FAQ: Playful Math Journaling

Posted on by Denise Gaskins
Girl student thinking about her math journal prompt

Ever since the school year started, I’ve been getting questions about how to use my new Math Journaling Adventures logbooks.

[SIDE NOTE: These logbooks are included in this month’s Thanksgiving Sale! You’ll get an automatic 10% discount off all print books, applied at checkout, no special code required.]

“I love the way your math books get my children thinking.

    “Finally, they are having fun with math!

      “But sometimes I have no idea what the journaling prompt is all about or how to teach it. Where can I buy a solutions manual?”

      Um, that’s not how math journals work.

      The cool thing about journaling prompts is that they have no “right” answer. They are explorations into different parts of the world of math, nature walks in the land of numbers, shapes, and patterns. Springboards into whatever our children want to investigate, whatever sparks their interest.

      A few of the problem-solving prompts may have specific answers, but it really doesn’t matter if our kids find the exact solution a math professional might give. If they write what makes sense to them, they’ve accomplished the goal.

      If later, they think of something they hadn’t noticed, or they want to change their answer — well, that is mathematical thinking, too.

      Continue reading FAQ: Playful Math Journaling

      📚 Thanksgiving Sale: ALL Print Books Discounted! 📚

      Posted on by Denise Gaskins
      Thanks in many languages

      November is the traditional month of thanksgiving, at least here in the U.S. The harvest is in, and we have holidays just around the corner. It’s a great time to take stock of our blessings and practice gratitude.

      I’m thankful for YOU! 😍 And for everyone who reads my books, blog, newsletter, etc., or backs my Kickstarter campaigns, supports my Patreon, or whatever way you choose to share the Playful Math adventure.

      But especially, for those of you who cut out the middleman and buy direct through my store or on Kickstarter.

      How It Happened

      I was updating my business bookkeeping last weekend (How do I get so far behind?!), and I noticed that my direct-to-you sales this year have blown far past my sales through the normal online retailers.

      Wow!

      So I decided it was time for a Thank-You sale.

      I can’t mark down my print books very often, because the cost of printing and shipping lurks like a monster behind the scenes, eager to take a bite out of every purchase. There’s nothing I can do about those fixed expenses, and they keep going up.

      But this feels like a month for celebration, so here we go:

      ALL PRINT BOOKS—paperback, hardcover, and spiral bound—are included in the “I’m Thankful for You” Sale. A 10% discount applies automatically at checkout, no discount code required.

      SHOP NOW

      This would be a great time to grab a book for someone on your holiday gift list—and treat yourself to something new, too.

      With my thanks!

       
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      Image at the top of the post copyright © tupungato / Depositphotos.

      Mental Math: Advanced Subtraction

      Posted on by Denise Gaskins
      mother and daughter talking about math homework

      As our children grow and develop their math skills, the mental math strategies grow with them.

      The basics of mental math don’t change:

      • Use friendly numbers.
      • Estimate and adjust the answer.

      But we have new ways to help children do math in their heads as the numbers get bigger and the problems more challenging.

      For example, how might kids figure out a multi-digit subtraction like 67 − 38?

      First, we need to adjust our mindset…

      Continue reading Mental Math: Advanced Subtraction

      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.

      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 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

          Two Hands-On Craft Projects

          Posted on by Denise Gaskins
          photo: Cutting a paper square

          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!

           
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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 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.