Welcome to the 152nd 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!

We didn’t have a volunteer host for January, so I’m squeezing this in between other commitments. This is my third no-host-emergency carnival in the last year, which is NOT sustainable. If you’d like to help keep the Playful Math Carnival alive, we desperately need hosts for 2022!

By tradition, we start the carnival with a puzzle or activity in honor of our 152nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

## Math Journaling with Prime Numbers

**Cool facts about 152:** The eighth prime number is 19, and 8 × 19 = 152. When you square 152, you get a number that contains all the digits from 0–4. You can make 152 as the sum of eight consecutive even numbers, or as the sum of four consecutive prime numbers.

But 152 has two real claims to fame:

- It’s the
*smallest*number that is the sum of the cubes of two distinct odd primes. - And it’s the
*largest known*even number you can write as the sum of two primes in exactly four ways.

**So here’s your math investigation prompt:**

*Play around with prime numbers. Explore their powers, their sums, and anything else about them you like.*

*What do you notice? What do you wonder?*

*What’s the most interesting number relationship you can find?*

## Our Final Dodeca-versary Party

The Playful Math Carnival (originally called “Math Teachers at Play”) is just wrapping up its 12th anniversary year. We’ve shared so many wonderful, creative math ideas through the years that I hate to lose track of them all.

Did you miss the earlier anniversary posts? Check out carnival editions 144, 147, and 150 for more playful math blasts from the past.

The posts in this 152nd edition are drawn from our fourth year of publication. We had 12 monthly carnivals from February 2012 to January 2013, with 11 different hosts:

- John Golden (@mathhombre) hosted #47.
- Bon Crowder (@MathFour) hosted #48.
- Karyn Tripp hosted #49.
- Erlina Ronda (@math4teaching) hosted #50.
- Sue VanHattum (@suevanhattum) hosted #51.
- I hosted #52 and #58.
- Motion Math hosted #53.
- Rebecka Peterson (@RebeckaMozdeh) hosted #54.
- Guillermo Bautista (@jr_bautista) hosted #55.
- Christy Knockleby (@housefulofchaos) hosted #56.
- Terrance Banks (@tbanks1906) hosted #57.

Far too many of these posts have been lost to the sands of time, but I’ve recovered what I could with the help of the Internet Archive’s Wayback Machine.

## 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
- What Comes Next?

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!

**Journaling with Math Art**

I’ve broken up the list of math links with art from the 2022 Joint Mathematics Meetings Gallery.

Math art is a wonderful playful math prompt. Ask your students to list what they see in a piece, and what it makes them wonder. Then encourage them to create their own art in a similar style.

## Talking Math with Kids

“The key to all of these activities is that we view numbers and quantities as ways of exploring, and we nurture our children’s sense of wonder about the world.”—David Wees, Raising mathematicians

**Young Children Explore Math**

- In #51, Christopher Danielson (@Trianglemancsd) talks with his daughter about What counts as a math question. (And here’s the Follow-up.)

- And Malke Rosenfeld (@mathinyourfeet) and her daughter have some serious fun finding Not Just Shapes.

- Then in #52, Malke entertains a tough audience with Scissor Stories: Tales of Transformation.

- In #57, Christa Fairbrother encourages math Engagement using a function box.

**Creating Math Art**

- In #47, Amy Bowers demonstrates how children can paint beautiful math art grids.

- And Becky Johnston shares a young learner’s Metamorphosis pictures, and wishes for a broader view of mathematical thinking.

- Then in #51, Becky and her son delight in The Very Escheriffic Day.

**Playing with Picture Books**

- In #47, Karyn Tripp creates a number web in What Equals What? With Math Fables.

- In #50, Malke Rosenfeld (@mathinyourfeet) and her daughter explore Sidewalk Math: Functions!

- In #52, Kristen and her girls wonder How Do You Count a Dozen Ducklings?

