“Play and rigor support each other.
“When students are invited to play with math, they learn more deeply, more robustly, and remember more consistently.
“Play is promoted as something that can engage kids and give them a more positive attitude about school, but it’s easy to assume that it’s not useful for learning, when in reality the opposite is true:
“The student who is playing tends to be the student who is learning most deeply.”
—Dan Finkel, Math for Love newsletter
“We know that algorithms are amazing human achievements, but they are not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.”
— Pam Harris, Math Is Figure-Out-Able Podcast
Whether you work with a math curriculum or take a less-traditional route to learning, do not be satisfied with mere pencil-and-paper competence. Instead, work on building your children’s mental math skills, because mental calculation forces a child to understand arithmetic at a much deeper level than is required by traditional pencil-and-paper methods.
Traditional algorithms (the math most of us learned in school) rely on memorizing and rigidly following the same set of rules for every problem, repeatedly applying the basic, single-digit math facts. Computers excel at this sort of step-by-step procedure, but children struggle with memory lapses and careless errors.
Mental math, on the other hand, relies on a child’s own creative mind to consider how numbers interact with each other in many ways. It teaches students the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.
The techniques that let us work with numbers in our heads reflect the fundamental properties of arithmetic. These principles are also fundamental to algebra, which explains why flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.
Your textbook may explain these properties in technical terms, but don’t be intimidated by the jargon. These are just common-sense rules for playing with numbers.
I continue to dig myself out of the avalanche of tasks that built up during the years that I spent mostly down south with my mom as she was weakening.
But here are two tidbits of mathy fun that came across my desk recently, which I think you’ll enjoy…
I think I’ve mentioned before how much I love the Numberhive game. They recently posted a series of print-and-play freebies for their new place value variation.
This cool-looking game is in prelaunch on the crowdfunding site Gamefound, but the creator has posted a free Mini Print & Play version you can download now, suitable for prealgebra and up. (The full game will have multiple variations, including a preschool level.)
Finally, the Math Journaling Adventures books and kids’ gear are now live in my store, and all my math game books are still on sale through the month of June.
Have fun playing math with your kids!
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Are you looking for more creative ways to play math with your kids? Join my free 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.
“Playful Math for the Summer” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © damedeeso / Depositphotos.
“If you stay with meaningful mental arithmetic longer, you will find that your child, if she is average, can do problems much more advanced than the level listed for her grade. You will find that she likes arithmetic more.
“And when she does get to abstractions, she will understand them better.
“She will not need two or three years of work in primary grades to learn how to write out something like a subtraction problem with two-digit numbers. She can learn that in a few moments of time, if you just wait.”
—Ruth Beechick, An Easy Start in Arithmetic
Mental math is doing calculations in your head, with perhaps the aid of scratch paper or a whiteboard to jot down notes along the way.
But you cannot simply transfer the standard pencil-and-paper calculations to a mental chalkboard. That’s far too complicated.
ALL my math game books are on sale now at the Playful Math Store.
What a great way to prepare for a summer of mathematical play!
We were eclectic homeschoolers back in the Dark Ages before there was an internet. Our primary curriculum was the public library.
As we went along, I noticed how many of our homeschooling friends felt uncomfortable with math, and even hated or feared the subject.
Math anxiety runs rampant in Western culture. By one researcher’s estimate, more than 90% of adults experience some level of math anxiety — that is, discomfort, avoidance, and even emotional pain when faced with a math calculation.
So I became a sort of “math evangelist” in the homeschooling community, spreading the news that we can find beauty and fun even in math.
If you’re into math education — 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?
In this edition, you’ll find everything from math puzzles and games to humor and much more — even an interesting math art game.
So if you want to mix up your math teaching and make it more enjoyable for your students (and for yourself), definitely check out the Playful Math Carnival. Happy reading!
On a friend’s blog, I found this delightful letter written by Charles Lutwidge Dodgson to a young man named Wilton Cox.
The pseudonym Lewis Carroll comes from an alteration of the Latinized name Carolus (for Charles) and the replacement of Lutwidge with Lewis.
One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.
Here are a few stories to read as you sip your morning brew. . .
Download your printable Morning Coffee journal
This week’s rabbit hole started with a thought-provoking blog post by Sara Van Der Werf…
“We are all mathematicians. We all have the power to notice, describe, and generalize patterns. You have all had this ability since birth.
“If we believe this then every day we must plan lessons that allow students to act as mathematicians. We must put something in front of our students to notice. We must put something in front of our students to describe, to generalize.”
—Sara Van Der Werf
Read more about how to develop mathematical thinking in this fourth installment of professional development for homeschooling parents.
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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: What Is Mathematics?” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.
On May 5, we celebrate one of the rarest math holidays: Square Root Day, 5/5/25.
Here are a few ideas for playing math with squares and roots.
Five is the square root of twenty-five, which means it is the number we can “square” (multiply times itself) to get 25.
The root is the base number from which the square grows. In physical terms, it is the side of the square.
Imagine a straight segment of length 5, perhaps a stick or a piece of chalk. Now lay that segment down and slide it sideways for a distance equal to its length. Drag the stick across sand, or pull the chalk across paper or a slate.
Notice how this sideways motion transforms the one-dimensional length into a two-dimensional shape, a square.
The area of this shape is the square of its root: 5 × 5 = 25.
What do you think would happen if you could drag the square through a third dimension, or drag that resulting shape through a fourth dimension?
How many shapes do you suppose might grow from that original root of 5?
Denise Gaskins' Let's Play Math 