Denise Gaskins' Let's Play Math

Geometric Math Art, Recovered

Posted on October 29, 2025September 11, 2025 by Denise Gaskins

I’ve been updating my old book files to a new publishing program, and in the process discovering anew how often websites change and disappear. So frustrating!

Thankfully, the Internet Archive keeps some things that we can look back at. It doesn’t always work, but today it came to the rescue and let me recover the wonderful workbook from the Metropolitan Museum of Art, Islamic Art And Geometric Design, plus some of the pattern pages at the old School of Islamic Geometric Design.

I reference these pages in my Geometric Coloring Designs series (available at my Playful Math Store), so I was glad to find they weren’t lost forever.

Math Art = a great way to spark energy when your students hit the mathematical doldrums.

If you’d like to play around with math art patterns, each image below links to Eric Broug’s step-by-step instructions for creating the design. Also, Broug made printable pages to get students started, which you can download here. No compass construction required!

Pattern 1

Pattern 2

Pattern 3

There are two more patterns on the old SIGD site, but I can’t get those instructions to load. That might be my antique rural internet connection, however, so feel free to do some exploring on your own.

And have fun drawing math with your kids!

* * *

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.

“Geometric Math Art, Recovered” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © Denise Gaskins.

How to Think like a School Math Genius

Posted on October 22, 2025September 4, 2025 by Denise Gaskins

$Teen student thinking$

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

“There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

“Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

—James Tanton

James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.

But his wonderful, old-fashioned site full of great insights and interesting problems is gone.

😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.

Continue reading How to Think like a School Math Genius

Fun New Math Story

Posted on October 15, 2025October 14, 2025 by Denise Gaskins

Hey, look! A new book from the folks at Natural Math, now on Kickstarter:

Modultown! A Math-Inspired Children’s Book

Experience a whimsical puzzle hunt in a new fantastic world full of friendship and surprises, from the authors of Funville Adventures.

When human siblings Emmy and Leo find themselves magically transported to Modultown, they make new friends and combine their different perspectives to solve challenges that flesh out the mechanics of modular arithmetic.

Playing in Modultown unlocks pathways into number theory, computer science, genetics, and other essential modern fields.

Back It Now

NOTE: If you haven’t explored Kickstarter before, it’s a wonderful place to discover new books and products from creators around the world.

In the old days, traditional publishing companies paid writers in advance to write the books the publisher wanted to see. In this new world, you get to choose and support the writers creating books you want to read.

* * *

Notice–Wonder–Discover: The Foundation of Learning Well

Posted on October 9, 2025October 8, 2025 by Denise Gaskins

Notebook on desk, with the words "Notice. Wonder. Discover."

Most of us were never taught how to teach. And we certainly weren’t taught what to do when NOTHING is working.

My friend Sonya Post is offering a new course that will help you rethink how learning actually works, how you can stop second-guessing yourself and start seeing real growth.

I’ve taken the earlier iterations of her course, and I’d recommend it to all parents.

Truly wonderful insights!

Find More Information

What the Course Covers

The course consists of six weekly online workshops, plus an optional bonus session:

Session 1: Orientation – Why Learning Feels Hard
The default scripts we carry from school, and how to overcome them.

Session 2: Notice – The First Act of Learning
Before anything can be learned, it must be seen.

Session 3: Structure – Why Look for Structure?
Structure is the beginning of understanding — and the root of algebraic thinking.

Session 4: Arbitrary vs. Necessary
Not all information deserves equal weight. Here’s how to make space for thinking.

Session 5: Wonder – Curiosity That Moves Forward
Wonder is not optional — it’s the engine of discovery, the heart of orientation, and the builder of wisdom.

Session 6: Discover – What Was Always There
Discovery is our response to insight, how we orient inward and express outward after recognizing something true.

Optional Bonus Session
Mothering as Orientation — A Christian Reflection.

The course begins October 14: Notice–Wonder–Discover Course.

More About Sonya

You may have heard me mention Sonya before. She created The Best Math Game Ever, and she teaches the math course I wish my kids and I could have taken:

A Revolutionary New Approach to Homeschool Math

And in fact, anyone who is taking one of her homeschool math courses (or signs up in the next few weeks) will get the Notice-Wonder-Discover Course included for free.

Sonya says:

“I don’t just build these resources — I use them. I’ve walked the road of frustration, math tears, and feeling lost about how to teach well. This course exists because I don’t want you to walk that road alone. This is the framework I wish I’d had years ago, and I can’t wait to share it with you.”

I really can’t praise Sonya’s work enough. If you’re struggling at all with your teaching or family life, she’ll turn you around and give you new perspective on how to move forward with grace.

Get the Notice–Wonder–Discover Course

* * *

Mental Math: Advanced Addition

Posted on October 8, 2025November 4, 2025 by Denise Gaskins

$photo of kids having fun with math$

Mental math is doing calculations with our minds, and perhaps with the aid of scratch paper or a whiteboard to jot down notes along the way.

