# Trigonometry Lesson 5 (Teachers)

### Exploring Covariation on a Unit Circle

In this lesson, Mary and Claire think about how an object’s height changes in relation to its angle of rotation as it moves along a circular path. They also explore what happens to the changes in height as the object moves. They explore how this relates to circular motion along different sizes of circles.

##### Episode 1: Making Sense

The students get a feel for how the height above a circular midline changes as they trace their fingers along a circular path. They think about when their height changes quickly and when it changes slowly.

##### Episode 2: Exploring

The students explore the path a fly takes as it travels along the tip of a fan blade at 8 stops. They think about the fly’s height above the middle of the fan and how that changes with the angle of rotation.

##### Episode 3: Repeating Your Reasoning

The students explore the path a fly takes as it travels along the tip of a fan blade at 12 stops. They think about the fly’s height above the middle of the fan and how that changes with the angle of rotation.

##### Episode 4: Reflecting

Mary and Claire reflect on the patterns they notice regarding how the height above the midline changes, and how the angle of rotation changes on any size circle.

### Mathematics in this Lesson

Targeted Understandings

This lesson can help students:

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Common Core Math Standards

Common Core Math Practices