Covariational Reasoning on the Square Task
In this lesson, Zoe and Gisele begin working on the N-gon Task sequence. Specifically, they explore how a point’s height varies as a function of the distance traveled for a point moving counterclockwise around a square. During this lesson, they manage changes to the varying quantities, discuss starting assumptions, and create a method for coordinating segments of their graph with segments of the shape.
Episode 1: Exploring
In this episode, Zoe and Gisel make sense of the N-gon Task sequence. They work to create a graph for a point, A, as it travels counterclockwise around a square with side length 10 that relates the height of the point as a function of its distance traveled.
Episode 2: Repeating Your Reasoning
Zoe and Gisele repeat their reasoning, this time dealing with a point traveling counterclockwise around a square with side length 7. In this episode, Zoe and Gisele explore an implicit assumption they made on their first graph.
Episode 3: Reflecting
Having created two similar graphs for squares of different side lengths, Zoe and Gisele describe the differences and how those differences are related to their starting assumptions.
Episode 4: Repeating Your Reasoning
Having chosen a convention for where their graphs should start going forward, Zoe and Gisele repeat their reasoning on one more square task to solidify their thinking.
Episode 5: Reflecting
After creating several graphs that relate the height as a function of distance for a point, A, traveling counterclockwise around a square of varying side lengths, Zoe and Gisele are ready to generalize their graph.