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!

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?

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.

**Click to tweet:** Math Teachers at Play #85: a smorgasbord of great ideas for learning, teaching, and playing around with math.

*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.

[Back to top.]

[Back to Table of Contents.]

*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.*

[Back to top.]

[Back to Table of Contents.]

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.”

[Back to top.]

[Back to Table of Contents.]

*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.

[Back to top.]

[Back to Table of Contents.]

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?

[Back to top.]

[Back to Table of Contents.]

*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.

[Back to top.]

[Back to Table of Contents.]

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!

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

]]>

Are you tired of flashcards and repetitive worksheets? Now your children can practice their math skills by playing games.

Math games pump up mental muscle, reduce the fear of failure, and develop a positive attitude toward mathematics. Through playful interaction, games strengthen a child’s intuitive understanding of numbers and build problem-solving strategies. Mastering a math game can be hard work, but kids do it willingly because it is fun.

*Counting & Number Bonds* features 21 kid-tested games, offering a variety of challenges for preschool and early-elementary learners. Young children can play with counting and number recognition while they learn the basic principle of good sportsmanship, to respond gracefully whether they win or lose. Older students will explore place value, build number sense, and begin practicing the math facts.

Buy now at:

- Amazon.com
- Amazon.uk
- Amazon.ca
- Amazon.au
- and all the other Amazons worldwide

*Addition & Subtraction* features 22 kid-tested games, offering a variety of challenges for elementary-age students. Children will strengthen their understanding of numbers and develop mental flexibility by playing with addition and subtraction, from the basic number facts to numbers in the hundreds and beyond. Logic games build strategic thinking skills, and dice games give students hands-on experience with probability.

Buy now at:

- Amazon.com
- Amazon.uk
- Amazon.ca
- Amazon.au
- and all the other Amazons worldwide

You don’t need a Kindle device to read Amazon ebooks. Click here to download the Kindle program for your computer, phone, or tablet.

For those of you who prefer to buy ebooks from iTunes, Barnes & Noble, Kobo, etc.—those versions are coming soon! The epub book format takes a bit more work, but I’m hoping for time to finish it up within a week or so.

Paperback editions are also in the works.

Featured photo above by Richard Riley via Flickr (CC BY 2.0).

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

]]>

Lay out the ace to six of each suit in a row, face up and not overlapping, one suit above another. You will have one column of four aces, a column of four twos, and so on—six columns in all.

The first player flips a card upside down and says its number value. Players alternate, each time turning down one card, mentally adding its value to the running total, and saying the new sum out loud. The player who exactly reaches thirty-one, or who forces the next player to go over that sum, wins the game.

For a shorter game, use only the ace to four of each suit. Play to a target sum of twenty-two.

Thirty-One comes from British mathematician Henry Dudeney’s classic book, *The Canterbury Puzzles*. According to Dudeney, “This is a game that used to be (and may be to this day, for aught I know) a favourite means of swindling employed by card-sharpers at racecourses and in railway carriages.”

Dudeney challenges his readers to find a rule by which a player can always win: “Now, the question is, in order to win, should you turn down the first card, or courteously request your opponent to do so? And how should you conduct your play?”

Dudeney, H. E. *The Canterbury Puzzles,* Thomas Nelson and Sons, 1919 (originally published 1907); available at Project Gutenberg or the Internet Archive.

http://www.gutenberg.org/ebooks/27635

https://archive.org/details/canterburypuzzle00dudeuoft

This post is an excerpt from my book *Addition & Subtraction: Math Games for Elementary Students*, coming this spring to bookstores all over the Internet.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

]]>

It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our *Math Teachers at Play* (MTaP) math education blog carnival.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

**Don’t procrastinate:** *The deadline for entries is next Monday, April 20 extended to Friday, April 24.* The carnival will be posted at … Well, we don’t have a host yet. Would you like to volunteer?

**Click to tweet about the carnival.**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog. If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

]]>

**Math Concepts:** counting up to five, thinking ahead.

**Players:** two or more.

**Equipment**: none.

Each player starts with both hands as fists, palm down, pointer fingers extended to show one point for each hand. On your turn, use one of your fingers to tap one hand:

- If you tap an opponent’s hand, that person must extend as many extra fingers on that hand (in addition to the points already there) as you have showing on the hand that tapped. Your own fingers don’t change.

- If you force your opponent to extend all the fingers and thumb on one hand, that makes a “dead hand” that must be put behind the player’s back, out of the game.

- If you tap your own hand, you can “split” fingers from one hand to the other. For instance, if you have three points on one hand and only one on the other, you may tap hands to rearrange them, putting out two fingers on each hand. Splits do not have to end up even, but each hand must end up with at least one point (and less than five, of course).

- You may even revive a dead hand if you have enough fingers on your other hand to split. A dead hand has lost all its points, so it starts at zero. When you tap it, you can share out the points from your other hand as you wish.

The last player with a live hand wins the game.

**House Rule:** Do you want a shorter game? Omit the splits. Or you could allow ordinary splits but not splitting fingers to dead hands.

**Nubs:** All splits must share the fingers evenly between the hands. If you have an odd number of points, this will leave you with “half fingers,” shown by curling those fingers down.

**Zombies:** (For advanced players.) If a hand is tapped with more fingers than are needed to put it out of the game, it comes back from the dead with the leftover points. For instance, if you have four fingers out, and your opponent taps you with a two-finger hand, that would fill up your hand with one point left over. Close your fist, and then hold out just the zombie point. In this variation, the only way to kill a hand is to give it exactly five points.

