The easiest way to introduce symmetry is by having third-grade students use their hands. Draw, trace or use clip art of polygons to create a large image of a symmetrical and then an asymmetrical polygon. Put one polygon on every sheet and give students a set of two sheets. Students need to cut out the polygons and figure out which ones they can fold in half perfectly, without any overlap on any side, and which ones they cannot fold perfectly. Once they find a polygon's line of symmetry, students should draw a dotted line on the fold to illustrate it. Have students come to the front of the class and place the symmetrical polygons on one side of the board and the asymmetrical polygons on the other side of the board. Discuss their findings.
Once students have a basic notion of symmetry, they can demonstrate their knowledge with math manipulatives. Give each table group a box of assorted math shapes, blocks and other objects. Have them sort the objects into piles of symmetrical and asymmetrical shapes. More advanced groups can use math tiles to create complex symmetrical shapes. Have them place a string across the shape to show its line of symmetry.
Dedicate one day as a symmetry day at school. Go on a walk around the school and look for symmetrical and asymmetrical objects. Have students bring a clipboard and pencil so they can sketch their discoveries as they go. Assign homework that has students search their houses for symmetrical objects. Students should draw these objects or bring a symmetrical object for show-and-tell.
Extend students' understanding of symmetry by moving beyond polygons and simple objects. Do an art project in which students have only half of an image from a magazine. Choose symmetrical images cut on the vertical, such as a face, bridge or building. Students can glue the image to a piece of paper and endeavor to create the missing half, maintaining symmetry.