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Geometry Unit 9 Plan – 21 Periods Unit of Study: Unit Circle Geometry Unit 9 Standard(s) to be Assessed HSG-CO.A.1 Know precise definitions of angle and circle based on the undefined notion of distance around a circular arc. HSG-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. HSG-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. HSF-TF.A.1 (supporting standard) Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. HSF-TF.A.2 (supporting standard) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. HSG-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. HSG-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Page 1 of 2 Learning Target to be Assessed Pre/Post Angle Relationships Assessment Item #s Unit Common Assessment Item #s LT1: Know the definitions of angle and circle based on distance around an arc. 1 LT2: Derive and calculate the length of an arc. 2, 3, 4 LT3: Define and determine radian measure. LT4: Derive the formula for area of a sector and use the formula to calculate the area of a sector. LT5: Derive the equation of a circle and apply the equation of a circle by recognizing its relationship to the center and radius, points on the circle, and graph. 5, 6 32 7, 8, 9 10, 11, 12, 13, 14 Geometry Unit 9 Plan – 21 Periods HSG-GPE.B.4 Use coordinate to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). LT6: Use coordinates to show that a point lies on a circle. 15 Note: HSG-C.A.l Prove that all circles are similar—This standard is not assessed in the district common assessment but should be addressed in instruction as possibly a demonstration. Instructional Information for Unit Circle Geometry Unit 9 (13 periods) Big Idea: Radian measure is an equivalent expression of degree measure; the unit circle relates right triangles and the equation circles. Essential Question: Why do we use radian measure? Resources: Formative Assessment Lessons: http://map.mathshell.org/materials/lessons.php Circles I Page 2 of 2