Equations on a Graphing Calculator
Lesson 11 of 17
Objective: SWBAT graph linear and non linear equations on a graphing calculator. SWBAT set appropriate viewing windows and use the trace feature to identify different points on the lines.
I begin class by telling students that I appreciate all of the hard work they have been doing making graphs in class to represent a variety of different situations. I let them know that today, I will be showing them how a graphing calculator can make graphs and help them explore the behavior of functions. I like to make a joke with students about how they will be mad at me after I show them what the calculator can do, because I have made them do so much work by hand. But I share with them the reasoning behind my method of waiting to teach them how to make graphs on the graphing calculator at this point. I let them know that making the graphs by hand helps them to better understand the concepts behind what they are learning. I explain that the graphing calculator is a tool that can help them in their work, but they must have a good understanding of graphing concepts in order to use it effectively.
I hand out Equations on a Graphing Calculator and let students know that we will work on the first problem as a class. Working in a whole class setting on the graphing calculator can be frustrating if the technology is not working properly. I check out my graphing calculators before class and make sure they are set up the way I want them. I often go through and clear out old equations and make sure viewing windows are set to the standard setting. I also like students to follow along at the Smartboard. I use wabbitemu software to show students what to do on the graphing calculator, so everyone can see and hear my actions on the calculator. In addition, as access to technology improves at my school, I have been using programs like desmos.com and plot.ly more and more frequently. Both run well on the Google Chromebooks that we have at school and the desmos app runs well in the Ipads.
Students in my classroom may have had different experiences with graphing calculators in previous classes. I find that everyone generally needs a refresher so I go through the first problem quite thoroughly. I show students where they can enter an equation, how to enter "X", and where they press the Graph button to actually see the graph. I make frequent trips around the room to make sure no one gets too far behind and ask people sitting at the same tables to help each other.
Students often struggle with how to set the viewing window. I spend A LOT of time on this part of the lesson as it is an important skill for students to master moving forward. I help students understand how to set the viewing window by asking them what the x- and y-axes should look like for the first problem situation. Elicit that for the x-axis (the predicted temperature) they need to know how many people to expect if the temperature is 75 degrees. I tell students they don't want that 75 to be right on the edge of the viewing window, they want to be able to see a little bit past that, so they might set the Xmin=0 and the Xmax=85. Follow a similar process for the y-axis. I find students can be quite intuitive about determining the scale for x and y once they have set the Min and Max points. I ask them how they decide on a good scale once they know the range they have to cover.
Once they are able to see a good visual of the graph, I bring students' attention to the questions in the activity. I ask them how they can use the graph to find the answers to these questions. I show students the TRACE button and help them zoom in in order to get an accurate value. I make sure students understand that one question is asking them to find a y-value and the other is giving them a y-value and asking them to find the corresponding x-value. Students may want to use the equations to answer the questions. I congratulate them on good thinking, but insist that they use the graphs. I allow them to use the equations to check their work instead.
This is a good point to make an explicit connection to CCSS REI 10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). I show students that they are using the graphing calculator to extend their graphs and explore different points - all of which are solutions to the equation.
Next, I let students get to work at their tables on the rest of the activity. I don't mind if students work together a little bit here, but I insist that they all use their own graphing calculators and keep track of their own answers. Too often, with graphing calculator activities, I see some students let others do the work for them because they don't fully understand how to use the calculator. I do find it helpful though to let students work together and help each other. Sometimes a student will have a better way of explaining the technology in a way that his/her peer will understand.
Issues I watch for:
- Make sure students know how to enter the parentheses in the second equation.
- Many students will struggle with the quadratic function. I encourage and show them how to use the zoom feature to get closer and closer to the number they are looking for. I encourage students to see just how close they can get! I show them the ZOOM Standard feature to help them get back to the main viewing window when they are moving on to the next point.
- I challenge students when they get to the quadratic table Out values. Most students will likely give only one In value for a given Out. Students may be confused at first, but I ask them to look at the shape of their graph again. I point to where they found one of the correct Out values and ask them if that same y-value occurs somewhere else on the graph. I show students that they can move their cursor straight across the graph horizontally by using the arrow keys (when the TRACE feature is not in use).
I leave the last few minutes of class to allow students to share out any questions they have or any tips that they want to share with other students. I like to close class with an exit ticket that gives structure to the end of class and gives students time to reflect on what they learned. A nice prompt for today's exit ticket is:
What part of using the graphing calculator did you like the best? How would you explain that piece to another student who has never used the calculator?
If I get a variety of responses to this prompt and good instructions for a future student, I might type them up and share them with the class at the beginning of the next lesson.
This material is adapted from the IMP Teacher’s Guide, © 2010 Interactive Mathematics Program. Some rights reserved.