In this lesson, students repeatedly test whether points are on a circle by finding the distance between the points and the circle’s center. As students carry out their testing, they look for and express regularity in repeated reasoning (MP8), eventually writing a generalized equation for a circle.

This lesson and the next several lessons require more algebraic fluency than did the previous lessons in this course. Depending on students’ familiarity and comfort with the algebra skills involved, it might make sense to spend more than one day on some lessons.