##
* *Reflection: Student Ownership
Angle and Degree Measure - Section 1: Warm-up

I have to say, my classes really enjoyed debating over the largest angle that could be made with the hands of a clock. Some, like Warm Up 2 and Warm Up 3, said that 6:00 or 9:15 where the biggest since they made 180^{o}. This is obviously a limited viewpoint of angles that will be expanded in this unit. Others said 12:00, which would be 360^{o}. My favorite, Warm Up 1, was 354^{o} at 11:59 as this student figured out the number of degree for one minute and took it away from 360. In a case like this, I don’t give my opinion during the discussion. I just make sure that the students are taking turns and not monopolizing the conversation. It always feels so great when classes get animated while discussing something mathematical.

*Student Ownership: Getting Excited About Sharing*

# Angle and Degree Measure

Lesson 1 of 19

## Objective: Students will be able to find angles on a coordinate plane.

*50 minutes*

#### Warm-up

*5 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 Video Narrative specifically explains this lesson’s Warm Up- Angles and Degree Measure, which asks students to identify the angles created by the hands of a clock.

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

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This lesson begins with a quick review of quadrants. Students finally get to see why quadrants are placed in this specific manner. This is a bit of a hook for the lesson.

Next, I give them the major vocabulary about angles in standard form on a coordinate plane.

After they get a little experience with the most basic angles on a coordinate plane, I introduce them to coterminal angles. We begin by look at the negative/positive version of a given angle. For example, for 250^{o}, we find the angle -110^{o}. I then make a bit of a show going all the way around from 250^{o} to 610^{o} and ask the students what angle that would be. This blows their minds. I ask them to find another positive and then a negative one. We discuss how many total coterminal angles there would be (**Math Practice 8**). Given this new information, I then ask them what numbers we can use for angles now and if there are any limitations thus connecting angle measures to the real number system.

We do a few additional example as needed to ensure that everything gets it.

#### Resources

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#### Locker Combination Activity

*20 min*

The next activity has the students turn locker combinations into degrees (**Math Practice 4**). Students decide on a locker combination, turn it into the appropriate degrees, and then trade with their partner to decode their partner's degrees back into a combination. As a reminder (I had to look this up), you have to pass the first number at least 3 times (going right) before you hit the first number. Then you have to go left and pass the next number one time before hitting it. Go right and stop on the final number without passing. It is important to review this process with the students before beginning the activity.

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#### Exit Ticket

*5 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 the students to list three angles co-terminal with 100^{o}.

#### Resources

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This Homework asks students to sketch a couple angles, some of which are larger than 180^{o}. Next it asks students to identify some coterminal angles. The extension activity in the homework asks students to find the angle measures that the small hand of a clock moves in time (**Math Practice 1**). I have included a blank clock with the minutes marked to provide a physical model to those students who require some scaffolding.

#### 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