Welcome to the 154th 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 154th 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

Since 154 is a nonagonal number, I think you might enjoy visiting some of my old “Adventures of Alexandria Jones” posts about figurate numbers:

- Alexandria Jones and the Puzzling Pythagorean Pebbles
- Puzzle: Figuring Out Figurate Numbers
- Game: Avoid Three, or Tic-Tac-No!

And then try this math journaling prompt: Build or draw your own nonagonal numbers — numbers built from 9-sided polygons.

How many nonagonal numbers can you find? What do you notice? Does it make you wonder?

## 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 help keep the Playful Math Carnival going? We need volunteer hosts! Find out more at the Playful Math Education Blog Carnival home page.

Note: The bonus math journaling prompts and images below are from my new book, *312 Things To Do with a Math Journal*. Have fun playing math with your kids!

## Talking Math with Kids

“Look at this one. It’s only this big. I thought it would be way bigger. Let’s make a bigger square, like twenty by twenty. Will that be a too-bigger pocket?”—Celeste Bancos, Origami Pockets and a Paper Pickup Truck

- Celeste Bancos (@CBancos) and son fiddle with paper in Origami Pockets and a Paper Pickup Truck. And don’t miss her delightful story Pickle and the Closet of Functions.

- And here’s one more math discussion from Celeste and Luke: These Snakes are Working Hard.

- John Golden (@mathhombre) and students play around with Early Elementary Math Games.

- Christopher Danielson (@Trianglemancsd) explains Pattern Machines: What They Are and Why You Need One.

- Cindy West launches discussion about a variety of topics with Picture Books That Teach Fractions, Ratios, Percentages, and Decimals and Problem Solving Picture Books for Math.

- Puzzles can be a wonderful prompt for math discussion. Can your children work together to find solutions to Sian Zelbo’s Same Sum Circles?

- Talk math with older kids, too! Fawn Nguyen (@fawnpnguyen) posts a slide deck of 90 Number Talks for Middle Schoolers — enough for a full school year if you do this routine every other day.

### Bowling (solitaire game)

Draw circles in a bowling-pin pattern. Write the numbers 1–10 in the circles. Roll two dice and cross out any combination of circles that exactly matches that sum. Those are the pins you knocked down. Roll again, trying to hit more pins.

If all the numbers left are 6 or less, you may choose to roll only one die. Can you knock down all the pins? What is your strategy?

—Denise Gaskins, *312 Things To Do with a Math Journal*

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## Exploring Elementary Arithmetic

“When interviewing students to learn how they reason, we’re often surprised, intrigued, and delighted. Their thinking stretches our own thinking and informs our instruction. Similarly, we think it’s also valuable for students to learn to listen to each other during class instruction. Understanding how their classmates reason can expand their own thinking.”—Marilyn Burns, What Was Nathan Thinking?

- Marilyn Burns (@mburnsmath) challenges students to think more deeply about math facts in What Was Nathan Thinking?

- Ganit Charcha (@GanitCharcha) explains how simple addition makes for an Amazing Mathematics-Based Card Trick your students can perform.

- Your children may enjoy these daily number challenge puzzles: Numble (find a 3-digit multiple of 3) and Nerdle (find a daily equation). Or create your own puzzles for each other with Michael Minas’s (@mminas8) new game Equationle.

- Does playing games really help kids learn? Dan Finkel (@MathforLove) relates a Prime Climb Success Story.

- Colleen Young (@ColleenYoung) organizes her Number Resources — including this Number Operations puzzle that builds understanding of multiplication, division, and place value. After they solve it, challenge your kids to create a similar puzzle of their own.

- Jenna Laib (@jennalaib) shares a fun slow-reveal graph slideshow in Why Biggest Isn’t Fastest in the Animal Kingdom.

### Triangular Numbers

You’ve heard of square numbers. Triangular numbers are their smaller cousins. Arrange dots in a bowling-pin pattern. Count the dots to find the triangular number: one dot in the first row (T_{1} = 1), two in the second row (T_{2} = 1 + 2), three in the third row (T_{3} = 1 + 2 + 3), etc.

Keep adding more dots. Each row is one dot longer than the previous row. How many triangular numbers can you find? Do you see any patterns? Can you think of any questions to ask?

—Denise Gaskins, *312 Things To Do with a Math Journal*

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## Adventuring into Algebra and Geometry

“As this had taken less time than I expected, I had to then think quick and come up with an extension…”—Michael Jacobs, A Nice Algebra Puzzle

- Michael Jacobs (@msbjacobs) and students play with pyramids in A Nice Algebra Puzzle.

- Nicole Whitty (@whittymath) sparks a Systems of Linear Equations Debate.

- Jo Morgan (@mathsjem) shares Sudeep Gokarakonda’s (@boss_maths) “Dose of Don” article about Symmetry puzzles for middle and high school students.

- And you can always go explore Don’s blog for yourself. Here are a few puzzles he collected to help students understand slope (or gradient).

- Henri Picciotto (@hpicciotto) updates his website to encourage Seeking Depth in Algebra 2 through activities and games.

### Everything Is a Rectangle

Draw any *quadrilateral *(four-sided shape) on your page. How can you convert it into a rectangle with the same area? For example, can you imagine cutting off one part and pasting it in a different place?

What if it’s an unusual shape like a kite or an arrowhead? Extra challenge: Can you convert shapes that are not quadrilaterals?

—Denise Gaskins, *312 Things To Do with a Math Journal*

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## Scaling the Slopes of High School Math

“Take a risk and find the guts to create something really personal, whether it’s funny or dark or thought-provoking or just mathematically beautiful. Just push yourself a bit out of your comfort zone and take a chance and have fun with it!”—Julia Schanen, Share Math Like Strogatz: An Interview with Julia Schanen

- Have your high school students heard of the Steven H. Strogatz Prize for Math Communication? Application deadline: April 27, 2022. Tim Chartier (@timchartier) interviews last year’s winner, Julia Schanen.

