Carnival 150: Keeping Playful Math Alive

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:

  • Risa Kawchuk plays a variation on Rock, Paper, Scissors for practicing addition and multiplication facts with mixed ages: Fingers! – A Math Game.
From Jeff’s blog: The more digits you use, the higher your score.
  • I love the games that John Golden (@mathhombre) invents, and his Integer Games were perfect to round out Kitten’s math lessons this week.
  • Pat Ballew (@ballew_pat) says, “Sometimes vectors make difficult problems look easy.” Check out his post Midpoint Madness for an example.
From Maria’s blog: Math games aren’t just for little kids!
  • Sue VanHattum (@suevanhattum) tells how she began reasoning through a problem in Tin Ceilings, Triangles, and Loving Math: “Coming up with a formula for n \times n 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.
  • James Tanton (@jamestanton) takes on the challenge of Multi-Choosing: How can we count the possibilities when repeat choices are allowed?
How many ways can we scoop it?

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.
  • 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.
From John’s blog: Can art be math? Try it and see.

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:

From my blog: The secret life of equations…

May 2011: Just the Basics

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

From John’s blog: What’s your mathematical superpower?

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:

From Jimmie’s blog: Notebooking helps students remember what they learn.
From John’s blog: Finding irrationals on the number line.
  • 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.
  • Colleen Young (@ColleenYoung) recommends a math puzzle flexible enough to cover topics from addition to complex numbers: Arithmagons.
From Colleen’s blog: Adapt this puzzle to fit your students.

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:

  • 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.
From John’s blog: For this turn, “Least Slope” wins.
Math and poetry DO mix.

August 2011: The Centered-Square Carnival

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

  • 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.
From Ashli’s blog: Spark a class discussion.

September 2011: And Baby Makes Three

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

Odd or even? It depends…

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:

If you ran the zoo…
  • John Golden (@mathhombre) starts a war in Area Battle: “A game for upper el to middle school to compare area and perimeter.”
From John’s blog: First, make your Area Battle cards.

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:

From Bogusia’s blog: Connect all the tiles in a single line to make a true equation.

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.
  • 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.
From Karyn’s blog: Hands-on exponential growth.
From Erlina’s blog: How many ways can you cross a chessboard?

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:

From Rebecca’s blog: What’s for breakfast? Let’s count…
From Jen’s blog: Lift the flaps to reveal the graphs.
How do mathematician parents raise their children?

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.

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