All ages – Page 3 – Denise Gaskins' Let's Play Math

Math Journal: Playing with My Own Ignorance

Posted on March 12, 2025February 24, 2025 by Denise Gaskins

Mary Everest Boole, wife of English mathematician George Boole, once described algebra as “thinking logically about the fact of our own ignorance.”

This definition made me chuckle. Like any human being, I am ignorant on many things, but I usually avoid thinking about that.

So I wondered what would happen if I took Mrs. Boole’s advice and tried thinking logically about my ignorance.

How far could I go?

Perhaps you’d like to try this experiment with your children. All you need is a pen and paper or a whiteboard and markers and a bit of curiosity.

And if you enjoy this exploration, check out my Math Journaling Adventures project to discover how playful writing activities can help your students learn mathematics. Preorder your books today!

Continue reading Math Journal: Playing with My Own Ignorance

Math Adventures Merchandise to Inspire Your Kids

Posted on March 11, 2025July 12, 2025 by Denise Gaskins

My new math book series, the Math Journaling Adventures, just launched on Kickstarter.

And I’m trying several new reward options I’ve never done before. (The “rewards” on Kickstarter are all the various things you can buy with your support pledge.)

This is going to be so much fun!

Check it out:

Math Journaling Adventures

Continue reading Math Adventures Merchandise to Inspire Your Kids

Playful Math 179: Our Sweet Sixteen Carnival

Posted on February 26, 2025February 28, 2025 by Denise Gaskins

Welcome to the sweet-16 birthday edition of the Playful Math Carnival. Originally called Math Teachers at Play, our first carnival was published in February 2009.

Each Playful Math Carnival offers 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.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a math activity in honor of our 179th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

NOTE: Our wonderful volunteer hosts have kept the Playful Math Carnival going when so many other blog carnivals died off. If you’d like to sign up to host the carnival for a month, email Denise for information.

Try These Prime Puzzles

Did you know there are 179 even-numbered days this year?

How many even-numbered days will there be in a leap year?

But there are 365 days in a standard year and 366 in a leap year. Shouldn’t there be half that many even-numbered days?

179 is a prime number, and it’s also a knockout prime. You can knock out any of the digits, and what’s left is still prime: 17, 19, or 79.

Can you find another knockout prime number?

179 is a twin prime. That means that one of its odd-numbered neighbors is also prime.

Is the other twin 177 or 181? Can you tell without looking it up?

Why are twin primes limited to the odd numbers? That doesn’t seem fair!

179 is also an emirp. That’s a special kind of prime that forms a different prime number when you write it backwards: 971 is also prime.

How many emirps can you find?

“A palindrome is a word that when written in reverse results in the same word. for example, ‘racecar’ reversed is still ‘racecar’. Related to palindromes are semordnilaps. These are words that when written in reverse result in a distinct valid word. For example, ‘stressed’ written in reverse is ‘desserts’. Not all words are palindromes or semordnilaps.

“While certainly not all numbers are palindromes, all non-palindromic numbers when written in reverse will form semordnilaps.

“Narrowing to primes brings back the same trichotomy as with words: some numbers are emirps, some numbers are palindromic primes, but some are neither.”

—The On-Line Encyclopedia of Integer Sequences A006567

Click here for all the mathy goodness!

Playful Math 178: Nicomachus’s Carnival

Posted on January 29, 2025January 28, 2025 by Denise Gaskins

Welcome to the 178th 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/activity in honor of our 178th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Activity: Nicomachus’s Theorem

Welcome to 2025, a perfectly square year — and the only one this century!

2025 = (20 + 25)²

When is the next time we’ll have a perfect-square year?
Can you find the only perfect square less than 2025 that works by this pattern? When you split the number’s digits into two smaller numbers and square their sum, you get back to that number.

2025 = the sum of all the numbers in the multiplication table, from 1×1 to 9×9

2025 = the sum of the first 9 perfect cubes

When is the next time this will happen, that the year is the sum of the first n perfect cubes?

