Irregular VS Regular Polygons

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Students will be able to group polygons into the categories of irregular and regular.

Big Idea

It’s okay to be irregular... if you are a two-dimensional shape.


10 minutes

Up until this lesson, I have focused on naming polygons and examining the attributes of each shape.  The next level of classifying shapes is determining if they are regular or irregular.  I expect that my fifth graders have some informal concept of regular and irregular shapes; they may have never been given the vocabulary.  In this lesson, we will use the terms regular and irregular to assist the class in further classifying polygons.

When I think about drawing a hexagon, a perfect honeycomb shape comes to mind.  Additionally, if I had to draw an octagon, I would imagine a stop sign.  These versions of polygons are for some reason more aesthetically appealing to the brain and can readily be recalled when considering these shapes.  For the elementary student, regular polygons have been used since kindergarten to name shapes and identify symmetry.  My goal in today’s lesson is to remind students that there is more than one way to think of polygons. 

I am going to ask the students to visualize a shape in their minds, describe it to me verbally, and then draw it.  After listening to student descriptions I will also make a drawing based and compare it to the student drawing.  I expect that students will draw a regular polygon similar to what I would have done.  However, I am deliberately drawing an irregular polygon.  The intention is to get students thinking about different versions of polygons.

I start this activity by asking students to close their eyes and think about the shape that I say.  I choose a hexagon.  After a few moments I ask them to open their eyes and tell me what they visualize so that I can try and draw it.  Most student responses are centered on the number of sides.  I tell them I have a pretty good idea of what they saw in their minds and I am going to draw it.  As I am drawing mine on a whiteboard I ask students to make a quick drawing on their whiteboards.  I give a few seconds for each of us to complete the drawing and tell them it is time for the big reveal to see if our shapes match. 

I reassure them that I’m pretty sure I know what their drawing looks like from the great descriptions they gave.  With boards revealed students are quite surprised to see the irregular polygon that I have drawn.  I begin to defend my shape saying I followed their descriptions and I really thought I was going to get it right.  I quickly say I would like a rematch and give them another polygon to visualize.  I play it up as much as possible that this time I will get it for sure.  Fifth grade is a great age because students are just starting to really understand irony and I love to use this to my advantage.  Some of them catch on to my antics but they still enjoy it. 

After these two examples of visualizing shapes I ask students if there is a way they could have given me a better description.  This discussion is a spring board into the main portion of the lesson. 


20 minutes

The majority of student comments in our math discussion center around one idea; my shape looked crazy.  I ask students to explain why my shape is so "crazy" compared to theirs.  Remember, the main goal of this lesson is distinguish between regular and irregular polygons. It is important that students understand that there is more than one way to draw a polygon.  By generating a definition through experience and discussion, distinction between regular and irregular polygons will be more apparent to the students.

For the remainder of this section of the lesson, I have a classroom discussion to really get my students engaged in thinking about classifying polygons.  After taking responses to the first question of why my shape was so "crazy" compared to theirs, I begin to model for the students my thought process in describing a polygon.

I start by asking a student to come up to the board and draw the example of a hexagon that they visualized and drew on their whiteboard.  I lead students in thinking by pretending this is the shape that I had visualized in my mind.  I describe the shape to them using terms such as congruent or same size.  I discuss the lengths of the sides, and the angles inside the shape.

After giving my description, I ask students to recap what I described in their own words.  I call on a few students to monitor for their new way of describing the polygon.

The process is repeated for another regular polygon, but this time I have the students begin to do the thinking by describing the polygon.  Students begin by talking to their neighbor about the polygon and then I bring the students back to the whole group to share out some ideas.

After drawing my example of an irregular polygon on the board, I ask the students to again discuss with their neighbors ways in which they would describe this polygon.  Once again, students return to a whole group discussion.

It can be difficult to keep all students engaged in conversation when it is used this extensively.  I have a lot of techniques I deploy in order to keep up the level of engagement.  My techniques are (1) constantly circulating the room, (2) calling on students who aren’t raising their hand, and (3) allowing students to talk to their neighbors.  Calling on students who are not participating does not have to be an unpleasant experience for them.  They can be asked to repeat what another student has just said or if they agree or disagree with what was just said.   If they are simply ignoring the whole discussion, whatever was just said can be repeated so that they can listen, and repeat it themselves.

As the discussion is wrapping up, I let the students know there is a way to classify polygons by giving them a name, instead of a description.  I introduce the terms regular and irregular to the students.  Most of them are relieved to find an easier way to describe the polygons.  I ask students to add these two new definitions to their vocabulary sheet:

Regular polygon – a polygon that has all side lengths the same and all angle measures the same. Irregular polygon – a polygon that has differing side lengths and angle measures.


15 minutes

To close the lesson I give students practice in classifying polygons based on the new definitions.  Using a given sheet of polygons, they separate the shapes into two groups; regular and irregular.   

I suggest students be given an opportunity to cut out the shapes to group them.  One caution - students will want to cut exactly around the shapes and this will be very time consuming.  I tell the students to just cut a circle around the shape and not to cut on the shape lines.  This saves a lot of time and allows the students to focus on what the task is actually about; classifying polygons into regular and irregular. 

As a challenge to early finishers, I tell them to write the name each polygon on the back of cut out shape.  Each shape should have two words to its name (i.e. regular hexagon) 

While students are working, I circulate the room and check for understanding by monitoring the grouping students created.