Plane Polygons

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The students will be able to sort and classify two-dimensional figures in a hierarchy based on properties.

Big Idea

Shape up!


One of the main standards in 5th grade geometry is for students to classify two-dimensional figures in a hierarchy based on properties (5.G.4).  I have been working with my class on lines, angles (types as well as measuring), congruency/similar, parallel etc.

In this standard, the students need to group shapes based on the properties of sides - parallel, perpendicular, congruent and number of sides; and properties of angles - types of angles, congruency. This builds deductive reasoning and precise vocabulary use. 

This lesson seems very simple, and there is a lot to be learned before this.  The more ways students can classify and discriminate shapes the better they will understand them.

There is a common misconception to look for while your students are sorting the shapes - students will think that the last category they put the shapes in is the only classification that can be used.  

Inclusion - Engaging Students

3 minutes

I believe that my students have a better understanding and reach a higher level thinking when I am able to tie their learning to their previous knowledge and their personal life.  I either do a strategy activity from Tribes or ask a questions that will relate to my students' lives and the lesson I am about to teach. 

Today I ask my students to talk about how they would group items in their desk and if some of these items were more important (hierarchy). 

 See the Classroom Video: Connection to Prior Knowledge

Most of the students grouped their shapes by the number of sides and angles and the shapes did not overlap into different categories.

Exploration of Polygon Shapes

30 minutes

Once my students have a chance to share their ideas about classifying and ordering the items in their desks, I link them to classifying and ordering geometric two-dimensional shapes based on their properties. I tell them that not only can we group things together we can also put them in order of how important they are - we can do this in science and now in math. 

I ask my students - What is the definition of geometry? In the past I have always said it is the study of lines and shapes but today I have a different definition for them.  Geometry is all about shapes and their properties.  I am now using the word properties to group the shapes. 

My next slide has Plane Geometric shape definition and Solid Geometric shape definition.  I also write on my board Geometry indicating it as subdivided into plane and solid shapes.  I ask my students to brainstorm some plane figures and solid figures.  There is an arrow off to the left side of my slide where I can slide my images of the two types of shapes under the definitions. 

Coming up later in this lesson students will be sorting and grouping shapes and I want to give them some math tools to do this.  In their bins they have a compass, protractor, rulers, definition cards and polygon tiles (left over from an old math program but you can Google polygon shapes and find numerous images to print off).  Because I seem to always mix up the names of the protractor and compass I have an image on a slide where I can slide the name next to the tool. 

Since I have not completly introduced the term properties to my students I make a point to do this with the next slide.  In each of the rectangles I have properties the students will need to be looking at to create their groups or subcategories of polygons. 

The next slide has Questions to ask yourself when you work together to sort your pieces....

By giving the students the words angles, sides, equal and parallel I am intentionally directing their ideas to include these when they group their shapes. 

Whenever I have my students work together in groups - which is really often because I believe students will build on each other’s ideas, it cements the ideas when they have to explain it to another person and it will be in more kid friendly language when coming from another student, and it creates leaders - I always review my class "rules" which are the four Tribes Agreements of Attentive Listening, Appreciations / No Put-Downs, The Right to Pass and Mutual Respect.   I also refer back to another Tribes lesson/strategy I've taught called "The Roles People Play."  You may hear some of my students talking about being helpers, organizers, leaders, encouragers not talkers, sitters, jokers or bosses.  I find negative behavior is greatly reduced during group work and if there is a disruption in learning my students can use these strategies to get the group back on task. 

Classroom Video: Diverse Entry Points

I walk around the room as each group works to sort all of their pieces, listening for students to be using the geometric terms we have covered in class and specifically the words for classification of angles, parallel, sides etc.  If I don't hear this I will guide the students to using them.

After the groups have finished their classifications I will have them walk through what I call a Table Tour or Student Self-Assessment.  Students will walk around the tables and write down how they think each table grouped their polygon tiles - once again giving the student’s time to practice vocabulary (MP6) and constructing viable arguments and critiquing the reasoning of others (MP3). 

On the next slide I put up the classification given in the CCSS and ask my students to once again critique the reasoning of others and to check their own work. 

Here is a link to the Geometry Shapes.  If you use Smart Notebook there is a Notebook file in the Resources. 

Reflection on Learning

10 minutes

It is important to always have your students reflect what they have learned.  This will more than double their retention of the content.  For this lesson I had my students popcorn answers to the question "What did you notice about how the other groups sorted their shapes?"  Not only did they have the time to sort their own shapes but also to look at how other students sorted their shapes. 

Classroom Video: Developing a Conceptual Understanding

The last slide is reflection questions - for content, collaborative and personal behavior.  Research states that if a person reflects on their learning retention of the knowledge doubles.  When students reflect on their behavior there is more positive behavior than negative.  Students are seeing themselves as leaders, helpers, organizers and encouragers.  The negative roles melt away.