Evidence of Student Vocabulary Knowledge Skills Instructional Achievement Level Descriptors Attainment/Assessment Students: Students know: Students understand/are able EEG-GPE.1. N/A Given the center (h, k) and to: radius (r) of a circle, Key features of a circle, Create a right triangle in a Explain and justify that every circle using the horizontal The Pythagorean Theorem, point on the circle is a and vertical shifts from the combination of a horizontal center as the legs and the The technique of completing the and vertical shift from the radius of the circle as the square. center with a length equal to hypotenuse, the radius, Convert an equation of a Create a right triangle from circle from general form to the center of a circle to a standard form using the general point on the circle, method of completing the and show that the legs of the square. right triangle are the absolute values of x-h and y-k, and the Circles represent a fixed hypotenuse is r, then apply distance in all directions in a Pythagorean theorem to show plane from a given point, and that r2 = (x - h)2 + (y - k)2. a right triangle may be created to show the relationship of the horizontal Given an equation of a circle and vertical shift to the in general form, distance, Complete the square to Rewriting algebraic rewrite the equation in the expressions or equations in form r2 = (x - h)2 + (y - k)2 equivalent forms often and determine the center and reveals significant features of radius. the expression, (i.e., circles written in standard form are useful for recognizing the center and radius of a circle).
Evidence of Student Attainment/Assessment Vocabulary Knowledge Skills Instructional Achievement Level Descriptors Students: Given the center (h, k) and radius (r) of a circle, Explain and justify that every point on the circle is a combination of a horizontal and vertical shift from the center with a length equal to the radius, Create a right triangle from the center of a circle to a general point on the circle, and show that the legs of the right triangle are the absolute values of x-h and y-k, and the hypotenuse is r, then apply Pythagorean theorem to show that r2 = (x - h)2 + (y - k)2. Given an equation of a circle in general form, Complete the square to rewrite the equation in the form r2 = (x - h)2 + (y - k)2 and determine the center and radius. Students know: Key features of a circle, The Pythagorean Theorem, The technique of completing the square. Students understand/are able to: Create a right triangle in a circle using the horizontal and vertical shifts from the center as the legs and the radius of the circle as the hypotenuse, Convert an equation of a circle from general form to standard form using the method of completing the square. Circles represent a fixed distance in all directions in a plane from a given point, and a right triangle may be created to show the relationship of the horizontal and vertical shift to the distance, Rewriting algebraic expressions or equations in equivalent forms often reveals significant features of the expression, (i.e., circles written in standard form are useful for recognizing the center and radius of a circle). EEG-GPE.1. N/A