But we cannot simply transfer the standard pencil-and-paper calculations to a mental chalkboard. That’s far too complicated.

We still want to follow our basic strategies of using friendly numbers, estimating, and adjusting the answer. So how can we help children do math in their heads as the numbers get bigger and the problems more challenging?

How might kids figure out a multi-digit addition like 87 + 39?

Here are three useful strategies…

Continue reading Mental Math: Advanced Addition

Mental Math: Early Division

Posted on October 1, 2025November 4, 2025 by Denise Gaskins

$Boy doing mental math calculation$

Mental math is doing calculations with our minds, though we can use scratch paper or whiteboards to make notes as we work.

Doing mental math, children use the basic principles of arithmetic to simplify problems so they can think about number relationships, mastering the basic structures of how numbers work, the same structures that underlie algebraic reasoning.

As always, we rely on two key mental-math strategies.

Use friendly numbers.
Estimate, then adjust.

Division is the mirror image of multiplication, the inverse operation that undoes multiplication, which means we are scaling numbers down into smaller parts. Important friendly numbers include halves, thirds, and tenths, plus the square numbers and any multiplication facts the student happens to remember.

Continue reading Mental Math: Early Division

Two Hands-On Craft Projects

Posted on September 24, 2025June 18, 2025 by Denise Gaskins

Here are a couple of fun foldable projects to try with your kids.

Both of the projects below start with squares of paper. Do you know how to convert any piece of paper into a square? Here are two methods.

Can you tell why they work, how each method creates a true square?
What if you didn’t have a rectangular page to start with — could you still create a square?

Minecraft Endless Card

A square flexagon. If you don’t care for Minecraft, just create four square designs of your own to fold, cut, and paste.

https://hattifant.com/minecraft-endless-card-paper-craft

What math do you notice in the finished card? What questions can you ask?

Origami Puzzle Purse

Write a decorative note to a friend, then fold it into a compact little puzzle.

https://hannaleetidd.com/blogs/news/how-to-make-a-victorian-love-token

What do you notice? What do you wonder?

Have fun folding math with your kids!

* * *

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 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.

“Two Hands-On Craft Projects” copyright © 2025 by Denise Gaskins. Image at the top of the blog copyright © Vejaa / Depositphotos.

Mental Math: Early Multiplication

Posted on September 17, 2025November 4, 2025 by Denise Gaskins

$mother and daughter talking math together$

Children learn best through interaction with others, and mental math prompts can lead to fascinating conversations, listening as our kids apply their creativity to the many ways numbers interact.

With mental math, students master the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.

And these 3Rs are the foundation of algebra, which explains why flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.

Let’s Try an Example

Multiplication involves scaling one number by another, making it grow twice as big, or three times as much, or eightfold the size. Multiplication by a fraction scales the opposite direction, shrinking to half or a third or five-ninths the original amount.

The key friendly numbers for multiplication and division are the doubles and the square numbers. As with addition and subtraction, students can estimate the answer using any math facts they know and then adjust as needed.

How many ways might children think their way through the most-missed multiplication fact, 8 × 7?

Continue reading Mental Math: Early Multiplication

FAQ: How To Start a Homeschool Math Club

Posted on September 10, 2025August 2, 2025 by Denise Gaskins

Denise Gaskins reading math with preschoolers

The question hits my inbox whenever parents start planning for a new school year:

“Hello! I am on the board of a homeschool co-op. We have had requests for a math club and wondered if you have any tips for starting one. We service children from K-10th and would need to try to meet the needs of as many ages as possible.”

There are several ways you might organize a homeschool math club, depending on the students you have and on your goals. I think you would have to split the students by age groups — it is very hard to keep that wide of a range of students interested. Then decide whether you want an activity-oriented club or a more academic focus.

When I started my first math club, I raided the math shelves in the children’s section at my library (510-519) for anything that interested me. I figured that if an activity didn’t interest me, I couldn’t make it fun for the kids. Over the years we have done a variety of games, puzzles, craft projects, and more — always looking for something that was NOT like whatever the kids would be doing in their textbooks at home.

Let’s look at the possibilities by grade level…

Continue reading FAQ: How To Start a Homeschool Math Club

Playful Math 182: The Storytelling Carnival

Posted on September 8, 2025September 6, 2025 by Denise Gaskins

Would you like some great ideas for reading and playing math with your kids?

Sue VanHattum put together a delightful collection of mathematical fiction in honor of Math Storytelling Day:

Math Storytelling (Playful Math Carnival 182)

What are you waiting for? Come join the fun!

Click Here to Read the Carnival Blog

Help Us Keep the Carnival Going

The Playful Math Blog Carnival wants you! We’re transitioning to a seasonal carnival, to make it easier on our volunteer hosts who collect links and write the carnival.

Every 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.
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 let me know!