Gift wrap and symmetry

This is a time of year when many of us are running around frantically shopping for gifts. Caught up in the spirit of the holidays, I was looking for some math-themed gift wrap as part of a holiday promotion for Geometiles.  In the middle of all the madness, this winter holiday giftwrap caught my eye because of its rotational symmetry. To most people “symmetry” means “mirror symmetry”. But to mathematicians, mirror symmetry is just one of the four types of symmetry used to classify patterns. The other three types of symmetry are rotational, translational, and glide reflection….
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An exercise in modeling a real life tile pattern

What a great exercise it would be for a child to figure out how to “model” this wall with only equilateral triangles and squares. This is exactly the kind of thinking that the writers of the Common Core Math standards illustrate in the draft of their Geometry Progression for Grades K-6, pp. 7, 11-12. Geometiles™ were used for the modeling task, as shown above….
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