Zome tilings

Saw a neat page in our Zome Geometry book last night:

Today we tried making a few of these shapes. The first was the non-convex pentagon tiling first:

 

A few thoughts from the kids:

Kid 1: (6th grade boy) The pattern keeps changing. We never saw the “one straight” until [pointing to the figure] here, and we never saw the “three straight” until here.

Kid 2: (6th grade girl): I think it is cool how the pattern seems like it isn’t going to work and then it fixes itself.

Kid 3: (4th grade boy) It is really interesting ’cause of the patterns. They almost discontinue, but then we saw something that helped us fix it.

Next we tried for a shape with Penrose tiles – I actually didn’t know that you could make the Penrose darts and kites out of Zome struts.

  

A few thoughts from the kids:

Kid 1: I think the shape has 3 fold symmetry and also two fold symmetry.

Kid 2: I’d never seen the Penrose shapes before and it cool how you can flip them. If you take the kite and reverse the part pointing out, you get the dart.

Kid 3: There are two different versions of the (zome) stars. That made building the shape hard.

Also, we’d played with Penrose tiles once before as a 3D printing project:

Penrose tiles and some simple 3d variations

And speaking of 3D printing . . . the last thing we did was take a look at Laura Taalman’s 3D printed pentagon program:

Using Laura Taalman’s 3D printed pentagons to talk math with kids

This last part was just for fun, but all three kids were really interested. Taalman’s work here is amazing.

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