Simplifying Symmetry For All

The word symmetry often brings to mind the red mirror devices used in schools to help students understand the concept. And when you ask people what symmetry is, this is often times their answer rather than the actual definition. Here you will learn what symmetry is (in words you can use to describe it to your students) and the different types of symmetry.

Symmetry is...

- a concept. It is not a something an object or shape is, but something that has.

- shown when an object or shape looks the same after a transformation has occurred, such as a reflection or a rotation, as described by Live Science.

- shown by a dotted line for 2-D shapes, referred to as a line of symmetry.

- shown by a plane for 3-D objects, referred to as a plane of symmetry.

Types of Symmetry

Reflective or Mirror

Generally, when people talk about symmetry, especially in the primary grades is mirror or reflective symmetry. That is, a shape or object can be cut in half such that the two halves are mirror images of each other.

Just as 2-D shapes can have more than one line of symmetry, 3-D objects can have more than one plane of symmetry.

Reciprocalnet.org (n.d.). "Examples of planes of symmetry" [Snapshot]. Retrieved from http://bit.ly/2zqLWJq

Rotational

"A shape has rotational symmetry, when you turn it around its centre point, it fits over a tracing of itself (or into an outline of itself) at least once before it has completed a full rotation" (Smalls, pp. 410).

Tutor Vista. (n.d.). "Words with rotational symmetry" [Snapshot]. Retrieved from http://bit.ly/2zE2233

In class we tested shapes for rotational symmetry and found that some had it, while others did not. To test, we traced the shape onto a piece of paper and then rotated the shape 90°, 180°, 270° and 360°. Like you can see with the "Z", the shape matches the original when turned 180°.

We can classify shapes based on the number of ways a shape fits into its outline. We call this order of rotational symmetry. Take a look at the star. You can see it has been rotated five times and each time it falls within the outline of its original shape. Therefore, the order of rotational symmetry is five. Now look at the right angle triangle. It only fits into the original outline when it has been rotated 360°. Therefore, its order of rotational symmetry is one.

BBC. (n.d.). "Order of rotational symmetry" [Snapshot]. Retrieved from http://bit.ly/2zE2233

It is important for students to be able to manipulate the material in order to better understand it and sometimes that can be hard with a topic such as symmetry.

Activities to help students understand symmetry

- Have students draw a line over the 2-D shape.

- Have students make the objects out of snap cubes and see if they can slide a piece of paper in between to shown symmetry.

- Have students mold 3-D objects out of clay and see if students can cut the object that would show symmetry.

- Using SMART board technology, rotate and reflect shapes and have a discussion comparing the original shapes with its transformation.

- Trace an outline of a shape and have students rotate the manipulative to see if it matches the outline, and if so when and how many times.

References:
Small, M. (2017). Making Math Meaningful to Canadian Students K-8, (3rd ed.). Nelson Education.