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
Common Core Math Standards
Common Core Math Practices