Playful Math Education Carnival 130

Play. Learn. Enjoy!

Welcome to the 130th edition of the Playful Math Education Blog Carnival, a feast of delectable tidbits of mathy fun.

The Playful Math Carnival is like a free online magazine devoted to learning, teaching, and playing around with math. It’s back-to-school time in the U.S., so this month’s edition focuses on establishing a creative math mindset from preschool to high school.

You’re sure to find something that will delight both you and your child.

By tradition, we start the carnival with a puzzle in honor of our 130th edition. But if you would like to jump straight to our featured blog posts, use our handy Table of Contents.


Some blog articles were submitted by their authors, others were drawn from the immense backlog in my rss reader, and the beautiful illustrations are from the 2019 Bridges Conference Mathematical Art Gallery.

If you’d like to skip directly to your area of interest, click one of these links:

Would you like to see YOUR favorite blog post in next month’s Playful Math blog carnival? Submissions are always open.

Submit an Entry

We need more 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!

Puzzle: Cake Numbers

Visual math promotes understanding. When children learn to see numbers, shapes, and relationships with their minds’ eye, they find new concepts easier to grasp.

The puzzle of cake numbers will stretch your students’ visualization skills. In math, a cake number is the maximum number of pieces we can cut a 3-dimensional cake into, using a planar (infinitely long, straight) knife.

Today’s carnival number 130 is a cake number.

Can you visualize how many cuts it would take to make 130 pieces of cake?

Start with a simpler puzzle to give your mental muscles a workout. Try a hands-on experiment with cake numbers:

  • Get a large block of cheese and a sharp knife.
  • See how many different pieces you can cut.
  • With zero cuts, of course, you get one piece — the whole cake.
  • With one cut, you get two pieces.
  • How many pieces can you get with two cuts? With three?

Here is a picture of four planes cutting through space. Can you count the pieces of cake?

Don’t get fooled! The first few cake numbers make the pattern look simple. But the fourth cut will not make 16 pieces.

For a simpler 2-dimensional puzzle, try cutting a flat pancake or pizza. Read more about pizza-cutting in Playful Math Carnival #106.

And if you’re still wondering, it takes nine cuts to make 130 pieces of cake.

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Talking Math with Kids

“Pisces Geometricus” by Flora Olivier

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Exploring Elementary Arithmetic

  • Counting rabbits can promote math skills, too — just ask Fibonacci. Kow-Cheong Yan (@MathPlus) looks at all the different ways to play with Rabbit Math.
“Prime 54” by Paul Ashwell

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Adventuring into Algebra and Geometry

“FIT” by Kris Empting-Obenland

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Scaling the Slopes of High School Math

  • Sue VanHattum (@suevanhattum) wants to prompt student curiousity with a hands-on review activity on the first day of class. Here are her ideas for geometry, precalculus, and more.
  • What math topics confuse your students? Or which ones stump you? Joseph Nebus (@nebusj) asks for topic suggestions to fill his Fall 2019 Mathematics A-To-Z. (Take time to explore some past topics at the bottom of the post.)
  • By the time they reach high school, most students believe that math is boring. Introduce your students to the “World’s Most Interesting Mathematicians” who share their favorite bits of mind-blowing math in The Big Internet Math-Off 2019.
“3D-Spirograph” by Alex Guerten

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Enjoying Recreational Puzzles and Math Art

“Conformal Chessboards in a Crop Field” by Hans Kuiper

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Teaching with Wisdom and Grace

“The Stijlish Seed of Life” by Emanuela Ughi

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Giving Credit Where It’s Due

“Teal cupcakes” photo (top) by Brooke Lark, “Five cupcakes” by Rae Goldman, and “Colorful layer cake” by Annie Spratt via Unsplash.

Art images are from the 2019 Bridges Conference mathematical art gallery.

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 week of September 23–27 at Find the Factors blog. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Older posts are welcome, as long as they haven’t been published in recent editions of this carnival.

Past posts and future hosts can be found on our blog carnival information page.

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