- Discover all of the Strogatz Prize 2020 and 2021 Winners.

- Sarah Carter (@mathequalslove) creates a free printable Parent Graphs of Trig Functions Clothespin Matching Activity.

- Bob Lochel (@bobloch) offers a new Statistical Power and Virtual Coins activity.

- Erick Lee (@TheErickLee) reviews derivative rules with Add ‘Em Up Activities.

- And don’t miss the 202nd Carnival of Mathematics.

### Explain a Mistake

Describe a mistake you made in math, or a problem you missed on a quiz or test. What went wrong? How will you avoid this error the next time? Do you understand the problem now, or is there something more you need to learn about it?

—Denise Gaskins, *312 Things To Do with a Math Journal*

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## Enjoying Recreational Puzzles and Math Art

“The answers to both can be found with an online search, and the latter can be computed in milliseconds by writing some code, but you’ll have more fun if you find the answers using that big lump of gray matter in your skull.”—Patrick Vennebush, The Great Puzzle Hunt

- Patrick Vennebush (@pvennebush) drops a couple of math puzzles and an algebra joke — and links to an upcoming online math event — in The Great Puzzle Hunt.

- JoAnne Growney (@MathyPoems) quotes one of my favorite math artists in A Poet with a Slide Rule.

- Paula Beardell Krieg (@PaulaKrieg) demonstrates a cute foldable T-Cut Origami Booklet.

- Sue VanHattum (@suevanhattum) posts a Logic Puzzle, Supposedly from Einstein.

- John Golden (@mathhombre) highlights the classic do-it-yourself board game of Agression. You may also enjoy playing Gordon Hamilton’s (@gamesbygord) Little Bit of Aggression maps with your kids.

- Patrick Honner (@MrHonner) explores What a Math Party Game Tells Us About Graph Theory.

- Tanya Khovanova shares a puzzle from the Kyiv Olympiad, 1978. Also, check out her post about Anti-Chiece Latin Squares.

- Matthew Scroggs (@mscroggs) provides tips for anyone who wants to Build your own MENACE.

- What do you do when you’re stumped on a math problem? Benjamin Leis (@benjamin_leis) explains his Two Circumcircles Walkthrough, while Sam Shah (@samjshah2) describes his experience with a tough Semicircle Puzzle. Pat Ballew (@ballew_pat) investigates patterns in Infinite Radical Sequences.

### Circle Pattern

Draw a circle. Draw another circle the same size, with its center at any point on the first circle’s circumference. At each point where the circles meet, draw another circle centered there. Continue drawing circles with their centers at each new intersection.

What do you see in this pattern? Can you think of any questions to ask?

—Denise Gaskins, *312 Things To Do with a Math Journal*

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## Teaching with Wisdom and Grace

“Everyone deserves a chance to experience what makes people fall in love in mathematics.”—Dan Finkel, 4 Reasons Play and Math Go Together

- Dan Finkel (@MathforLove) explains 4 Reasons Play and Math Go Together. And don’t miss his interview with Kent Haines (@KentHaines) on the Heinemann (@HeinemannPub) podcast: Math Games Galore!

- Simon Gregg (@Simon_Gregg) ruminates on a learning adventure at the beach in Why play?

- Chris Wright shares thoughts about early math in Waxing Philosophical.

- Elisa Waingort (@ElisaW5) ponders things that have changed — and what has not — in Challenge: I used to think…

- Mark Chubb (@MarkChubb3) examines What Makes Math Interesting Anyway? and how we can encourage creativity in our classrooms.

- Amplify (@Amplify) offers a free printable set of Mathematician Profile Cards to get middle and high school students talking.

- Ben Orlin (@benorlin) argues for teacherly humility in I can’t multiply 2573 by 389.

- Michael Pershan (@mpershan) raises the question: What’s the difference between worked examples done well and done poorly?

- Melissa Dean (@Dean_of_math) celebrates The Power of the Hexagon to prompt student thinking and discussion.

- Anna Blinstein (@ablinstein) relates her experience implementing Consolidation — that is, wrapping up the big ideas at the end of class to help students make key connections.

- And for my contribution to the carnival: If you enjoyed the math prompts scattered throughout this carnival, check out my four-part Math Journaling Series: Part 1: The Foundation, Part 2: Practical Tips, Part 3: Types of Prompts (with Examples), and Part 4: Responding to Your Child’s Writing.

### Reinvent Your Homework

Find a page of calculations in your math book, or download a worksheet online. Choose two or three of the questions. Write a story problem to match each calculation.

For example, for the calculation 3/4 × 8, you might imagine a recipe that takes 3/4 cup of flour. But you are planning a party and need to make eight times that amount. How much flour will you need in all?

—Denise Gaskins, *312 Things To Do with a Math Journal*

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## Giving Credit Where It’s Due

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 take place at John Golden’s Math Hombre blog sometime during the month of April.

Would you like to take a turn hosting the Playful Math Carnival? Visit our blog carnival information page for more details.

Playful Math Carnival Home Page

Math journaling prompts and images (except as noted below) are from *312 Things To Do with a Math Journal*.

Nonagonal-Number.gif: Referenced on Wolfram/Alpha: Nonagonal Number, CC BY-SA 4.0, via Wikimedia Commons.

Photos above: “Purple beach” photo by Nick Dunn on Unsplash. “Homework photo 1” by Anoushka P, and “Homework photo 2” by Antoine Dautry on Unsplash (license terms).

good one! prek-12 coverage…

Thanks! It’s always fun to find so many treasures.