A circle is the best shape to demonstrate symmetry, since no matter where you fold it, so long as you go through the center point, you will have two equal halves in size and shape that mirror each other. Demonstrate this by folding a circle through its center point, showing how each side matches the other perfectly, so that when folding the paper no single piece of the paper sticks out. Do this for many center lines around the circle.
The only way three sides can make a shape is to form a triangle. Out of paper, make one triangle with three congruent angles and side lengths. Show its symmetry by folding it over on itself through the center point, splitting one of the angles evenly in half. Do this with all three angles. Show where it is not symmetrical by folding it through its center point without splitting any angle so that one point of the triangle meets the center of its base. Make another with two equal long sides and one short side. Show its symmetry by folding it in half through its center point, splitting the angle of different degree from the other two. Show how it's not symmetrical by folding it through its center point, splitting one of the two equal angles. Your pupil will see that some of the paper sticks out.
Using a square, a rectangle, a trapezoid and a parallelogram, continue to physically show symmetry and asymmetry by folding the shapes over through their focal points. Your students should be able to notice by now how different angles and side lengths play into the definition of symmetry. They may even be able to predict which fold lines will prove to be an axis of symmetry.
At the end of your activities, the children should be ready to learn about the axis of symmetry, which is the line the shapes have been folded over when they make an equal shape on each side. Have the students identify each axis of symmetry for each shape, noting that each one goes through the focal point. Now have them study the fold lines that don't create symmetry. They should notice that some of these also go through the focal point. Explain to them that each side of the shape must also be equal to make it symmetrical.