*[Photo by shonk.]*

Welcome to the ** Math Teachers At Play** blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.

Let’s start the mathematical fun with a couple of puzzles in honor of our 20th edition: First, the shape to our right is an ** icosahedron**, one of the Platonic solids. Each face is an equilateral triangle — can you count them? For more fun, make your own model.

[Graphic from Wolfram MathWorld.]A rooted tree consists of a fixed node (the circled dot) with branches growing from it. I think many of the “trees” look more like bushes, but mathematicians didn’t ask my opinion before assigning the name.

Anyway, if you have only one node, then all you have is a root, waiting to grow. Two nodes will give you the root with a single branch. With three nodes, you have two possible trees: one long branch, or two short ones. Etc.

Puzzle: How many nodes will you need in order to have 20 possible trees?

And now, on to the carnival itself. Below are a number of math-related posts, submitted by the bloggers or drawn from my overflowing blog reader, plus some suggestions for how you might contribute to our next edition, all tied together with some twists of visual humor from the FAIL Blog. Have fun browsing!

## ELEMENTARY CONCEPTS

As Liping Ma showed, there is more to understanding and teaching elementary mathematics than we often realize. Do you have a game, activity, or anecdote about teaching math to young students? Please share!

- Quirky Momma points out some sneaky Ways Your Preschooler Can Learn Through Chores.

- Ruralmama shares some real life math in Grocery Math Count.

- Tom DeRosa gives instructions for the Ultimate Number Line Game: Number Sense on a Massive Scale.

- John Golden presents an upper-elementary game (adaptable to 1st or 2nd grade) that will give your students practice on comparison and decomposition, as well as strategy and adjustment for calculation: Pick On Someone Your Own Size.

- Have you looked at Mathwire recently? They offer a great assortment of elementary math activites and games, such as Pascal’s Pumpkins and other Seasonal Topics.

## ARITHMETIC

This section is for arithmetic and number theory at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.

- Ashley Allain describes her family’s learning adventure in Just SCRATCHing the Surface of Fractions.

- Maria Miller shows us how to work Percentages with Mental Math.

- Also on the topic of percents, politicalmath explains Why Take Math? So Your Ignorance Isn’t Broadcast Nationwide on the AP Wire.

- Simon Job shares a fun video for Introducing Probability.

- I have been creating fantasy word problems lately, but my Narnia blog post isn’t quite ready to go. Instead, I’ll offer some insights on thinking through word problems. This is one of my favorite articles from the archive: Reading to Learn Math.

## BASIC ALGEBRA & GEOMETRY

Can you explain why we never divide by zero, or what is wrong with distributing the square in the expression ? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.

- Rachel Lynette presents a geometric variation on the game
*Battleship*in Symmetry Game: Guess My Grid.

- Maria Miller explains that organizing the information into a chart can be helpful when solving Mixture Problems — Algebra 1.

- Dan Greene shares a creative approach to coordinate graphing in XKCD Based Lesson: The Coordinate Plane.

- Dave Marain offers geometry and exponent puzzlers in The Return of the WarmUp Challenges!

- Zac links to a “real-world math tutorial” for algebra students: Calculating Takeoff Speeds.

## ADVANCED MATH

Like most adults, I have forgotten enough math to fill several textbooks. I’m eager to learn again — but math books can be so-o-o tedious. Can you make upper-level math topics come alive, so they will stick in my (or a student’s) mind?

- Jonathan challenges his class with More Puzzle Extension: Expressing n as the Sum of Consecutive Integers.

- Mr. Sweeney revises a James Bond scenario in Sick of Security Camera Problems.

- Khalid Azad clears up students’ confusion with A Visual, Intuitive Guide to Imaginary Numbers.

- The 59th Carnival of Mathematics features 59 blog posts (counting the multi-part posts and the carnival post itself) on a wide variety of interesting topics.

## MATHEMATICAL PUZZLES

Recreational mathematics has a long and fascinating history. What kind of math do you do, just for the fun of it?

- MiaZagora plays around with logic in Word Puzzle Wednesday.

- John Cook wonders about Counterfeit Coins and Rare Diseases.

- Tanya Khovanova has some fun with assumptions in Hassan’s Horses.

- 10-Minute Math cooks up a puzzle: The Cone Problem.

- Exercise your mind daily with a problem from the American Mathematics Competitions (AMC-8, AMC-10, or AMC-12) at MAA Minute Math.

## ABOUT TEACHING MATH

Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

- Brent Yorgey recommends Logicomix: An Epic Search for Truth.

- Kate Novak offers some guidance for Building a Better Worksheet.

- Jackie comes up with a creative way to check her students’ understanding of vocabulary in Formative Assessment?

- Dan Meyer passes on the cautionary tale of Clever Hans: “Take-home lesson: never underestimate your ability to fool yourself into believing your students understand something when really what they are doing is watching you.”

And that rounds up this edition of the ** Math Teachers at Play** carnival. I hope you enjoyed the ride. The next installment of our carnival will open on December 18th. 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 index 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!

Claim your two free learning guide booklets, and be one of the first to hear about new books, revisions, and sales or other promotions.

Denise,

how do I submit a blog to you for the next carnival? thanks. here is my email add. gpbautista1@gmail.com.

Check the end of the post above. We always tell how to submit a post to the next carnival. You can go to the blog carnival index page and click “Submit” in the sidebar, or you can use the handy submission form link.