Math school year in review part 1 – our tiling projects

Roughly a year ago the boys started their first year in school after 5 years of home schooling. Both kid’s packets for the next school year arrived last week. That got me daydreaming about the math we’ve done in the last year. Turns out that we’ve done a lot and I wanted to write about some of it before it all slips out of my mind.

One subject that we’ve spent a fair amount of time on this year is tilings. Not by design but I just happened to see a lot of neat tiling ideas in the last year.  Here’s a review of the tiling projects we did in the last 12 months:

(1) The project from Zome Geometry that got us going

This project was one of the few ones that I didn’t film.  The reason was that we had several kids from the neighborhood over working on it and I don’t feel comfortable filming kids that aren’t mine!

Anyway, this was a really fun project from Zome Geometry by George Hart and Henri Picciotto

Zome Tilings

IMG_0555

(2) That project led to two 3d versions:

The natural thing to do after this project was to look at ways that you could cover 3 dimensional space with shapes – again we made use of our Zometool set:

Tiling 3-dimensional space with our Zometool set

Honeycombs

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(3) A problem from a UK math exam led to a fun tiling project

I saw this neat problem from a UK math test circulating on Twitter back in February.

The UK Intermediate mathematics challenge part 2

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(4) A domino counting exercise form Jim Propp

We’d done a couple of projects based on Jim Propp’s blog, he thought that we might enjoy studying how 2×1 dominoes tile a 2xN square.  The project was so fun that we actually did it twice!

A fun counting exercise for kids suggested by Jim Propp

Counting 2xN domino tilings

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(5) Propp’s suggestion above came after we did these two projects on the Arctic Circle Theorem

I learned about the Arctic Circle theorem from a graduate student at MIT who thought it might be possible to share this fairly advanced mathematical idea with kids:

The Arctic Circle Theorem

A second example from tiling the Aztec diamond

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(6) Dan Anderson’s Gosper Curves

Maybe stretching a little to call this tilining, but we had fun exploring how the Gosper Island’s that Dan Anderson sent us fit together:

Dan Anderson’s Gosper curves

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(7) Inspiration from Eugenia Cheng’s Shapes video

I saw this neat video from Eugenia Cheng over the summer:

Thinking about how to use it with my kids inspired these two projects:

Tiling pentagon cookies

Learning about tiling pentagons from Laura Taalman and Evelyn Lamb

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(8) Richard Stanly’s Tiling presentation

Finally, just last week I stumbled on a presentation that Richard Stanley – a math professor at MIT who specializes in combinatorics – had put together about tilings.  There were a couple of ideas that were accessible to kids:

Talking through some examples from Richard Stanley’s tiling presentation

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