Erika Pallone and David Witte
K306 Lesson Plan
Geometry I
Polygons and Angle Sum
Coach Elaboration
I. Rationale and Goals
The goal for this lesson is for students to be able to name the different polygons
based on the number of sides in the polygon, to have students recognize the difference
between polygons and regular polygons, learn the formula needed to calculate the angle
sum of any polygon, and make connections between geometrical shapes and algebraic
formulas. This lesson is necessary because it will help with further math classes when
learning patterns, volume, area, triangle theorems, etc.
This lesson meets the Indiana Content Standards:
 G.2.1. Identify and describe regular polygons.
 G.2.2. Find measures of interior and exterior angles of polygons, justifying the
method used.
and also the National Council for Mathematics Standards 2 and 3, Algebra and Geometry
respectively:
Mathematics instructional programs should include attention to patterns, functions,
symbols, and models, as well as geometry and spatial sense, to enable all students to:
 Understand patterns, relations and functions
 Represent and analyze mathematical situations and structures using algebraic
symbols
 draw geometric objects with specified properties, such as side lengths or angle
measures
 use geometric models to represent and explain numerical and algebraic relationships
 recognize and apply geometric ideas and relationships in areas outside the
mathematics classroom, such as art, science, and everyday life
II. Concepts and Other Content
The general idea for our lesson is to teach students the definition and various
properties of polygons. After this lesson, students will be able to calculate the angle sum
of any polygon just by knowing how many sides the polygon has. The following is an
outline for our lesson:
1. Teacher will introduce Polygons:
 Definition: closed many-sided geometric figure
 Properties:
o Each segment intersects two others each at an end point
o Each vertex has exactly 2 line segments coming out of it
o Regular polygon: each angle has same measure and each line
segment is of equal length
2. Students will fill in left column in table of polygons:
Polygon
Number of Sides
Regular Polygon
(all angles are equal and length of
all sides are equal)
3
Equilateral Triangle
Triangle
4
Quadrilateral
Square
5
Pentagon
Regular Pentagon
6
Regular Hexagon
Hexagon
7
Heptagon
Regular Heptagon
8
Octagon
Regular Octagon
10
Decagon
Regular Decagon
12
Regular Dodecagon
Dodecagon
3. Teacher will explain drawing diagonals in a polygon:
 Definition of a Diagonal: line formed by connecting 2 vertices of a
polygon which is not already a side
4. Teacher will show that drawing diagonals leads to triangles:
 Draw all the diagonals of a polygon without crossing edges – leads to just
drawing all the diagonals that come out of one vertex
o No matter what vertex you start at, you will end with the same number of
triangles
o Number of triangles formed will always be two less than the number of
sides (remember that the number of sides = n so number of triangles = n –
2)
Number of sides for the
polygon = n
Number of triangles formed
by diagonals from 1 vertex
4
5
6
7
8
10
12
:
:
n
2
3
4
5
6
8
10
Difference between number
of sides and number of
triangles
4–2=2
5–3=2
6–4=2
7–5=2
8–6=2
10 – 8= 2
12 – 10 = 2
n-2
n – (n – 2) = 2
5. Teacher reminds students that the sum of the angles of a triangle is always 180 degrees
 Therefore, (# triangles in a certain polygon)*(180 degrees) = sum of angles in that
polygon which leads to (n – 2)*(180 degrees) = sum of all angles of n-gon
6. Students will then get into groups and fill in the table given below:
Polygon: n =
number of
sides
3
4
5
6
7
8
9
10
50
100
Number of
diagonals
from each
vertex
(n - 3)
Number of
triangles
possible
(n – 2)
Total
number of
degrees in
polygon
(n – 2)*180
Can you find a relationship
between the names of the
polygons and a common
name or event? (sports,
animals, science, buildings,
etc.) Try to come up with
at least 2 examples.
Answers: Relate prefixes to sports: triathlon, decathlon or certain chemicals: octane,
pentane, pentagon (building) quadriplegic, octopus, etc.
During this portion of the lesson, the teachers will walk around and “coach elaborate”
with the students asking questions such as:

Why do you think the number of triangles will be the same no matter what vertex
you start with?
 Why do you think the number of triangles is always three less than the number of
sides?
 Why can’t diagonals intersect?
 Why is a triangle the smallest possible polygon?
 If you start with a triangle and find all the answers, what will happen to the
answers when you add one side and start with a quadrilateral? What if you add 5
sides?
 Why do we use triangles to find the angle sum?
The teacher will make sure that each student in the group answers at least one question to
get a more general idea of what the class knows as a whole.
6. Teachers will lead a whole class discussion where the groups will tell the class what
they got as answers for the table and for the question asked.
III. Performance Objectives
By the end of this lesson students will be able to identify a polygon, and to
distinguish between regular and irregular polygons. Students will be able to calculate the
angle sum of any polygons using the method of drawing diagonals and creating triangles.
Also, students will be able to relate prefixes of polygons to other items they come across
in daily life.
IV. Teaching Strategies and Student Learning Activities
At the beginning of class, the teacher will introduce the students to polygons
giving them the definition and properties of polygons. Students will then be asked to
draw their own polygons in the table given to them. The main portion of this lesson will
be a lecture by the teacher on drawing diagonals of a polygon, finding the number of
triangles, and using the number of triangles to find the total sum of the angles in any
polygon. This portion of the lesson will be teacher centered with students taking notes.
Next, we will hand out a table to the students which they will be required to complete in
groups. By working in groups, students will practice social skills while having the
opportunity to discuss problems with their classmates if they do not fully understand the
day’s lessons. Similarly, students will have the opportunity to explain to other classmates
what they have learned that day if their classmate is confused. During group work, the
teachers will be walking around to the groups asking them open ended questions to see
what the students know and what they are having trouble with. At the end of the lesson,
the teacher will ask each group to share their answers to the worksheets with the rest of
the class. This lesson will be continued the next day elaborating on the total number of
diagonals that can be drawn and the degree of each angle in a regular polygon.
This lesson is adapted to special needs students in a few different ways. First, the
teachers are handing out two tables so that students will not have to write down an
abundance of notes. These worksheets can be used at a later date as a review or a study
guide for a test. Secondly, students will be working in groups which are beneficial to
practicing social skills. Furthermore, the teachers will be walking around during class
performing a formative assessment of the students while asking them open-ended
questions about the day’s topic. This will allow the teacher to judge the knowledge of the
students and find out if there are any students which need additional instruction or review
of the material.
V. Materials
 Dry Erase Markers
 Table of polygons for each student
 In-class worksheet for each student
VI. Assessment
The students will be formatively assessed by the teachers during group work as
the “coach elaboration” questions are asked. Also, at the end of the lesson, students will
be formatively assessed as we are going over the worksheet. The teacher will ask
questions as the answers to the worksheet are being given such as, “How did you come
up with that answer?” and “How do you know that is true?”
VII. Resources
 Coach Elaboration Teaching Strategy
 Haenisch, Siegfried. Geometry. Minnesota: American Guidance Service, Inc.,
2001. 154-159.