Today students will be working with their graphing calculators. If you do not have access to a whole class set, I think this activity would also work nicely with students working in pairs and sharing calculators. I am going to have all of my students use their own calculator, but work in teams to discuss their findings.
Today’s activity is very prescriptive in telling students how to solve a rational equation on the graphing calculator. The goal is not for students to establish their own understanding and their own procedure for how to solve by graphing. The goals are as follows:
As students work to make these connections they are engaging in MP2. The strategy of writing a system is powerful for students. They can use it to check (or estimate) solutions to an equation. This strategy is even more powerful when students leverage graphing technology (MP5).
Today's lesson may seem a bit procedural, but I think there are some deeper understandings that students are developing. To get students thinking in the right direction, I begin by posing these questions to students:
It is important that students can articulate that they are looking for the values of x that make both sides of equation equal. Then I will pose the problem in the discovery activity and ask students, "How do you think that I cab solve this equation by graphing?"
I am hoping to lead students into the big idea here: We can graph each side of the equation as a separate function and use the graph to estimate the solution of the resulting system. Once this idea is raised, I will pass out Solving Rational Equations by Graphing and have students work through these examples. There are many practice problems here, so I don’t necessarily expect my student to finish them all.
As students work through this activity, there are some secondary learning targets that I also hope are hit:
To wrap-up today’s learning and insure students made the desired connections, I will have them answer the following question (see page 3 of the flipchart):
How are the solutions of a rational equation related to the intersection points formed by the graphs of the two separate functions made equal by the equation?
I think it is important that students can articulate in some way that the equation is broken into two functions and that we are finding the solution where these two graphs meet because this is where both sides (or both functions) are equal.