You can prepare your children for high school math by playing with positive and negative integers, number properties, mixed operations, algebraic functions, coordinate geometry, and more. Prealgebra & Geometry features 41 kid-tested games, offering a variety of challenges for students in 4–9th grades and beyond.

A true understanding of mathematics requires more than the ability to memorize procedures. This book helps your children learn to think mathematically, giving them a strong foundation for future learning.

And don’t worry if you’ve forgotten all the math you learned in school. I’ve included plenty of definitions and explanations throughout the book. It’s like having a painless math refresher course as you play.

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.

Would you like to snag 100+ easy, no-prep resources for creative problem-solving, number play, math art, word problems, mini-essays, brainteasers, patterns, research projects, and much more?

It may look like Cimorene has lain down on the job, but don’t be fooled! She’s hard at work, creating a math investigation for your students to explore.

Cats know how important it can be for students to experiment with math and try new things. Playing with ideas is how kittens (and humans!) learn.

Cimorene wants you to know that the Make 100 Math Rebels Kickstarter offers a great way for human children to learn math through play. She encourages you to go watch the video and read all about the project:

Too often, school math can seem stiff and rigid. To children, it can feel like “Do what I say, whether it makes sense or not.” But cats know that kids are like kittens — they can make sense of ideas just fine if we give them time to play around.

So Cimorene says you should download the free sample journaling pages from the Math Rebels Kickstarter page. The beautiful parchment design makes doing math an adventure.

Cimorene’s math puzzle is a classic geometry problem from the ancient Kingdom of Cats: Squaring the Circle.

Draw a circle on your journal page. Can you draw a square (or rectangle) that has the same area?

How would you even begin such a task?

Notice Cimorene’s hint in the photo above: Try drawing the square that just touches the edges of your circle. (We call those just-touching lines “tangents” to the circle.)

What do you notice? Do the square and the circle have the same area? How close are they?

The tangent square sets an upper limit on the area of the circle. You can see that any square that exactly matches the circle would have to be smaller than the tangent square.

Can you find a square that sets a lower limit on the area of the circle? That is, a square that must have less area than the circle?

What’s the biggest square you can draw inside your circle? Can you find a square that has all four corners on the circle?

We call that biggest-inside square “inscribed” in the circle. Any polygon whose corners all sit on the circle is an inscribed polygon.

Play around with circles and squares. How close can you get to matching their size?

Further Exploration

After you have explored for awhile on your own, Cimorene has one more twist in her puzzle.

Divide the width of the circle in thirds, and then in thirds again. (That is, cut the diameter into nine parts.) Draw a square with sides measured by eight such parts.

You can try this on your journaling page by drawing a circle that is nine squares wide. Then draw a square overlapping it, with sides that are eight squares in length.

How closely do the areas match?

Playing with Pi

Here’s a surprise: Cimorene’s puzzle isn’t really about squares, but about calculus.

The problem of Squaring the Circle is really a much bigger question: Finding the area of a square, rectangle, or other polygon is relatively easy, but how can we discover the area of a curved shape?

For a circle, the area is related to the number pi, which is the number of times you would have to walk across the circle to equal the distance of one time walking around it.

So the problem of Squaring the Circle is really the same as asking, “What is the value of pi?”

Can you figure out what approximate value for pi matches the 8/9 square used in the ancient Kingdom of Cats?

If you’d like to learn more about pi, get ready for a celebration: Pi Day is coming soon! Every year, millions of children celebrate math on March 14th, because if you write the date as 3/14, it’s the same as the first three digits of pi.

Find out more about playing with pi in my Pi Day Round-Up post.

My February playful math newsletter went out yesterday morning to all subscribers.

This month’s issue featured a couple of string art projects for Valentine’s Day, the cardioid curve, make-your-own math art, and the link between string art and calculus.

If you didn’t see it, check your Updates or Promotions tab (in Gmail) or your Spam folder. And to make sure you get all the future newsletters, add denise (dot) gaskins (at) tabletopacademypress (dotcom) to your contacts or address book.

Not a subscriber? Don’t miss next month’s playful math activities! Click the link below to sign up today, and we’ll send you our free math and writing booklets, too.

As a Bonus: You’ll receive my 8-week email series “Playful Math for Families” and be one of the first to hear about any new books, revisions, and sales or other promotions

To help spread the news about my Math Rebel Kickstarter, I’m hosting a math game book giveaway.

Three lucky readers will win a paperback copy of my book Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play (US shipping only) OR a free copy of any digital book from my publisher’s online store.

The Sampler contains short excerpts from five of my most popular titles. It’s a wonderful way to get started with playful math.

And math games are great for journaling, too! You can play pencil-and-paper games right on the journal page. And for any game, you can use the page for keeping score and writing notes about your strategy for winning.

The Giveaway is over. Congratulations to winners Angela, Gina, and Linda!

But there’s still time left to get in on the Math Rebellion Project. Don’t miss out on this wonderful chance to launch your children on an adventure of creative, playful math.

Deadline for entries is Friday, February 12, 2021.

Winners will be chosen by Rafflecopter’s random generator and will be contacted by email. You must respond to that email within 48 hours, or we will choose a new winner.

And I’d love to hear your input! Please leave a comment below to let me know what you think of the Math Rebellion project.

Puck is concerned that some people don’t understand the idea behind the Math Rebel journals. He decided to create a journaling prompt so your children can experience the joy of creative reasoning (and save cats from their mortal enemy!)

Journaling is a great way to help children learn to see with mathematical eyes. Not just to remember what we tell them, but to create their own math.

Many people know it’s important for students to do hands-on experiments in science. But Puck realized that most adults don’t know how to do a math experiment.

My publishing company welcomes our two newest employees. Cimorene and Puck will head up our promotions department. Because cats know the internet, and they know how to make people do whatever they want.

Or at least, that’s what they tell me.

Today, Cimorene wants people to back the Make 100 Math Rebels Kickstarter. She thinks everyone should order one of the paperback or hardcover book sets. Because books come in boxes. And boxes are important to cats.

Puck agrees that boxes are a good thing. But he thinks people should choose any pledge level they like. Puck values curiosity and creative thinking, and the Math Rebel project is all about teaching students to explore ideas and think creatively about math.

I’d love to see children all around the world learning math as a creative, thought-provoking, liberal-arts adventure. Not just school math, but true mathematical thinking.

So, now that the Kickstarter’s running full-steam — closing in on our third Stretch Goal! — I’ve been working full-time on the reward books.

At the $5 pledge level and above, backers will get this digital book of 100 Math Journal Prompts.

Except, I’m thinking now it will really be 104 prompts because I plan to release them on my publisher’s online store as two booklets of printable task cards. At four cards per page, a 50-card booklet will have a half-page blank space. And since I’ve collected plenty of prompts (enough to make five booklets, if the funding hits all our Stretch Goals) it’s easy to add a couple more activities to each book.

And besides, creating the prompts is so much fun. I’m happy to throw in some extras!

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically. To make sense of math concepts and persevere in figuring things out. To notice the numbers, shapes, and patterns all around. To wonder about big ideas.

Journaling is a great way to help children learn to see with mathematical eyes. Not just to remember what we tell them, but to create their own math.

Get started with creative math journaling today. Visit the Make 100 Math Rebels Kickstarter page to download the free “How To Be a Math Rebel” sampler pictured above, which contains one of my all-time favorite math prompts.

It doesn’t matter whether your students are homeschooled or in a classroom, distance learning or in person. Everyone can enjoy the experience of playing around with math.