Investigating Radians

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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.

Warm-Up: Clicker Questions

5 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.

Investigation: What is a radian?

35 minutes

Supplies Needed

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...

Student 1

student 2

Student 3

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

Closure: Clicker Checks

10 minutes

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