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From Angles to Art: The Hidden Math in Pop-Up Cards Revealed

Header image for blog post on about how math can be used to make pop-up cards.
See how math sneaks it's way into making pop-up cards!

Hi, art lovers!

I recently had an incredible experience in the studio while engrossed in creating some delightful wintry pop-up cards. To my surprise, I found myself delving into the realm of mathematics—yes, you heard that right!

You might be wondering how the precise, structured world of math could intertwine with the free-spirited, creative haven of my art studio. Well, the answer is surprisingly simple—math and art share a common foundation in SHAPES, ANGLES, and PATTERNS! This enlightening revelation dawned on me while working on my latest YouTube video, serving as a delightful reminder of this intrinsic connection.

artist and arts educator Emma Tipping posing with a mini pop-up card, completed for a YouTube video
Lil ole me posing with a snowy forest mini pop-up card!

As an avid creator of pop-up cards, especially those adorning beautifully wrapped gifts, I find joy in this unique artistic expression. While some people revel in extreme activities like bungee jumping or conquering literal lofty peaks, my passion lies in the art of wrapping presents and adding a touch of whimsy with cute pop-up cards. To each their own, right?! After enlisting the help of my creative assistant, we embarked on a project to craft a charming Snowy Forest Mini pop-up card.

Now, this is the first time I’ve created a tutorial for a pop-up card, but I have made pop-up cards many times in the past. I particularly nerded out in the pop-up card world about two decades ago when Robert Sabuda published a bunch of fabulous pop-up card patterns on his website. I discovered Sabuda when I was visiting my parents in Kansas City and found a copy of his pop-up book, The Wonderful Wizard of Oz (If you’re ever looking for a fantastically amazing object that simultaneously celebrates American literature and the jewels of Midwest America, this is the book for you!).

But I digress. As I was practicing my pop-up card before making the actual video, it slowly dawned on me that I was using a lot of math to make my pop-up card. I was thinking about angles, how to make multiple triangles at once, and debating about whether to design my card in quarters or thirds. Then, suddenly, I realized- "Wow, I use math when I make art all the time!"

I think this all fell into place because I just finished illustrating the book We Didn't Learn Math This Way! A K-5 Guide for the Confused Adult published by Singapore Math (available now!).

Illustrator Emma Tipping holds the book, "We Didn't Learn Math This Way: A K-5 Guide for the Confused Adult", available on
The go-to-math-guide for parents everywhere!

Over the course of the two plus years it took to create and publish this book, I had ample opportunity to think deeply about elementary school mathematics, how it’s changed since I was a kid, and how it all relates to early art education. I’ve been particularly thinking a lot about how that moment in prek and kindergarten when kids are learning basic shapes is a ripe moment when math education and art education overlap. I really struggled with math in school, but I absolutely kicked the ball out of the park in geometry. Why? Because I’m a visual learner, a visual thinker, and because I’ve been creating art almost my entire life! Understanding that a square is actually a kind of rectangle? No brainer. Understanding the importance of angles in triangles and how those angles relate to one another? No problem, got it. Understanding how negative space and positive space interact? I’m here for it.

And there’s something else really cool I want to share with you here. After graduating from William Allen High School Arts Academy, in Allentown, PA, I spent a year or two studying at the Barnstone Studios in nearby Coplay, PA (now in Thurmont, MD since Barnstone's passing). Mathematics and geometry were a huge part of the curriculum there. We were constantly discussing curves, angles, and diagonals, and in particular, the golden ratio, which anybody who knows about art and design knows plays a significant part in art theory and art history, particularly, it is argued, during the Renaissance period.

Beautiful image of the golden ratio demonstrates the connection between art and math.
The Golden Ratio is studied by many artists.

Studying with Barnstone led me to add an extra level of structure to my artwork. This additional level of structure and visual understanding, and the ability to see hidden patterns and shapes within an art piece, or within the world that you’re trying to recreate, is a huge part of creating art and developing visual literacy.

OK, so how does this art jargon relate to making cute little pop-up cards with kids? Well, my assistant couldn’t quite believe it, but by the time I was done with this pop-up card project, we had talked about right angles, I had demonstrated how three triangles can fit together snugly within a rectangle, shown how useful knowledge of basic fractions can be when making art, and I even broke out the vocabulary term "parallel lines." While I knew theoretically that art and math had a lot of intersections, it was awesome to get back into the studio and see how math immediately informed my art-making!

Let's talk real talk. Math is AWESOME and POWERFUL. But there are lots of kids out there who struggle to connect with math. Either it's taught in ways that don't appeal to their type of intelligence or it's not demonstrated how math can enrich their own lives, or BOTH! Imagine how amped our kids would be about math if we could prove to them everyday how useful basic mathematical concepts can be when being creative and making art. I think the crisis of math confidence that we are witnessing in American schools would fizzle out over night!

So if you have reluctant mathematicians in your home or classroom, consider showing them this silly video of me goofing around in the studio, making mini pop-up cards. In case you want to check out these math concepts in action, you can check out my list of terms here, along with the exact moment that they occur in the video:

  • Fourths... 3:15

  • Parallel lines... 5:40

  • Three triangles in a rectangle... 6:14

  • Right angles... 6:50

If you and your young artists love this video, please like and subscribe.

And don't forget to download the project guide here the video to help you and your kiddos easily cut out the paper pieces you’ll need for your pop-up.

Now, let’s get poppin'!


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