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

      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!

       
      * * *

      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.

      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!

       
      * * *

      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.

      Hints for the Patty Paper Trisection

      Posted on by Denise Gaskins
      drafting tools

      No peeking! This post is for those of you who have given the trisection proof a good workout on your own.

      If you have a question about the proof or a solution you would like to share, please post a comment here.

      But if you haven’t yet worked at the puzzle, go back and give it a try.

      When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.

      Continue reading Hints for the Patty Paper Trisection

      Puzzle: Patty Paper Trisection

      Posted on by Denise Gaskins
      student using drafting tools

      One of the great unsolved problems of antiquity was to trisect any angle, to cut it into thirds with only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass.

      Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator.

      One “cheat” that works is to fold your paper.

      I will show you how it works, and your job is to show why.

      Continue reading Puzzle: Patty Paper Trisection

      Happy Pythagorean Triple Day!

      Posted on by Denise Gaskins
      Pythagorean Theorem demonstrated with tangrams

      Thursday is Pythagorean Triple Day, one of the rarest math holidays.

      The numbers of Thursday’s date: 7/24/25 or 24/7/25, fit the pattern of the Pythagorean Theorem: 7 squared + 24 squared = 25 squared.

      Any three numbers that fit the a2 + b2 = c2 pattern form a Pythagorean Triple.

      Continue reading Happy Pythagorean Triple Day!

      Playful Math for the Summer

      Posted on by Denise Gaskins
      playful dog at the beach

      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…

      Numberhive Place Value

      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.

      DiceCulus Core Game — Mini PnP

      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.)

      Math Journaling and Games

      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!

       
      * * *

      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.

      Monday is Square Root Day

      Posted on by Denise Gaskins
      square tree with roots

      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.

      What is a Square Root?

      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?

      Continue reading Monday is Square Root Day