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

Skit: The Handshake Problem

Posted on by Denise Gaskins
The handshake problem

If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?

Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned.

I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students presented this skit.

Download a Printable Script

Cast

1-3 narrators (or more, if you have a large group)
7 friends (non-speaking parts, adjust to fit your group)

Props

Each friend will need a sheet of paper with a number written on it big and bold enough to be read by the audience. The numbers needed are 0, 1, 2, 3, … up to one less than the number of friends. Each friend keeps his paper in a pocket until needed.

Continue reading Skit: The Handshake Problem

Math Journal: The 1-2-3 Puzzle

Posted on by Denise Gaskins
colorful numbers 1, 2, 3

Math Journaling Adventures series by Denise GaskinsThere’s still time to check out my Math Journaling Adventures project and discover how playful writing activities will help your students learn mathematics. Preorder your books today!

Meanwhile, here’s a math puzzle to share with your kids…

Write down any whole number. It can be a single-digit number, or as big as you like. For example:

64,861,287,124,425,928

Now, count up the number of even digits (including zeros), the number of odd digits, and the total number of digits your number contains. Write those counted numbers down in order, like this:

64,861,287,124,425,928
even 12, odd 5, total 17

Continue reading Math Journal: The 1-2-3 Puzzle

Only Two Days Left for Math Journaling Adventures

Posted on by Denise Gaskins
Math Journaling Adventures series by Denise Gaskins
  • If you’re a parent trying to help your child learn math…
  • Or a teacher looking for creative ideas for your classroom…
  • Or a homeschooling parent hoping to enrich your student’s understanding…

Then you’ll love the Math Journaling Adventures series because these logbooks guide your children to explore mathematics at a deeper level, building a strong foundation to support future learning.

It’s a fun way to enrich any math curriculum, and great for unschoolers, too.

But you have to ACT FAST: The Kickstarter campaign ends in 2 days!

Order Your Copy Today ❯

Continue reading Only Two Days Left for Math Journaling Adventures

Math Journal: Three Quick Number Games

Posted on by Denise Gaskins
photo of family playing a dice game

Math Journaling Adventures Kickstarter projectHere are three quick math games you can fit in whenever you have a few minutes’ free time. Have fun playing math with your kids!

And if you enjoy these games, check out my Math Journaling Adventures project to discover how similar playful writing activities can help your students learn mathematics. Preorder your books today!

Continue reading Math Journal: Three Quick Number Games