What Is Thinking Thursday?

Posted on by Denise Gaskins
Thinking Thursday math journal prompt

There’s a new math journaling prompt this week.

Have your kids tried it yet?

This week’s prompt features one of my explain-your-reasoning to get kids thinking (and writing) about math while avoiding the formality that turns so many students away from geometry proofs. Or you might prefer last week’s prompt, featuring a classic math brainteaser and encouraging students to create their own related puzzles.

Or, if you’re reading this post later and missed those, there’s another great new prompt this week for you to explore.

Check it out:

Visit Thinking Thursday

Continue reading What Is Thinking Thursday?

What Is Math Game Monday?

Posted on by Denise Gaskins
Learn a new math game every week, for free

There’s a new Math Game Monday this week.

Have your kids tried it yet?

This week’s game is one of my favorites for upper-elementary and middle school students, offering plenty of practice doing estimation and mental math with fractions. Or you might prefer last week’s game, featuring a classic two-player logic puzzle that develops strategic reasoning.

Or, if you’re reading this post later and missed those, there’s another great new game this week for you to play.

Check it out:

Visit Math Game Monday

Continue reading What Is Math Game Monday?

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.

      Continue reading Geometric Math Art, Recovered

      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?

      Continue reading Two Hands-On Craft Projects

      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!