## 4-way representation – solving a system of trig equations, video narrative, modeling - Section 3: Modeling

*4-way representation – solving a system of trig equations, video narrative, modeling*

# 4-way Representation - Trig System of Equations

Lesson 15 of 16

## 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.

*50 minutes*

#### Review 3-2-1 Assessments

*5 min*

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.

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#### Warm-Up

*5 min*

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:

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

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#### Application

*10 min*

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.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Discovering Trig Identities (Day 1 of 4)
- LESSON 2: Discovering Trig Identities (Day 2 of 4)
- LESSON 3: Discovering Trig Identities (Day 3 of 4)
- LESSON 4: Discovering Trig Identities (Day 4 of 4)
- LESSON 5: Simplifying Basic Trig Expressions – Connect the Dots
- LESSON 6: Verifying Trig Identities (Day 1 of 2)
- LESSON 7: Verifying Trig Identities (day 2 of 2)
- LESSON 8: Solving Basic Trigonometric Equations
- LESSON 9: Group Quiz - Solving Trig Equations
- LESSON 10: Solving Quadratic Trig Equations (Day 1 of 2)
- LESSON 11: Solving Quadratic Trig Equations (Day 2 of 2)
- LESSON 12: Puzzle - Solving Variety of Trig Equations
- LESSON 13: Sum and Difference Identities
- LESSON 14: Error Analysis - Sum and Difference Identities
- LESSON 15: 4-way Representation - Trig System of Equations
- LESSON 16: Review for test