Conversion Factors: How Old Are You in Nanoseconds?

Posted on by Denise Gaskins
birthday cupcake with sparkler

Homeschool Memories

[Based on a problem I made up for my co-op students, once upon a time…]

Conversion factors are special fractions that contain problem-solving information. Why are they called conversion factors?

  • “Conversion” means change, and conversion factors help you change the numbers and units in your problem.
  • “Factors” are things you multiply with. So to use a conversion factor, you will multiply it by something.

For instance, if I am driving an average of 60 mph on the highway, I can use that rate as a conversion factor. I may use the fraction:

Or I may flip it over to make:

It all depends on what problem I want to solve.

After driving two hours, how far have I gone?

But if I am planning to go 240 more miles, how much longer will it take?

Any rate can be used as a conversion factor. You can recognize them by their form: this per that. Miles per hour, dollars per gallon, cm per meter, and many, many more.

Of course, you will need to use the rate that is relevant to the problem you are trying to solve. If I were trying to figure out how far a tank of gas would take me, it wouldn’t be any help to know that an M1A1 Abrams tank would get about 1/3 mile per gallon. I won’t be driving one of those.

Continue reading Conversion Factors: How Old Are You in Nanoseconds?

Column Jumping: An Investigation

Posted on by Denise Gaskins
man jumping on rock columns

Charlotte Mason's Living Math ebook editionIn my new book, Charlotte Mason’s Living Math, I encourage families to explore the world of math by asking big, open-ended questions.

[Now available exclusively in my Playful Math Store! Ebook only at the moment, but print editions are coming soon.]

Here’s an example of such a question, an excerpt from my earlier book, 70+ Things To Do with a Hundred Chart: Number, Shape, and Logic Activities from Preschool to Middle School.

Have fun exploring math with your kids!

Continue reading Column Jumping: An Investigation

Make Your Own Nim Games

Posted on by Denise Gaskins
tower of rocks on a beach

Nim is a pure strategy game for two players. On each turn, players remove an option until finally no choice remains.

Game options might include:

  • How many stones to take from a pile.
  • Which position to claim on a gameboard.
  • How far to count in a given sequence.

The rules can vary at the players’ whim (as long as both players agree). How many possibilities do you start with, what are the rules for removing options, and how do you win or lose the game? Everything is open to change. And with every tweak, players must reanalyze their strategy.

Continue reading Make Your Own Nim Games

Playful Math 184: Carnival of Living Math

Posted on by Denise Gaskins
Playful Math Carnival 184

Welcome to the 184th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

With all the links, a blog carnival can feel overwhelming. Bookmark this article, so you can take your time reading the posts.

“Living math” means bringing our children face-to-face with the big ideas of mathematics to help them develop their reasoning skills. When the ideas of math come to life for our children, their minds delight in seeing how numbers and shapes connect to each other and exploring these relationships.

Scattered between the playful math links below, you’ll find quotations from my new book Charlotte Mason’s Living Math, along with several paintings of children playing and learning which I considered for the book but ran out of room.

“The lesson” by Rafael Frederico, 1895.

By tradition, we start the carnival with a puzzle/activity in honor of our 184th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Continue reading Playful Math 184: Carnival of Living Math

Math Prompt: True-False-True

Posted on by Denise Gaskins
girl writing in a notebook, sitting on couch with her corgi

Book, Charlotte Mason's Living MathOne of the stretch goals for my Charlotte Mason’s Living Math Kickstarter campaign is to add a math journaling prompt to the end of each chapter. So, I’ve been playing around with ideas to get readers writing.

Since the book’s all about how to build mathematical reasoning, I’m looking for ways to prompt creative thinking and flexibility in math calculations.

Check Out the Kickstarter

I found some fun ideas in Guy Gattegno and Martin Hoffman’s Handbook of Activities for the Teaching of Mathematics (which you can download here), including the following riff off a puzzle created by Lewis Carroll.

Continue reading Math Prompt: True-False-True

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.

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.

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