Welcome to the 162nd 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/activity in honor of our 162nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

## Try This Puzzle/Activity

The number 162 is a *palindromic product*:

162 = 3 x 3 x 2 x 3 x 3

and 162 = 9 x 2 x 9

- How would you define palindromic products?
- What other numbers can you find that are palindromic products?
- What do you notice about palindromic products?
- What questions can you ask?

Make a conjecture about palindromic products. (A *conjecture *is a statement you think might be true.)

Make another conjecture. How many can you make? Can you think of a way to investigate whether your conjectures are true or false?

## 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.

- 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

And in honor of my new *Tabletop Math Games Collection* — available for preorder now on Kickstarter — each section includes a video of a math game you can play with your kids.

Find out more about the project and download a free 4-game sampler file in my blog post New Project: The Tabletop Math Games Collection.

Enjoy!

## Talking Math with Kids

“This is what continuous provision is all about: a place where children can return again and again and make something, trying out new ideas, combining things they’ve done before, learning from each other.”—Simon Gregg, Folding, cutting, sticking, drawing

- Dan Finkel (@MathforLove) looks back over 3.5 years of Counting with very young children. And check out this 21st Century Pattern Block Play Idea that should work just fine with regular blocks, too.

- Jenna Laib (@jennalaib) plays a classic math game with younger students in Facilitating Number Boxes, Part 2 – Supporting Reasoning with Representations.

- Simon Gregg (@Simon_Gregg) considers the types of thought involved in Folding, cutting, sticking, drawing.

- Celeste Bancos (@CBancos) continues the delightful adventures of Baby Pickle with The Negative Minus-One-Hundred Function. And don’t miss the fun of Polyomino Play.

- Christopher Danielson (@Trianglemancsd) ponders Rectangles, zucchinis, and kindergartners.

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## Exploring Elementary Arithmetic

“Clearly, we had a lot of mathematical brilliance within the room. Sometimes, the less precise answer is more fun!”—Jenna Laib, “What Are You Hoping For?”

- Amy Michaels offers suggestions for Using Picture Books to Teach Homeschool Math.

- For my own carnival entry, check out the first post in my new math journaling series,
*Thinking Thursday.*It’s a math game prompt, a great way to get kids thinking creatively about numbers: Bowling.

- Iva Sallay (@findthefactors) posts interesting number facts along with her times-table puzzles. Try your hand at these: 1730 Level One, 1731 Level Two, 1732 Level Three, 1733 Level Four, and 1735 Level Five.

- Kelli Pearson (@ArtfulMath) reviews Kitten Math: The Math Workbook That Makes Kids Go “Awww!”

- Jenna Laib (@jennalaib) probes student thinking in “What Are You Hoping For?”: Facilitating the Number Boxes Game to Develop Reasoning.

- You’ve Got This Math shares a Battleship-style game for practicing Decimals on the Number Line.

- Michael Jacobs (@msbjacobs) shares a puzzle that helps build understanding: How Coding Revealed a Decimal Misconception.

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## Adventuring into Algebra and Geometry

“As you guess, check or eliminate your way to the solution, think of the power and elegance of these codes and all the secrets your system might reveal.”—Patrick Honner, The Basic Algebra Behind Secret Codes

- Dylan Kane (@dylanpkane) uncovers a wealth of nonsense by Asking ChatGPT About 7th Grade Math. Can your students correct the computer’s messed-up explanations?

- Henri Picciotto (@hpicciotto) shares a variety of puzzles to help students explore Rate of Change.

- Erick Lee (@TheErickLee) creates a Secret Message Activity to review arithmetic sequences. And don’t miss his fun puzzle about the Impossible Triangles.

- Patrick Honner (@MrHonner) explains The Basic Algebra Behind Secret Codes and Space Communication.

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## Scaling the Slopes of High School Math

“We might even be dismissive about the thing we aren’t familiar with because why take the energy to be curious about that new thing if the familiar thing will serve the needs well enough?”—Kate Ertmann , why Sometimes I Feel Like A Logarithm

- Sarah Carter (@mathequalslove) shares a set of precalculus puzzles: Odd One Out Coterminal Angles Activity. And your students might enjoy some of her Fun Conic Sections Activities or the Calculus Graph Sketching Activity for Connecting f, f’, and f”.

