Geometric Math Art, Recovered

Posted on by Denise Gaskins
Geometric pattern 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

Geometric design pattern by Eric Broug

Pattern 2

Geometric design pattern by Eric Broug

Pattern 3

Geometric design pattern by Eric Broug

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!

 
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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.

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“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 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 by Denise Gaskins
      Characters from Modultown math story

      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.

      Support Math Joy for All

       
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      Images copyright ©2025 Natural Math.

      Notice–Wonder–Discover: The Foundation of Learning Well

      Posted on 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:

      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.

      Sign up now, before it’s too late:

      Get the Notice–Wonder–Discover Course

       
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      Featured image above copyright © Sonya Post.

      Mental Math: Advanced Addition

      Posted on 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 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