Geometry : Unit #8 - Circles : Lesson #9

Finding the Circle Formula

Objective: SWBAT derive the formula for a circle using Pythagorean Theorem and apply it.
Standards: HSG-GPE.A.1
Subject(s): Math
90 minutes
1 Do Now, Exploration - 35 minutes
Finding the Circle Formula_Video Narrative_ Beginning.wmv
2 Practice with Circle Formula - 25 minutes

Practice with the Circle Formula:


Once students have derived the formula for a circle using the Pythagorean Theorem, teachers can help students work through the first two examples of page two of the lesson.  The first example asks students to write the equation of a circle given a point and a radius, while the second question asks students to find the formula given two points.  This will require students to use a prior skill of calculating length using the distance formula.  Teachers should give students time to talk through with a partner how to solve this question before telling them to use the distance formula, a graphical representations can help for students to visualize this. 


We will then ask students to graph a circle when given the formula.  Example 3 can be tricky for students since there are no h and k term for students.  

New Standard and Scaffolding for All Learners
Standards Alignment
3 Finish Notes, Activity/Homework and Exit Ticket - 15 minutes

Finishing Class notes:

Page 4 of notes asks students to find the area and circumference of a circle when given the formula of the circle.  There is a review activity which digs deeper into the idea and differences behind perimeter/circumference and area.  This review may not be necessary for students who have a strong understanding of these topics, and could be kept in the notes for classes who could use a reinforcement of these topics. 



The last part of the lesson includes a host of practice questions for students to apply their knowledge.  If teachers have a chance, they can review questions #8 and #9 with students since question #8 asks students to write the equation of a circle, and the other ask students to graph a circle when given the equation of a circle. 


Exit Ticket:

The exit ticket for this lesson asks students to determine the radius and center for a given circle, and also to write the equation of a circle when given the center and radius length.  

Adding Extra Practice
Intervention and Extension