What does completing the square have to do with circles? Math pupils use completing the square and other algebraic techniques to rewrite equations of circles in center-radius form. They then analyze equations of the form x^2 + y^2 + Ax + By + C = 0 to determine if the solution set is a point, a circle, or the empty set.

Concepts

circles, equation of a circle, completing the square

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Additional Tags

math

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Instructional Ideas

• Provide algebra tiles for learners who are still struggling with completing the square, factoring trinomials, etc.

Classroom Considerations

• The lesson relies heavily on algebraic processes, such as completing the square; be sure your class is up-to-date on their algebra skills
• Individuals also need to be familiar with how to write the equation of a circle (previous lesson)
• In the nineteenth installment of a 23-part module

Pros

• Teacher resource indicates tips for differentiating instruction for advanced/struggling learners, as well as for English language learners
• Includes answer key to all worksheets, including exit tickets and exercises
• Problem set includes a wide variety of exercises, which includes determining from their equations whether two circles are externally tangent

Cons

• None

Common Core

HSG-GPE.A.1