Finger-counting games are common in eastern Asia—and they must be contagious, since my daughters caught them from their Korean friends at college. Middle school teacher Nico Rowinsky shared Chopsticks (which is simpler than the version my daughters brought home) in a comment on the “Tiny Math Games” post at Dan Meyer’s blog.

This post is an excerpt from my book *Counting & Number Bonds: Math Games for Early Learners*, coming this spring to bookstores all over the Internet.

]]>

The April “Let’s Play Math” newsletter went out Monday morning to everyone who signed up for Tabletop Academy Press math updates. If you’re not on the mailing list, you can still join in the fun:

And remember: Newsletter subscribers are always the first to hear about new books, revisions, and sales or other promotions.

Math Snack: Math Treks

Playful, no-preparation math activities for all agesCreated by Maria Droujkova, a Math Trek is a “virtual reality” game, played at the intersection between the real world and your imagination. Participants explore their towns and communities, start noticing mathematics everywhere, and grow their math eyes.

Math Treks are like scavenger hunts for math. Gather a group of friends, choose a topic, and go for a walk to see how much math you can find. Take pictures to share and compare. My math club families have enjoyed a Multiplication Trek (looking for things in groups and arrays) around our local library and a Symmetry Trek through the woods.

If you have time for a little preparation, Maria posted several Math Trek game sheets you can download and print. …

]]>

Six years ago, my homeschool co-op classes had fun creating this April calendar to hand out at our end-of-semester party. Looking at my regular calendar today, I noticed that April this year starts on Wednesday, just like it did back then. I wonder when’s the next time that will happen?

A math calendar is not as easy to read as a traditional calendar — it is more like a puzzle. The expression in each square simplifies to that day’s date, so your family can treat each day like a mini-review quiz: “Do you remember how to calculate this?”

The calendar my students made is appropriate for middle school and beyond, but you can make a math calendar with puzzles for any age or skill level. Better yet, encourage the kids to make puzzles of their own.

**At home:**

Post the calendar on your refrigerator. Use each math puzzle as a daily review “mini-quiz” for your children (or yourself).

**In the classroom:**

Post today’s calculation on the board as a warm-up puzzle. Encourage your students to make up “Today is…” puzzles of their own.

**As a puzzle:**

Cut the calendar squares apart, then challenge your students to arrange them in ascending (or descending) order.

If you like, you may use the following worksheet:

Submission details here: Kids’ Project — More Math Calendars?

]]>

**But Before You Go…**

I’m running out of carnival hosts! Would you like to volunteer? It’s a bit of work, but great fun, too. Leave a comment here, or send me an email.

**Excerpt:**

Welcome to the 84th Math Teachers at Play Blog Carnival!

84 is a portentous number. It’s the sum of twin primes (What’s the previous sum of twin primes? Next?). It’s thrice perfect, twice everything. It’s positively Orwellian. It’s even a town in Pennsylvania.

84 puzzler 1:

Number the intersections of these five circles with the integers 1 to 20 so that the points on each circle sum to the same.It was a good month for math reading related posts …

]]>

**Please Note:** We need volunteers to host future carnivals! See below for more information.

If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s *Math Teachers at Play* (MTaP) math education blog carnival.

- Click here to submit your blog post.
- Browse all the past editions of the
*Math Teachers at Play*blog carnival

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

**Don’t procrastinate:** *The deadline for entries is this Friday, March 20.* The carnival will be posted next week at Math Hombre.

**Click to tweet about the carnival.**

(No spam, I promise! You will have a chance to edit or cancel the tweet.)

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

**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!**Arithmetic/Pre-Algebra:**This section is for arithmetic lessons and number theory puzzles at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.**Beginning Algebra and Geometry:**Can you explain why we never divide by zero, how to bisect an angle, 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.**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?**Mathematical Recreations:**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!

We need more hosts! Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog.

If you think you’d like to join in the fun, read the instructions on our Math Teachers at Play page. Then leave a comment or email me to let me know which month you’d like to take.

While you’re waiting for next week’s *Math Teachers at Play* carnival, you may enjoy:

- Last month’s Math(s) Teachers at Play – 83rd Edition
- Carnival of Mathematics
- Carnaval de Matemáticas

]]>

]]>

- the Happy Birthday, Einstein! video series
- Happy Birthday, Einstein (Part 2)
- Happy Birthday, Einstein (Part 3)
- Happy Birthday, Einstein (Part 4)
- Albert Einstein’s math biography
- Math-related quotes from Albert Einstein

]]>

An extra note from Dr. Grime: “Since pi39 ends in 0, you may think we could use pi38 instead, which has even fewer digits. Unfortunately, the rounding errors of pi38 are ten times larger than the rounding errors of pi39 — more than a hydrogen atom. So that extra decimal place makes a difference, even if it’s 0.”

]]>

Do you have a favorite family activity for celebrating Pi Day? I’d love to hear it!

]]>

Unending digits …

Why not keep it simple, like

Twenty-two sevenths?—Luke Anderson

Encourage your students to make their own Pi Day haiku with these tips from *Mr. L’s Math*:

And remember, Pi Day is also Albert Einstein’s birthday! Check out this series of short videos about his life and work: Happy Birthday, Einstein.

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Luke Anderson, via TeachPi.org. Background photo courtesy of Robert Couse-Baker (CC BY 2.0) via Flickr.

]]>

Hat tip: Singing Banana.

]]>