- And Cynthia Hockman-Chupp (@love2learn2day) considers the options for Organizing Your Children’s Math Library. It’s a pretty big job, since she collects examples of Math in Children’s Literature.

- In #58, Yelena McManaman gets addicted to iconic numbers in 1+1=2 but Mostly it Doesn’t, and your children can join in by contributing to A scavenger hunt game about unitizing.

**Young Math Games**

- In #47, Lilac Mohr shares Homemade Math Manipulatives: Sorting Hearts. Also they play Blocks in Socks: Early Math Game.

- In #49, Malke Rosenfeld (@mathinyourfeet) tells how her daughter invented A Game of Her Own: Discovering Division.

- In #51, Christy Knockleby (@housefulofchaos) and her son make up an Endless Patterning Game.

**Teaching Young Math**

- In #48, Malke Rosenfeld (@mathinyourfeet) relates her daughter’s path to Hundreds (Chart) Happiness.

- In #51, Carole Fullerton demonstrates how Missing Part Cards Lay the Foundation for Subtraction.

- And I describe one of my favorite playful math lessons: Tell Me a (Math) Story.

- In #52, Timon Piccini (@mrpicc112) ponders how important talking is to math: Language and Conceptual Understanding.

- In #55, Beth Schaubroeck collects resources for Elementary School Enrichment.

- In #58, David Wees (@davidwees) shares a variety of ways to nurture our children’s sense of wonder about numbers in Raising mathematicians.

- Are there times you doubt that anything is sinking in, or wonder if you’re not doing enough of the “right” kind of math? In #58, Malke finds reassurance in Found Math: How My Kid Shows Me She’s Learning.

**Older Children Talk Math**

- In #48, Sue Downing (@susandowning) listens to 2nd-graders inventing their own multiplication puzzles: Marvelous Math Play Date.

- In #51, Feanor translates Vitya’s Maths, a beautiful story of a boy solving a word problem.

- In #52, Christopher Danielson (@Trianglemancsd) demonstrates how much easier it is for elementary students to explain their answers (and to self-correct) through conversation: If you keep at it, it will pay off.

- In #53, DoriAnn Haskins and son explore Alex the Great and Fractions.

- In #55, Rodi Steinig and students discuss Popcorn, Nose Rings, and Parameters.

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## Exploring Elementary Arithmetic

“For my children, most maths curricula probably work just fine for a while. And then … well, they just get bored of doing the same thing day in day out. And boredom is definitely not a good learning state!”—Lucinda Leo, The Perfect Math Curriculum

**Playing with Numbers**

- In #52, Bon Crowder (@MathFour) plans a Birthday Party Fibonacci Style.

- And I explore what it means to profoundly understand elementary math: PUFM 1.4 Subtraction. Then in #55, I discuss PUFM Multiplication Part 2.

- In #55, Angie Eakland challenges her upper-elementary students to create math clocks: What Time Is It?

- Getting “the answer” is only the beginning of mathematics. In #58, Bon Crowder (@MathFour) shows how the real fun comes in extending the puzzle and asking new questions.

**Let’s Read Math**

- In #47, Christy Knockleby (@housefulofchaos) interrupts her regular homeschooling program to enjoy A few more math books and activities.

- In #48, Lucinda Leo (@lucindaleo) reviews Ed Zaccaro’s book
*Primary Grade Challenge Math*: The Perfect Math Curriculum.

- In #58, Mama Squirrel enjoys a recent thrift store treasure: Praise for The Number Devil.

- And Malke Rosenfeld (@mathinyourfeet) finds a “gold mine” in Ten Times Better, Longer, Faster, Farther: Understanding Scale.

**Elementary Math Games**

- In #47, John Golden (@mathhombre) writes up one of his favorite games, Fraction Catch.

- In #49, Malke Rosenfeld (@mathinyourfeet) adapts a math game that’s Totally Territorial: Cats, Maps, Area & Multiplication.

