Playful Math Carnival #142: Math Art Edition

Welcome to the 142nd 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.

Seriously, plan on coming back to this post several times. There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 142nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Activity: Planar Graphs

According to the OEIS Wiki, 142 is “the number of planar graphs with six vertices.”

What does that mean?

And how can our students play with it?

A planar graph is a set of vertices connected (or not) by edges. Each edge links two vertices, and the edges cannot intersect each other. The graph doesn’t have to be fully connected, and individual vertices may float free.

Children can model planar graphs with three-dimensional constructions using small balls of playdough (vertices) connected by toothpicks (edges).

Let’s start with something smaller than 142. If you roll four balls of playdough, how many different ways can you connect them? The picture shows five possibilities. How many more can you find?

Sort your planar graphs into categories. How are they similar? How are they different?

A wise mathematician once said, “Learning is having new questions to ask.” How many different questions can you think of to ask about planar graphs?

Play the Planarity game to untangle connected planar graphs (or check your phone store for a similar app).

Or play Sprouts, a pencil-and-paper planar-graph game.

For deeper study, elementary and middle-school students will enjoy Joel David Hamkins’s Graph coloring & chromatic numbers and Graph theory for kids. Older students can dive into Oscar Levin’s Discrete Mathematics: An Open Introduction. Here’s the section on planar graphs.

[“Geöffneter Berg” by Paul Klee, 1914.]


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

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

Art images below are from the 2020 Bridges Conference Gallery.

[“Four Dodecahedra” by Ulrich Mikloweit.]

Talking Math with Kids

“Math is not just adding, subtracting, multiplying and dividing. It is the mystery of numbers within numbers and the discovery of how numbers keep changing the world.”

—Savannah Sanders, Never Give Up

  • The anonymous Urban Mama relates her son’s experience with different aspects of counting in Math Books We Love.

[“Los tres Amigos” by Zdenka Guadarrama.]

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Exploring Elementary Arithmetic

“Almost no one teaches finding common denominators as a prelude to dividing fractions (which is sort of a shame because it makes division of fractions work like multiplication … the way kids think it should.)”

—Pat Ballew, Division of Fractions by the Alien Method

  • Iva Sallay’s (@findthefactors) blog is full of multiplication puzzles that are fun for students and adults. Can you solve her Mystery Message? Here are the first three clues.

[“Concise Lesson in Uniform Partitions” by Conan Chadbourne.]

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Adventuring into Algebra and Geometry

“Working with a student who has not yet been taught simultaneous equations or ‘rules’ of solving equations with two unknowns is fun — for the student as well as for the teacher. Both of us are experiencing Aha moments in almost every session!”

—Rupesh Gesota, Math Coach blog

[“Tangent to a flower” by Jana Kopfová.]

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Scaling the Slopes of High School Math

“We must have empathy, and we must have humility, and we must understand what we have done badly in the past. We must catch ourselves when we repeat the patterns that brought us to past evils. We must do more than only calculate. “

—Joseph Nebus, My All 2020 Mathematics A to Z: Statistics

  • Joseph Nebus (@nebusj) continues his fascinating A to Z posts with a look at the dangerous history of Statistics.
  • The Mathematics News Snapshots for High School (MNS) project offers insight into modern mathematical puzzles like Catalan’s Conjecture.

[“Heresy” by Hanne Kekkonen.]

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Enjoying Recreational Puzzles and Math Art

“This is the wonderful thing about just thinking and playing with half-formed thoughts: often exciting ideas will flash into your brain when you least expect them.”

—James Tanton, Math and Cats

  • If you’d like your students to think about how math affects politics, there’s still time to play with The Gerrymander Math Project before next week’s Election Day.
  • Art is one of my favorite ways to play with math ideas. Sophia Wood (@fractalkitty) hosts the Mathober Doodles challenge. There’s still time to catch the last few days, or you can just ignore the dates and start at the beginning.
  • Don’t forget Annie Perkins’s (@anniek_p) Math Art Challenge — an evergreen resource of mathematical inspiration for your students.

[“Five 7 Crossing Links” by Annie Perkins.]

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Teaching with Wisdom and Grace

“Thinking is everything in mathematics. Thinking is where joy is to be found … A math class should be an environment where students feel free to share their thinking, and feel no shame about brainstorming.”

—Francis Su, Teach math like you’d teach writing

  • Jenna Laib (@jennalaib) helps her sixth-grade students learn the value of failure and frustration with Johnny Upgrade.
  • The Mathematics Teachers Association of the Nova Scotia Teachers Union (@MTA_NS) publishes all of their Mathematics Matters newsletters online for free. The Saskatchewan Mathematics Teachers’ Society (@SMTSca) posts each issue of The Variable. And the British Columbia Association of Math Teachers (@BCAMT) shares their eVector newsletter, too. Great resources full of creative math!

[“Red Cylinder with self intersections” by Gabriele Meyer.]

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Credits, and a Cry for Help

Art images are from the 2020 Bridges Conference Gallery. Quotes are from the linked blog posts.

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 is planned for late November or early December at Arithmophobia No More 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 Education Blog Carnival, please speak up!

[“Conformal Cosmatesque” by Steve Pomerantz.]

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