Today we visited symmetry. My students know what symmetry is, however, there were a few terms that I wanted them to learn:
- Axis of Symmetry - a line through a shape so that each side is a mirror immage
- Reflectional Symmetry - a type of symmetry where one half is the reflection of the other
- Rotational Symmetry - the shape can be rotated some amount and still looks the same.
Our activity today came from "Kaleidoscopic Octagon: Link Geometry, Measurement, and Art" by Karyn Mazo is from a magazine called Challenge that was published by Good Apple in 1999, Issue 83 pp. 14-15.
In the article, the author gives an idea for explaining the math involved in the art as follows:
A lesson in spatial logic, patterning,
geometry and measurement.
The students folded their paper vertically,
horizontally, and diagonally. Using rulers
they measured from the midpoint of their
folds to construct a regular octagon.
Then the students created patterns which
they reproduced in each section of the octagon.
We followed her instructions to create the octagon. Please watch our video: Perfect Octagon from a Square. Then I had the students create a design in one triangular section of the octagon. Since my focus is creating reflectional symmetry and rotational symmetry, I required the students to use a "mira" math reflector. This tool allows the kids to see a reflection of their design in the mira, while also allowing them to see their pencil through the mira in order to trace the design as a perfect reflection.
Here is Mrs. Dittrich's class using the miras to create their kaleidoscopic octagon:
We will finish up the octagons tomorrow.