Having students experiment with making symmetrical shapes helps in teaching symmetry. Bring in square sheets of paper and have students fold them in half twice. Give each student a pair of scissors and let them make as many cuts as they want. When they unfold them, they will see a beautiful snowflake with both a horizontal and a vertical line of symmetry. You can also have students experiment with making snowflakes online, which allows them to see the symmetrical results of cuts immediately.
Part of learning about symmetry is being able to recognize it in everyday objects and symbols. Teach your students symmetry by asking them to go through the alphabet and find all the letters that have symmetry. Be sure to have them mark down which letters have horizontal symmetry, vertical symmetry or both. You can do this individually or together as a class. Then have students try to think of words that are symmetrical, such as "MOM." Students should find as many words as they can that have either one or two axes of symmetry.
Games that force students to make symmetrical shapes on the fly can help them learn symmetry. Break your class into pairs. Give each student an eight-by-eight grid of blank squares. Label the rows with the letters A through H and the columns with the numbers one to eight. Have students make a symmetrical pattern by shading in squares on the grid without showing their partner. Students must take turn guessing a square on their partner's grid, such as B5. If the square is shaded, the student takes another guess. If it is blank, it is his partner's turn. The first student in each game to correctly identify their partner's entire pattern wins.
Symmetry is not just about geometrical patterns on paper. It can also involve movement. Tell your class that you and your image in a mirror are symmetrical to one another. You can demonstrate this by bringing a mirror into class. Break your class into pairs and have one student in each pair act as a mirror to his partner's actions. Let them act out some movements together, and then have them switch roles.