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WHOSE LINE IS IT ANYWAYS? Class/Course Title: Duration/Time Frame: Geometry Full class period or 60 min. CTE/Core Standards: Geometry-Circles: MACC.912.GC.2, MACC.912.GC.5 and Modeling with Geometry: MACC.912.GMG.1 CTE: 06.0 engineering principles. Demonstrate an understanding of 09.0 Build, program, and configure a robot to perform predefined tasks Teacher: Michael Chase Lesson Objective: Students will determine which straight lines represent the perimeter or circumference of given polygons and circles. Materials: Various two dimensional polygons with length measurements and various circles with diameter or radius measurements. CTE/Core Benchmarks: Core: MACC.912.GC.2 Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. MACC.912.GC.5 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. MACC.912.GMG.1 Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* CTE: 06.03- Name the six simple machines (i.e. lever, inclined plane, wheel and axle, screw, wedge, and pulley) and describe their application to robotics. 1 09.05- Formulate examples of how the robot might be used or adapted for use in a manufacturing or other environment. 09.06- Create and present a proposal, including drawings and specifications, describing the robot, the tasks and rationale, and the results. Key Terms/Vocabulary: Core: Perimeter, circumference, radius, diameter, arc, arc length CTE: Wheel circumference and axle, rotations, distance, diameter, Anticipatory Set/Introduction: How are the perimeter of polygons and the circumference of circles alike? How are they different? Can they ever be equal? Exploration/Investigation: Core: Students will try to decide what straight line matches with the perimeter of given polygons and the circumference of given circles. Practice Problem Solving/Applications: Core: Students will calculate the perimeter of given polygons and calculate the circumference of given circles. These measurements will help students to make their matches. CTE: Students will complete the Wheels and Distance worksheet. Check for Understanding: Core: Students will again be asked to compare perimeter and circumference and explain their findings based on their calculations during class. Closure/Summary: Core: The teacher can review the use of formulas to calculate perimeter and circumference. Students should also discuss any situations where their answers were the same measurement. Reflections: Core: As a homework assignment, students can work on review questions incorporating real-world examples. Modifications and/or Accommodations: Core/CTE: Pair or group students or the calculations can be first completed as a class with students then completing the remaining calculations individually. 2