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Lesson Plan Guide Georgia Learning Connections *TITLE: Interior angles of polygons *Annotation Students will use GSP to create polygons, find the sum of the degrees of the interior angles, and compare them to the number of sides in the figure. This lesson will be a hands-on activity. *Primary Learning Outcome: The students will be able to determine the sum of the interior angles of any polygon given the number of sides. If it is a regular polygon, students will be able to determine the number of degrees in each angle. What is the sum of the interior angles of a regular polygon with n sides? How many degrees are in each angle? Additional Learning Outcomes: What is a polygon? What does it mean for a polygon to be regular? Students should have a working knowledge of how to create figures and how to measure angles using GSP. *Assessed QCC: The learner will be able to apply the property that the sum of the interior angles of a triangle is 180 degrees in order to obtain problem solutions. GA QCC #22 – Eighth grade QCC #28 – Pre- Algebra Determine the formula for the sum of the interior angles of a regular polygon. Non-Assessed QCC: Classify triangles according to the measures of their angles. Relate the number of sides of a polygon to the number of diagonals from one vertex *Total Duration: Approximately 2 hours. Students will need time to get instructions, explore examples, and make conclusions. Teacher needs to make sure that a class discussion of discoveries is conducted to conclude the activity. *Materials and Equipment: Computer with GSP Paper and Pencil Georgia Learning Connections 2000 Georgia Department of Education Technology Connection: GSP Procedures: Step One Students will go to a computer and open GSP. They will create a three-sided figure by making three points on the sheet and connecting them with line segments. They will then calculate the degrees in each angle and add them. Students will create a table on their paper and record the number of sides and the sum of the angles. Estimated Time: This step should take about 5 minutes Step Two Students will create figures of four, five and six-sides. They will measure the angles of each and find the sum of the interior angles. Estimated Time: This step should take about 20 minutes Step Four Students will calculate the difference between the sides and the sum of the interior angles. Estimated Time: This step should take about 5 minutes Step Five Students will derive a formula for finding the sum of the interior angle of any polygon Estimated Time: This step should take about 30 minutes Step Six Students will test their theory by constructing several examples in GSP to confirm their thoughts. Estimated Time: This step should take about 30 minutes Step Seven Class discussion of discoveries made through investigations Estimated Time: This step should take about 30 minutes Georgia Learning Connections 2000 Georgia Department of Education *Assessment: Teacher will assess this lesson through observing the activity as students work and determining if students arrived at the correct formula for finding the sum of the interior angles of a polygon. Teachers could quiz students by giving them a quiz with different polygons that students must determine the sum of the interior angles. Extension: Would the formula change if the polygon were concave? How do the interior angles compare to the exterior angles? What is the sum of the exterior angles? Accommodation: Students could work in pairs. Students could be directed to look for triangles that would be created by connecting one vertex to every other vertex and comparing the number of triangles with the number of sides. (Hint: How many degrees are in a triangle?) Georgia Learning Connections 2000 Georgia Department of Education