Fantastic Figures

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SWBAT understand the relationships among categories of plane figures.

Big Idea

Students sort figures according to properties, and analyze properties of figures and how they interrelate.


15 minutes

Students are given a picture of a geometric object and are told that their task, as a team, is to become an expert on that geometric object.  I break the task down with the students and remind them to share their expertise with their team. 

Students will:

  • Write the name (names) of a geometric object in the center of the Graphic Organizer.
  • Complete the graphic organizer for a figure.
  • For “Examples” and “Non-examples” think about objects in the real world.
  • Be able to defend any information on the graphic organizer.
  • Post the graphic organizer in the classroom, and plan how to share your expertise with your classmates.
  • Students will participate in a Gallery Walk.

Guided Practice

15 minutes

Prior to beginning, I assess the students’ knowledge of the vocabulary used in this game by engaging students in a class discussion in which they find examples, define, and/or illustrate the geometric terms.

I use Geometry Plane Figures on an ActivBoard to discuss points, line segments, rays, and lines. This presentation is about 25 slides of information, like a PowerPoint presentation. It has a handful of multiple choice questions, and solid examples which help to support instruction in a new format. If you don't have an interactive board, pictures of geometry plane figures, or drawings, can be used.

My goal here isn't to cover these terms as rote memorization.  Instead, I want my students to examine the figures closely, define and identify the characteristics of these geometric figures.

Independent Practice

15 minutes

Students work in pairs to sort a variety of polygon shapes.

Students are encouraged to classify shapes and create categories, which they can be associated with. As I rotate throughout the classroom, I ask students in their groups the following questions:

  • What are ways to classify triangles?
  • Why can’t trapezoids and kites be classified as parallelograms?
  • Which quadrilaterals have opposite angles congruent and why is this true of certain quadrilaterals?
  • How many lines of symmetry does a regular polygon have?

This concept builds from Grade 3 when students described, analyzed, and compared properties of 2-D shapes. They compared and classified shapes by their sides and angles, and connected these with definitions of shapes. In Grade 4, they built, drew, and analyzed 2-D shapes to deepen their understanding of the properties of 2-D shapes. They learned about parallel and perpendicular lines, and the the presence or absence of angles of a specified size to classify 2-D shapes. Now, I'm asking my students to classify 2-D shapes in a hierarchy based on properties.

In the conversations between students, I am listening for students to use the details they've learned in earlier grades, (Grades 3 and 4), to accurately describe the attributes of shapes. To support the rigor during share, I encourage my students to classify and discriminate shapes in more than just one way; the more ways that students can classify and discriminate shapes, the better they can understand them. The shapes are not limited to quadrilaterals.

Here, students begin to work on objective 5.G.4 (Classify two dimensional figures in a hierarchy based on properties.)

Students share out their hierarchy graphic organizers

To provide extra support, you can have students list attributes of the shapes like the number of sides, number of angles, types of lines, etc. The important thing is that they need to determine what's alike and what's different about the 2 shapes in order to get a larger classification for the shapes and and be able to explain these properties. I'm asking my students, "Why is a square always a rectangle?" "Why is a rectangle not always a square?" At first, the students are really confused, but through inquiry and support in their small groups, students begin manipulating the shapes and forming conjectures about what I might be getting at. Students need to be expected to use precision in justifying and explaining their reasoning.


15 minutes

To incorporate literacy into math, we read the book Shape Up, by David Adler. This book contains directions for creating an assortment of shapes using:

  • Slices of American cheese
  • Toothpick
  • Pretzel sticks
  • Plain paper
  • Graph paper
  • Pencil
  • Plastic knife
  • Slice of bread


The shapes, beginning with triangles and going all the way to dodecagons, are defined and explained in simple terms. I have bags full of each material for each group of about 4 students. If you wanted, you could have a bag for each student. After reading the story, I have students go back to their seats to attempt to recreate the shapes. In their cooperative groups, I;m facilitating instruction by walking around with the book. Since this isn't an assessment, I might "flash" a specific page of the book to a specific group who might be having trouble with a shape. (This is after I've heard some attempt to try within the group.) This is especially helpful with the dodecagon shape.


1 minutes

The polygons figures on the Polygon Capture Game worksheet can also be used for various sorting games and activities.

More polygons can be added by the students or teacher. These might include figures that are more complex to capture, such as a kite or non-convex hexagon. Non-polygons, such as figures with curves, can be added to the basic deck.

Exit Ticket

5 minutes

As an exit ticket, students picks one question to respond to on a post-it note:

  • How can I classify and understand relationships among 2D figures using their attributes?
  • How many ways can I classify polygons?
  • What are the different attributes of polygons that help me classify them into groups?
  • What strategy will you use to capture the most polygons?