How to Teach Polygons and Quadrilaterals

 How to Teach Polygons and Quads

Looking for how to teach classifying polygons for upper elementary math students?

Let's talk about what they need to know, plus some teaching tips for polygons and quadrilaterals. We will also discuss how to differentiate instruction.

What to look for in this post:
  • Progression of classifying polygons standards for upper elementary school
  • Vocabulary associated with polygons and quadrilaterals
  • Classifying shapes by different categories
  • Teaching polygons and quadrilaterals using the CRA Model
  • Demonstration of teaching classification of polygons
  • Polygon and quadrilateral activities within the CRA model
  • Milestones for students learning to classify polygons
  • Tips for teaching polygons
  • Differentiation for classifying polygons and quadrilaterals
  • Resources for teaching polygons and quadrilaterals

If you prefer to hear me talk through this, here is a video featuring all of this content:

[0:24] Progression of classifying polygons standards for upper elementary school

In this post, we are diving into what the standards require in terms of classifying polygons, quadrilaterals, and triangles in upper elementary math classrooms.

First, let’s take a look at the progression of classifying polygons standards. In third grade, students are expected to classify polygons, and more specifically, quadrilaterals. In fourth grade, the standards move toward them classifying polygons and right triangles. In fifth grade, students continue to classify polygons but they also need to be able to classify all triangles.

Across these standards, the vocabulary increases. I have found, however, that when teaching third grade I still have to use a fair amount of vocabulary that is not explicitly mentioned until the fourth grade standards. At all levels, students are expected to classify polygons into multiple categories.

[1:37] Vocabulary associated with polygons and quadrilaterals

I mentioned vocabulary, and here is a list of the terms that should be known in third, fourth, and fifth grades:


Polygon, closed, right angle, congruent, parallel, opposite side, triangle, quadrilateral, parallelogram, trapezoid, square, rhombus, rectangle, pentagon, hexagon, octagon, nonagon, decagon


Perpendicular, acute angle, obtuse angle, straight angle, reflex angle, acute triangle, obtuse triangle, right triangle, isosceles triangle, scalene triangle, equilateral triangle

I have found that I can’t teach quadrilaterals in third grade without first explaining right angles and parallel lines. If I am teaching about equal sides, why wouldn’t I use the word congruent?

[2:56] Classifying shapes by different categories

In third grade, the primary focus is on students classifying shapes by the number of sides and the number of angles. In fourth grade, students must also explain how to classify polygons based on whether their lines are parallel or perpendicular. This is when they are first introduced to these concepts around classifying shapes.

Fourth grade new learning is classifying right triangles. Now again, why would I not go ahead and teach them about acute and obtuse triangles if I am already teaching them about those types of angles? They also must be able to classify right triangles by their sides.

In fifth grade, the standards and vocabulary are primarily review, except that now they are classifying all triangles rather than just right triangles.

[4:01] Teaching polygons and quadrilaterals using the CRA Model

When it comes to instruction, I like to use the CRA model of teaching (Concrete, Representational, Abstract). At the concrete level, we introduce things in a hands-on way to students. They use manipulatives, allowing them to “touch” the math. At the representational level, we use pictures, drawings, and other visuals to represent the math. Lastly, the abstract level involves equations or algorithms. There are no visual components, and students can do things with fluency.

We want to be sure we don’t skip straight to abstract, and that we allow students to move through the concrete and representational stages first. When teaching how to classify polygons through the CRA model, I like to begin with geo boards. I then move to pictures, and finally to the abstract descriptions and explanations without the use of pictures.

[5:24] Demonstration of teaching classification of polygons

If you want to watch the full demonstration, go to the YouTube video and move to the time stamp listed above.

In the video, you will see that I use a free digital geo board to show how I would set up my introduction to this topic for third graders. If your students have access to devices, you don’t have to spend money on physical geo boards because they can use these instead. In addition, if you use the digital version then you don’t have to worry about rubber bands flying across your classroom!

I start by explaining that a polygon is any 2-dimensional shape that is closed and made up of only straight lines. We talk about open and closed shapes, and I tell them that “every end needs a friend” for a shape to be closed. If the shape is not closed, it is not a polygon. We also talk about how a circle is not a polygon, because it does not have all straight lines.

Quote: For a shape to be closed, every end needs a friend.

After we go through examples of polygons and non-polygons, we move through the generic names of polygons based on the number of sides and angles. They are familiar with triangles, of course, but I like to have them make two completely different triangles using different colors on their geo boards. We work through all the polygons, through decagons, and they have to make two different examples of each polygon.

Going through all of these usually takes up one lesson. On day two, we go back to the geo boards and focus on quadrilaterals. If you are teaching fourth and fifth grades, it is probably worth the time to review all of this as well. Still using the geo boards, I talk to them about right angles and I establish that the corner of a piece of paper is a benchmark for a right angle. I have them make multiple right angles on the geo board, and they have to check them against the corner of a piece of paper.

Next, I have students make a rectangle and I introduce the term ‘opposite sides’. I have them take two blue rubber bands and show one set of opposite sides, and then they have to take two red rubber bands and show the second set of opposite sides.

