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

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Learning outcomes

The students will learn that congruent figures are figures that are the same shape and size.

Teacher planning

Time required for lesson

1 hour


  • Overhead projector
  • Overhead of dotted paper
  • Examples of congruent figures and figures that are not congruent
  • Dotted paper
  • Rulers
  • Scissors
  • Construction Paper
  • Congruent objects or shapes to pass out to students


Students need to know what the word “same” means. They also need to understand what the words “shape” and “size” means.


  1. Review with students that a figure has a line of symmetry if you can fold the figure so both parts match exactly.
  2. Show examples in the classroom and have students find examples of things that have a line of symmetry.

Teacher Input

  1. Introduce a new vocabulary word: congruent. Figures that are the same shape and same shape are called congruent.
  2. Ask students: “When are figures congruent?” (When they have the same size and shape.) Explain to students that if two figures are two different shapes or sizes, they cannot be congruent.
  3. Teacher shows examples of figures that are congruent in the classroom. Teacher should ask students if they can find a pair of congruent figures in the classroom. Examples might be matching books, rulers, name tags, blocks, etc.
  4. Explain that all books are not congruent. The books must be the exact shape and size. Two exact 3rd grade spelling books would be congruent, but not a spelling book and a science book. Explain to students that two televisions screen would not always be congruent, because some are bigger than others.

Guided Practice

  1. On an overhead, draw 3 squares on the dotted paper. Each student should have a piece of the dotted paper.
  2. They draw squares just like the one on the overhead. Two of the squares are three dots long on each side. Label these squares 1 and 2. One square is four dots long on each side. Label this square 3. Students should cut out the squares.
  3. Teacher should ask students what they notice about the squares. Squares 1 and 2 are the same size and shape. Square 3 has the same shape, but it is not the same size. In order to be a congruent figure,” the figure must be the same size and same shape.

Independent Practice

  1. Give each child a piece of construction paper. Ask students to cut out congruent figures. They can cut out several small ones or one big one. Remember that they must be the same size and same shape. If you cut it out, the figures can lay right on top of each other and they are exactly the same.
  2. After sufficient time is given, allow some students to share their congruent figures.


  • Teacher can have several congruent shapes cut out of paper and objects that are congruent. (Examples: scissors, books, rulers) There should be 2 congruent objects. Pass out the objects and let the students get up and find a student with an object that is congruent to their object. *Remember the objects can be different colors, just so they have the same size and same shape.
  • Review the definition of congruent figures. Ask students questions such as: “Are two pennies congruent?” “Are two sheets of paper congruent?” “Are two tabletops congruent?” “Is a penny congruent with a dime? They are both round, but are they the same size?”
  • Teachers may ask other questions about things that are congruent.

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

        • Geometry
          • 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.
        • Kindergarten

          • K.G.5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

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.