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This lesson provided by:
 Author: Cathy Jones System: Alabama Department of Education School: Alabama Department of Education

General Lesson Information
 Lesson Plan ID: 26412 Title: Arc Lengths and Sector Areas Overview/Annotation: Students will work in cooperative groups to discover the relationships between arc length, central angle measure, and circumference.  They will also discover the relationship between circle area, central angle measures, and sector area.  Students will share their discoveries and create formulas for calculating arc length and sector area.  Then they will practice these skills in a journal entry and solving a real-life extension.This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

Associated Standards and Objectives
Content Standard(s):
 MA2015 (9-12) Geometry 28. 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. [G-C5]

Local/National Standards:

Geometry 9-12

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

• explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.

Primary Learning Objective(s):

Students will find the area of a sector given its arc length and radius.

Students will find the arc length of a sector given its area and radius.

Students will find the area and/or arc length of a circle given the measure of the central angle and radius.

Students will review computing the area and circumference of circles.

Students will review constructing and measuring angles.

Students will use inductive reasoning to compare their measurements and calculations and to generalize their results.

Preparation Information
 Total Duration: 91 to 120 Minutes Materials and Resources: Materials in AMSTI Kit for Geometry:   natural cotton string, protractors, rulers, safety compasses, calculators, measuring tapes Other Materials:  Approximately 8 cans of various sizes (example:  soup, vegetable, peanut, coke, potato chip) Technology Resources Needed: The websites below offer step by step directions and/or online calculators for computing the area of a sector or arc length of a circle.  TeacherTube tutorial links are also included.  Web links are not necessary for teaching the content, but can be helpful as you prepare to teach the lesson and can provide a mechanism for students to review lesson content.Calculators (AMSTI kit), CTX projector (optional), document camera or overhead projectorhttp://www.analyzemath.com/Geometry_calculators/arc_length_area_sector.htmlhttp://www.math-prof.com/Geom/Geom_Ch_32.asphttp://www.easycalculation.com/area/circle.phphttp://www.easycalculation.com/area/learn-circle.phphttp://www.teachertube.com/viewVideo.php?video_id=1423&title=Geo_Screencast__Sector_Areahttp://www.youtube.com/watch?v=anV3HI-1vyY&feature=related Background/Preparation: Students should be able to calculate the area and circumference of a circle.Students should be familiar with vocabulary related to a circle (arc, central angle, radius, diameter, chord, area, circumference).Students should know how to find an angle’s measure.

Procedures/Activities: