Do you enjoy math? I hope so!

If not, browsing this post just may change your mind.

Welcome to the 123rd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun.

The Playful Math Carnival is like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school. This month’s edition features articles from bloggers all across the internet.^{†}

You’re sure to find something that will delight both you and your child.

By tradition, we start the carnival with a puzzle in honor of our 123rd edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

^{†}Or more, depending on how you count. And on whether I keep finding things to squeeze in under the looming deadline. But if there are more, then there are certainly 36. Right?

## The 1-2-3 Puzzle

Write down any whole number. It can be a single-digit number, or as big as you like.

For example:

64,861,287,124,425,928

Now, count up the number of even digits (including zeros), the number of odd digits, and the total number of digits it contains. Write those numbers down in order, like this:

even 12, odd 5, total 17

Then, string those numbers together to make a new long number, like so:

12,517

Perform the same operation on this new number. Count the even digits, odd digits, and total length:

even 1, odd 4, total 5

And do it again:

145

even 1, odd 2, total 3

If you keep going, will your number always turn into 123?

## Contents

And now, on to the main attraction: the blog posts. Some 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.

- Talking Math with Kids
- 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

This month’s carnival is sponsored by my new book of playful math, 70+ Things To Do with a Hundred Chart: Number, Shape, and Logic Activities from Preschool to Middle School. So along with the blog post links below, I’ll be sharing a few of my favorite hundred chart games and activities. I hope you enjoy them. 🙂

“This book is a treasure trove of amazing math games! I never imagined that so many math concepts could be taught using the hundreds chart.”

—Susie Davis, reader review

Would you like to see YOUR favorite blog post in next month’s carnival? Submissions are always open!

## Talking Math with Kids

**Playing Math on a Hundred Chart:** Practice counting and strategic thinking with Rachel Capes’s (@YouveGotThis1) Free Number Puzzle Game to Develop Number Sense (free registration required). This game offers plenty of chances to talk with your child about number patterns and which numbers come before or after another number.

- Andrew Shauver (@hs_math_phys) and son explore the importance of units for measuring hot chocolate in Math Talk by Necessity: a 4-year-old’s story.

- Deanna McLennan (@McLennan1977) and students head outside for Puddle Play – Rethinking the Math Classroom. “What had originally looked to be a damper on our outdoor fun turned into a complex and layered opportunity for rich math thinking…”

- Picture books can prompt wonderful math conversations. Kelly Darke (@KellyDarkeMath) and daughter Siena read Two Books about One.

- Malke Rosenfeld (@mathinyourfeet) reports from Inside the Whole-Body Newspaper Build Project with some fantastic reflections on construction and collaboration.

- Adam Hillman (@witenry) creates colorful art with common objects. His Instagram gallery is a delightful resource to spark mathematical conversations.

- And when you need a dose of mathematical cuteness to brighten your day, be sure to check out the Talking Math With Your Kids (#tmyk) feed on Twitter.

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## Exploring Elementary Arithmetic

**Playing Math on a Hundred Chart:** Challenge a friend to a subtraction face-off with Euclid’s Game on a Hundred Chart. For older students: Can you find the connection between this game and the Euclidean Algorithm?

- Are your kids trying to learn their math facts? Michael Pershan (@mpershan) demonstrates The absolute best way to practice flash cards with elementary students.

- David Butler (@DavidKButlerUoA) shares a challenging interactive Letters and Numbers Game.

- Kyle Pearce (@MathletePearce) connects measurement, multiplication, fractions, and candy for grades K–8 in Exploring Proportional Relationships Developmentally.

- I love Jess Prior’s (@Fortyninecubed) “Minimally Different” puzzles. Check out his new set about Sharing in a Ratio.

- Mike Lawler (@mikeandallie) and sons discuss A really neat way for kids to experience prime and composite numbers. It’s almost hypnotic!

- For my entry to the carnival, here’s an excerpt from my Hundred Chart book: Playing Complex Fractions with Your Kids. It’s a hands-on way to begin making sense of an often-scary topic.

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## Adventuring into Algebra and Geometry

**Playing Math on a Hundred Chart:** Students must spot and describe number patterns with Stuart Kay’s Blank 100 Grid Number Investigations (free registration required). The activity covers odds, evens, multiples, factors, primes, square numbers, cube numbers, triangular numbers, powers of 2 and 3, and other familiar number sequences.

- Amie Albrecht (@nomad_penguin) finds a variety of ways for students to explore the properties of shapes in A lesson plan (of sorts) for quadrilaterals. And don’t miss John Golden’s (@mathhombre) Quadrilateral Vacation from the comments section.

- Craig Barton (@mrbartonmaths) highlights a cool resource to help your students make sense of graphs: Speed-Time Graph Spiders.

- Phyllis Bergenholtz (About) creates her own algebra tiles in Hands-on Algebra: The Distributive Property.

- Bob Lochel (@bobloch) brings the power of Desmos to bear in a lesson on Golfing with Linear Equations.

- Michael Pershan (@mpershan) challenges his students with geometry puzzles in I kind of like these congruent triangle problems I made. And check out these triangles-and-more Area Mazes from John Rowe (@MrJohnRowe).

- How can we support students learning to write geometry proofs? Max Ray-Riek (@maxrayriek) and Tina Cardone (@crstn85) present Proof in IM’s High School Geometry (A Sneak Preview).

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## Scaling the Slopes of High School Math

**Playing Math on a Hundred Chart:** Examine the mathematics of gerrymandering. Choose two colors and shade in the squares on a hundred chart at random so that forty squares are one color and sixty the other color. Can your students create ten voting districts that will guarantee (1) a proportional representation? (2) A win for the minority color? (3) The greatest possible margin of victory for the majority color?

