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* *Reflection: Connection to Prior Knowledge
Discovering Trig Identities (Day 2 of 4) - Section 2: Investigation

When looking over my students’ work, I was intrigued by the various answers being given for question 4. Technically, students should already have prior knowledge of how changing the ‘a’ value would affect the graph. We just got done studying the key aspects of trigonometric functions and how parameter changes affect the graphs in the last unit. This question showed me that my student either did not retain much of that knowledge or were not connecting to their prior knowledge for this question.

Here is a variety of levels of answers for question 4 that I observed:

Good use of mathematical vocabulary

Could be better with more detail

True (but not the answer I expected yet)

I wondered if the difficulty with this question stemmed a bit from the language of the question. During class, I had many students ask me what the worksheet meant by the word parameter. I thought I had used that term when we studied trigonometric functions in the last unit (or at least in the whole first semester when we studied a variety of other functions!) When I followed up with the prompting question of “As *a* changes how does the graph change?” many more of my students were able to understand the question. Apparently, I need to work more on using the prompting question “As the PARAMETER *a *changes, how does the graph change?” I think that would help my students in the future with this type of question.

Even once students understood the question, I still got a few wrong answers. I think these two examples would be great for a Favorite No activity. They would provide a great opportunity to help students be more precise with their mathematical language (Mathematical Practice 6).

Good Opportunity for a Favorite No

*Connection to Prior Knowledge: Student Work - Question 4*

# Discovering Trig Identities (Day 2 of 4)

Lesson 2 of 16

## Objective: SWBAT visualize and interpret the trigonometric identities with a focus today on negative angle identities.

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#### Closure

*15 min*

Today’s closure to the lesson is very important!

At the end of a discovery activity it is important for communicate to students about what they have learned. First, I will have students complete another page in their trig identities book with the negative angle identities. I ran this as a whole group discussion. I asked the students to share what they found and then filtered any incorrect answers by asking the class if they agreed. Then I explicitly summarized the identities on the board just to be sure that every student was getting the correct information (MP6).

Next, I will have students complete the closure questions on Pages 5-7 of Discovering Trig Identities. I plan to provide about 10 minutes for students to work through the last 3 questions on the flipchart (pages 5-7) and to allow a bit of time to go over the last question (MP1). The last question is intended to just see what they came up with. The purpose of this last question is to first communicate to students where we are going with this, but also it gives a great preview to the teacher of who will most likely become a leader in the class for simplifying identities (MP2).

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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