*[Feature photo by Tomruen via Wikimedia Commons.]*

Do you enjoy math? I hope so! If not, browsing the articles linked in this post just may change your mind.

Welcome to the 85th edition of the ** Math Teachers At Play** math education blog carnival—a 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.

By tradition, we start the carnival with a short puzzle or activity. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Let the mathematical fun begin!

## TRY THIS PUZZLE

In honor of our 85th edition, I present: the *centered triangular numbers.*

You can build centered triangles with stones in a sandbox, or with any small manipulative that won’t roll away. Like all figurate numbers, the centered triangles start with the number one: a single stone. Imagine this as a triangle with a stone at each corner and sides of length zero.

Around this, you build the next triangle, which has 2 stones on each side. The sides are one unit long. Four stones in all, so the second centered triangular number is 4.

Then build a 3-stones-per-side triangle centered around that. Each new side is 2 units long, and we’ve used a total of 10 stones so far. The third centered triangular number is ten.

Keep building triangles centered around each other, each with one more stone per side. Each triangle’s sides are one unit longer than the sides of the triangle just inside it.

- 85 is a centered triangular number. How many triangles will you need to use up 85 stones? (Don’t forget to count the first stone as a triangle.)
- Can you find a pattern in the numbers?
- What other centered polygon shapes can you build?
- High school students: Can you find an equation to fit the pattern?

## 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.

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

And since I’ve been in a bookish mood lately, each section includes a link to one of my favorite under-appreciated (5 reviews or fewer) math book. The covers link to Amazon.com, where I get a few cent’s commission if you actually buy something—but you should be able to borrow all these books through your local library or library loan system.

## EARLY LEARNING ACTIVITIES

*Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers* by Alexander Zvonkin

This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s—what he tried, what worked, what failed, but most important, what the kids experienced.

- Phil Rowlands (@Help_Your_Child) explains that play is fundamental to ensuring young children learn effectively and discusses the Cuisenaire rod maniulatives.

- Thomas Hobson (@TheTeacherTom) slows down to model “safe and proper woodworking procedures” while the children keep track—debating, frequently recounting, always rearranging, stacking, building, making patterns.

- Tracy Zager (@TracyZager) creates an opportunity for kindergarten kids to play with body-scale number lines, records what happens, and wonders how to make it better. Lots of great comments here.

- Julie (@jmommymom) finds patterns and shapes in a circular grid: Creative Math Art for Kindergarten.

- Pam Odd (@pameladonnis) introduces her children to one of her childhood favorite craft activities in Reinforcing Math Concepts with Picture Pie.

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## ELEMENTARY EXPLORATION AND MIDDLE SCHOOL MASTERY

*More Math Games & Activities from Around the World* by Claudia Zaslavsky

Math, history, art, and world cultures come together in this delightful book for kids, even for those who find traditional math lessons boring. More than 70 games, puzzles, and projects encourage kids to hone their math skills as they calculate, measure, and solve problems.

- Joe Schwartz (@JSchwartz10a) and students puzzle over how to count from 6 to 8.

- Joshua Greene (@JoshuaGreene19) and son find math in the trash, with a nudge or two from Grandma.

- Kristin Gray (@MathMinds) seeks understanding after her students uncover something she never learned.

- Julie (@jmommymom) and family read the math fairy tale book
*The Man Who Counted: A Collection of Mathematical Adventures*and try their hand at the Four 4s challenge.

- Spencer Olmsted’s class is on fire with math patterns. “It’s a wonderful thing to connect a physical model, the ordered pairs that describe it, and a graph—it’s practically poetry.”

- And for my own (@letsplaymath)contribution to the carnival, here’s a math-and-strategy card game from British mathematician Henry Dudeney’s classic book,
*The Canterbury Puzzles.*

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## ADVENTURES IN BASIC ALGEBRA & GEOMETRY

Mathematical Cavalcade by Brian Bolt

This collection of puzzles, games and activities is designed to stimulate and challenge people of all ages who enjoy puzzles with a mathematical flavor. The second part of the book contains a commentary giving hints and solutions.

