Kindergartners are able to discuss symmetry any time of the year, but you can choose to do it when you want to make paper shapes, such as a paper heart. Teach kids how folding a heart in half creates two equal sides. Show them that the line of symmetry is the fold line; they can trace it with their fingers or their pencils. Have students trace a heart stencil, cut out the shape and fold it in half to make a symmetrical Valentine.
Give a child a folded paper and ask her to create a picture with crayons on one side of the fold line. Next, she should recolor the picture again with heavy crayon. Fold the paper inside out, with the colored side in. Have her rub the paper vigorously with her fist. When she opens the paper, the first half of the picture should be recreated on the other side of the fold line from the crayon rubbing. Discuss how the fold cuts the picture in half, or two equal parts.
Another way to discuss symmetry goes beyond the fold line. Upper elementary students can discover there are multiple lines of symmetry for a single figure. For example, give fourth graders circles of different sizes. Ask them to use their rulers and pencils to draw different lines of symmetry. They should discover that a circle has an infinite number of lines of symmetry.
Give children a number of shapes that appear to be related but might have different lines of symmetry. A group of four-sided figures called quadrilaterals might include a trapezoid, a diamond, a rectangle, a square and a rhombus. Ask the children to draw the lines of symmetry in each one. For example, a square would have four lines of symmetry -- the horizontal and vertical lines and two diagonals.