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# Error Analysis - Sum and Difference Identities

Lesson 14 of 16

## Objective: SWBAT to apply the sum and difference identities to find exact values of trigonometric ratios of angles that are not derived from special triangles.

## Big Idea: Students become teachers as they grade each other's work and find errors in applying the sum and difference identities.

*50 minutes*

#### Homework Quiz

*7 min*

Today's class begins with a **Homework Quiz**. Students will have 7 minutes to complete **Homework Quiz: Trig Equations #7-8** covering the content of Homework 7 and Homework 8.

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#### Summarize Past Learning

*3 min*

Once students have completed the homework quiz I will ask them to take out their **identities book**. I will ask students to take a minute to review the identities we learned yesterday since they were not on the quiz. Then, I will have them add the Sum and Difference Identities for tangent to their books. The students will apply this identity in their work today.

I plan to structure today’s lesson so that students complete their work in teams. My students will sit in teams of 3 so that they can discuss the problems. All students will complete their own work, using their team as a resource for help or quick check-ins. I will also encourage my students to use their notes or texts to help them complete this activity. * *

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#### Application

*30 min*

The work required for today’s activity can definitely be adjusted based on students’ mathematical ability and the pace at which they work. For struggling students, encourage them to just go through and find the first place an error was made and just write what it should have been. Don’t have these students go all the way through and finish the problem correctly. On the other hand, require all students that you think are ready to advance their learning to actually find the correct answer to the problem.

With a colored marker, pen, or pencil students should correct the work provided on Student Worksheet: Error Analysis over Sum and Diff. They should circle where the error occurs and correct that error. If time permits, students should complete the problem all the way to find the correct answer. While students are identifying these errors in their teams the following mathematical practice standards will be addressed: * ***MP1**, **MP2**, **MP3****,*** ***MP5****, *** ***MP6**, **MP7**, * ***MP8.**

Another scaffold that I had to provide for today’s lesson is to help students recall the rules for radical operations and for adding/subtracting fractions. I use some basic suggestive prompts:

- Before we can add/subtract fractions, what must we do?
- Are they like terms? Can you add them together?
- Try an example you know: What’s the square root of 3 times the square root of 3?

With such prompting, most of my students are able to recall the rules. If i need to take things a little further, I may make up an example of a simpler problem and walk the students through it.

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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