And by Nicomachus’s theorem:

2025 = 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³
so it must also = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)²

Try it for yourself with small numbers: Get some blocks, and build the first few perfect cubes. Then see if you can rearrange the block to form the sum of those numbers squared.

Can you show that…

1³ = 1²
1³ + 2³ = (1 + 2)²
1³ + 2³ + 3³ = (1 + 2 + 3)²
1³ + 2³ + 3³ + 4³ = (1 + 2 + 3 + 4)²
1³ + 2³ + 3³ + 4³ + 5³ = (1 + 2 + 3 + 4 + 5)²

Older Students: Can you see that the pattern would continue as long as you want? How might you prove that?

Here’s the formula for triangular numbers, to get you started:

(1 + 2 + 3 + … + n) = n(n + 1)/2

Click here for all the mathy goodness!

Puzzle: Henry Dudeney’s Pebble Game

Posted on December 18, 2024November 22, 2024 by Denise Gaskins

photo of girl playing with pebbles on the beach

English mathematician and puzzle-meister Henry Ernest Dudeney once wrote:

“It may be said generally that a game is a contest of skill for two or more persons, into which we enter either for amusement or to win a prize. A puzzle is something to be done or solved by the individual.

“The example that I give here is apparently a game, but, as in every case one player may win if he only play correctly, it is in reality a puzzle. The interest, therefore, lies in attempting to discover the leading method of play.”

Below is the puzzle game as Dudeney explained it.

Play it for fun at first, then see if you can solve the puzzle.

Continue reading Puzzle: Henry Dudeney’s Pebble Game

Holiday Countdown Craft

Posted on December 11, 2024January 1, 2025 by Denise Gaskins

Marking time is hard for children (and often for us adults, as well).

I don’t mean telling time, which has its own difficulties. But waiting, marking time until the Big Day or Important Event arrives.

Whether you’re counting down the days to Christmas, or the hours until New Year’s Day, or waiting for a birthday or visit to Grandma — it’s never easy to sit idly during the interim.

Holiday Countdown

Here’s a fun little craft that can make the waiting easier, or at least make it easier to keep track of how much longer until the time is right.

It’s a spinning time-piece for kids to decorate and put together (with a bit of adult help wielding a craft knife).

Holiday Countdown is a 28-page printable file includes illustrated instructions, along with countdown timers for birthday, Christmas, and New Year’s Eve celebrations, plus blank timers you can adapt to any occasion.

Buy Now

Mandala Version, with Video Instructions

The ever-creative Manja designed a mandala-coloring version of the countdown timer for New Year’s Eve. Read all about it (and find the download links) on her Hattifant blog.

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Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.

This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

“Holiday Countdown Craft” copyright © 2024 by Denise Gaskins. Image at the top of the post copyright © BrianAJackson / Depositphotos.

Math Games for the Holidays

Posted on December 4, 2024November 22, 2024 by Denise Gaskins

Are you looking for fun ways to keep your children busy (and learning!) through the holidays? Here are two printable activity guides you might enjoy:

Snowman Drive

(My newest game activity.)

Players roll the dice and build their creative snowman (or snowbeast). Will you make a fearless pirate or a dapper aristocrat — or a high-scoring snow spider?

A Snowman Drive is a family-friendly party that can also serve as a fundraiser for your church, homeschool group, or organization. The Drive consists of several rounds of the Snowman Game played on a single worksheet, with prizes for the top-scoring players and overall champion.

This activity book includes game instructions and gameboard pages for single-family or group play.

For ages 5 and up.

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Download a PDF preview file.
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FORMAT: 13-page printable PDF file with your choice of 8.5″×11″ (letter size) or A4 pages.

Buy Now

Christmas Tree Math Games

(Number play on a triangular hundred chart.)

Christmas Tree Math Games features 4 easy-to-learn games and 6 additional activities for primary and middle-grade students. All you need is a set of dice and a few colorful markers.

