The "cut and trace" method allows children to draw symmetrical shapes by following mechanical steps, even if they do not yet understand the concept of symmetry. Let each child cut a shape out of corrugated cardboard, leaving one straight edge of the cardboard intact. Help the child use a marker to color a line along the straight edge on both faces of the cardboard. Trace around the cardboard cutout onto a sheet of paper. Flip the cardboard over and line up its colored edge with the straight edge of the tracing. Trace the cutout again to create a symmetrical shape.
This technique uses tracing paper to help students visualize the mirror-image halves of a symmetrical shape. Give each student a sheet of tracing paper folded in half. Each student should draw a wiggly line that starts and ends on the fold. Have students look at their paper from both sides to see that the wiggle turns into a mirror image of itself when viewed from behind. Fold over the papers and trace the wiggly shape onto the other half. Unfolding the paper will create a shape with a line of symmetry along the fold.
Students can combine careful folding, cutting and tracing to create shapes with multiple lines of symmetry. Have each student fold a piece of thin cardboard in half. Fold again along a perpendicular line to create quarters. If desired, students may fold the paper in half a third and fourth time, with each fold aligning the two folded edges produced by the previous fold. Make a cut along the unfolded end that starts on one folded edge and ends on the other. Unfold and trace the shape to create a flower, snowflake or other shape with multiple lines of symmetry.
Drawing symmetrical shapes on graph paper can help students begin to develop an intuition for the graphical transformations that lead to symmetry. Draw a center point on a sheet of graph paper. Draw multiple points near the center point. Find the mirror images of each point by counting the same rise and opposite run, or vice versa, starting from the center point. For example, the mirror image of a point at (1, 2) is (-1, 2) or (1, -2), depending on the line of symmetry. Connect all the points in an outline to create a whole, symmetrical shape.