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 requires more algebraic fluency than the previous lessons in this course, as do the next several lessons. Depending on students’ familiarity and comfort with the algebra skills involved, it might make sense to spend more than one day on some lessons.
Lesson overview
 4.1 Warmup: Going the Distance (5 minutes)

4.2 Activity: Circling the Problem (15 minutes)
 Includes "Are you Ready for More?" extension problem
 4.3 Activity: Building an Equation for a Circle (15 minutes)
 Lesson Synthesis
 4.4 Cooldown: Writing Circle Equations (5 minutes)
Learning goals:
 Generalize (using words and other representations) the process of repeated distance calculations to derive an equation for a circle in the coordinate plane.
Learning goals (student facing):
 Let’s build an equation for a circle.
Learning targets (student facing):
 I can derive an equation for a circle in the coordinate plane.
Required materials:
 Scientific calculators
Standards:
 This lesson builds on the standard: CCSS.HSGGPE.B.4MS.GGPE.4MO.G.GPE.B.3
 This lesson builds towards the standard: CCSS.HSGGPE.A.1MS.GGPE.1MO.G.GPE.A.1
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