Welcome to the 160th 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 160th 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

Appropriately for an October carnival, 160 is an *evil* number.

A number is evil if it has an even number of ones in binary form. Can you find the binary version of 160? (Hint: Exploding Dots.)

160 is also a *polyiamond* number. If you connect 9 equilateral triangles side-to-side, a complete set of 9-iamond shapes would have 160 pieces.

But sets that large can be overwhelming. Try playing with smaller sets of polyiamonds. Download some triangle-dot graph paper and see how many different polyiamond shapes you can make.

What do you notice? Does it make you wonder?

What designs can you create with your polyiamonds?

*Photo by Daiga Ellaby on Unsplash*

## 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

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

## Talking Math with Kids

“It’s funny to me how S and N both have a low threshold for ‘school-ification.’ They’ll happily mathematize the world, but once it starts to feel like a lesson…”—Jenna Laib, Rush Hour Conversations

- Jenna Laib (@jennalaib) and children deal with real-life data in Rush Hour Conversations.

- Kate Pickle (@katepickle) shares a fun way to get kids talking about symmetry, patterns, and geometry: Shape Mandala Drawing for Kids – Free Printable Templates.

- Dan Finkel (@MathforLove) and Katherine Cook pose questions to get students thinking: Upscale Pattern Block Provocation.

- Want to get your kids playing with math? Christopher Danielson (@Trianglemancsd) explains how to Design for Engagement.

- And if you haven’t sampled Danielson’s delicious stories about talking math with kids, here’s a tasty place to start: Canned pumpkin.

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*Image by Ilya Lisauskas from Pexels*

## Exploring Elementary Arithmetic

“May your classroom be filled with math joy and rich math talk all year long.”—Steve Wyborney, 170 New Esti-Mysteries

- Michael Minas (@mminas8) and sons demonstrate a new game: 3 Little Pigs vs the Big Bad Wolf.

- Tad Watanabe (@watanabeKSU) talks about Subtraction strategies, focusing on an important early-learner strategy missing from Pam Harris’s (@pwharris) big Master Mental-Math Strategies List.

- Steve Wyborney (@SteveWyborney) posts 170 New Esti-Mysteries to help kids build estimation skills.

- Sue O’Connell (@SueOConnellMath) raids the library for ways we can Use Literature to Make Sense of Math Operations.

- MMMathMania (@MMMathMania) demonstrates a place-value game: Lock it Down.

- NRICH maths (@nrichmaths) challenges students to send in their own answers to the Playing with Coins and Mathematical Sudokus puzzles. (Secondary students use this link.) And then try making your own puzzles with the Mathdoku Editor.

- John Golden (@mathhombre) shares two games invented by his students: Sorry, It’s Fractions, and Fraction Reaction.

- Joseph Nebus (@nebusj) links to more than 10,000 answers to a traditional puzzle in Some Fun Ways to Write Numbers but Complicated. (For example, our carnival number 160 = 12 + 3 × 4 + 5 + 6 × 7 + 89 = 98 + 7 × 6 + 5 + 4 × 3 + 2 + 1.)

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*Photo by Tolga Ulkan on Unsplash*

## Adventuring into Algebra and Geometry

“We all needed the opportunity to think for ourselves, and to experience success as a result. How else could we become resilient, confident, creative people?”—Audrey McLaren, Playing in math using Desmos

- Audrey McLaren (@a_mcsquared) gives tips for Playing in math using Desmos.

- Sarah Carter (@mathequalslove) collects 8 Fun & Engaging Coordinate Plane Activities.

- Tad Watanabe (@watanabeKSU) demonstrates a rate-situations approach to teaching Arithmetic with integers: Multiplication.

- Jenna Laib (@jennalaib) creates slow-reveal graphs to intrigue students: Number of Websites Online and Hawaiian Native Bird Species.

- John Golden (@mathhombre) shares two math games invented by his students: polyGONE, and Binomial Battleship.

- Mr Rowlandson (@Mr_Rowlandson) lays out a series of hands-on activities to get students (and teachers) Thinking About Pythagoras’ Theorem.

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*Photo by Johannes Plenio on Unsplash *

## Scaling the Slopes of High School Math

“Pose challenges to yourself. Get data sets you would like to see represented graphically and create those graphics. Learn by doing things.”—Alberto Cairo, Getting Graphic with Alberto Cairo

- Patrick Honner (@MrHonner) asks How Big Is Infinity?

- Teaching Statistics? Sarah Carter (@mathequalslove) collects 53 Fun and Interesting Statistics Activities.

