Playful Math Education Carnival 147

Welcome to the 147th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing. There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle in honor of our 147th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Puzzle #147: Iva Sallay’s Great Hexahex

Iva Sallay (@findthefactors) has hosted many delightful editions of the Playful Math Carnival, including the recent #146, and she wrote a fantastic post about how to bring the carnival to your own blog:

In that post, she tells the story of a mathematical contortionist, the Great Hexahex:

Hexahex knows how to bend himself into 82 different “free” positions. He wants to stretch himself a little bit and add 65 more “one-sided” positions for a total of 147 contortions in his repertoire.

Reflections (mirror images) count as distinct “one-sided” positions if they are not mere rotations of any other position.

Below is a graphic showing those first 82 positions (and a link to download a printable version), followed by their reflections across a horizontal line. Put an X above the 17 positions in the bottom three rows that do not qualify as distinct. Then count up the remaining shapes.

You will see that Hexahex can indeed contort himself 147 ways!

Continuing Our Dodeca-versary Party

As I mentioned back in Carnival #144, this year is the 12th anniversary of the Playful Math Education Blog Carnival (originally titled Math Teachers at Play). We’ve shared so many wonderful, playful, creative math ideas through the years that I hate to lose track of them all.

Since Iva did such a wonderful job of collecting and linking to current mathy treasures in her “You Can Host” article, I decided to make this edition another blast from the past.

The posts in this 147th edition are drawn from our second year of publication. We had 12 monthly carnivals from February 2010 to January 2011, with 11 different hosts:


And now, on to the main attraction: the blog posts. If you’d like to skip directly to your area of interest, click one of these links.

Would you like to the Playful Math Carnival on your blog? We’d love to have you join us! Click for details:

Carnival Home Page

Playing with Preschool and Early Elementary Math

  • In #30, Clemencia Rosado used pennies and paperclips to practice counting in M for Math Games.

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Exploring Elementary Arithmetic

  • In #30, Michelle Martin helped her 4th- and 5th-grade students visualize large numbers in Every Vote Counts.

Learning Math Through Games

Fun with Fractions and Ratios

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Adventuring into Algebra and Geometry

Algebra Activities

Getting into Geometry

Algebra and Geometry Games

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Scaling the Slopes of High School Math

Advanced Algebra and Geometry

Cruising on to Calculus

  • In #27, Pat Ballew (@ballew_pat) stumped his pre-calc students by asking the simple question, “Given Two Points, write the equation of a line containing the two points…” but in three dimensions.

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Enjoying Recreational Puzzles and Problems

Sharing Math with Friends

  • In #29, Sol Lederman described how to impress your friends with magical math: 12 Cent Math Trick — even kids can do it!

Book Reviews

Counting, Probability, and Discrete Math

And Plenty of Puzzles

  • In #23, Toomai introduced his kids to the puzzling Rep-tiles.

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Teaching with Wisdom and Grace

Understanding Mathematics

  • In #24, Fëanor translated a delightful story in which a hapless student struggles with a challenging word problem and “Nikolai Nosov demonstrates why he is possibly the finest expositor of mathematical pedagogy in children’s literature anywhere.” Check it out: Vitya’s Maths.

Understanding Education

Homeschooling Math

  • In #29, John Golden (@mathhombre) offered guidelines for homeschoolers on choosing a math program. This post contains one of my favorite quotes on teaching: “The toughest thing for a homeschooler is the same as for a school teacher — shifting from a weak tea vision of math being grinding calculations to a rich frothy mug of math as an active way of thinking.”
  • In #24, Kendra posted tips for homeschoolers who dream of teaching elementary math without a textbook (perhaps using some of the activities and games above): Organizing a Math Lesson.

Playing in the Classroom

Teacher Tricks and Tips

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Giving Credit Where It’s Due

Carnival graphics are from The Hexahex puzzle was created by Iva Sallay.

And that rounds up this edition of the Playful Math Education Blog Carnival. I hope you enjoyed the ride!

The next installment of our carnival will cover July and August at Kelly Darke’s Math Book Magic blog. Visit our blog carnival information page for more details.

photo by Mike Licht via flickr

We need 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 Playful Math Education Blog Carnival, please speak up!

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