K-12 Teaching and Learning From the UNC School of Education


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  • Congruent figures: This is a fun, hands-on activity to help students identify congruent figures.
  • Our geometric world: The students will use newspaper and magazine pictures to recognize geometric figures within the real world. They will make a collage of pictures showing various geometric shapes. They will write a summary of the shapes that are represented in their collage.
  • Polyhedra: Faces, edges, and verticies (3-D marshmallow models): Students will review the names of 3 dimensional shapes, create the shapes using marshmallows and toothpicks, and find relationships among the faces, verticies, and edges of different 3-D polyhedra.

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Learning outcomes

Students will:

  • create a symmetrical tree that includes congruent shapes.
  • identify congruency and symmetry in shapes when given a group of shapes.

Teacher planning

Time required for lesson

1 hour


  • Scissors
  • White construction paper
  • Green construction paper
  • Red construction paper
  • String


  • Students will need to know a minimal amount about symmetry and congruence. Furthermore, it is important that students have some knowledge of what happens to a shape that has been flipped, turned, or slid.
  • To make the snowflake you will need to get 8×12 white construction paper. Cut it in half hamburger style, and place 2 pieces on top of each other. Then, fold the papers in half once. Staple the papers twice in the crease that you have created.


  1. Review previous concepts in geometry. Direct students through 2 dimensional shapes and their names.
  2. Then, ask students if shapes have any special qualities that they can think of. Draw 2 similar shapes on the board or overhead. Draw one shape smaller than the other. Have students to tell what they see that is alike and different about the shapes. Explain that these shapes that look alike, but are different sizes, are called similar.
  3. Then, draw 2 more shapes. These shapes need to be the same shape and same size, but have a different orientation. Have students to tell what is alike about these shapes. Is there any thing different about these shapes? (Yes, they are turned or flipped.) Tell the students that shapes that have the same shape and size are called congruent. I often have my students to remember congruent by using the word congroovy. The 2 o’s in groovy are congruent. Write the word congroovy on the board and have the students to find what letter is congruent in the word.
  4. Ask students what they think would happen if a shape was folded. Show students a shape that has been cut out of construction paper. Fold the paper and allow the students to see what happens. Make sure that at some point the shape can be folded to show a line of symmetry. Explain that when a shape can be folded and the 2 sides perfectly match this is called symmetry. Ask the students to think of the 2 m’s in the word symmetry. Tell them that they can remember symmetry by pretending that the m doesn’t have a hook on the front. If you were to fold the m’s in half the m would be congruent. Ask students what objects in their environment have symmetry.
  5. If no one mentions the human body, mention to the class that maybe the human body could be symmetrical. Have three volunteers come to the front. Allow two of the students to use a piece of string to find the line of symmetry in the third person. Ask if there are any more possible ways that the string could be placed to show symmetry.
  6. Hand each student a pre-stapled snowflake packet. Tell the students that they are going to practice making symmetrical snowflakes. Allow the students to use scissors to cut small designs out of the prefolded packets. Tell them not to cut the staples out. (It holds together the two pages.) Then, allow the students to open their snowflakes and viola! you have a 3 dimensional snowflake with symmetry.
  7. For a final project, hand students a piece or two of green construction paper and 1 piece of red and yellow paper. Give the students these goals:
    • Make a tree that is symmetrical and has one line of symmetry.
    • Add congruent ornaments out of yellow and red paper to the tree.
  8. End the lesson by having some students present their symmetrical trees with congruent ornaments to the class. Have the students to explain why the tree is symmetrical and the ornaments are congruent.


Use the following rubric to give each student a grade on this project:

  • 4: (Complete Understanding of Symmetry and Congruence)Student’s tree has one line of symmetry and at least 3 types of congruent ornaments.
  • 3: (Moderate Understanding) Student’s tree has one line of symmetry and ornaments are nearly congruent and at least 2 different kinds of ornaments on the tree.
  • 2: (Minimal Understanding) Student’s tree almost looks symmetrical and none of the ornaments are congruent on the tree.
  • 1: Student has completed a tree without a line of symmetry and little or no ornaments on the tree.

Supplemental information


Students can also be given a group of objects with lines of symmetry and congruence. Have the students to color all shapes with 1 line of congruence red, 2 lines -green, and 3 or more - yellow. Then, have students to draw a line matching congruent shapes to one another.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 1

        • Geometry
          • 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape,...

North Carolina curriculum alignment

Mathematics (2004)

Grade 3

  • Goal 3: Geometry - The learner will recognize and use basic geometric properties of two- and three-dimensional figures.
    • Objective 3.01: Use appropriate vocabulary to compare, describe, and classify two- and three-dimensional figures.