Turtle Tessellation Tiles and Pentagon Spirals

We are finished with our homeschooling year. Well…almost.  We didn’t get to math this year, and so as we shift our focus to more fun, and a less strictly academic theme to our schooling (because who are we kidding? Homeschooling is a lifestyle; there really is no “summer break,”) we will be doing our math for the year.  As part of that unit, we will be exploring tessellations, tiling, geometry and patterns for both the kids. (Currently they are 11 and 5 years old.)  In keeping with our summer fun (oh, again, who am I kidding? I always do this,) I went and looked for some fun, hands-on manipulatives for the kids to explore the topics. Boy did I hit the jackpot.  Look what I found!!! Turtle tessellation tiles and spiraling pentagons at Talking Math with your Kids.
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There is so much opportunity here and all in play.  Spatial arrangement and awareness, patterns, symmetry, and so much more. Just in my and my 11-year-old’s short (30 min maybe) exploration of these tiles I noticed the following.

1. The pentagons have the same length for every side.

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2.To spiral the pentagons, one has to rotate the form to change direction. (otherwise it will make a circle, which is still really cool. It took us a while to figure this one out.
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3.The turtles have different symmetry depending on how you arrange them. In one spot where four meet, you have 2 lines of symmetry. At another point where all four meet, you find radial symmetry.

4. One could do an infinite (I have not tested this hypothesis) number of patterns with the turtles with light and dark.

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5. They are irresistible, and it is impossible not to learn through playing.

I can’t wait to explore them more.

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