Math games build mental flexibility and strategic reasoning in players of all ages. And even people who hated math in school can enjoy the friendly challenge of a game.

These are NOT the typical memory-and-speed-based math games you’ve probably seen online, but true battles of wit and skill (plus a bit of luck).

Perfect ice-breakers for family gatherings, classroom warmups, or for launching a group game night. You’ll be surprised how much fun thinking hard can be!

Christmas Tree Math Games includes instructions and tips for the teacher, math game pages for handouts or learning centers, plus a variety of dot-grid journaling paper.

For ages 6 and up.

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Download a PDF preview file.
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FORMAT: 30-page printable PDF file with your choice of 8.5″×11″ (letter size) or A4 pages.

Buy Now

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Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my email newsletter.

This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

“Math Games for the Holidays” copyright © 2024 by Denise Gaskins. Image at the top of the post copyright © prarinya / Depositphotos.

Quick Note: Black Weekend Sale

Posted on November 29, 2024November 22, 2024 by Denise Gaskins

This Weekend Only

For US customers, ALL merchandise items at my Playful Math Store are on sale for the Black Friday/Small Business Saturday/Cyber Monday season.

Display your mathy spirit for everyone to see. And they make great gifts, too!

Plus, each purchase comes with a free bonus book — see product listings for details.

Check it out:

Playful Math Merch Sale

(International readers: I’m sorry. Due to tax issues, merchandise is only available in the US for now.)

Math Art Sale Almost Over

Remember, for November I’ve put all my digital printable math art activities on sale for 20% off. (Discount calculated automatically at checkout.)

Just a few days left to take advantage of that discount!

Gratis Games and Playful Math News

Posted on November 19, 2024November 19, 2024 by Denise Gaskins

Do you want to help your children learn math?

Teach them to play.

Grab a free copy of my Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play, which contains short excerpts from my most popular titles. It’s a great way to get started with playful math. 😍

As a bonus, I’ll add you to my Playful Math News email subscription and send you monthly tips and activity ideas for playing math with your kids.

From time to time, I’ll even throw in a free sample of whatever I’ve been working on — an early draft of something that will eventually show up in one of my books or printable activity guides.

For example, check out this fun freebie I sent last April:

The Arithmetic Fairy

Don’t miss out on all this mathy goodness. Sign up today!

Get the Games Book Now

New Book: Farzanah and the 17 Camels

Posted on August 26, 2024August 22, 2024 by Denise Gaskins

illustration from Farzanah and the 17 Camels

Now’s your chance to promote creative math for kids, with Sue Looney’s new book on Kickstarter: Farzanah and the 17 Camels.

You can order the book in digital or paperback format, get multiple copies for a classroom or book club, or just donate to support the project.

Visit the Kickstarter

Farzanah and the 17 Camels celebrates the excitement and the rewards of solving a challenging and intriguing math problem. Set against the backdrop of the ancient Silk Road, with bustling markets, stunning carpets, fun characters, and camels, the story draws readers into the magic of Farzanah’s surroundings.

As Farzanah searches for an unusual approach, a way of solving the problem that no one else could think of, she follows the wise advice of her mother:

“My dear Farzanah, don’t be discouraged,” said Mama. “Sometimes, being stuck is exactly where you need to be. I find the best thing I can do is to step away. I free my mind to think about other things. It is in that space that the magic happens. I am able to look at things from a different perspective. With wait time and wishful thinking comes the solution.”

Farzanah embodies the joy of productive struggle in mathematical problem-solving. She is patient, persistent, and curious, using these qualities to tackle a perplexing dilemma that has troubled everyone.

For a bonus math puzzle you can play today, based on Farzanah’s life, download Farzanah’s Sheep Dilemma.

Looney’s earlier book, Ying and the Magic Turtle, is available on the Natural Math website. Or check out her Same But Different discussion prompts for all ages on her website.

Visit the Kickstarter

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