- Stephen Cavadino (@srcav) says, “I love it when my student talk maths well, and this post looks at an interesting discussion my year 9s had on perimeter.”

- Tina Cardone (@crstn85) gets a seasonal reminder that extended wait time and letting kids ask us for help rather than continuing the conversation as soon as they have responded really does work.

- Bridget Dunbar (@BridgetDunbar) uses Fawn Nguyen’s Visual Patterns website to help her students understand finding the constant rate of change between two points.

- Bryan Anderson (@Anderson02B) begins a series of linear pattern challenge posts: Linear Patterns 180.

- Mrs. E (@MrsETeachesMath) diagrams the relationships in the Quadrilateral Family Tree. “Just like all families, they have some issues, however, they all get along and are happy together.”

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## ADVANCED MATHEMATICAL ENDEAVORS

*A Decade of the Berkeley Math Circle: The American Experience* by Zvezdelina Stankova, Tom Rike

A wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik’s cube and abstract algebra… Also features 300 problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions.

- Manan Shah (@shahlock) relates what he really learned in Calculus class, aside from Calculus, in Pigeonholed: What’s Your Major?

- Dan MacKinnon (@mathrecreation) uses The Geometer’s Sketchpad to construct patterns through iteration. Working through how to build iterations helps teach basic principles of geometric construction as well as more advanced ideas (self similarity, limits).

- Bob Lochel (@bobloch) develops a new perspective on imaginary numbers. “The bulbs have gone off. I GET this now! What I appreciate most here is that we don’t need to wait until deep into algebra 2 to think about the imaginary unit.”

- Michael Fenton (@mjfenton) offers a Polar Graphing Sorting Activity to help students establish some connections between polar and Cartesian forms.

- Have you ever wondered where Euler’s Formula comes from? See how arithmetic, geometry, trigonometry, and calculus dance together on the complex plane to create mathematical beauty.

- And don’t miss the Carnival of Mathematics #121.

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## PUZZLING RECREATIONS

The Universe in a Handkerchief: Lewis Carroll’s Mathematical Recreations, Games, Puzzles, and Word Plays by Martin Gardner

Puzzles and paradoxes from Lewis Carroll, the author of Alice in Wonderland, whose interests ranged from inventing new games like Arithmetical Croquet to important problems in symbolic logic and propositional calculus. Written by Carroll expert and well-known mathematics author Martin Gardner.

- Joel David Hamkins shares a new booklet of Math for eight-year-olds: graph theory for kids. Download, print, explore, and enjoy!

- Sam Blanco (@SamBlancoBCBA) reviews a strewable puzzle resources for upper-elementary and middle school kids (and adults!): Visual Brainstorms.

- Samantha Oestreicher (@SamanthaOestrei) applies the measuring rod of mathematics to the world of books and their movies: An Unexpectedly Long Journey.

- Mike Lawler (@mikeandallie) and sons investigate how scaling affects area and perimeter in a variation of The “rope around the Earth” problem.

- Mario Livio (@Mario_Livio) leads NOVA viewers on a mathematical mystery tour—an exploration of math’s astonishing power across the centuries. Is math a human invention or the discovery of the language of the universe?

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## TEACHING TIPS

*Common Core Math For Parents For Dummies* by Christopher Danielson

Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math.

- Stephen Cavadino (@srcav) points out how a new textbook nearly ruins a nice puzzle: A missed opportunity?

- Sue VanHattum (@suevanhattum) reports the first sighting of her book,
*Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers*. Have you ordered your copy yet?

- Jennifer Smith (@4mulaFun) discusses several techniques you can use to help children review and understand what they write in their notebooks.

- Several authors at Heinemann Publishing (@HeinemannPub) unpack, examine, and reflect on the Standards for Mathematical Practice and how they can help students grow into confident, proficient mathematicians.

- Ben Orlin (@benorlin) ponders The Math Ceiling: Where’s your cognitive breaking point? and sets off a storm of thought-provoking comments.

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## LOOKING AHEAD

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 sometime during the week of May 25-29 at ZenoMath. 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 volunteers for the fall semester. 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!