4-way Representation - Trig System of Equations

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Objective

SWBAT use multiple representations to solve a system of trigonometric equations.

Big Idea

All students are challenged to represent their solutions to a system of trig equations in four different ways.

Review 3-2-1 Assessments

5 minutes

I will take some time at the start of class today to review the 3-2-1 Assessment from yesterday's closing segment. Today, I will address only the questions. If I don’t find time to address all of these today, I will keep them up and come back to them at the beginning/end of class throughout the next week. I only remove a Sticky Note once I have answered the question, and then I know which questions have not been answered.

These assessments shed light on the ways that some of my students are struggling. I had a couple of comments like “Can you start over? I am so lost.” Being that these were anonymous, I encouraged kids that wrote these things to see me for help outside of class.  It is a nice formative assessment of the class as a whole. Are they ready to move on? If not, you may want to back it up and take a day to review. These next few days students will be modeling with real world data, so it may be too challenging if they don’t have the pre-requisite skills from the beginning of this unit. 

Warm-Up

5 minutes

After reviewing some questions from yesterday, I will begin students work today by asking them to complete the problem on Page 2 of  the 4-way Representation Flipchart. This problem requires students to recall how to solve a system of equations. Depending on a student’s solution methods, it may also require a student to review solving a quadratic equation. 

I expect my students will solve the problem in many different ways:

  1. Graphing – putting in both equations and finding where the two functions intersect
  2. Graphing – setting the two equations equal to each other and graphing in standard form, found x-intercepts
  3. Table – put in both equations and find where the table values say they are equal
  4. Table – using standard form of combined equations and finding where equal to zero
  5. Algebraically – substitution method and then used quadratic formula or factor
  6. Algebraically – elimination method and then used quadratic formula or factor

It would be awesome for students to present all these different methods to help remind their peers of them, but I tend to think that would take too long. Instead, I plan to remind students by identifying all of the solution methods I am seeing. I will most likely encourage students to use Methods 3 and 4 above to check their answers, but not to solve the system. It is an inefficient method when working in the set of real numbers.

If I model the solution, I will use Method #5. I think that this will be most helpful in scaffolding the remainder of the lesson. 

Modeling

30 minutes

Application

10 minutes

For the last 10 minutes of class, have students complete the Yo-Yo Problem on the back side of the Student Worksheet: 4-way representation. This problem guides students through writing a function to model the motion of a yo-yo. So, it is not necessarily closing out the learning from today’s lesson, but reviewing past concepts from the last unit in context. Students can text in their answers (see Page 4 of Flipchart). I will use the information they text in to judge what they remember from the last unit about writing trig functions.

Teacher's Note: If my students need more time on the 4-way model, I will assign this closure problem as homework and address it at the start of class tomorrow.