# Lotsa Snowflakes

I was going to do a class for 6-10 year olds today. The plan was to explore symmetry with snowflakes. But nobody signed up and the class got cancelled. Which meant a luxuriously slow Saturday morning spent with the Rocket Boy, his best friend A, A’s little brother, and their mom… cutting snowflakes.

The boys loved it! Yes, they are big important 9-year olds who build robots, create video games, and “hang out” and “chill”. And yet, the snowflakes are irresistible!

It was completely a “go at your own speed, do what you want” kind of thing. I did draw their attention to symmetries they created. A. folded and cut square snowflakes with four lines of symmetry. He cut out an entire collection!

Rocket Boy folded this way and that with lots of asymmetrical folds. Yet he always had at least one line of symmetry. We looked at the reflection and glide opportunities embedded in his designs.

Little M. was perhaps the most enthusiastic and tenacious snowflake designer. He mastered the 4-lines of symmetry design. Then he switched to just folding the paper in half (it was a pretty heavy paper, so folding it more than once made it difficult for little hands to cut). His design element of choice was triangles. Unfolded, they formed beautiful Christmas trees and, sometimes, funny faces.

At some point we also discussed how to make a circular snowflake out of a rectangular sheet of paper. And made some paper Christmas trees decorated with the left-over “confetti”.

This went on for almost an hour before the older boys decided to go jump on the trampoline. Now that we’ve got a lovely collection, perhaps we can experiment some more, but in a more structured way. The questions I’d like to explore

• how to fold paper for a snowflake with 6,8, 10 lines of symmetry?
• how to fold paper for a snowflake with an odd number of lines of symmetry? Is it possible?
• starting with a particular end result (such as a Yoda snowflake), how to fold and where to cut?
• are folds always commutative? Would folding THIS way, then THAT way produce a different snowflake from folding THAT way first, then THIS way?
• trying fold-and-cut models.
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