Circles and Completing the Square (Day 1 of 2)

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SWBAT find the equation of a circle, convert equations of conics by completing the square, and graph a circle given an equation in standard or general form.

Big Idea

Use TRIANGLES and SQUARES to find the equation of a CIRCLE?! Students use prior knowledge of perfect squares and the Pythagorean Theorem to find equations for circles.

Warm-up: Clicker Questions

5 minutes

Using clickers, students should classify the conics on pages 2-7 of the Flipchart. For this exercise, I give students 40 seconds to respond to each question. I will discourage calculator use during today's warmup.

Explanation: Circles and Completing the Square

40 minutes

As you transition from the Warm-up, each student should receive the  Student Handout - Circles and Completing the Square. This aligns to the notes on pages 8-15 of the flipchart.

Students begin by developing the standard form equation of a circle centered at the origin based on their knowledge of the Pythagorean Theorem. In Problem 2, they then work to derive the equation of the circle that has shifted away from the origin. I predict students to struggle a bit here, so I will be stepping in and helping teams to identify he values of the legs of the right triangle. At this point, it is important for students to connect what each variable in the standard form of the circle represent. I will use page 11 in the flipchart to help facilitate this discussion and encourage students to jot this down in their notes.

I plan to continue to teach this lesson in a very stop-and-go type lesson. Students do a section in their team and then we stop and discuss it as a class. So next students will apply the standard form equation of a circle by writing the equations from graphs of circles, Problem 3. When all students have worked through this, present the solutions. Students will then complete Questions 4 and 5 on the packet. This is the most important section to me. I want to be sure my students have plenty of time to develop their own understanding here of how to write a perfect binomial squared. This learning will be essential as students will be completing the square on every conic section we study to help convert to standard form. I believe that by having students establish the patterns that arise in perfect square binomials it helps them to better understand the process of completing the square and factoring to a binomial squared.  Since I really didn’t want to rush my students through this section, I predict stdents will need to continue their work on this section tomorrow.

I describe the mathematical practice goals for this section in this video narrative.

The Circles, Video Narrative, Explanation of Notes and Handout provides more detail on how the students' worksheet aligns to the flipchart file and how to use the flipchart file!



Closure: Confidence with Circles

5 minutes

I am going to present pgae 16 of the Flipchart and have students answer the question. Before presenting the answers I will poll the students on their confidence to solve the problem using a clicker poll.


If you got further in today's lesson than questions 4-5, you can also use the questions on pages 17-18 of the flipchart to close out the lesson.


Assign Homework 2 - Conic Sections for homework tonight.