Welcome to the 150th 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 October, so I’m squeezing this in between extended-family situations that require my time. If you’d like to help keep the Playful Math Carnival alive, we desperately need hosts for 2022!

## Try These Sum-Difference Puzzles

By tradition, we start the carnival with a puzzle/activity in honor of our 150th edition. This puzzle comes from the archives of Iva Sallay’s delightful Find the Factors blog.

**Copy the puzzle diagrams below.** Write numbers in the boxes to make true statements going uphill, and use the same numbers to make true statements going downhill:

**Six has two factor pairs.** One of those factor pairs adds up to 5, and the other one subtracts to 5. Can you place those factors in the proper boxes to complete the first puzzle?

**150 has six factor pairs.** One of those factor pairs adds up to 25, and another one subtracts to 25. If you can identify those factor pairs, then you can complete the second puzzle!

How are the two puzzles related?

Iva also posts one of my favorite multiplication puzzles, her scrambled times tables. Check out puzzle #150 in this post (it’s Level 3, or medium difficulty) and then browser her site for plenty more.

## Playful Math Carnival #150

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

This month’s carnival continues our Playful Math Dodecaversary. As I mentioned back in Carnival #144, 2021 is the 12th anniversary of the Playful Math Education Blog Carnival (originally titled Math Teachers at Play). We’ve shared so many wonderful, playful, creative math ideas through the years.

But blogs and websites disappear every day. I hate to lose track of it all, so I’m trying to rescue what I can.

The posts in this 150th carnival are drawn from our third year of publication. We had twelve carnivals from February 2011 to January 2012, with nine different volunteer hosts. I don’t have time to organize the posts, so I’ll just hit the highlights month by month…

## February 2011: The Limericks Carnival

I hosted Carnival #35, and for fun I scattered math poetry between the 35 posts. (It was cool to hit that number, but later I had to delete one post when its blog got eaten by a spam site.) These were my favorite submissions:

- Sally Haughey (@SallyHaughey) applies her imagination to “number recognition, one to one correspondence, counting, taking turns, and beginning addition” in Make Your Own Math Games – Fit for Royality!

- Cassy Turner (@Cassyt) shows how a common trick used by elementary teachers may backfire, causing a student to stumble: Understanding trumps tricks.

- Risa Kawchuk plays a variation on Rock, Paper, Scissors for practicing addition and multiplication facts with mixed ages: Fingers! – A Math Game.

- Sue Downing (@susandowning) finds a wonderful visual for creating Equivalent Fractions, which would also be helpful for an older student doing unit conversions.

- I’m a sucker for Four-4s variations. Jeff Trevaskis (@webmaths) shares a worksheet puzzle/game for practicing Order of Operations.

- I love the games that John Golden (@mathhombre) invents, and his Integer Games were perfect to round out Kitten’s math lessons this week.

- For a practical geometry exercise, Dan MacKinnon (@mathrecreation) constructs angle bisectors and parallel lines in simple origami and math – paper cup.

- Mimi Yang (@untilnextstop) offers a hands-on Trick for Teaching Basic Trig to confused students. Read the comments for a bonus tip on introducing trig ratios, and then see day 2 of the lesson: Not Enough Information?

- Shawn Cornally (@ThinkThankThunk) puts his foot in his mouth, and his students figure out exactly how far down it went, in How I Teach Calculus: A Comedy (The Papoose is Imminent).

- Pat Ballew (@ballew_pat) says, “Sometimes vectors make difficult problems look easy.” Check out his post Midpoint Madness for an example.

- Shecky Riemann (@SheckyR) offers up a “little quickie recursive brain workout” in Weekend Miscellany.

- Maria Andersen (@busynessgirl) creates a New Math Game: Antiderivative Block and says that “watching students play this game was the most fun I have ever had in a math class.”

- Sue VanHattum (@suevanhattum) tells how she began reasoning through a problem in Tin Ceilings, Triangles, and Loving Math: “Coming up with a formula for squares is a hard problem (which I’m not done with yet). But just looking for different size triangles, and maybe coloring some in, would be fun for a young kid, I think.”

- In the “made me laugh” department: John Cook (@JohnDCook) finds out that science education, too, is “much more complicated than you expected” (reference to quote by E. G. Begle) when he tries to solve for Final velocity with his daughter. And then Pat chimes in with a follow-up story about related rates.

- I wish I could sit in the back of the room when Jonathan Halabi (@Jd2718x) starts Teaching off topic (yet again). He follows up with a thought-provoking addendum on division of fractions.

