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.
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.
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.
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…
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.
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.)
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!
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“Playful Math for the Summer” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © damedeeso / Depositphotos.
ALL my math game books are on sale now at the Playful Math Store.
What a great way to prepare for a summer of mathematical play!
On a friend’s blog, I found this delightful letter written by Charles Lutwidge Dodgson to a young man named Wilton Cox.
The pseudonym Lewis Carroll comes from an alteration of the Latinized name Carolus (for Charles) and the replacement of Lutwidge with Lewis.
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.
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?
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.
1-3 narrators (or more, if you have a large group)
7 friends (non-speaking parts, adjust to fit your group)
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.
There’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
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!
Continue reading Only Two Days Left for Math Journaling Adventures
Denise Gaskins' Let's Play Math 