Grade Level/ Course (HS): Geometry Unit 5 Standard: G.C. 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. Domain: Circles Cluster: Find arc lengths and areas of sectors of circles. Quarter 1: Quarter 2: Quarter 3: Quarter 4: Recall how to find the area and circumference of a circle. Explain that 1° = Π/180 radians Recall from G.C.1, that all circles are similar. Determine the constant of proportionality (scale factor). Justify the radii of any two circles (r1 and r2) and the arc lengths (s1 and s2) determined by congruent central angles are proportional, such that r1 /s1 = r2/s2 Verify that the constant of a proportion is the same as the radian measure, of the given central Θ, angle. Conclude s = r Θ From Appendix A: Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course. Make sense of Reason abstractly Construct viable Model with Use appropriate tools Attend to precision. Look for and make use Look for and express problems and and quantitatively. arguments and mathematics. strategically. of structure. regularity in repeated persevere in solving critique the reasoning. them. reasoning of others.
Grade Level/ Course (HS): Geometry Unit 5 Standard: G.C. 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. Domain: Circles Cluster: Find arc lengths and areas of sectors of circles. Quarter 1: Quarter 2: Quarter 3: Quarter 4: Recall how to find the area and circumference of a circle. Explain that 1° = Π/180 radians Recall from G.C.1, that all circles are similar. Determine the constant of proportionality (scale factor). Justify the radii of any two circles (r1 and r2) and the arc lengths (s1 and s2) determined by congruent central angles are proportional, such that r1 /s1 = r2/s2 Verify that the constant of a proportion is the same as the radian measure, Θ, of the given central angle. Conclude s = r Θ From Appendix A: Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
Geometry-Pacing-Guide-Version-3.docx