# Math Teachers at Play #20

[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!

• 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.

## 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.

• 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 $\left(a + b \right)^2$? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.

## 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?

• 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?

## 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!

• 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!

## 7 thoughts on “Math Teachers at Play #20”

1. Pingback: Weekend miscellany
2. 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.

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