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G-C-1-3

Page history last edited by Brenda Butz 6 years, 3 months ago

G.C.1.3 Recognize and write the radius r, center (h,k), and standard form of the equation of a circle (x-h)²+(y-k)²=r² with and without graphs.

In a Nutshell

Students will learn to state the value of the radius and the center of a circle given either an equation of a circle or a graph. Students will also learn to write the equation of a circle in standard form given the radius and the center or the graph of a circle.

Student Actions	Teacher Actions
Develop accurate and appropriate procedural fluency: Students will develop procedural fluency by learning to write the equation of a graph when given the center and the radius, write the equation when given a graph of the circle, and name the center and radius when given the equation of a circle.	Teachers will use and connect the mathematical representations between the graph of a circle in the coordinate plane and the algebraic equation in a variety of problems. Teachers will pose purposeful questions about circles located in all four quadrants, so students are exposed to both positive and negative coordinates of the center.
Key Understandings	Misconceptions
Students understand how to recognize and write the center of the circle and the length of the radius when given the equation of a circle written in standard form. Students understand how to locate and write the center point of the center and find the length of the radius when given a graph of a circle. Students understand that the distance from the center of a circle to any point on the circle is the same and that distance is the measurement of the radii.	Students don’t realize that the minus sign in the equation of a circle does not give them the correct sign for their x or y value of the center. Students forget to take the square root when finding the radius of the circle. Students will forget to square the radius when writing the standard form of a circle. Students think circles in the 3rd quadrant have a negative radius because x and y are both negative.