- Inspire your students to represent data in creative ways with these fun examples from Randall Munroe (@xkcd): Road Space Comparison and Easy or Hard.

- Check out Tim Chartier’s (@timchartier) interviews with modern mathematician: Getting Graphic with Alberto Cairo and Hoop Math from the Sideline with Dean Oliver.

- Pat Ballew (@ballew_pat) explores The Harmony of the Harmonic Mean. And investigates Which Platonic Solid is Most-Spherical? (and The Archimedian Solids)

- Also, Ballew looks for A Non-calculus Explanation for the Volume of a Bead. Arjen Dijksman (@materion) responds with the graphical comparison of Volume of a bead vs. volume of a sphere.

- Sue VanHattum (@suevanhattum) shares a Calc II: Lovely Arc Length Example.

- And don’t miss the 209th Carnival of Mathematics.

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*Photo by Takahiro Sakamoto on Unsplash*

## Enjoying Recreational Puzzles and Math Art

“Number theory is like poetry

they are both of the same kind

they start a fire in your mind…”—Olga Taussky-Todd, Number theory is like poetry

- Sian Zelbo (@SianZelbo) poses the Map Folding Problem. Can your kids solve it?

- Paula Beardell Krieg (@PaulaKrieg) demonstrates how to make your own intriguing math toy: Kaleidocycle, revisited.

- Sarah Carter (@mathequalslove) posts a plethora of puzzles, including the Halloween Symbols Puzzle and Pentominoes Jack-o’-lantern Halloween Puzzle.

- Joseph Nebus (@nebusj) investigates How Pop-Up Cards and Books Work.

- Tanya Khovanova shares More Math Jokes. (And still more…)

- JoAnne Growney (@MathyPoems) offers a poetic quote about math proofs: Women in Mathematics — Netherlands. And I enjoyed Olga Taussky-Todd’s description of how Number theory is like poetry.

- Inspire your students to write combinational poetry with Growney’s post Arts-based Math Education — Meet one of the Stars.

- Get your students playing with math art. Explore John Golden’s (@mathhombre) Miscellanea Tumbler and notice, wonder, create!

- And if you have high school students, encourage them to enter their favorite art, writing, or video about math to the Steven H. Strogatz Prize for Math Communication. (Deadline next April, 2023. See the 2022 winners.)

- For my entry to the carnival: Help students of all ages build number skills and mathematical thinking when you Get a Weekly Dose of Playful Math.

- Pat Ballew (@ballew_pat) relates A Brief History of the River Crossing Problem.

- Mathologer (@Mathologer) explores the deep mathematics of the iconic Pythagoras twisted squares.

- Pamela E. Harris (@DPeharris) and students turn a combinatorics problem into a Choose Your Own (Math) Adventure. What a fun way to think about mathematics!

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*Photo by Nadine Primeau on Unsplash*

## Teaching with Wisdom and Grace

“You can never improve as a teacher unless at some point you listen to the students.”—David Butler, Four levels of listening

- Christopher Danielson (@Trianglemancsd) shares thoughts On Being a Math Person (or Not).

- Simon Gregg (@Simon_Gregg) considers children’s thinking in The design cycle, sped up.

- Sue VanHattum (@suevanhattum) asks What does it mean when we feel we “understand” something?

- Check out the handy Calendar of Mathsy Moments 2022-2023 from Maths Ed (@MathsEdIdeas).

- Jenna Laib (@jennalaib) ponders how we might respond to student work in Restless Teachers.

- Betsy Mays (@Betsymays123) offers a printable template to give students a chance to show mastery of their test mistakes: Aftermath.

- Robert Kaplinsky (@robertkaplinsky) shares 5 Struggles Your Foster Students Wished You Knew.

- James Propp (@JimPropp) extols the value of Teaching with Magic Paper.

- Melissa Dean (@Dean_of_math) struggles with Walking the Assessment Talk and dreams of a classroom where Product is(n’t) king.

- David Butler (@DavidKButlerUoA) explores Four levels of listening, and warns about the danger of teaching Arbitrary mnemonics.

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*Photo by Annie Spratt on Unsplash*

## Giving Credit Where It’s Due

The spooky cat picture is by bess.hamiti@gmail.com from Pixabay.

The polyiamonds chart is by Eric W. Weisstein. “Polyiamond.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/Polyiamond.html.

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 months of November-December at Nature Study Australia. 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!

*Photo by Sage Friedman on Unsplash*