Welcome to the 144th 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 would start the carnival with a puzzle/activity in honor of our 144th edition. But this time, I want to take a peek back at the history of our carnival.

But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

## 12 Years of Playful Math

144 is a perfect square — 12^{2} to be exact. And since this month marks exactly 12 years since the Playful Math Education Blog Carnival began, it seems like a perfect time to remember where we came from.

In February 2009, I posted the inaugural edition of the Math Teachers at Play blog carnival. At first, the carnival appeared biweekly, but we soon switched to our current once-a-month schedule.

#### Why Create a Blog Carnival?

It was the heyday of blog carnivals, and the Carnival of Mathematics was going strong at issue #49.

I really did (and still do) enjoy the Carnival of Mathematics, most of the time, but I had to admit that many of the posts went right over my head. And my middle-school level contributions often felt out of place (to me, at least), like toddlers at a high society cocktail party. On the other hand, the more general edu-blog carnivals (which have since died away) had grown so large it was nearly impossible to browse all their posts.

So I wanted something smaller and more “relevant” — more tightly targeted to my interests. And not finding the type of blog carnival I wanted, I decided to create it.

I’ve been delighted at how the online math community rallied to support the carnival. Without our wonderful volunteer hosts, the Math Teachers at Play/Playful Math Education Carnival would have perished long ago.

#### Our First Year

The posts in this 144th edition are drawn from our first year. We had 22 carnivals, with 11 different hosts:

- As the carnival founder, I hosted #1, #2, #5, #8, and #20.
- Kate Nowak (@k8nowak) jumped on board to host #3.
- Homeschooler Misty hosted #4, #7, and #9.
- Tom DeRosa hosted #6 and #16.
- Maria Miller hosted #10 and #15(a). Yes, there’s a story behind the latter number.
- Sue VanHattum (@suevanhattum) hosted #11, #14, #19, and #21. And solved the Mystery of the Mixed-Up Numbers (see Carnival 19).
- Jason Dyer (@jdyer) hosted #12.
- Heather Woodie (@HeatherBSW) hosted #13.
- Maria Droujkova (@MariaDroujkova) hosted #15(b).
- Dan Mackinnon (@mathrecreation) hosted #17 and created the beautiful title graphic below.
- John Golden (@mathhombre) wrapped up our first year with #22.

Some of these articles have been lost to the sands of time (I particularly miss Kate’s and Misty’s blogs), but I’ve recovered what I could with the help of the Internet Archive’s Wayback Machine.

As you browse the articles below, whenever you find one you enjoy, do take time to explore the blogger’s other posts. There’s a wealth of mathy goodness to be found on these old sites!

## Contents

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.

- Playing with Preschool and Early Elementary Math
- Exploring Elementary Arithmetic
- Adventuring into Algebra and Geometry
- Scaling the Slopes of High School Math
- Enjoying Recreational Puzzles and Math Art
- Teaching with Wisdom and Grace
- Giving Credit Where It’s Due

Would you like to host next month’s Playful Math Carnival on *your *blog? We’d love to have you join us! Click for details:

## Playing with Preschool and Early Elementary Math

- In #8, a homeschooling headmistress shared several great ideas about teaching math to young children: Math the Play Way.

- In #15(a), Toomai introduced a kindergarten class to research mathematics: Sequences and Creative Math for Kindergartners.

- Then in #17, David Richeson (@divbyzero) put together a great list of activities in Kindergarten Mathematics. [Follow-up post here.]

- In #14, Maria Miller described a simple, playful way to Learn to Recognize Coins.

- In #21, homeschooler Kendra and her sons played with estimation after reading the book Counting on Frank.

- In #8, Jimmie Lanley staged a shopping trip to let her daughter play around with Hands-on Estimating.

- In #15(b), I explored several thinking strategies for Mental Math: Addition.

#### Games for Early Math Topics

- In #5, Tanya Khovanova posed a few Subtraction Problems, Russian Style. Fun!

- In #9, Maria Miller introduced the 10-Out card game.

- In #12, homeschooler Kendra invented a Clock Game.

- And in #17, Kendra played around with making change: Piggy Bank Math Game.

- In #13, John Golden (@mathhombre) shared a fun Shel Silverstein poem and two Money Games.

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## Exploring Elementary Arithmetic

- In #2, I posted a quick puzzle that works with almost any grade level: Math Warm-Up: Today is February 4 x 3 x 2 x 1.

- In #3, Cassy Turner (@Cassyt) explained how to use Number Strings
*without numbers.*

- In #1, Dave Marain (@dmarain) asked Was the First Super Bowl More or Less Than a BILLION Seconds Ago?

