LESSON PLAN # 3

 

Name: Laura Galaviz

 

Title of lesson: Regular Polygons: Central, Interior and Exterior Angles

 

Date of lesson: TBA

 

Length of lesson: 50 minutes

 

Description of the class:

                     Name of course: Geometry                                                       

                     Grade level: 9-10

                     Honors or regular: Honors or regular

 

Source of the lesson:

            http://mason.gmu.edu/~mmankus/tripoly/regpoly.htm

 

TEKS addressed:

b. 2 (B): The student makes and verifies conjectures about angles, lines, polygons, circles, and three-dimensional figures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

c. (1) The student uses numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.

 

I.       Overview

Students will explore the measures of central, interior and exterior angles of regular polygons. They will calculate the sums of the measures of each of these angles. They will make generalizations for regular n- polygons.

 

II.  Performance or learner outcomes

            Students will be able to:

1)      Define central, interior and exterior angles of polygons

2)      Explore the relationship of the number of sides of a regular polygon to its central, interior and exterior angles

3)      Formulate conjectures about central, interior, and exterior angles of a regular n-polygon.

   

III. Resources, materials and supplies needed

·        Investigation Worksheets

·        Transparency of Investigation Worksheet for Teacher

·        Regular Polygon Printout

 

IV. Supplementary materials, handouts.

·        Attached

Five-E Organization

 

Teacher Does:                                                  Student Does:

Engage: What is a polygon? What is a regular polygon?   Review definitions of central, interior and exterior angles. Ask students to define. First have them write and draw what they think they mean on a sheet of paper and then share with the class.   Central Angle: the angle formed by two adjacent vertices and the center of the polygon Interior Angle: the angle inside formed by two adjacent sides of a polygon Exterior Angle: the supplement of an interior angle of a polygon (Review “supplement”)

Students will state what a regular polygon is.   Students will give definitions for central, interior and exterior angles.                     Students will recall the meaning of supplement and compliment.

Evaluate: Teacher will ask students to define each of the concepts. Teacher will call on random students.

 

Teacher Does:                                                  Student Does:

Explore: Teacher will group students to where there are no more than 3 per group   Ask students to investigate the relationship of the number of sides of a regular polygon and the central, interior and exterior angles.   In addition, students should find the sum of the measures of central, interior and exterior angles.   Then they should form conjectures about the central, interior and exterior angles of regular n polygons.

Students will form into groups of no more than 3.   Students will work on the investigation (3 parts).            Students will make conjectures for each of the measure of angles of a regular n-gon.

Evaluate: Teacher will walk around and talk to each of the groups to make sure each of the students are working. Teacher will ask students to explain how they got each of their solutions.

 

 

Teacher Does:                                                  Student Does:

Explain:   When groups are finished with the exploration, have different students present their conjectures for each of the angles for regular n polygons. Emphasize the importance of explaining the process taken thoroughly. Discuss as a class why these conjectures are true or untrue if they make inaccurate conjectures.

Students will present their conjectures on the board and give a thorough explanation. Students who solved using a different method will also present. Students will engage in classroom discussion.

Evaluate: Teacher will be aware of the different methods students used to form their conjectures. Teacher will have these students present their work.

 

Teacher Does:                                                  Student Does:

Extend/Elaborate: If students only used one method to find the measure of central, interior and exterior angles, have them think about how to use a different method to find these angles.  For example, students can think about breaking apart the polygon into triangles as shown below: Have them write a conjecture about the interior angles of a regular polygon using this method. [Hint: Notice there are _______ triangles and the sum of the measures of the angles of each triangle is _______.]     In addition, students can answer the following question: What is the area of a regular n-gon?

Students will use different methods to solve the same problems.                                       Students will think about how to find the area of a regular n-gon? [Hint: use formula for area of triangle.]

Evaluate:  Teacher will walk around to each of the groups and discuss with them their different approach to the problem. Teacher will answer any questions.

 

Name:

Date:

 

Investigation:

 

1. Explore the relationship of the number of sides of a regular polygon and the Central Angles. Fill in the following table and make a generalization about Regular N-gons.

 

 

 

2. Write a conjecture about the Central Angles of a Regular Polygon.

 

 

Name:

Date:

 

Investigation:

 

1. Explore the relationship of the number of sides of a regular polygon and the Interior Angles. Fill in the following table and make a generalization about Regular N-gons.

 

 

 

2. Write a conjecture about Interior Angles of a Regular Polygon.

 

 

Name:

Date:

 

Investigation:

 

1. Explore the relationship of the number of sides of a regular polygon and the Exterior Angles. Fill in the following table and make a generalization about Regular N-gons.

 

 

 

2. Write a conjecture about Exterior Angles of a Regular Polygons.

 

Regular Polygons