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# Circles and Completing the Square (Day 2 of 2)

Lesson 5 of 13

## Objective: 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.

*50 minutes*

At the start of today's lesson, I expect students to complete their work on the Student Handout - Circles and Completing the Square that was started in yesterday's lessons. This aligns to the notes on pages 8-15 of the flipchart file. 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!

At the end of yesterday’s lesson, my students left off working on Questions 4-5 of their handout. Here it is essential that students are able to identity the patterns in perfect binomial squares. It is easy to see whether or not students have identified these patterns when students are asked to complete Question 5e. Encourage students to read through the next example and try to complete Question 6a. I found that many of my students benefited from actually seeing an example done out. So I let them struggle a bit and then I modeled Question 6a and had my students complete 6b and 6c in their teams. Question 6b does give students a bit of a challenge as the x coordinate of the center is at 0.

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

##### Resources (5)

#### Resources

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I am going to present pages 17-18 of the Flipchart and have students answer the questions. Before presenting the answers I will poll the students on their confidence to solve the problem using a clicker poll.

I have allowed 10 minutes for today's closure because I find that my students still require quite a bit of time to write one general form equation into standard form.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Cutting Conics
- LESSON 2: Name that Conic
- LESSON 3: Human Conics: Circles and Ellipses
- LESSON 4: Circles and Completing the Square (Day 1 of 2)
- LESSON 5: Circles and Completing the Square (Day 2 of 2)
- LESSON 6: Ellipses
- LESSON 7: Human Conics: Parabolas
- LESSON 8: Parabolas
- LESSON 9: Parabola Problem Partner Critiques
- LESSON 10: Hyperbolas
- LESSON 11: Non-Linear Systems of Equations
- LESSON 12: Conic Sections Test Review
- LESSON 13: Conic Sections Unit Test