- My contribution to the carnival is a quote from Maria Droujkova (@MariaDroujkova): What to Do When You’re Stuck. Does it work? Dave Lanovaz (@DaveLanovaz) offers a great example in his post Looking for Wrong Answers.

- James Tanton (@jamestanton) takes on the challenge of Multi-Choosing: How can we count the possibilities when repeat choices are allowed?

## March 2011: The Squangular Carnival

John Golden (@mathhombre) hosted Carnival #36 with a delightful collection of posts. These were my favorites:

- John leads off the carnival with my Times Tac Toe game. It’s a variation of gomoku, which is always fun.

- Chris McGinn shares a fun reflectional symmetry activity in Mirror Imaging Monsters.

- Erlina Ronda (@math4teaching) introduces negative numbers with a sorting activity.

- John Cook (@JohnDCook) invents a new class of prime numbers called the Limerick Primes. Can your students find one?

- For his own entry, John explores the difference between teaching rules (Do we line up the decimal point or not?) and doing mathematics (and making conjectures) in Knot Fun.

## April 2011: The Number Puzzle Carnival

Caroline Mukisa (@mathsinsider) hosted Carnival #37, featuring several fun calculations with the numbers 3, 7, and 37. These were my favorite posts:

- Crewton Ramone (@CrewtonRamone) and sons are Playing with Nines (multiplication).

- Cynthia Hockman-Chupp (@love2learn2day) explores growing patterns with snap cubes.

- Dan Finkel (@MathforLove) and Katherine Cook create a playful One Minute Math Video: Adding 1000 numbers versus opening a bag of chips. Your kids will love this one!

- James Tanton (@jamestanton) shares his mathematical “why” in What Made Me a Mathematician (and why I approach mathematics teaching the way I do).

- My daughter Kitten plays with negative numbers in Backwards Math and then solves a creative identity crisis in More Backwards Math.

## May 2011: Just the Basics

Guillermo Bautista (@jr_bautista) hosted a bare-bones Carnival #38. These were my favorite entries:

- Susan Carpenter’s 1st and 2nd grade classroom plays with growing patterns in http://susan-carpenter.blogspot.com/2011/03/one-more-math-post.html.

- Dan Finkel (@MathforLove) presents Squares of Differences: subtraction practice toward a greater purpose, saying, “Squares of differences are a great puzzle, a motivator of arithmetic practice, and a springboard to some very deep, elegant ideas in mathematics.”

- John Golden (@mathhombre) creates a super-hero-themed game to introduce exponents: Power Up.

## June 2011: The Math Humor Carnival

I hosted Carnival #39, featuring several treats from Mike Cook’s Canonical List of Math Jokes. These were my favorite submissions:

- Christopher Danielson (@Trianglemancsd) has an interesting circular conversation with a 4-year old.

- Bon Crowder (@MathFour) encourages teachers to think deeply about preschool math in Counting Isn’t an Inherent Concept.

- Mathwire links to a variety of geometric explorations in Problem Solving: Pattern Blocks.

- Rachel Lynette presents a Math Scavenger Hunt to try with your students.

- Jimmie Quick (@jimmieaquick) presents Notebooking With Creative Interviews, saying, “A lesson about the googol turns into a fun creative writing exercise.” Be sure to check out her other math notebooking pages and her very thorough math notebooking lens, too.

- Yan Kow Cheong (@MathPlus) has fun adding spice to NCTM’s search for “real-life problems” in Censored Math Questions from Singapore.

- Bree Pickford-Murray (@btwnthenumbers) asks her students to write a proof, and they discover the importance of clear definitions: Rosie’s Round Table.

- Sue VanHattum (@suevanhattum) found a great resource for older students: RISPs: Rich Starting Points.

- Dave Richeson (@divbyzero) points out the problem-solving value of Extreme examples and counterexamples.

- John Scammell (@thescamdog) shows students how to create a Pythagorean spiral on card stock to explore irrational numbers in Radical Number Line.

- Tanya Khovanova shares several Recent Geeky Jokes, plus instructions from John Conway on the best way to walk up the stairs. Okay, so those aren’t really puzzles — but these two posts are.

- Rebecca Hanson (@AuthenticMaths?) shows how a simple warm-up exercise can develop deep understanding in her series How do the Chinese do it? [parts 2, 3, 4, 5, 6, 7].

- David Cox (@dcox21) encourages students, “Embrace the conflict that arises when what you thought was true turns out to be, well, not so much.” Check out his post ( )conceptions.

