The Angles of a Polygon

Lesson Plan

Course: Math A

Unit: Study of Polygons

Lesson Title: Angles of a Polygon

Description: Students will learn what a polygon is, along with the difference between regular and irregular polygons.  Students will learn rules for determining the sum of the interior angles of any polygon and for determining the measure of each exterior angle in a regular polygon.  Students will take the information they have learned and complete practice assignments along with a final assessment.

Learner Characteristics and Context: This is an online multimedia supported lesson for ninth grade students.  This lesson is designed for students who have some familiarity with basic geometric concepts and angle measurement.

Objectives:

  • After completing the lesson the student will be able to:
    1. Define polygon;
    2. Explain the difference between regular and irregular polygons;
    3. State the rule for determining the sum of the interior angles of any polygon;
    4. Apply the rule to any polygon;
    5. Draw an exterior angle of a regular polygon;
    6. State the rule for determining the measure of each exterior angle of a regular polygon;
    7. Apply the rule to any regular polygon.
       

Related Standards:

New York State Math Standards

Students will: understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Examination Standards for State Math A Exam

4.13 sum of interior angles of a polygon
4.14 sum of exterior angles of a polygon 

Timeline: This lesson should be completed in two class periods (45 minutes each), given one computer per student is available.  This includes all assessments.  Part of a third class will be dedicated to large group discussion of the lesson.

Learning Activities: 

  • In this lesson the student will:
    1. Read definitions and view examples to learn the difference between regular and irregular polygons;
    2. Complete a quiz about regular and irregular polygons (to be downloaded and turned in); 
    3. View a presentation that shows them how the rule for determining the sum of the interior angles is derived along with examples for using the rule;
    4. Work through practice exercises involving the interior angles of polygons;
    5. View another presentation in which students will see how to draw an exterior angle and then learn the rule for determining the measure of each exterior angle in a regular polygon;
    6. Work through practice exercises involving the exterior angles of polygons;
    7. Complete a final assessment covering all objectives (to be downloaded and turned in).

Materials:

  • The lesson will be made available online.
  • Computer and Internet access for each student.  The computers must have Microsoft Word and Microsoft PowerPoint installed.  A printer must be connected to each computer.

Instructional Message Descriptions:

Objectives & Instructional Message Descriptions  Multimedia Representations
1
Define polygon:

Define what a polygon is and identify the characteristics.

Text is used for the definitions.  Images are used to show examples of polygons throughout the background of the site.
2
Explain the difference between regular and irregular polygons:

Describe the difference between regular and irregular polygons.

Text is used for the definitions.  Images are used to compare regular and irregular polygons.
3
State the rule for determining the sum of the interior angles of any polygon:

Derive the rule and explain what the variable represents.

A presentation containing text, images, animation and audio is used to derive the rule and show how it is used.
4
Apply the rule to any polygon:

Apply the rule to an irregular polygon by inputting the number of sides to get the angle measure.

An example of applying the rule is shown in the presentation mentioned in #3.  Text is used to provide practice exercises.
5
Draw an exterior angle of a regular polygon:

Demonstrate how to draw an exterior angle.

A presentation containing text, images, animation and audio is used to show how an exterior angle is drawn.
6
State the rule for determining the measure of each exterior angle of a regular polygon:


Give the rule and explain what the variable represents.

The presentation, mentioned in #5, gives the rule and shows how it is applied to regular polygons.
7
 
Apply the rule to any regular polygon:

Give a polygon and input the number of sides to get the total exterior angle sum.

Text is used to provide practice exercises.  The presentation, mentioned in #5, also demonstrates examples.

Assessment: Students will submit both their polygon quiz and final assessment.

References:

Dressler I., & Keenan E. (2002).  Mathematics A.  New York:  AMSCO School Publications, Inc.

Murray, M. (1999).  Sum of interior and exterior angles of polygons.  Oswego City School District Regents Exam Prep.  Retrieved July 26, 2004, from:  http://www.regentsprep.org