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# Building the Unit Circle (Day 1 of 2)

Lesson 4 of 10

## Objective: SWBAT identify special angles in the unit circle and find the coordinates of these angles.

## Big Idea: Students use prior knowledge of circles and angles, and their cut-out special triangle templates, to build the unit circle.

*50 minutes*

#### Warm-up

*5 min*

To warm-up for today's lesson, I ask students to practice converting from radian angle measurement to degrees. I display the problem on page 2 of today's flipchart, Flipchart_Building the Unit Circle. Students can text in their answers as they complete the warm-up. The warm-up will prove to be helpful for some students as they build their Unit Circle.

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#### Building the Unit Circle

*40 min*

After the warm-up problem, I presented page 3 of the Flipchart_Building the Unit Circle to quickly introduce what a Unit Circle is. I just wanted to emphasize that this is a special circle that has a radius of 1.

Next, students should work through the Student Handout - Building the Unit Circle. They will also need the Unit Circle Template to complete their work.

The Building the Unit Circle handout outlines EXACTLY what students need to do. I found it helpful to have struggling students begin by labeling the degree measurements on the two circles (divided into 8 sections and 12 sections) located on their handout and then transfer these numbers to their Unit Circle Template. If students had a hard time visualizing the two circles transposed on top of each other, I had them highlight the sections like this: Day 1 building.

Furthermore, if students asked for help with converting radian measurements I really tried to guide students into thinking about a full rotation as 2pi radians and then working from there to figure out how much 1/12 of a rotation would be and how much 1/8 of a rotation would be. I noted that many of my students, however, were actually converting each degree measurement to radians using the ration pi/180. I did not intervene as I think it is important for them to develop their own understandings, so whatever works for them! However, at the end of day 2 I did take time to point out how we could have divided the total rotation in radians into sections just as we had done with the degree measurements.

I set the goal of having all students minimally be through question 10 at the conclusion of today’s lesson. Many students were able to also complete question 11 though in the allotted time.

**Supplies: **Students each need a pair of scissors for today’s lesson.

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To close out today's lesson, students will complete a Postcard to Absent Student. Directions for this assignment are located on page 4 of today's Flipchart_Building the Unit Circle. My goal for this closure is for students to stop and reflect on what they have learned so far. It will allow them another repetition of what they did today so hopefully these important concepts of building the unit circle will stick with them! Also, the cards come in useful to actually catch up absent students when they return 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: Angles and Rotations
- LESSON 2: Investigating Radians
- LESSON 3: Radians Formalized
- LESSON 4: Building the Unit Circle (Day 1 of 2)
- LESSON 5: Building the Unit Circle (Day 2 of 2)
- LESSON 6: What does the unit circle tell us? (Day 1 of 2)
- LESSON 7: What does the unit circle tell us? (Day 2 of 2)
- LESSON 8: Periodicity and Symmetry
- LESSON 9: Unit Circle Cake Walk (and other fun Unit Circle activities!)
- LESSON 10: Group Quiz - Unit Circle Applications