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# Investigating Radians

Lesson 2 of 10

## Objective: SWBAT explain how radian angle measurements are derived and how to convert from radians to degree angle measurements.

## Big Idea: Students use cylinders and string to investigate radian angle measurements and then use their findings to develop a method to convert from radian to degrees.

*50 minutes*

To begin today’s lesson, students should answer the clicker questions on pages 2-3 of the Flipchart - Investigating Radians.pdf. I want students to recall how to find the circumference of a circle. It is important that they are familiar with the fact that the distance around the circle will always be equal to 2pi times the radius of that circle. This fact will be very important in the next section of the lesson as we encourage students to attend to precision **(MP6)** in the investigation of radian measurement.

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For today’s investigation, we need a few supplies, Investigating Radians, Supplies Needed.MP4, as students complete the Student Handout - Investigatng Radians.docx.

Students will begin by measuring the radius of a cross section of their cylinder. They will then mark a midpoint on their string and make marks equal to one radius in both directions. They should use one color as they mark the radii length to the right and a different color as they mark the radii length to the left (for positive and negative angle rotations). They will then use this string to determine how many radii fit around their cylinder. Many students will answer maybe 6.2 or 6.3 and feel they are being precise. It is important here that we guide students to the more precise answer of 2pi. To help facilitate this connection I plan to just ask for a more precise answer and let them ponder it for a bit. Eventually I will remind kids to think about today’s warm-up problem.

Next, students will be lead (in questions #1-5) to determine how many radians relate to how many degrees. And then they will eventually derive on their own how to convert radian measurements. Check out the Student Handout - Investigatng Radians.docx to see how we will step kids into this.

Some pictures of students hard at work...

Here are the mathematical practices addressed in today’s lesson: Investigating Radians, Mathematical Practices.MP4

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#### Closure: Clicker Checks

*10 min*

To close out today’s learning and insure students are able to meet the learning target, I want to poll my class and see which students are able to convert basic problems from radian angle measurements to degrees and vice a versa. Although these problems are very basic and skill oriented, it will give us a great picture of whom really understood today’s investigation and whether or not they were able to derive a correct method to convert between angle measurements. The four closure questions are located on pages 4-7 of today’s flipchart, Flipchart - Investigating Radians.pdf

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Hi Tiffany, thanks so much for posting this lesson. I am going to try this tomorrow, except I have a block schedule, so I plan on doing both this exploratory lesson and the formalizing lesson after it in one day. I listened to your reflection video and was trying to think of how to get students to make that jump from approximate to exact answers. I think I am going to try having them solve for both the exact and approximate answers in the warm-up. During the exploration, I am going to make a chart on the whiteboard of each cylinders approximate answers of "how many radiuses fit around the circle" to then see if we can use the approximations to get a more exact answer. I know a couple of my students will be able to make the jump, so to solidify it for everyone, I am also going to show them this gif at the end as well: https://en.wikipedia.org/wiki/File:Circle_radians.gif

| one year ago | Reply

Hi Tiffany! I used this activity with my students the other day. They were SO engaged and didn't catch on until the very end of the activity...which is great!

This is my second year teaching Pre-Calculus and wanted to make this year a lot more engaging. I am following your activities for this unit and I am very excited!

| one year ago | Reply##### Similar Lessons

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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