- John is back in #51 with a superhero game for multiplication and division of fractions: Size the Day.

- In #52, Patricia Stohr-Hunt shares a free “I have, who has?” card game in Monday Math Freebies: Numbers to 20.

- Meanwhile, I play Tens Concentration and Math War with my homeschool co-op students.

- And Patrick Vennebush (@pvennebush) creates a multiplication version of Nim in Great Gift for a Math Dad.

- In #53, Colleen Young (@ColleenYoung) collects her favorite Mathematics Games. Click a tab at the top of her blog and explore!

- Malke is back in #56, where she invwents a New Math Game: Factor Dominoes.

**Playing with Programming**

- In #51, DrTechniko (@drtechniko) explains How To Train Your Robot. It’s a great game for family math night!

- In #52, David Wees (@davidwees) posts Kindergarteners programming and Programming with 3rd graders.

- In #58, Christy Knockleby (@housefulofchaos) describes What I want my children to practice through computer programming.

- Older students love learning to command the computer, too. My daughter Kitten enjoys Al Sweigart’s free Python programming books, especially
*Invent Your Own Computer Games*.

**Moving Beyond the Basics**

- In #49, Pat Ballew (@ballew_pat) stands in awe of a math calculation with Three Times the Symmetry.

- In #51, David Coffey (@delta_dc) helps students decide When it makes sense to use a calculator.

- And Christy Knockleby (@housefulofchaos) creates binary cards for adding up The sum of the powers of two.

- In #52, Crewton Ramone (@CrewtonRamone) teaches Long Division With Base Ten Blocks.

- In #54, Dan MacKinnon (@mathrecreation) takes A deep dive into the multiplication table.

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## Adventuring into Algebra and Geometry

“I point out to them that are almost always multiple methods in math. Teachers may have told them that there is only one way to do things in the past, but that is bullsh*t.”—John Golden, Guess My Rule

**Playing with Puzzles**

- In #47, Maria Miller posts a Triangle area problem.

- In #48, John Golden (@mathhombre) shares the graphic adventures of Mr. Slope Guy.

- In #51, David Cox (@dcox21) offers a geometric algebra puzzle: Did I Get It?

- And Mimi Yang (@untilnextstop) poses a puzzle to prompt Estimation of Circular Areas.

- In #52, yofx relates a Pythagorean puzzle: Scharezade + Math.

- In #55, Pat Ballew (@ballew_pat) analyzes a challenging puzzle in Students’ Difficulty with Geometry.

- In #56, Erlina Ronda (@math4teaching) shares two puzzles: Semicircle Road Trip #1 and #2.

**Getting into Games**

- In #51, I explain the Function Machine game. And John Golden shows how it works in the classroom: Guess My Rule.

- In #55, Alexandre Muñiz (@two_star) details The Making of Angle Find: A Geometric Game. You can play the game here.

- And John Golden (@mathhombre) plays with integer inequalities: Greater Than.

**Teaching Middle School Math**

- In #48, Bree Pickford-Murray (@btwnthenumbers) comes up with a creative way to get her middle-school students involved in solving math problems: Math Emergency!

- In #49, Fawn Nguyen (@fawnpnguyen) shares Always-Sometimes-Never (ASN) questions for middle-school math.

- In #51, Geoff Krall (@geoffkrall) introduces The Great Inquiry Based Curriculum Mapping Project for algebra and beyond (later adapted into his Common Core Problem Based Curriculum Maps, which begin at grade 4).

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## Scaling the Slopes of High School Math

“I would argue that application is not the most important reason we teach mathematics. The most important thing we teach kids is mathematical thinking.”—John Chase, Why Calculus still belongs at the top

**Puzzling It Out**

- In #47, Luis R. Guzman, Jr., introduces A Complex Problem for students.

- In #51, Kate Nowak uses a wonderful, puzzle-based approach to Introducing Logs. I like Sue’s idea to simplify the notation further: P
_{2}(8)=3.

