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**.

**Click here to find Winer’s own notes about the lesson**, along with all the puzzle handouts.

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.

## Table Of Contents

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.

**
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- Early Learning Activities
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips

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**.

**Sarah Dees**(@FrugalFun4Boys) comes up with a way to do**Sorting, Counting, and Graphing for Preschoolers**. “We were able to get in lots of counting practice and conversations about more and less and which group was the greatest. And, it kept him busy for quite awhile, which is always a good thing.”

**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…

- Writing numbers correctly is often a struggle for young kids.
**Christina Tondevold**(@BuildMathMinds) explains**How I Got My Daughter to Stop Writing 501 as 5001 in 10 Minutes**.

**Marilyn Burns**(@mburnsmath) shares counting and addition activities based on the picture book**Chrysanthemum—An Oldie but Goodie**.

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## 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.”

- How often have you found that students are taught “tricks” to remember math rules—but they still make mistakes, because the rules don’t make sense?
**Ellie Nix**(Bloglovin’)explains**Why I’m Not Teaching Decimal Operations “Rules”**.

- Old math contest problems can lead to interesting discussions.
**Mike Lawler**(@mikeandallie) and his sons dig for deeper understanding of fractions in**Two fraction problems – what a difference!**and**Dividing Fractions**.

- For my own contribution to the carnival, I’ve posted a couple of hands-on arithmetic explorations in
**A Penny for Your Math**.

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## 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…”

- I love following
**Rodi Steinig**‘s Math Circle blog posts. Her latest series explores Compass Art and touches on a variety of Euclidean geometry topics. Read the story in order:**Intro to Geometry**,**The Evolution of a Question**,**Fun with Euclid**,**More Fun with Euclid**, and**Do Ghosts Have Guts?**

**Pat Ballew**(@OnThisDayinMath) discusses five graphics from*The Puzzle Universe, A History of Mathematics in 315 Puzzles*in**Is this a Proof of the Pythagorean Theorem, and to Whom?**Have you seen these picture proofs before? Which of them make the most sense to your students?

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## Advanced Mathematical Endeavors

**Andrew Irving**and**Ebrahim Patel**(@TheBeesMaths) answer the question**“What are Complex Numbers?”**Students may also like to know**“What’s the point of a matrix?”**

**Sam Shah**(@samjshah) has his precalculus students**Playing with Blocks: Three Dimensional Visual Sequences**.

- The
**Math Curmudgeon**(@MathCurmudgeon) shares three related-rates puzzles, with related questions:**The Ladder Problem**,**The Balloon Problem**, and**The Conical Tank**.

**Ben Orlin**(@benorlin) spins a horrific yarn in**The Differentiation: A Survivor’s Tale**: “Is the Differentiation a plague, a storm, a vengeful god come to smite the wayward and the weak?”

- And don’t miss the
**128th Carnival of Mathematics**.

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## Puzzling Recreations

- Two of the
**Three J’s**have fun analyzing strategy for the**Love Letter game**.

- More games! If you’re looking for good gift ideas,
**Kansas Mom**reviews several of her favorites in**Just Playing Games: Math Games Our Family Enjoys**.

**Burkard Polster**(@Mathologer) plays around with modular multiplication in**Times Tables, Mandelbrot and the Heart of Mathematics**.

**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**.

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## Teaching Tips

- Ever wonder what exactly to do with all the math manipulatives that came with your math curriculum?
**Kate Snow**(@katesmathhelp) shares**Six Things You Need to Know About Math Manipulatives**. See also**How to use (and when to STOP using) homeschool math manipulatives**.

- 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…”

**Teri Owens**(Google+) shares the classroom game platform**Kahoot! – educational and fun – especially for reviewing**.

**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…

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## Credits

- Turkey photo by
**Teddy Llovet**via Flickr. (CC BY 2.0) - Snub dodecahedron from
**MAA Number-a-Day**. - Videos are from
**Vi Hart**.

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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