## PowerPoint- Radians - Section 2: The Unit Circle

# Radians Day 2 of 2

Lesson 5 of 19

## Objective: Students will be able to use radians to measure angles.

## Big Idea: The stars in the sky are not necessarily the best way to measure angles, this lesson explains why.

*45 minutes*

#### Warm Up and Homework Check

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The resource video specifically explains this lesson’s Warm Up- Radians Day 2 asks students to describe the similarities and differences between radians and degrees.

I also use this time to correct and record the previous day's Homework.

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#### The Unit Circle

*15 min*

This is the second day of a two day lesson. In the previous lesson, the students built the concept of radian. Today, we will take that concept, add it to the unit circle, and practice converting radians to degrees and vice versa. I pass out the Radian Measure and the Unit Circle sheet. The students fill in the radian and degree measures today and put in the coordinates and discuss the trig ratios in the next lesson (**Math Practice 2**).

One place where students struggle is in the fact that a circle is 2π. When you divide it, half of a of a circle is π, and this can be confusing. Verbal repetition is a good method to help students remember. I will often repeat a key concept several times (not over and over in a row) but emphasizing it. It is extremely important to note that 90^{o }is the same as π/2. They should know this but some will struggle.

#### Resources

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The final goal is to give the students an opportunity to figure out a method for converting Degrees to Radians. I ask "What if I wanted to know how many radians are equal to 140^{o}?". If time is short, this can be done as a whole class discussion, otherwise, I have them work as pairs and then ask for volunteers to share. Be careful not to just give students formula but "build" it so they can make sense as to why it works. After our discussion, I ask the students to write out, in their own words how to find convert from degrees to radians. For example, they could say that you could rewrite the degrees as a percent of 180 and this is equivalent to the number of πs (**Math Practice** 3)**. **

Next the students will be asked to convert 55^{o}, 110^{o}, and 440^{o} into radians to practice this new skill. Notice that these are multiples of each other. Some students may catch on to this and use it to find the radian measure (**Math Practice 7**). ** **The better the students connect radians as a fractional part of a circle the better, as this is key to conceptually understanding radians.

The wrap up portion of this lesson asks students to figure out how to convert radians to degrees. This may prove more challenging and require more scaffolding. I may want to ask the students guiding questions like "How would you undo what you did in the last type of problem?". Again, I have them write a quick explanation of the process rather than copying a formula. There are a few practice problems to finish off this lesson.

#### Resources

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to convert radians to degrees.

#### Resources

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The homework is straightforward practice on converting radians into degrees and vice versa. The remainder of the unit requires students to be comfortable converting between degrees and radians so it is important to that the skill is fairly well mastered at this point.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Angle and Degree Measure
- LESSON 2: Trigonometric Ratios
- LESSON 3: Trigonometric Ratios of General Angles
- LESSON 4: Radians Day 1 of 2
- LESSON 5: Radians Day 2 of 2
- LESSON 6: The Unit Circle Day 1 of 2
- LESSON 7: The Unit Circle Day 2 of 2
- LESSON 8: Graphs of Sine and Cosine
- LESSON 9: Period and Amplitude
- LESSON 10: Period Puzzle
- LESSON 11: Transformations of Sine and Cosine Graphs
- LESSON 12: Graph of Tangent
- LESSON 13: Model Trigonometry with a Ferris Wheel Day 1 of 2
- LESSON 14: Model Trigonometry with a Ferris Wheel Day 2 of 2
- LESSON 15: Modeling Average Temperature with Trigonometry
- LESSON 16: Pythagorean Identity
- LESSON 17: Trigonometric Functions Review Day 1
- LESSON 18: Trigonometric Functions Review Day 2
- LESSON 19: Trigonometric Functions Test