Playful Math Education 142

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.]

Click here for all the mathy goodness!

Working on the Playful Math Carnival

Every time I put together a Playful Math Education Blog Carnival, it becomes my favorite blog post of all time.

At least until the next edition.

I’m always delighted by the posts I discover. There’s so much richness in the math blogging community. This month’s carnival is no different.

I think you’re going to love it!

Hint of Things to Come

The Paul Klee painting above is from the carnival. Isn’t it beautiful?

In the carnival post, I use the image to complement a math activity about graphs.

But I think it’s also a wonderful reminder of how connections (between individual bloggers or between math topics in a carnival) make a richer whole than any of us could create on our own.

Would You Like to Help?

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, please speak up!

CREDITS: “Geöffneter Berg” by Paul Klee, 1914 via John Golden’s (Mathhombre) Miscellanea.

Playful Math Carnival 141 via Nebusresearch

Check out the latest carnival of playful math:

Joseph put together this huge collection of mathematical inspiration, activities, teaching tips, puzzles, and more.

He writes:

    “I am an amusement park enthusiast: I’ve ridden at least 250 different roller coasters at least once each. This includes all the wooden Möbius-strip roller coasters out there. Also all three racing merry-go-rounds. The oldest roller coaster still standing. And I had hoped, this year, to get to the centennial years for the Jackrabbit roller coaster at Kennywood Amusement Park (Pittsburgh) and Jack Rabbit roller coaster at Seabreeze Park (Rochester, New York). Jackrabbit (with spelling variants) used to be a quite popular roller coaster name.
    “So plans went awry and it seems unlikely we’ll get to any amusement parks this year. No county fairs or carnivals. We can still go to virtual ones, though. Amusement parks and midway games inspire many mathematical questions.
    “So let’s take some in…”

Click Here to Read the Carnival Blog

Continue reading Playful Math Carnival 141 via Nebusresearch

Playful Math 140 at Find the Factors

Check out new Playful Math Blog Carnival at Find the Factors blog:

A blog carnival is like a free online monthly magazine of mathematical adventures. And this edition is a great one!

Iva put together a huge collection of articles on learning, teaching, and playing around with math. There’s such a wealth of interesting things to read, you’ll want to bookmark the post and come back to it again and again.

Click here to go read the carnival blog

Continue reading Playful Math 140 at Find the Factors

Playful Math Carnival 139 at Math Mama Writes

Okay, yes, this link is way late. Again. It’s a good thing these math carnivals are full of evergreen fun!

[TEASER: Watch this space for an exciting announcement next week. I may not have been blogging, but I haven’t been idle…]

Meanwhile, do check out the latest carnival of games, activity ideas, and inspirations for mathematical delight:

Sue put together this summer collection of mathematical activities. She writes:

“Most mathematicians are in it at least partially for the fun of it. We like to play with numbers, shapes, and logic. The more you play with math with your kids, the more likely they are to enjoy it.”

Sue edited the wonderful book Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, so she knows all about the joy of learning math.

Each monthly Playful Math Education Blog Carnival brings you a great new collection of puzzles, math conversations, teaching tips, and all sorts of mathy fun.

It’s like a free online magazine of mathematical adventures, helpful and inspiring no matter when you read them. Enjoy!

Click Here to Read the Carnival Blog

Help Us Keep the Carnival Going

The Playful Math Blog Carnival wants you!

The carnival is a joint effort. We depend on our volunteer hosts to collect blog posts and write the carnival each month.

Putting together a blog carnival can be a lot of work, but it’s a great opportunity to share the work of bloggers you admire and to discover new math-friends online. I love that part of being a host!

Classroom teachers, homeschoolers, college professors, unschoolers, or anyone who likes to play around with math — if you would like to take a turn hosting the carnival, please speak up.

Playful Math 138 @ Math Hombre Blog

Wow, the pandemic and the lockdowns really threw me off-kilter. Or maybe it’s just that I’ve been mono-focused on finishing my new book. This poor blog has sure suffered lately.

Unfortunately, I let last month’s carnival pass me by. I only noticed it, because Sue put out a call-for-entries to her own carnival, which is coming soon.

But the last one was great, and you really don’t want to miss it!

Check out spring Playful Math Blog Carnival at Math Hombre blog:

John put together a great collection of number puzzles, games, and math art. Plus special memories of John Conway and Don Steward.

It’s like a free online monthly magazine of mathematical adventures. Enjoy!

Click here to go read the carnival blog

Continue reading Playful Math 138 @ Math Hombre Blog

Playful Math Carnival 137 @ Life Through A Mathematician’s Eyes

Check out the latest carnival of playful math:

Ioana put together this April collection of mathematical activities. She writes:

“When I first agreed to do this Carnival, I could not imagine that I will be writing and preparing for it in lockdown. But here we are, a strange situation with a stressful environment. With this in mind, we have to hope for the better. With this in mind, the Carnival is split into Learning Resources & Activities and Relaxation Time. With all that is happening around us, we need to look for activities that relax us.”

Continue reading Playful Math Carnival 137 @ Life Through A Mathematician’s Eyes

Playful Math Carnival 136 @ Nebusresearch Blog

Check out the new playful math blog carnival at nebusresearch blog. Joseph Nebus put together a great collection of math art, puzzles, games, teaching tips, and an inspiring bit of hope in troubled times:

It’s like a free online magazine of mathematical adventures.

Enjoy!

Click here to go read the carnival blog

Do You Want More Ways to Play with Math?

Past carnivals are still full of mathy treasure. See them all on Pinterest:

And if you’re a blogger, be sure to submit your blog post for next month’s carnival!

Playful Math Carnival #135 at Find the Factors

Check out the latest carnival of playful math for all ages:

Iva Sallay put together this collection of mathematical links — art, geometry, poetry, games, picture books, math history, probability, and much more.

Each monthly Playful Math Education Blog Carnival brings you a great new collection of puzzles, math conversations, teaching tips, and all sorts of mathy fun.

It’s like a free online magazine of mathematical adventures, helpful and inspiring no matter when you read them. Enjoy!

Click Here to Read the Carnival Blog

Help Us Keep the Carnival Going

The Playful Math Blog Carnival wants you!

The carnival is a joint effort. We depend on our volunteer hosts to collect blog posts and write the carnival each month.

Putting together a blog carnival can be a lot of work, but it’s a great opportunity to share the work of bloggers you admire and to discover new math-friends online. I love that part of being a host!

Classroom teachers, homeschoolers, college professors, unschoolers, or anyone who likes to play around with math — if you would like to take a turn hosting the carnival, please speak up.

And if you’re a blogger, be sure to submit your blog post for next month’s carnival!

Playing with Math 134 @ Math Misery Blog

Check out the latest carnival of playful math:

Manan Shah put together this collection of mathematical fun targeted primarily at high school teachers and students.

Each monthly Playful Math Education Blog Carnival brings you a great new collection of puzzles, math conversations, teaching tips, and all sorts of mathy fun.

It’s like a free online magazine of mathematical adventures, helpful and inspiring no matter when you read them. Enjoy!

Click Here to Read the Carnival Blog

Help Us Keep the Carnival Going

The Playful Math Blog Carnival wants you!

The carnival is a joint effort. We depend on our volunteer hosts to collect blog posts and write the carnival each month.

Putting together a blog carnival can be a lot of work, but it’s a great opportunity to share the work of bloggers you admire and to discover new math-friends online. I love that part of being a host!

Classroom teachers, homeschoolers, college professors, unschoolers, or anyone who likes to play around with math — if you would like to take a turn hosting the carnival, please speak up.