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# Simplifying Basic Trig Expressions – Connect the Dots

Lesson 5 of 16

## Objective: SWBAT use trigonometric identities to simplify basic expressions.

#### Homework Quiz & Warm Up

*15 min*

At the start of class today, students will take their Homework Quiz for the week. When students finish the quiz I will let them start to work on Page 3 of the Simplifying Basic Trig Identities flipchart. The point in these problems is to review algebraic rules and concepts that will be useful when simplifying trigonometric identities. I will make sure to model these problems as a review a little later in the lesson.

As students are working, I will be thinking about how to group the students. Today's activity is going to be challenging for most students. Perseverance is important today. I plan to have students work in teams of 2-3. Today is a great day to encourage a team mentality in the classroom. We are all here to learn and help each other. Today is going to be challenging, but together they can do it!

**Teacher's Note about Homework Quizzes:** Every Friday for homework quizzes, I ask 10 questions from the homework and students have 7 minutes to text in their answers. The score they receive on this quiz is their score for the week of homework. Homework quizzes rock! No handling students’ papers, no grading (or minimal grading if you don’t have clickers), and you still get great feedback on students understandings and misconceptions. If you don’t have access to clickers, just have the kids write it down. Watch the Accessing a Homework Quiz* *video if you would like to print out the Homework Quiz.

##### Resources (6)

#### Resources

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#### Application

*30 min*

During the middle part of today’s lesson students will work with their table mates to simplify the identities and find their matching answers. They will need to work hard to identify the correct matches and explain their thinking clearly to the other members of their group (MP2). The task is challenging because students need to interpret the expressions and recall both identities and algebraic skills (MP7). I expect my students to actively use their trig identities books to help them simplify these identities. Once students finish the activity they can connect the dots on the last page to check their answers.

During this time, I will monitor the classroom to keep teams on task. I will make regular efforts to encourage team work. I will avoid being a resource for knowledge that I expect students to possess at this point, either in their minds or their trig identity books. One strategy I like to use to ensure students are only asking good questions (and to help me to remember not to help students too much and to make them think for themselves!) are **Question Cubes**. No cube, no question.

If students are emerging as leaders in simplifying trig identities and they complete their work quickly, I will allow them to tutor peers. It really is much more difficult to **explain** how to simplify a trig expression than it is to actually do it. By having students tutor, I think it gives them an opportunity to dive deeper into their own thinking, while helping catch struggling students up (MP3).

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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