- In #3, Pagetutor demonstrated What A Trillion Dollars Looks Like. Like, in cash money. Stacked on pallets.

- In #21, I showed how to use diagrams to solve 4th grade story problems.

#### Mastering Multiplication

- In #8, David Van Couvering (@dcouvering) wrote about times table stars: Now THAT is the way to learn math.

- In #6, Jason Dyer (@jdyer) created a puzzle with Hot Dogs and Buns (Least Common Multiple).

- In #14, Jimmie Lanley posted resources for Living Math with Factors, Multiples, and Primes.

- In #2, Mathmom recounted her students’ adventure in factoring: Numbers with exactly four factors.

- In #9, Heather Lewis began to explore The First Bunch of Ways to Multiply. [You can find the whole list at 25+ Ways to Multiply.]

- In #15(b), John Cook (@JohnDCook) discussed a prime-numbers conjecture that’s Easy to guess, hard to prove — and accessible to children.

#### Learning Math Through Games

- Also in #11, John Golden (@mathhombre) played with measurement, dice, and a bit of strategy in Michigan Smith (cousin to Indiana Jones, doncha know).

- Then in #14, John was Running Out of Options.

- And in #20, John playtested Pick On Someone Your Own Size.

- Also in #20, Tom DeRosa described his Ultimate Number Line Game: Number Sense on a Massive Scale.

- In #22, I hosted the annual Mathematics Game. It’s a great way to build flexible number skills, and it’s new every year!

#### Tackling Tougher Topics

- In #13, Jimmie Lanley and her daughter built Platonic Polyhedra.

- In #16, I shared a challenging research question: Do Your Students Understand Division?

- Then in #20, I offered some insights on thinking through word problems: Reading to Learn Math.

- In #11, Tony Cookson (@prof_cookson) explored department store discounts: 30-20-10 Pricing.

- In #15(a), Tom DeRosa posted a real-life Erasing Debt Activity with a printable activity sheet.

- In #4, Maria Miller demonstrated how to teach Division of fractions conceptually.

- In #13, Pat Ballew (@ballew_pat) discussed the common-denominator approach to fraction division: Ours is Not to Reason Why, Just Flip and Multiply.

- And in #16, Pat reflected on Student Confusion about Order of Operations.

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## Adventuring into Algebra and Geometry

#### Algebra Activities

- In #10, Jeff Goldstein (@doctorjeff) asked What Can You Do With a Humongous Piece of Xerox Paper? You probably won’t believe the answers!

- In #19, I tackled a tough word problem: Algebra: A Problem in Translation.

- In #4, Jon Ingram shared Ten 16th century word problems from
*The Whetstone of Witte*, the first book on algebra ever published in English. [You may have to scroll down for the puzzles. The Wayback Machine recovered the article, but the page formatting lookes broken.]

- In #20, Maria Miller explained how to use a chart when solving Mixture Problems.

- In #1, Dan Wekselgreene (@dwekselgreene) posted a puzzle worksheet for Factoring Trinomials.

- In #14, Sam Shah (@samjshah) opined about quadratics: Factoring, Schmactoring.

- In #19, Bert Speelpenning discussed the value of Deferred Computation – the Pythagorean Spiral.

- In #13, Matthew Bardoe (@BardoeMatthew) demonstrated Visualizing Numbers Real and Imaginary.

- And in #20, Khalid Azad (@betterexplained) did the same thing in much more depth: A Visual, Intuitive Guide to Imaginary Numbers.

#### Angles and Graphs

- In #20, Jackie Ballarini (@JackieB) came up with a creative way to check her students’ understanding of angle vocabulary in Formative Assessment?

- In #7, Jason Dyer (@jdyer) suggested an open-ended discussion about the Plat Diviseur.

- In #16, John Golden (@mathhombre) discussed teaching about Angles.

- In #7, Pat Ballew (@ballew_pat) played with words: Left Angles and Language Reversals.

- In #20, Dan Wekselgreene (@dwekselgreene) created an XKCD Based Lesson: The Coordinate Plane.

- Then in #22, Dan explored Representations of Linear Equations.

#### Geometry Games

- In #20, Rachel Lynette shared a Symmetry Game: Guess My Grid.

- In #19, John Golden (@mathhombre) created the Blokus-style Area Block game.

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## Scaling the Slopes of High School Math

#### Advanced Algebra and Geometry

- In #8, Brent Yorgey explained the Babylonian method to calculate Square roots with pencil and paper.

- In #7, John Cook (@JohnDCook) connected Fibonacci and geometric sequences.