- Elias Wirth (About) details the challenge of measuring length in From Coastlines To Fractals.

- Brian P (@_b_p) shocks his students during a classroom discussion in One graph. Ten minutes. An important conversation. He also links to
*The New York Times*‘s What’s Going On in This Graph? blog. What a rich resource!

- Elissa Miller (@misscalcul8) shares a delicious math art project: Unit Circle Art IV.

- Sarah Carter (@mathequalslove) gamifies the textbook’s lesson on parent functions, and it turns into her “best lesson of the year so far”: Twelve Basic Functions Challenge in Pre-Calculus.

- Chris Bolognese (@EulersNephew) challenges his students to use their rectangular, polar, and parametric graphing skills in the Coloring Book Project.

- The good folks at NrichMaths (@nrichmaths) want to get secondary students Thinking Mathematically. To that end, they host a variety of Live Problems — math puzzles that students can solve and submit their answers.

- And don’t miss the 163rd Carnival of Mathematics.

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## Enjoying Recreational Puzzles and Math Art

**Playing Math on a Hundred Chart:** Dive into one of the classic games of recreational math with Hundred Chart Nim. When mathematicians study a problem, they often try making small changes, just to see what will happen. Encourage your students to alter the rules and make their own Nim games.

- Kent Haines (@KentHaines) introduces kids to a different way to look at the world with the game Map Wars — Can you color in the entire map?

- Dan Finkel (@MathforLove) has made it to #18 in his series of recreational math posts: A Mathematician at Play 18: A Roll of the Dice.

- Simon Singh (@SLSingh) sends out a wide variety of interesting puzzles from his Parallelograms website.

- The Public Math team (About) invites you to share Math Zines with your kids — mini-books about counting, division, and fractal patterns. How cute!

- Benjamin Leis (@benjamin_leis) offers inspiration and links to help you start your own math circle in Math Circle Talk Slide Deck.

- Clarissa Grandi (@c0mplexnumber) demonstrates how to make a beautiful golden pentagram in Construct-a-Christmas-card.

- If you love Raymond Smullyan’s puzzles (and who doesn’t?), you’ll definitely want to explore Dan MacKinnon’s (@mathrecreation) set of riddles with The unreliable guards.

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## Teaching with Wisdom and Grace

**Playing Math on a Hundred Chart:** Joe Schwartz (@JSchwartz10a) details the development of a playful math lesson in “I Like This Game Because You Have to Think Hard.” Grab a blank grid and some colored pencils and have some fun!

- Jenna Laib (@jennalaib) notices how a rich problem provides a deep mathematical experience for students of all ability levels, without the need for well-intentioned but heavy-handed differentiation. No More Mathematical Matchmaking: The Return of the Inaba Place Value Puzzles.

- Homeschoolers, Lynna Sutherland (@hswotrainingwls) shows you how to be successful with a relaxed approach to Math: Often the Last Subject to be Deschooled.

- Calli Wright (@CalliWrights) compiles The Big List of Board Games that Inspire Mathematical Thinking.

- Mark Chubb (@MarkChubb3) ponders the value of mathematical surprise in building young mathematicians: Reasoning and Proving.

- Jess Prior (@Fortyninecubed) analyzes the development of a math lesson over years of teaching: Reflections on Dividing Fractions.

- Dan Meyer (@ddmeyer) warns that the modern edu-fad of “celebrating mistakes” is not the same as respecting a student’s thinking: That Isn’t a Mistake, and the follow-up post What Do You Do with the Ideas You Used to Call “Mistakes”?

- We teach, yes. But there’s always plenty more to learn, too! Deepen your own understanding of math with Joseph Nebus’s (@Nebusj) ongoing Mathematics A to Z series. Or check out some of the books in Shecky Riemann’s (@SheckyR) Book Mentions.

- Sunil Singh (@Mathgarden) argues that The Whiteness of Math Education Will Never Be Changed Without Teaching Math History — Properly.

- Marian Dingle (@dingleteach) explains how mathematical definitions are metaphors for many societal realities: Measures of Center.

- Anne Schwartz (@sophgermain) weighs in on Why white teachers don’t like talking about a lack of diversity.

- Robert Berry (@robertqberry) launches reflection-provoking conversations with Truly Wonderful and Getting Better.

- And Francis Su’s (@mathyawp) Mathematics for Human Flourishing is always worth a re-read.

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## Giving Credit Where It’s Due

PUZZLE CREDITS:

“123 Iteration Puzzle” from Archimedes Lab via Pat Ballew.

Number Puzzle Game created by Rachel Capes.

Euclid’s Game created by Alexander Bogomolny.

“Blank 100 Grid Number Investigations” by Stuart Kay.

“Gerrymandering Challenge” from the Metric Geometry and Gerrymandering Group via Chris Bolognese.

Number Grid Tic-Tac-Toe game created by Joe Schwartz at Exit 10A blog.

PHOTO CREDITS:

“Girl with bubbles” photo (top) by pan xiaozhen and “Dragon” photo by Tarik Haiga on Unsplash.

“Solving number puzzle” photo by Rachel Capes.

“Dirty numbers” photo by Håkan Dahlström via Flickr (CC BY 2.0).

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 open sometime during the week of January 28–31 at Life Through A Mathematician’s Eyes. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Older posts are welcome, as long as they haven’t been published in recent editions of this carnival.

Past posts and future hosts can be found on our blog carnival information 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 Playful Math Education Blog Carnival, please speak up!

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