## 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 149 via Nature Study Australia

Check out the latest carnival of playful 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.

Johanna put together a beautiful collection of mathematical resources and activities for studying math in nature, biometric data, journaling, math poetry, and other delights.

### 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 Carnival 148 via Math Book Magic

Check out the latest carnival of playful 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.

Kelly put together this magical collection of mathematical games, activities, art projects, hands-on fun, math storybooks, and inspiration.

### 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 Education Carnival 147

Welcome to the 147th 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!

By tradition, we start the carnival with a puzzle in honor of our 147th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

## Playful Math Carnival 146 via Find the Factors

Check out the latest carnival of playful 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.

Iva put together this huge and amazing collection of mathematical games, activities, art projects, hands-on fun, math storybooks, poetry, and more.

### 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 Carnival 145 via Math Hombre

Check out the latest carnival of playful 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.

John put together this wonderful collection of mathematical games, art projects, books, math essays, puzzles, and more.

Continue reading Playful Math Carnival 145 via Math Hombre

## Playful Math Carnival 144: Anniversary Edition

Welcome to the 144th 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!

By tradition, we would start the carnival with a puzzle/activity in honor of our 144th edition. But this time, I want to take a peek back at the history of our carnival.

## Playful Math Carnival 143 via Learning Well at Home

Check out the latest carnival of playful 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.

Sonya put together this wonderful collection of mathematical games, art projects, holiday activities, paper crafts (LOTS of snowflakes!), and more.

She writes:

“It doesn’t matter where you look, there are always things to count and lots of things to wonder about. How many snowflakes in a snowman? How many points are on a star? How many turkeys do we eat every year? Does anyone actually eat all the fruitcake that is sold each year?
“Here is Winter and her holidays by the numbers…
“This was probably my favorite Playful Math Education Blog Carnival to write. There is so much out there to explore that I’m sure I’ve barely scratched the surface.
“Come back because I’m going to keep adding to this post…”

—Sonya Post, Carnival #143

## 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.

## 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.