- And in #15(a), John asked What is the shape of the Earth?

- In #2, Pat Ballew (@ballew_pat) wondered Why Bother with Vectors?

- Then in #3, Pat discussed the centroid: Just an Average Point.

- And in #12, Pat explored a A Mandelbrot-like Set for Quadratics.

- And then in #19, Pat offered Notes on Cyclic Quadrilaterals.

#### Trigonometry

- In #16, Sue VanHattum (@suevanhattum) played trig improv in The Joy of Tutoring.

- In #9, John Golden (@mathhombre) created Trig Rummy.

- In #16, John Cook (@JohnDCook) asked How many trig functions are there?

- In #20, Mr. Sweeney revised a James Bond scenario in Sick of Security Camera Problems.

#### Calculus

- In #8, Robert Talbert (@RobertTalbert) shared Four things I used to think about calculus, and what I’ve replaced them with.

- In #21, Pat Ballew (@ballew_pat) had Fun with Parabolas in Calculus.

- In #5, Sam Shah (@samjshah) offered a valuable problem-solving mantra: Take what you don’t know…

- In #21, Brent Yorgey explained a proof that pi is irrational, which he thought calculus students should be able to follow.

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## Enjoying Recreational Puzzles and Math Art

#### Crafts and Math Art

- In #1, Heather Lewis constructed A Pop-Up Sierpinski Valentine Card. (Bookmark it to try with your students next year.)

- In #2, Jason Dyer (@jdyer) challenged us to spot An Ancient Typo in some Chinese math art.

- In #13, Dan Mackinnon (@mathrecreation) created geometrical window patterns with Post-It notes.

- In #14, John Golden (@mathhombre) explained how to create One Page Wonder, a storybook that can be read in lots of different orders, like some weird form of poetry.

- Also in #14, Dan Mackinnon (@mathrecreation) examined origami and its mathematical side. An older post of his on Sonobe units also looks helpful.

- In #21, Rachel Lynette made a DIY Soma Cube puzzle. (It would make a great gift!) You may also enjoy the History of Soma Cube website, which includes plenty of puzzles.

- In #9, Pat Ballew (@ballew_pat) shared two optical illusions Fool me once, Fool me Everytime? I’m amazed how strong the second one is, even
*with*the circle in place.

- Then in #10, John Cook (@JohnDCook) discussed an amazing Optical illusion, mathematical illusion.

- In #11, Mike Croucher (@walkingrandomly) experimented with Wheels on Wheels on Wheels — a spirograph extravaganza.

#### Poetry and Stories

- In #4, Sue VanHattum (@suevanhattum) presented Math Salons and Base Eight.

- And in #22, Sue challenged us to Write a Kids’ Poem about Math. [Note: The missing image probably contained this poem.]

- Also in #22, John Golden (@mathhombre) asked his class to write a number that, when you say it out loud properly, has haiku form. One possibility: 22,220,220.

- In #6, Vlorbik wrote a Calculus Poem.

- Then in #17, Travis posted Calculus Haiku – The Derivative.

- In #15(b), Pat Ballew (@ballew_pat) told the story of Pi and the 47 Ronin. 300 years later, the incense is still perpetually burning.

#### Book Reviews

- In #17, Sue VanHattum (@suevanhattum) commented on Seymour Papert’s Mindstorms: Children, Computers, and Powerful Ideas.

- Also in #17, Tom DeRosa enjoyed Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin.

- In #19, Jim Holt reviewed a comic book about the quest for logical certainty in mathematics. And in #20, Brent Yorgey liked it, too: Logicomix: An Epic Search for Truth.

- In #22, Antonio Cangiano interviewed Derrick Niederman, author of Number Freak.

- In #19, Tanya Khovanova discussed The Geometric Transformations and shared sample puzzles.

- Also in #19, Dan Mackinnon (@mathrecreation) dug into math history with Mathematics in Ancient Iraq: A Social History.

#### Counting, Probability, and Discrete Math

- In #13, Tom DeRosa collected resources for Discrete Math for the High School Classroom (and Part 2).

- And in #14, Tom shared 3 fun probability games and projects.

- In #5, Brent Yorgey challenged his readers to try Distributing cookies and explained four possible solutions.

- In #14, Jonathan Halabi (@Jd2718x) posed a tricky counting puzzle.

- And in #20, Jonathan described how his class throught through Expressing n as the Sum of Consecutive Integers.

- In #22, Pat Ballew (@ballew_pat) played around with Lotteries and Math.

