Regular vs. Irregular Polygons

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SWBAT classify 2-D shapes by their properties.

Big Idea

Students will complete a powerpoint presentation and will explore the difference between regular and irregular polygons.

Teacher Demonstration

40 minutes

Powerpoint Presentation

To review previously discussed properties and to introduce new properties, I created a Google Powerpoint, 2D Shapes & Properties, and shared it with students. Next, students opened the presentation in their Google Documents and copied the presentation to make the presentation their own. 

Goal & Introduction

I began today by introducing the goal: I can classify 2D-shapes by their properties. I included the goal on the first slide, Goal, as I wanted students to have a purpose for learning. 


Next, we moved on to the second slide to discuss Properties. We reflected upon the Properties Poster that was introduced yesterday to insert a definition of properties in the speech bubble:  characteristics that describe something. I like to keep definitions short for easy memorization!

Reviewing Angles

We then moved on to the next slide, Right Angle Slide, which provided an opportunity for students to make a bulleted list to explain a right angle and to draw an example of a right angle using the drawing tools. Again, we reflected on previously taught vocabulary to complete this page: Right Angle Poster. Students absolutely loved being able to create examples on the computer! Here's an example of student work on this slide: Student Example of Right Angle.

We then reviewed and completed slides for other angle posters: Acute Angle Poster and Obtuse Angle Poster.

Other Properties

At this point, we continued in the same fashion, introducing, discussing, and completing a slide for each of the following properties: 


Student Work 

Here's a Student Example of 2D Shapes & Properties.

Student Exploration

40 minutes

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. 


For the rest of today's lesson, I wanted to provide students with the opportunity to classify 2D shapes by their properties. So I printed examples of regular and irregular triangles, quadrilaterals, pentagons, and hexagons for each group to examine: Regular vs Irregular. To scaffold this activity, I only handed out one page at a time to groups (front & back). 

Getting Started

I explained: Now that we have an understanding of shape properties, we are going to use this understanding to determine the difference between regular polygons and irregular polygons! I projected a copy of the first page of triangles. I continued: For example, this page shows a regular triangle and two irregular triangles. Today, I want you to investigate what makes these triangle types special! 

Constructing Viable Arguments

I purposefully created an open-ended investigation based on the question, What is the difference between regular and irregular polygons? This way, students would naturally engage in Math Practice 3: Construct viable arguments and critique the reasoning of others. They were determined to find the answer to this question on their own by investigating shape properties! 

Monitoring Student Understanding

While students were working, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Again... Math Practice 3). 

  1. What have you noticed so far? 
  2. Have are the properties of a regular triangle?
  3. What argument can you make based upon the evidence gathered?
  4. How is a regular pentagon different from an irregular pentagon?
  5. What is your next step going to be? 


I cut out copies of each shape to provide Concrete Models for students when determining the number of lines of symmetry. Often times, students need to be able to fold shapes in order to determine the number of lines of symmetry so I had these concrete models handy just in case any students needed them! Here, a couple students are Determining Lines of Symmetry. Through questioning and guidance, I encourage these students to construct an argument based on their investigation: Constructing an Argument

I loved watching this group make constructing evidence-based arguments: Relying on Evidence.

Here, Constructing an Argument about Regular Polygons, a pair of students reflect back on all the evidence gathered so far to make an argument about all regular polygons. 


20 minutes

To bring closure to this lesson, I invited students to the front carpet with the papers from their investigation. We then created the following poster altogether: Regular vs Irregular Polygons Poster. You can see that we ran out of room and time! We weren't able to fit hexagons on the poster, although I'm not sure they were needed for students to make a conjecture about all regular polygons. You will also see that we weren't able to make any final observations about all irregular polygons. 

I started by placing a regular triangle in the Regular Polygon column and asked: What did you discover when investigating the regular triangle? I labeled the poster with student responses, "It has all congruent angles." "The angles are 60 degrees each!" "It has all congruent sides!" "Each side is about 12 cm!" "That means it's an acute equilateral!" "There are three lines of symmetry!"

We continued on in the same manner with the other shapes. At then end, I asked students: What argument can you make about all regular polygons? Students agreed, "All regular polygons have all congruent sides, are symmetrical, and have all congruent angles!" 

Looking back on the investigation format of this lesson, I feel that students purposefully applied their knowledge of properties to classify 2D shapes. 

As a side note, the label next to the irregular pentagons on the poster should read: All sides are not congruent.