Welcome to my math blog! The purpose of this blog is to help you stay informed about our learning and experiences that have taken place during our math class. I have also included links your child (and you) may want to use in order to supplement math learning in 5th grade.

## Monday, March 28, 2016

### Kaleidoscopic Octagon

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 image
• 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:

Kaleidoscopic Octagon

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.  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.