- In #54, Rebecka Peterson (@RebeckaMozdeh) plays with a couple of Calculus puzzlers.

- In #58, Amy Gruen (@sqrt_1) shares a sorting puzzle that Sextupled the Time It Takes To Teach End Behavior of polynomial functions to her Algebra 2 students.

- And a former student of mine investigates number series in Fibonacci Multiplication.

**Math in the Real World**

- In #52, Sam Shah (@samjshah2) wraps up the school year with some real-world math in Wealth Inequality: A Calculus Investigation.

- And John Berray’s (@johnberray) students apply geometric series to a 1792 Penny.

- Also in #52, Rachel Thomas (@math_rachel) explains how math is used to keep track of offenders and undertake search and rescue operations: Conic section hide and seek.

**Teaching High School Math**

- In #47, Derek Bruff (@derekbruff) pushes students to confront the weakness of intuition: Prediction Questions, Simulations, and Times for Telling.

- In #51, Nat Banting (@NatBanting) walks us through his students’ Soft Drink Project: The Framework, The Brainstorm, The Design, The Math, The Show.

- In #57, Pat Ballew (@ballew_pat) takes a closer look at the centroid: Just an Average Point.

- In #58, Sam Shah (@samjshah2) uses GeoGebra to play with Families of Curves. Beautiful!

- And Pat investigates square pyramid numbers in Some Notes on the Sum of Squares of the Integers.

- Also in #58, Arthur Benjamin argues that statistics should be the new summit of the high school curriculum. John Chase (@mrchasemath) disagrees: Why Calculus still belongs at the top.

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## Enjoying Recreational Puzzles and Math Art

“If you’re not a math buff, but secretly always wanted to be, you can do no better than start here. If you are already an established math buff I don’t promise you’ll learn a lot new, but you’ll be highly entertained along the way, and likely see some things you already knew from fresh or different angles.”—Shecky Riemann, Joy to the Word (of Math)

**Math Circle Puzzles**

- In #47, Rodi Steinig explores a puzzle with children: What We Did in Math Circle, and Why We Did It.

- In #49, Sue VanHattum (@suevanhattum) describes how The Oakland Math Circle does Spot It.

- In #52, Fawn Nguyen (@fawnpnguyen) shares several wonderful puzzles from her Math Teachers’ Circle. (A few of them no longer work, since the graphics are lost to history.)

- And Rodi reminds us that some math problems need to be pondered: The List, My Shirt, and Taking a Break from a Problem.

**Classic Conundrums**

- In #51, Dan MacKinnon (@mathrecreation) shares five puzzles On the island of liars and truthers.

- In #52, Pat Ballew (@ballew_pat) highlights a couple of Nice Old Geometry Problems.

- And Shecky Riemann (@SheckyR) offers a new version of a classic logic puzzle that is easy enough for elementary students.

- Also in #52, Dave Richeson (@divbyzero) dips into history to challenge us with Puzzler: a squarable region from Leonardo da Vinci.

- Back again in #58, Pat explores Geometric Vanishes, A Little History. “For 450 years, puzzles that can be rearranged to change the area have been keeping us spellbound.”

**And Other Stumpers**

- In #48, the IMACS staff challenge us to solve the Mystery of the Lost Dog.

- In #51, Robert Abbott (inventor of the card game Eleusis) shares some great Logic mazes.

- In #52, William Emeny (@Maths_Master) poses the Square number snakes and rings puzzle. (Can your kids spot the error?)

- And Fawn Nguyen (@fawnpnguyen) collects a variety of puzzles and activities in Last Math Lessons.

- Also in #52, David Coffey (@delta_dc) investigates the eternal question: How long until we “Pig Out”? And here’s Part II.

- In #57, Sue VanHattum (@suevanhattum) posts two Holiday Logic Puzzles.