#### And Plenty of Puzzles

- In #20, Tanya Khovanova had some fun with assumptions in Hassan’s Horses.

- In #22, Lee Bradley issued a Pieces of Eight number challenge.

- In #21, Sue VanHattum (@suevanhattum) made a puzzle: Holiday Logic.

- And in #22, Sue posed several questions about Pythagorean Triples.

- In #8, Jeff Trevaskis (@webmaths) shared the puzzle of 4 Buried Soldiers.

- In #1, Tanya Khovanova translated Five Linguistics Puzzles from the Russian book
*200 Problems in Linguistics and Mathematics*.

- Then in #2, Heather Lewis followed Tanya’s post with Language Puzzles, Part II.

- In #11, Jonathan Halabi (@Jd2718x) posted 5 challenging logic puzzles and talked about how to use them with students.

- In #14, Tanya Khovanova presented a group of puzzles and explained the concept of ‘revealing coefficient’, in her post titled Unrevealing Coin Weighings.

- In #4, Praveen Puri (@PuriConsulting) asked What’s the Chance That the Patient Has the Disease?

- In #14, Chad Orzel (@orzelc) offered an estimation contest; Mary O’Keefe analyzed the contest, first in terms of winner’s curse, and then in terms of information cascades. Sue VanHattum chimed in with tips for improving your estimation skills. The contest’s over, but the posts are still fun.

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## Teaching with Wisdom and Grace

#### Understanding Mathematics

- In #17, Alison Blank put together an inspired and inspiring Prezi presentation: Math is Not Linear.

- In #14, Marcus du Sautoy (@MarcusduSautoy) explored The secret life of numbers.

- In #11, Sue VanHattum (@suevanhattum) pondered how Math is Like Mountain Climbing.

- Also in #11, Dan Mackinnon (@mathrecreation) posted a series on Metaphors and Mathematics. Here are Part 2 and Part 3.

- In #8, Pat Ballew (@ballew_pat) discussed Logic Diagrams, A Brief History.

#### Homeschooling Math

- In #2, Mama Squirrel shared her family’s long Journey Through Miquon Math.

- In #5, I described how we use Buddy Math, which works with almost any math program.

- In #8, Heather Woodie (@HeatherBSW) explained how she uses Math Journaling.

- Also in #8, Child’s Play played with the mathematics of circles: Trampoline Math.

#### Playing in the Classroom

- In #21, Jonathan Halabi (@Jd2718x) got his students thinking with “What’s a question that someone else might get wrong?”

- In #17, Kate Nowak (@k8nowak) introduced Speed Dating for classroom review.

- And in #22, Kate shared her method For Your Low Tech Non-Clicker-Having, Non-Polleverywhere, Formative Assessment Needs.

- In #21, Riley Lark (@rileylark) described his no-prep Bag of Tricks #1 — Index Cards.

- Also in #21, Dan Wekselgreene (@dwekselgreene) explained how he adapts the Review game: Trashketball to keep lower-skilled students involved.

#### Continuing Our Own Education

- In #20, Kate Nowak (@k8nowak) offered guidance for Building a Better Worksheet. [I hadn’t heard of Pizzazz-type puzzles: Chose a book, click sample pages.]

- Also in #20, Dan Meyer (@ddmeyer) shared a link to Ben Blum-Smith’s (@benblumsmith) cautionary tale of Clever Hans: Required Reading for Math Teachers. “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.”

- In #12, Casey described what it’s like Living with Dyscalculia.

- In #19, Jason Dyer (@jdyer) explored students’ trouble with reading in “When vocabulary isn’t the issue” and “A reading experiment“. The puzzle given in that second post looks fun!

- In #10, Rick Regan (@DoctorBinary) compared teaching approaches when he taught his mother binary numbers.

- In #14, John Golden (@mathhombre) gave an introduction to Polya and emphasized the cyclical nature of problem-solving. [The PDF link is broken, but I found the article here.]

- In #2, Sam Shah (@samjshah) asked calculus teachers, How do you introduce integrals?

- In #15(b), Tom DeRosa presented his 52 Teachers, 52 Lessons Project. He never made it all the way to 52, but still worth reading.

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## Giving Credit Where It’s Due

Math Teachers at Play Blog Carnival logo created by Dan Mackinnon for Carnival #17. Circus graphics are by alextrou92 and macrovector via depositphotos.com.

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

**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!

Hi Denise!

Hooray for #144! Thanks for the shout-out. Here’s an updated link for the Number Strings: https://singaporemathsource.com/?s=strings

Thanks! I fixed it.

amazing work here

Thank you! It was a lot of fun digging out old treasures. 🙂