectangles and other graphing-calculator techniques.

Key Questions What scales have you assigned to the calculator’s display? What do you want to see? What sort of numbers do you want to see that aren’t in your viewing window? Are these in the x- or the y-direction?

Supplemental Activity Mystery Graph (reinforcement) is a graph-interpretation activity in which students are given the graph of a nonlinear function, but not its equation, and are asked to find a number of values for the function.