Do it with Graphs

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Objective

SWBAT solve problems involving rational, radical, absolute value and exponential equations graphically.

Big Idea

Graphing calculators and complicated problems...a great way to get your students doing it with graphs!

Set the Stage

10 minutes

I begin class with two equations on the board and ask my students to find the zeros for each. (MP1)  Most students will try some variation of division or simple inspection to find the solutions and after they've worked individually and/or collaboratively for a few minutes I ask if anyone has the answers.  If there are any volunteers, I ask them to explain their work to the class and if not, I suggest that maybe this is a job for their graphing calculators!

After giving my students time to enter the first equation into their calculators, I ask them how they can find the solutions using the graph. Some students will be fairly competent with this, but there are several who will need help to fully utilize the options for finding zeros with their graphing calculator.  (MP5) I've included basic instructions on the equations sheet, which can either be given directly to students, or can be read to them.

When everyone has successfully utilized the calculator to find the zeros for the first problem, I encourage them to try the second problem and post their solutions on the front board as they find them and be prepared to explain how they got them. (MP2) I check for understanding and confidence using fist-to-five and give a few additional examples to work through if necessary.  We close this section by discussing the advantages to using a calculator (speed, accuracy of plotting, flexibility of view- table, trace, calc, etc) and disadvantages (may have to rewrite equation, window adjustments, making sense of the answers).

Put it into Action

35 minutes

Team Practice (10 minutes): I use individual whiteboards and markers for this section, but you can use plain paper instead.   For this section I have my students team up to graphically solve Graphing Practice Problems with an emphasis on what the solutions represent in terms of the original problem.  They work through a few practice problems with answers provided first to be sure they understand the process and expectations. (MP1) 

Team Competition (25 minutes): After about ten minutes or when all teams indicate they're ready to compete I review the rules of the contest then have each team get a white board and marker.  The rules are included on the Graphing Competition Problems, which has all the contest problems and solutions.  I read one problem then allow three to five minutes before having a simultaneous display of the answers on the whiteboards. (MP1, MP3) Points are awarded as indicated in the rules and posted on the board.  If you choose to use paper rather than whiteboards, you can have teams exchange papers and check each others answers - they generally are pretty tough on each other! My video explains why I chose this strategy for reinforcing this lesson.

Wrap it Up

5 minutes

To close this lesson I give each student a notecard and ask them to describe one benefit they see about solving equations using a graphing calculator and one problem they have with it.  These reflections focus student thinking on both the tool, the graphing calculator, and the process, finding solutions to an assortment of equations graphically. (MP5)  They also give me insights into areas that students may still be struggling with in using calculators with proficiency.