The goal of this lesson is for students to begin their exploration of the unit circle, defined as a circle of radius 1 centered at the origin, which they continue in the following lesson and use throughout the remainder of the unit. They focus first on the symmetric nature of the \((x,y)\) coordinates of points on the unit circle and then learn that these points can also be defined by their angle of rotation, which leads to working with radian angle measurements.
This lesson builds on the geometry course where students learned that all circles are similar and examined arcs intercepted by given angles. That work lead to defining the radian measure of an angle as the ratio of the arc length traveled to the radius of the circle. This means that 1 radian is the angle when the length of the arc it intersects on a circle of radius \(r\) is \(r\). Students also learned that by this definition, and because \(\pi\) is the ratio of the circumference of the circle to its diameter, there are \(2\pi\) radians in a full circle. This lesson includes an optional activity if students need practice recalling the definition of radian measurement.
Students look for regularity in repeated reasoning as they apply radian measure to examine the distance a wheel travels as it rolls for several angles, reasoning that the measure of the angle of revolution corresponds to the distance traveled when the radius is 1 (MP8).
Lesson overview
 3.1 Warmup: Finding Coordinates of Points on the Unit Circle (10 minutes)
 3.2 Activity: Which Point? (10 minutes)
 3.3 Optional Activity: Measuring Circles (15 minutes)

3.4 Activity: Around a Bike Wheel (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 3.5 Cooldown: Radian measure (5 minutes)
Learning goals:
 Calculate the radian angle measurement a point on a wheel rotates through by relating it to the distance traveled by the wheel.
 Describe characteristics of points on a unit circle.
Learning goals (student facing):
 Let’s learn about the unit circle.
Learning targets (student facing):
 I understand that a radian angle measurement is the ratio of the arc length to the radius of the circle.
 I understand that points on a unit circle can be defined by their coordinates or by an angle of rotation.
Required materials:
 Circular objects of different sizes
 Ribbon or string
Required preparation:
 Acquire 1 round object per student if using the optional activity Measuring Circles.
 Be prepared to display applets for all to see during the activity syntheses of the activities “Measuring Circles” and “Around a Bike Wheel."
 Devices are required for the digital version of the extension in “Around a Bike Wheel,” ideally 1 per student.
Glossary:
 unit circle  The circle in the coordinate plane with radius 1 and center the origin.
 Access the complete Algebra 2 Course glossary.
Standards:
 This lesson builds on the standards: CCSS.HSGC.A.1MS.GC.1CCSS.HSGC.B.5MS.GC.5CCSS.HSGSRT.C.8MS.GSRT.8MO.G.C.A.1MO.G.C.B.5MO.G.SRT.C.7
 This lesson builds towards the standards: CCSS.HSFTF.A.2MS.FTF.2CCSS.HSFTF.C.8MS.FTF.8
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