Once they have practiced creating different shapes on their geo boards, I like to call out a specific shape and have everyone make it. They can then hold up physical geo boards or you can check their screens. I might say something like, “Make me a quadrilateral with one pair of opposite sides.” For fourth and fifth grades, you would then move on to introducing different types of triangles.

[10:16] Polygon and quadrilateral activities within the CRA model

The geo board work all falls under the concrete part of teaching polygons. Representational activities include drawing the shapes, and abstract activities involve asking students to classify a shape based only on a description of attributes or to tell the attributes of a named shape without a picture to go along with it.

If students do not have a solid foundation with their shapes, and if they have not gotten to build and play with them, then they are probably not going to be very successful at the abstract level.

[10:53] Milestones for students learning to classify polygons

The first major milestone for your students is the ability to classify polygons by their sides and angles. As they move on to fourth and fifth grades, they will have to use more terms to classify polygons and gain a deeper understanding of sides and angles.

The second big milestone is that your students can classify quadrilaterals (third grade) or the different types of triangles (fourth and fifth grades) into multiple categories. The keyword here is MULTIPLE.

Third grade students should be able to answer questions like:
  • Which shapes are polygons? (when shown an array)
  • Name this polygon. (when shown a picture)
  • What name best describes a polygon with X number of sides?
They should also be able to draw a quadrilateral that is not a trapezoid, parallelogram, square, rhombus, or rectangle.

[12:54] Tips for teaching polygons

(1) Make sure you are showing students figures in different positions.

They shouldn’t always think a right angle has to look like an “L”. It can be on its side or turned a different way, just as a square can.

(2) Make sure you include irregular polygons.

Students may be more hesitant to classify polygons that do not have congruent sides.

(3) Check your trapezoid definition.

This one is kind of a big deal, and it may be something you haven’t thought about before. There are actually two different definitions for a trapezoid. The traditional definition states that there is only one set of parallel lines in a trapezoid. There is, however, also a Euclid definition stating that there is AT LEAST one set of parallel lines. In higher level math, like calculus, sometimes a trapezoid will use this definition of at least one set of parallel lines versus the definition of only one set of parallel lines.

(4) Have analogies prepared for categories of polygon classification.

In the PowerPoint that I use to teach, we talk about different foods and I relate all foods to a quadrilateral. We discuss that there are specific types of foods that we can categorize. For example, there are donuts and then there are frosted donuts, filled donuts, and frosted, filled donuts. I like to have something to relate to so students can understand the hierarchy of classifying shapes.

(5) Use an anchor chart.

Especially as your students are learning this new vocabulary, it is helpful to provide them something they can reference. I have an anchor chart for classifying polygons as well as one for classifying quadrilaterals.

[15:56] Differentiation for classifying polygons and quadrilaterals

If students are having trouble, I can just about guarantee that it is because they need help with the vocabulary. So, the first intervention would be vocabulary review and practice. Second, make sure they can classify quadrilaterals in at least one way before moving on to two ways. If students need a challenge, have them classify shapes in multiple ways. Students can write explanations for their classifications as well. You can provide terms they have to use in their explanations, such as right angles, parallel lines, congruent lines, or opposite sides. If they are ready for a challenge, students can also begin to learn more advanced vocabulary.

Looking for more resources for teaching about polygons and quadrilaterals?

I have created a polygons and quadrilaterals no-prep bundle, especially focusing on third grade standards. It includes:
  • A PowerPoint (not only the class notes that you would share on the board but also student notes with blanks that they can fill in)
  • An exit ticket for the lesson
  • A game that can be played as scoot or task cards
  • A worksheet for identifying polygons and quadrilaterals (fun classification practices that students can do in a maze worksheet)
  • Two anchor charts: Classifying Polygons and Classifying Quadrilaterals (full page and half page sizes available; can also be printed as a poster for your wall)
  • Matching game for classifying polygons (leveled)
  • Matching game for classifying quadrilaterals (leveled)
  • Quadrilateral tic tac toe
  • A dice game where students have to name figures, classify shapes, and answer questions
The bundle is available on Teachers Pay Teachers.

Polygons and Quadrilaterals: No-Prep Bundle

You can also grab this free download, which is a teaching guide including everything we talked about in this post. It includes the progression of the standards, the different strategies for teaching vocabulary, my five teaching tips, as well as the milestones, interventions, and enrichment ideas.

Teaching Tool - Free Download - Polygons and Triangles

Teaching Tool - Free Download - Polygons and Quadrilaterals

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How to Teach Metric Conversions for Fourth and Fifth Grades

Check out these related YouTube videos:
How to Teach Adding and Subtracting Mixed Numbers
How to Teach Adding and Subtracting Fractions with Like Denominators
How to Teach Adding and Subtracting Fractions with Unlike Denominators
How to Teach Third Grade Measurement
How to Teach Converting Measurements for Fourth and Fifth Grades
How to Teach Polygons and Quadrilaterals for Third Grade

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