A third-grade lesson on congruence should begin with a full explanation of the concept. Tell students that two shapes are congruent if they are identical in shape and size. Draw identical squares or triangles on the board to demonstrate this. Ask students to think of and name congruent objects in their homes or in the classroom. They might name such things as desks, dinner plates and stereo speakers. For each object named, ask the entire class if the objects are congruent or not.
When students have mastered the concept of congruence, third-graders should be able to identify it on the spot. Make an activity sheet with a number of pairs of shapes and figures, some of which are congruent and some of which are not. Ask students to write "congruent" or "incongruent" next to each pair. Make sure that at least one pair is of two figures identical in shape but of different sizes. Take up the activity sheet as a class so students can identify their mistakes immediately.
Students in the third grade should be able to explain why two shapes are or aren't congruent. Make another activity sheet pairs of shapes that are or aren't congruent. Leave space for students to identify congruence and write a short explanation. For example, for congruent hexagons, students should write that the two shapes have six sides of equal length, identical angles and are of identical size. Take the sheet up as a class, and ask different students to provide their explanations aloud.
To have fully learned congruence, third-graders must demonstrate that they can produce congruent figures. Make another activity sheet with single shapes, each of which is followed by a blank space. Challenge students to draw a congruent shape next to each figure on the page. Begin with simple geometrical shapes such as rectangles and octagons. End with more complex shapes, such as flags or houses. You can include colored shapes that require students to use colored pencils or markers.