Equations of Circles (Lesson 0.2)
Unit 0 - Day 2
Define a circle as the set of points one radius away from a center; understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane
Write the equation of a circle given a center and a radius using transformations of the unit circle
Identify the center and radius given an equation in standard form
Quick Lesson Plan
The idea behind the experience is to connect the distance formula learned the previous day with the equation of a circle in the coordinate plane. They will start out with something they know in a context they appreciate (who doesn’t love pizza?) and then work through numbers one through six in their groups. They may struggle with number 5, so ask questions that will help students arrive at the idea of using the two coordinates (Pizza Hut’s location and the generic person) with the distance formula to find an equation.
After debriefing #1-6 (see below), the students can use Desmos to investigate the effects of transformations on the equation of a circle for #7-11.
It’s important to define a circle as the set of points one radius away from a center, which is why much of the questioning on page 1 revolves around connecting the length of the radius to the locations of Iris, Kamairah, and Leo. Have them justify their responses using the distance formula so they can connect the distance formula to the equation of a circle in the coordinate plane. Be sure to tie the equation of a circle on page 2 to the horizontal and vertical shifts of the center and the enlargement of the radius.