- Avery Pickford (@averypickford) offers a thought-provoking series about Teaching Problem Solving [parts 2, 3]. (Part 3 is his wonderfully thorough “Mathematical Habits of Mind” list.)

- Colleen Young (@ColleenYoung) recommends a math puzzle flexible enough to cover topics from addition to complex numbers: Arithmagons.

## July 2011: The Word-Puzzle Carnival

Sue VanHattum (@suevanhattum) collected 40 posts for Carnival #40, plus an intriguing puzzle about the word “forty.” These were my favorite posts:

- Bon Crowder (@MathFour) looks through her young daughter’s eyes at the commutative and associative properties, along with substitution, in How to Teach Math Concepts at the Dinner Table.

- Rachel Lynette offers a symmetry game called Guess My Grid, with a free game board to download.

- Toomai shares a series of posts on building a computer from first principles, using paper and then wood to create a simple adding machine. Here’s his first post, and you can follow the arrows to each new one.

- Alexandre Borovik (@AVBorovik) blogs about The greatest calamity in the history of science and the importance of very round numbers.

- John Golden (@mathhombre) has another cool game, called Linear War.

- Dan MacKinnon (@mathrecreation) discovers the Hidato, or a king’s tour puzzles, and then makes up his own Kixote, or knight’s path puzzles.

- Allison Johnson (@infinigons) posts about mathematical fearlessness and the lessons she took from solving a hard problem in Putting myself in my kids’ shoes.

- For my entry, I share some Quotations on Teaching Math from several of my favorite bloggers.

- John Cook (@JohnDCook) posts a sweet collection of Geeky limericks, with several more in the comments.

- JoAnne Growney (@MathyPoems) shares poem about Seeking a universal language.

## August 2011: The Centered-Square Carnival

Mimi Yang (@untilnextstop) hosted Carnival #41. These were my favorite entries:

- Sue Downing (@susandowning) tells how her tutoring students deal with a bad math problem in Was the Bus Empty?

- Alexander Bogomolny (@CutTheKnotMath) shares a series of Engaging Math Activities for the Summer Break.

- Kate Nowak presents a Good Problem: Follow That Diagonal. It’s a nice rich puzzle to keep in the back of your pocket, because it is tied to various concepts but also works well as a standalone task.

- Gary Antonick and Katherine Cook celebrate Avoid Triangles at all Costs (ATAAC) Day with a puzzle challenge (and here’s Part 2), and discuss the value of questioning in mathematics.

- Ashli Black (@mythagon) describes one of her favorite warm-up activities: What’s the Question?

## September 2011: And Baby Makes Three

Bon Crowder (@MathFour) spins a moving tale in Carnival #42. These were my favorite posts:

- Miss Pi considers how to get her students Asking Good Questions.

- My daughter and I investigate The (Mathematical) Trouble with Pizza.

- Kudzayi Chakahwata (@Kudzayi_C) shares 5 Tips for Coaxing Dreaded Maths Corrections from Your Child.

- Dan MacKinnon (@mathrecreation) explains Tesseracts and factor lattices, a geometric way to envision multiplication relationships. Challenge your children to draw a few.

- John Cook (@JohnDCook) explains the problem of finding Odd numbers in odd bases.

## October 2011: Fast Food, Crime Drama and More

Caroline Mukisa (@mathsinsider) hosted the savory Carnival #43. Unfortunately, the “Crime Drama” (analyzing blood spatter) post was beyond my ability to recover. These were my favorite articles:

- Kristen (@Teaching_Stars) plays an Ancient Roman finger game in Math Play Day.

- Bon Crowder (@MathFour) explores the difference between motivation and inspiration in teaching children.

- Dan MacKinnon (@mathrecreation) adds depth to our thinking about elementary patterns in Grade one functions.

- Rodi Steinig debates an Animal Voting Plan with her math circle students.

- Alexander Bogomolny (@CutTheKnotMath) ponders the questions, When am I ever going to use this? Why do we need to learn this? Includes a summary of Samuel Otten’s (@ottensam) article Cornered by the Real World: A Defense of Mathematics.

- I pose Leonhard’s Block Puzzles, a treat from my old Mathematical Adventures of Alexandria Jones newsletter.

- Natasha interviews the designer of Thinkfun’s Chocolate Fix: Mark Engelberg, Game and Puzzle Inventor.

