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.