Cluster: Find arc lengths and areas of sectors mathematical content and develop their Students will of circles ability to apply that knowledge to Derive and apply the formula for arc problems. Derive using similarity the fact that the length; Task(s) length of the arc intercepted by an angle Derive the fact that the length of the arc is proportional to the radius, and define intercepted by an angle is proportional to the radian measure of the angle as the Circles and their Relationships among Central the radius; constant of proportionality; derive the Angles, Arcs and Chords Task , p.15 Define and apply radian measure. formula for the area of a sector. Investigating Angle Relationships in Circles Explore the relationship between inscribed Tasks, p. 46 & p.52 angles and central angles and their intercepted arcs. Enduring Understanding(s) Use the following lesson(s) first to Vocabulary Domain: introduce concepts/build conceptual The properties of polygons, lines, and angles Sector of a circle, segment of a circle Cluster: Find arc lengths and areas of sectors understanding. can be used to understand circles; the of circles properties of circles can be used to solve Derive using similarity the fact that the problems involving polygons, lines and angles. length of the arc intercepted by an angle Writing in Math/Discussion Use the textbook resources to address is proportional to the radius, and define If the radius of a circle doubles, will the procedural skill and fluency. the radian measure of the angle as the Essential Question(s) measure of a sector of that circle double? Will constant of proportionality; derive the Lesson 11-3 – Areas of Circles, pp.782 - How can the properties of circles, polygons, it double if the arc measure of that sector formula for the area of a sector. 788 lines and angles be useful when solving doubles? geometric problems? Use the following resources to deepen students' conceptual understanding of mathematical content and develop their Objective(s): Ticket Out the Door ability to apply that knowledge to Students will problems. Have students describe how to find the area of Derive a formula for the area of a a circle, given its circumference. Task(s) sector of a circle; Arc Length and Area of Sector Tasks, p. 82 & Find the area of circles and sectors of p.91 circles. (select from the tasks) ACT Practice (sample problems to prepare for the ACT)
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.
GEOMETRY%20Q4%20Revised%20EBB.docx