Denise Gaskins

Geometric Math Art, Recovered

Posted on October 29, 2025September 19, 2026 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.

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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.

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Fun New Math Story

Posted on October 15, 2025September 19, 2026 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.

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Notice, Wonder, Discover: The Foundation of Learning Well

Posted on October 9, 2025September 19, 2026 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 free orientation 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

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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…

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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.

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Two Hands-On Craft Projects

Posted on September 24, 2025September 19, 2026 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?

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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?

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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…

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