Cluster: Find arc lengths and areas of sectors of circles 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. Students will Derive and apply the formula for arc length; Derive the fact that the length of the arc intercepted by an angle is proportional to the radius; Define and apply radian measure. Explore the relationship between inscribed angles and central angles and their intercepted arcs. mathematical content and develop their ability to apply that knowledge to problems. Task(s) Circles and their Relationships among Central Angles, Arcs and Chords Task , p.15 Investigating Angle Relationships in Circles Tasks, p. 46 & p.52 Domain: Cluster: Find arc lengths and areas of sectors of circles 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. Enduring Understanding(s) The properties of polygons, lines, and angles can be used to understand circles; the properties of circles can be used to solve problems involving polygons, lines and angles. Essential Question(s) How can the properties of circles, polygons, lines and angles be useful when solving geometric problems? Objective(s): Students will Derive a formula for the area of a sector of a circle; Find the area of circles and sectors of circles. Use the following lesson(s) first to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural skill and fluency. Lesson 11-3 – Areas of Circles, pp.782 - 788 Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to problems. Task(s) Arc Length and Area of Sector Tasks, p. 82 & p.91 (select from the tasks) ACT Practice (sample problems to prepare for the ACT) Vocabulary Sector of a circle, segment of a circle Writing in Math/Discussion If the radius of a circle doubles, will the measure of a sector of that circle double? Will it double if the arc measure of that sector doubles? Ticket Out the Door Have students describe how to find the area of a circle, given its circumference.
RESOURCE TOOLBOX The Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students. Textbook Resources Comprehensive Geometry Help: Standards (Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.) Videos Tasks Inside Math Tasks Illustrative Math Tasks SCS Math Tasks NWEA MAP