I have a new podcast interview, and I think you’ll enjoy it!
Check out Pam Barnhill’s Homeschool Better Together on your favorite podcast app, or listen on the website:
Here’s an excerpt…
Podcast: Making Math a Delight
Blog
Playful Math 179: Our Sweet Sixteen Carnival
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.”
Coming Soon: Math Journaling Adventures
Coming Soon! On March 3, I’ll be launching the first installment in my new book series, the Math Journaling Adventures.
You’ll love these books because they make creative math investigations open-and-go for busy parents and teachers.
And the Kickstarter prelaunch page is now live. That means you can sign up to get an email from Kickstarter as soon as the campaign launches:
If you back the campaign on launch day, you can catch a great deal with the Earlybird discount pledge levels.
Morning Coffee: Professional Development for Homeschooling Parents and Other Teachers
Lately, I’ve spent most of my writing time thinking about the value of narration—the Charlotte Mason approach to teaching by getting kids to put ideas in their own words.
For students, I’m writing a new series of Math Adventure Journals to get them thinking about math and putting those thoughts into words. If you’re interested, sign up to be notified when the Kickstarter goes live.
But we parents can harness the value of narration in our own learning. After all, one of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.
To that end, I’ve decided to relaunch my “Morning Coffee” series of professional development posts for homeschooling parents.
Here’s How It Works
As I read articles and follow rabbit trails around the internet, I’ll collect the posts that speak to me. Then I’ll share these in a printable format with journaling pages for your response.
Since I’m interested in math education, many of the articles I read will be about math—but the principles of learning apply to every subject we teach.
To kick off the series, let’s start with one of my favorite articles ever…
Morning Coffee # 1: Learning to Ask Good Questions
Download your printable Morning Coffee journal
David Butler’s post Twelve matchsticks: focus or funnel presents an interesting math puzzle. But even better, it opens up a rabbit hole of thought-provoking posts about how to talk with children—or anyone:
“The approach where you have an idea in your head of how it should be done and you try to get the student to fill in the blanks is called funnelling. It’s actually a rather unpleasant experience as a student to be funnelled by a teacher. You don’t know what the teacher is getting at, and often you feel like there is a key piece of information they are withholding from you, and when it comes, the punchline feels rather flat.”
The printable file includes links to three more articles as I follow the rabbit around the internet. Enjoy!
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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.
“Morning Coffee: Professional Development for Homeschooling Parents and Other Teachers” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.
Playful Math 178: Nicomachus’s Carnival
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
FAQ: Can I Use Your Books as a Math Curriculum?
I recently listened to you on Cindy Rollins’ podcast, and I was captivated by your perspective on math. It was exciting, freeing, and wonder-filled. I would absolutely love to be able to teach in the ways you described.
We use early-elementary Saxon Math right now, which is thorough, but has SO MUCH to do that I’ve always struggled to do it all. Then I feel like I’m missing things, and I never know quite what is important. And yet, the actual lessons move so slowly that my kids get bored with the repetition.
I use a published curriculum because I have no idea of an appropriate scope and sequence, or similar flow of learning. With your playful approach to math, how do I know where to start, and what to do each day?
Do you have a suggested order to approach your books to have a full math approach? A sort of curriculum, per se, using your books.
[For those who missed my chat with Cindy Rollins about a Charlotte Mason approach to math, you can listen to it here.]
Continue reading FAQ: Can I Use Your Books as a Math Curriculum?
FAQ: Real Math for Early Learners
“I love your image of math as a nature walk. My children are ready to start their homeschooling journey, and I want to put them on the right track from the beginning. How can I help them think about math and problem-solving without using a textbook?”
The most difficult part of teaching our children real math is to change our own way of thinking about the subject you’ve already taken that step, so it looks like your family’s learning journey is off to a great start.
[For readers who are wondering what I mean by math as a nature walk, check out this post. You may also enjoy my article on natural learning: Math with Young Children.]
Memories: The Oral Story Problem Game
Homeschool Memories…
Perhaps you’ve heard me mention the oral story problem game. It was one of my favorite ways to get my children thinking about math, back in our early days of homeschooling. We played in the car on the way to soccer practice, or while we washed dishes, or sitting in the lobby waiting for a doctor’s appointment.
The rules are simple: I’ll make up a math problem for you to solve. And then you make up one for me.
The kids always loved trying to stump me.
This problem from Henry Ernest Dudeney’s Amusements in Mathematics reminded me of those days. This is exactly the way my eldest loved to torture me…
Start the New Year Right: Playful Math Carnival 177 via Math Hombre
If you’re looking for an entertaining way to weather the coming storm — or just curious about how learning math could possibly be fun — you’ll definitely want to check out the latest edition of the Playful Math Carnival.
It’s a collection of awesome blog posts curated by John Golden and published on the Math Hombre website:
The whole point of the carnival is to show that math doesn’t have to be tedious or repetitive. Through a bunch of fun and engaging posts, we celebrate math that’s playful, creative, and totally relevant to everyday life.
Because what could be more relevant than having fun while we learn?
Continue reading Start the New Year Right: Playful Math Carnival 177 via Math Hombre
Puzzle: Henry Dudeney’s Pebble Game
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.
Denise Gaskins' Let's Play Math 