- Annie Kate shares Questions for Math Students after Finishing a Problem. These would be great for a math journal or exit ticket.

- John Golden (@mathhombre) starts a war in Area Battle: “A game for upper el to middle school to compare area and perimeter.”

## November 2011: The Hexa-Trex Carnival

Bogusia Gierus hosted the short Carnival #44. While you’re there, play with the Daily Hexa-Trex puzzles and then encourage your students to make up their own. These were my favorites:

- Alexander Bogomolny (@CutTheKnotMath) gives us a very intriguing geometric / visualization puzzle: Wrapping a Cube.

- Erlina Ronda (@math4teaching) helps students make connections in The Counting Principle, Pascal’s Triangle, and Powers of 2.

- Jason Dyer (@jdyer) challenges us to analyze student errors in Focus on fixing bugs rather than overwriting procedures.

## December 2011: Just the Links, Ma’am

Virtual Math Tutor (@vmathtutor) went back to the basics for Carnival #45. These were my favorite entries:

- Tiger’s Mum plays with
*Sir Cumference and All the King’s Tens*in Spicing up math.

- Tom DeRosa encourages students to review with an Equations vs. Inequalities Mini-Poster Project.

- Susan Carpenter’s 1st and 2nd grade classroom explores traditional body-based measurements in A Measuring Quandry.

- Karyn Tripp shares math activities to go along with the story book One Grain of Rice.

- Kitten and I continue our counting lessons with More Than One Way to Solve It, Again.

- Jason Dyer (@jdyer) discusses The Educational Problem with Teaching Multiplication as Repeated Addition.

- Alexander Bogomolny (@CutTheKnotMath) continues his series Thought Provokers to Start a Class With.

- Erlina Ronda (@math4teaching) follows her counting post from last month with Pascal’s triangle and Counting Permutations.

## January 2012: Celebrating Books about Math

I wrapped up our third year with Carnival #46, seasoned with a variety of my favorite “living books” for math. These were my favorite submissions:

- Kristen and her girls play with the
*First Grade Diary*and other Cuisenaire rod activities in For the Love of the Rods. (And they review*12 Ways to Get to 11*, too.)

- MathWire offers a bit of seasonal fun in Snowman Probability and the Last Snowman Standing Game.

- While Mama makes dinner, Malke Rosenfeld’s (@mathinyourfeet) daughter creates Marshmallow Math: Solids & Sculpture. (And the story continues here, here, here, and here.)

- IMACS presents a clock-based game in An Introduction to Modular Addition and adds a couple new rules in More Modular Arithmetic.

- Rebecca Haden offers as series of counting challenges in her lesson plan, Combinatorics for Breakfast. What, no Spam?!

- Mimi Yang’s (@untilnextstop) class has been Learning from Our (Algebra) Mistakes. (The missing resources she links to are My Favorite No and The Row Game.)

- Riley Lark gives his students the run-around in What did you do to the x-axis?!? Using the most relevant context possible.

- Sue VanHattum (@suevanhattum) reviews
*Math Girls: A Novel Way to Learn Some Deep Math*: “I would highly recommend this book for anyone at the level of pre-calculus and above who enjoys math.”

- Gary Antonick and James Tanton (@jamestanton) share a few puzzles that elementary-age children can understand but adults can enjoy exploring as well: Numberplay: Tanton Wordless.

- Jen’s students add a “Types of Graphs” foldable to their math journals. Be sure to check out her other math journal ideas, too.

- Can you solve Pat Ballew’s (@ballew_pat) puzzle about an Interesting Rectangle Partitioning?

- John Cook (@JohnDCook) presents A Renaissance math puzzle. Intrigued, Thony Christie (@rmathematicus) digs into history in The story of a problem.

- Christopher Danielson (@Trianglemancsd) argues that being a good teacher is not about problem-solving skills, It’s about understanding.

- Math Rules wonders, “How much of a class should be conceptual and how much should be procedural?“

- Bon Crowder (@MathFour) hosts an interesting series of interviews with Mathematician Parents.

## That’s All, Folks!

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 November/December 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 — if you would like to take a turn hosting the Playful Math Education Blog Carnival, please speak up!

CREDITS: Blog photos belong to their original bloggers. “Green seedling” photo by Noah Buscher. “Ice cream flavors” photo by Lama Roscu. “Tea and writing” photo by Sixteen Miles Out. “Odd number” photo by Kai Gradert. “Giraffe” photo by Alexander Ross. “Beach sunset” photo by Dvir Adler. All via Unsplash.