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Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

*[Feature photo above by Christiaan Triebert via flickr (CC BY 2.0).]*

Have you ever heard of *Math Storytelling Day*? On September 25, people around the world celebrate mathematics by telling stories together. The stories can be real — like my story below — or fictional like the tale of Wizard Mathys from Fantasia and his crystal ball communication system.

Check out these posts for more information:

- Happy Math Storytelling Day
- Math Storytelling Day resources
- Moebius Noodles: Math Storytelling Day archive

My story begins with an unexpected adventure in pain. Appendicitis sidewhacked my life last week, but that’s not the story. It’s just the setting. During my recovery, I spent a lot of time in the smaller room of my hospital suite. I noticed this semi-random pattern in the floor tile, which made me wonder:

- Did they choose the pattern to keep their customers from getting bored while they were … occupied?
- Is the randomness real? Or can I find a line of symmetry or a set of tiles that repeat?
- If I take pictures from enough different angles, could I transfer the whole floor to graph paper for further study?
- And if the nurse finds me doing this, will she send me to a different ward of the hospital? Do hospitals have psychiatric wards, or is that only in the movies?
- What is the biggest chunk of squares I could “break out” from this pattern that would create the illusion of a regular, repeating tessellation?

I gave up on the graph paper idea (for now) and printed the pictures to play with. By my definition, “broken” pattern chunks need to be contiguous along the sides of the tiles, like pentominoes. Also, the edge of the chunk must be a clean break along the mortar lines. The piece can zigzag all over the place, but it isn’t allowed to come back and touch itself anywhere, even at a corner. No holes allowed.

I’m counting the plain squares as the unit and each of the smaller rectangles as a half square. So far, the biggest chunk of repeating tiles I’ve managed to break out is 283 squares.

Have you and your children created any mathematical stories this year? I’d love to hear them! Please share your links in the comments section below.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

*[Feature photo (above) by U.S. Army RDECOM. Photo (right) by Stephan Mosel. (CC BY 2.0)]*

On your mark… Get set… Go play some math!

Welcome to the 76th edition of the ** Math Teachers At Play** math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

By tradition, we start the carnival with a puzzle in honor of our 76th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.

Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.

On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.

Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.

For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system *Telephone numbers*.

**Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?**

T(0) = ?

T(1) = ?

T(2) = ?

T(3) = ?

T(4) = 10 connection patterns (as above)

T(5) = ?

T(6) = ?

and so on.

**Hint: **Don’t forget to count the state of the system when no one is on the ~~phone~~ crystal ball.

- Printable version: Crystal Ball Connection Patterns.

*[Wizard photo by Sean McGrath. (CC BY 2.0)]*

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; I’ve drawn others from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents:

*[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]*

I hear so many people say they hated geometry because of the proofs, but I’ve always loved a challenging puzzle. I found the following puzzle at a blog carnival during my first year of blogging. Don’t worry about the arbitrary two-column format you learned in high school — just think about what is true and how you know it must be so.

**I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:**

One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.

One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why …

*[Click here to go read Puzzle: Patty Paper Trisection.]*

Don’t miss any of *“Let’s Play Math!”*: Subscribe in a reader, or get updates by Email.

*[Feature photo above by hom26 via Flickr.]*

My free time lately has gone to local events and to book editing. I hope to put up a series of blog posts sometime soon, based on the Homeschool Math FAQs chapter I’m adding to the paperback version of *Let’s Play Math*. [And of course, I’ll update the ebook whenever I finally publish the paperback, so those of you who already bought a copy should be able to get the new version without paying extra.]

But in the meantime, as I was browsing my blog archives for an interesting “Throw-Back Thursday” post, I stumbled across this old geometry puzzle from Dave Marain over at MathNotations blog:

Jake shows Jack a piece of wood he cut out in the machine shop: a circular arc bounded by a chord. Jake claimed that the arc was not a semicircle. In fact, he claimed it was shorter than a semicircle, i.e., segment AB was not a diameter and arc ACB was less than 180 degrees.

Jack knew this was impossible and argued: “Don’t you see, Jake, that O must be the center of the circle and that OA, OB and OC are radii.”

Jake wasn’t buying this, since he had measured everything precisely. He argued that just because they could be radii didn’t prove they had to be.

Which boy do you agree with?

**Pick one side of the debate, and try to find at least three different ways to prove your point.**

If you have a student in geometry or higher math, print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.

Dave offers many other puzzles to challenge your math students. While you are at his blog, do take some time to browse past articles.

Get all our new math tips and games: Subscribe in a reader, or get updates by Email.

Last week, Kitten and I reached her textbook’s chapter on graphing linear equations, and a minor mistake with negative numbers threw her into an “I can’t do it!” funk. It’s not easy teaching a perfectionist kid.

Usually her mood improves if we switch to a slightly more advanced topic, and luckily I had saved these worksheets on my desktop, waiting for just such an opportunity. Today’s lesson:

**Some fun(ish) worksheets**

“For tomorrow, students will be graphing systems of inequalities, so I decided to create a little Ohio Jones adventure (Indiana’s lesser known brother)…”

I offered to give her a hint, but she wanted to try it totally on her own. It took her about 40 minutes to work through the first few rooms of the Lost Templo de los Dulces and explain her solutions to me. I’m sure she’ll speed up with experience.

So far, she’s enjoying it much more than the textbook lesson. It’s fascinating to me how the mere hint of fantasy adventure can change graphing equations from *boring* to *cool*. Thanks, Dan!

*[Feature photo above by David Reimann via Bridges 2013 Gallery. Number 70 (right) from Wikimedia Commons (CC-BY-SA-3.0-2.5-2.0-1.0).]*

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 70th edition of the ** Math Teachers At Play** math education blog carnival — a smorgasbord of 42+ links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 70th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

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