**Mathematical Art**

- In #51, Justin Lanier (@j_lanier) shares Slides and Twists, Life in Life, and Star Art.

- In #56, John Golden (@mathhombre) turns math into art: Exponential Potential.

- In #57, Malke Rosenfeld (@mathinyourfeet) creates Mathematical Star Ornaments.

- In #58, John and his son Xavier investigate conjectures about an origami cube in Family Math: Origami.

**Playful Math Books**

- In #47, Peter Rowlett (@peterrowlett) collects a list of Favourite popular mathematics books.

- In #48, I offer a brief review of Fermat’s Enigma.

- Then in #49, I discover Raymond Smullyan Excerpts at Dover Publications.

- In #55, Shecky Riemann (@SheckyR) reviews Steven Strogatz’s
*The Joy of x*: Joy to the Word (of Math).

- In #56, I share Who Killed Professor X?

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## Teaching with Wisdom and Grace

“Be creative. Look for strange relationships. Use diagrams. Use humor. Use analogies. Use mnemonics. Use anything that makes the ideas more vivid. Don’t stop until it makes sense, or that mathematical gap will haunt you. Mental toughness is critical — we often give up too easily.”—Kalid Azad, How to Develop a Mindset for Math

**Tips and Resources**

- In #49, John Golden (@mathhombre) discusses the value of Math Memoirs to help us understand a student’s thinking. (I love this post! The video he mentions has moved to here.)

- In #52, Jen Runde wraps up a year of math journaling with a Culminating Mind Map.

- And Patrick Honner (@MrHonner) gets his students to write Reflections on Math Class.

- Also in #52, Colleen Young (@ColleenYoung) links to several resources for Rich Questions in Mathematics. (Some are lost to time, but many still work.)

- And in #58, Colleen resolves that This year I will… take full advantage of all the math tips and resources she’s collected over the years.

**Creative Math Classrooms**

- In #47, Bon Crowder (@MathFour) explains How to Create an Inquiry Zone for Math Learning that makes math feel safe.

- And Jason Buell lays out some nuts and bolts of Complex Instruction.

- In #50, Erlina Ronda (@math4teaching) answers the question “What is Lesson Study?” and suggests a framework for Planning and Analyzing Mathematics Lessons.

- In #52, Druin (@druinok) demonstrates how to take Cornell Notes in Math Class.

- In #54, Remi Smith (@reminoodle) ends each semester with Review Games by Students for Students. Cool!

**Help for Homeschoolers**

- In #53, I investigate how Benezet’s experiment helped students build number sense.

- In #54, I help homeschoolers answer the question How Can I Teach Math If I Don’t Understand It?

- And Christy Knockleby (@housefulofchaos) shares 5 Steps to Creating Homemade Board Games to Practice Math Skills with Children at Different Levels. See also: Homemade Board Game Ideas.

**Building a Healthy Math Mindset**

- In #47, David Coffey (@delta_dc) discusses how to support students in being problem finders, not just problem solvers: Whose problem is it?

- In #50, with help from James Tanton (@jamestanton), I explore Thinking (and Teaching) like a Mathematician.

- In #52, Sue VanHattum (@suevanhattum) ponders the difficult task of Teaching for Understanding.

- In #53, Bon Crowder (@MathFour) shares how her creativity got squished in high school: Dumb Questions? Aren’t They All?

- And Rodi Steinig explains “The idea of a Math Circle is to not tell anyone anything.”

- In #58, Sue Jones (@geonz) thinks learning math should be Like a back float.

- And Kalid Azad (@betterexplained) wraps up the year with a wealth of insights about learning and teaching math in his How to Develop a Mindset for Math series.

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## What Comes Next?

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 month of February at Iva Sallay’s Find the Factors blog. 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 Carnival, click for details:

*CREDIT: “Lego Minifig Party” photo (top) courtesy of Hello I’m Nik on Unsplash.*