## Hotel Infinity: Part Five

Tova Brown concludes her exploration of the Hilbert’s Hotel Paradox with a look at the cardinality of the real numbers.

You run a hotel with an infinite number of rooms. You pride yourself on accommodating everyone, even guests arriving in infinitely large groups — but some infinities are more infinite than others, as it turns out.

Check out Tova Brown’s growing collection of videos that explore advanced math concepts through story-telling.

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## Hotel Infinity: Part Four

Tova Brown dives deeper into Hilbert’s Hotel Paradox, considering the difference between rational numbers and reals.

You run an infinitely large hotel, and are happy to realize that you can accommodate an infinite number of infinite groups of guests.

However, a delicate diplomatic situation arises when a portal to another universe opens, introducing a different kind of guest, in a different kind of group.

Can you make room for them all?

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## Hotel Infinity: Part Three

Tova Brown continues to examine Hilbert’s Hotel Paradox, pondering infinite sets of infinite sets.

As the proprietor of an infinitely large hotel, you pride yourself on welcoming everyone, even when the rooms are full. Your hotel becomes very popular among infinite sports teams, as a result.

Recruitment season presents a challenge, however, when many infinite teams arrive at once. How many infinite teams can stay in a single infinite hotel?

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## Hotel Infinity: Part Two

Tova Brown explores the second part of Hilbert’s Hotel Paradox. What’s infinity plus infinity?

Running an infinite hotel has its perks. Even when the rooms are full you can always find space for new guests, so you proudly welcome everyone who appears at your door.

When two guests arrive at once, you make room. When ten guests arrive, you accommodate them easily. When a crowd of hundreds appears, you welcome them all.

Is there no limit to your hospitality?

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## Hotel Infinity: Part One

Tova Brown’s introduction to Hilbert’s Hotel Paradox, a riddle about the nature of infinity…

Once upon a time, there was a hotel with an infinite number of rooms. You might be thinking this is impossible, and if so you’re right. A hotel like this could never exist in the real world.

But fortunately we’re not talking about the real world, we’re talking about math. And when we do math we can make up whatever rules we want, just to see what happens.

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## Math Teachers at Play #92

Welcome to the 92nd edition of the Math Teachers At Play math education blog carnival‌—‌a monthly 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.

Let the mathematical fun begin!

By tradition, we start the carnival with a couple of puzzles in honor of our 92nd edition…

### Puzzle #1

92 is a pentagonal number, so I was delighted when Lisa Winer‘s (@Lisaqt314) carnival submission came in. Her class spent some time playing around with figurate number puzzles‌—‌including pentagonal numbers‌—‌and collaborated on a blog post about their discoveries.

What fun!

### Puzzle #2

Or, try your hand at the classic Queen’s Puzzle:

• What is the maximum number of queens that can be placed on an chessboard such that no two attack one another?

Spoiler: Don’t peek! But the answer is here‌—‌and the cool thing is that there are 92 different ways to do it.

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

Along the way, I’ve thrown in some videos in honor of the holiday season.

Please: If you enjoy the carnival, would you consider sending in an entry for next month’s edition? Or volunteering to host sometime in 2016?

## Early Learning Activities

• Kids can enjoy making up math problems, but sometimes they can get a bit carried away. Just ask A. O. Fradkin (@aofradkin) about her daughter’s Gruesome Math.
• Nancy Smith (@nancyqsmith) notices her students struggling with the equal sign in Equality. Strong opinions, and even a few tears. It will be interesting to hear what tomorrow brings…

## Elementary Exploration And Middle School Mastery

• Joshua Greene (@JoshuaGreene19) offers some great ways to tweak an already-wonderful multiplication game in Times square variations. “It was really interesting to see the different strategies that the students took to determining what would go on their boards.”
• For my own contribution to the carnival, I’ve posted a couple of hands-on arithmetic explorations in A Penny for Your Math.

## Adventures in Basic Algebra & Geometry

• Tina Cardone (@crstn85) experiments with Bar Models in Algebra to help her students think about linear equations. “I did not require students to draw a model, but I refused to discuss an incorrect equation with them until they had a model. Kids would tell me ‘I don’t know how to do fractions or percents’ but when I told them to draw a bar, and then draw 4/5, they could do that without assistance…”

## Puzzling Recreations

• Pradeep Mutalik challenges readers to “infer the simple rule behind a number sequence that spikes up and down like the beating of a heart” in Be Still My Pulsating Sequence.

## Teaching Tips

• How can we get a peek at how our children are thinking? Kristin Gray (@mathminds) starts with a typical set of 1st Grade Story Problems and tweaks them into a lively Notice/Wonder Lesson. “When I told them they would get to choose how many students were at each stop, they were so excited! I gave them a paper with the sentence at the top, let them choose a partner and sent them on their way…”
• Tracy Zager (@tracyzager) talks about her own mathematical journey in The Steep Part of the Learning Curve: “The more math I learn, the better math teacher I am. I keep growing as a learner; I know more about where my kids are headed; and I understand more about what building is going on top of the foundation we construct in elementary school.”
• And finally, you may be interested in my new blog post series exploring what it means to understand math. Check out the first post Understanding Math: A Cultural Problem. More to come soon…

## Credits

And that rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.

The December 2015 installment of our carnival will open sometime during the week of December 21-25 at Math Misery? blog. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past posts and future hosts can be found on our blog carnival information page.

We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself)‌—‌if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!

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## Everyone Can Learn Math

Here’s a new video from Jo Boaler at YouCubed.org.

### Boaler’s Four Key Research-Based Messages

There is a huge elephant standing in most math classrooms, it is the idea that only some students can do well in math. Students believe it, parents believe and teachers believe it. The myth that math is a gift that some students have and some do not, is one of the most damaging ideas that pervades education in the US and that stands in the way of students’ math achievement.

—Jo Boaler
Unlocking Children’s Math Potential

### A Wealth of Resources

The YouCubed site is full of encouragement and help for families learning math.

— and plenty more!

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