Sorting Polygons

This is a lesson plan begins with the discussing the attributes of polygons. The students then sort the polygons in Venn Diagrams, according to these attributes. Extensions to fundamental ideas about probability and statistics are also included. This is a lesson plan that is complete with objectives, materials, and a learning plan. It also has practice activities for the students and extension activities.

Standards & Objectives

Academic standards
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles...
GLE 0206.1.1
Use mathematical language, symbols, and definitions while developing mathematical reasoning.
GLE 0206.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0206.1.3
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0206.1.4
Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution...
GLE 0206.1.5
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
GLE 0206.1.6
Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
GLE 0206.1.7
Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
GLE 0206.1.8
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and...
GLE 0306.4.1
Describe, compare, and analyze properties of polygons.
GLE 0406.4.1
Understand and use the properties of lines, segments, angles, polygons, and circles.
GLE 0506.4.1
Use basic formulas and visualization to find the area of geometric figures.
GLE 0606.4.1
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other...
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
Learning objectives: 

Learning Objectives:

Students will:

  • Precisely describe, classify, and understand relationships among types of two-dimensional objects using their defining properties.
  • Use Venn Diagrams to sort polygons according to certain attributes.
  • Understand and apply basic concepts of probability.

NCTM Standards and Expectations

  • Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.
  • Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.

Lesson Variations

Blooms taxonomy level: 
Extension suggestions: 


  •  One can design activities that use sets of polygons to reinforce ideas about probability and statistics. For instance, when holding a bag containing the diagrams, a teacher can ask, "What is the probability of drawing at random a regular polygon from this set of polygons?" A more difficult question is "Given that you have selected a triangle, what is the probability that you have selected an isosceles triangle?"
  • Another task asks students to sort the polygons into groups determined by the number of sides. They construct a bar graph showing the frequency of three-sided polygons, four-sided polygons, and so on. Having students draw a circle graph showing the percent of polygons in each category will enrich their understanding of percents and angle measurement.

Helpful Hints


  • Blank Transparencies
  • Shapes Activity Sheet 
  • Sorting Cards Activity Sheet 
  • Venn Diagram with One Circle Overhead 
  • Venn Diagram with Two Intersecting Circles Overhead 
  • Venn Diagram with Three Intersecting Circles Overhead 
  • Venn Diagram with One Circle Inside Another Circle Overhead