- Pat Ballew’s (@ballew_pat) blog is always a trove of mathy treasures. Check out the fun tidbits in So You Thought You Knew Everything About Equilateral Triangles, Expanded Version.

- Sometimes you meet math in unexpected places, even within yourself. Kate Ertmann (@GOK8) explains why Sometimes I Feel Like A Logarithm.

- And don’t miss our sister carnival, the 211th Carnival of Mathematics.

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## Enjoying Recreational Puzzles and Math Art

“Numbers and variables floating away.

Oh, I wonder, what shall I learn today?”—Miranda Jedlinski, Forest of Numbers

- Steve Phelps (@MathTechCoach) shares The best thing I have seen on Twitter in a while. Delightful!

- Celeste Bancos (@CBancos) experiments with Edge-Release Structures With Small Children.

- Becky Warren (@becky_k_warren) makes a printable math zine about Truchet Tiles and Quilting.

- Paula Beardell Krieg (@PaulaKrieg) constructs a beautiful Excavated Dodecahedron (with printable template). For an easier project, try her Cube with Curves or the Simplest Flexagon.

- I’m pretty sure I’ve said this before, but here’s one of my favorite math art prompts: Go to John Golden’s (@Mathhombre) Miscellanea tumblr. Choose any picture that speaks to you. Notice and wonder about the math. Then create a related math art image of your own.

- JoAnne Growney (@MathyPoems) shares links and congratulates the AMS 2023 Math-Poetry Contest Winners.

- I love Lewis Carroll puzzles, don’t you? Alex Bellos (@alexbellos) asks Can you solve it? Lewis Carroll fan fiction.

- Celebrate the winter weather with Sarah Carter’s (@mathequalslove) challenging Snowflake Puzzle. Or get ready for Valentine’s Day with her Pentominoes Heart Puzzle.

- Jonathan Halabi (@Jd2718x) poses a puzzling Dice Question. Then follows it up with Another Dice Question.

- Tanya Khovanova explores number patterns and relationships In Search of a Tribonacci Building.

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## Teaching with Wisdom and Grace

“Unfortunately, since parents and schools overemphasize the value of the right answers, even the ‘best’ students may be the worst at learning from mistakes.”—Julia Brodsky, Mistakes As Markers Of Growth

- I love a good quotation, don’t you? George Couros (@gcouros) curates 20 Inspirational Quotes to Start off 2023. And if you like those, check out my own growing collection of Math & Education Quotations.

- How do you review math topics in the classroom? Druin (@druinok) shares several Review Games I Want to Try.

- Dan Meyer (@ddmeyer) remembers What Math Teachers Were Sharing on Twitter in 2022.

- John Golden (@Mathhombre) shares his list of favorite Math Podcasts. Do you have any to add?

- If your homeschool students are struggling with math, Adena encourages you to Do These Three Simple Exercises Before Math Lessons.

- Michael Pershan (@mpershan) explains why Chatbots (mostly) won’t change education.

- Dylan Kane (@dylanpkane) pushes back on lazy thinking with The Benefits of Traditional Assessment. And don’t miss his thoughts on Memory, Remembering, and a Few Minutes of Teaching.

- Julia Brodsky (@artofinquiry) reflects on Mistakes As Markers Of Growth: From Valuing “Right Answers” To Embracing Uncertainty.

- Keith Devlin (@profkeithdevlin) considers Playful Math – Is there a “there” there?

- Simon Gregg (@Simon_Gregg) reviews an advance copy of Jim Noble’s (@teachmaths) upcoming book, Mathematics Lessons to Look Forward To.

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## Giving Credit Where It’s Due

Balloons photo by Adi Goldstein on Unsplash. Confetti photo by Matheus Frade on Unsplash.

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 next month at The Montessori Cosmos. Visit our blog carnival information page for more details.

**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!

Palindromic product?

A number n, n∈ℕ, is a “palindromic product” ⟺ n = a*b*a, a∈ℕ, a∈ℕ, a,b≠1

How’s that?

Might also think of one as any number that is a multiple of a perfect square.

Would 16 be included? 2*4*2?

I think the fact that a palindromic product is the multiple of a perfect square would definitely follow as a corollary of your definition.

But why not allow b=1? That still fits the palindromic form, and then all multiples of perfect squares are included, even the square itself:

25 = 5 x 1 x 5