Symmetry is an important math and spatial awareness skill. Your child can develop this skill while drawing, painting, and playing. While drawing, fold (or have our child fold) a piece of paper so that the fold divides the paper in half vertically. You can help your child make one butterfly wing on one side of the fold. He or she can then decorate the wing in any way desired. Now ask your child to copy or match that decorated wing as exactly as possible on the other side of the fold. He or she may need your help to draw the other wing. When your child has finished the butterfly, explain that the sides match and have symmetry.
Try this same procedure with simple shapes such as circles, squares, and triangles. Your child can draw the decorations or glue on pieces of paper or stickers. The complexity of the decorations will depend on your child's ability, which will grow with practice.
It will be fun to create symmetry with small toys or objects, too. Place a ruler or stick vertically on a surface. Your child can place the toys or objects in a certain pattern on one side, maybe arranged in a design or by color. Then he or she can create the same pattern on the other side. It can be fun to play this as a game with two players. One player closes his or her eyes while the first player creates the design on one side. Once he or she is finished, the second player opens his or her eyes and must create the symmetrical design on the other side. The only catch to this activity is having enough objects to create two matching sides!