Hey, everyone!

It’s been a minute since we’ve given you all an update; so, let’s remedy that.

After a busy summer of traveling, math conferences, and teaching classes, we’re knuckling down on layout, cover design, and the book’s supplemental materials. All that being said, the new estimated delivery date is September 2026. As we’re sure you’re aware, this is later than we originally planned, but we appreciate your understanding and support. If you are planning on teaching out of the book in August or September, please contact us for the current draft.

While we work on getting the book ready for printing, make sure you’ve completed the backer survey so we know where to ship your copy (or copies)!

Meanwhile, here’s a glimpse at our work on the cover. This is one of the first back-and-front cover drafts from a couple of years ago, which we call “the superhero ensemble,” and the front cover you saw during crowdfunding this spring:

That’s good, but AL is an action hero in the book, so we wanted her doing things on the cover. Math things. Maybe:

Great, mission accomplished! But now we are missing those “ready for anything” vibes from the first covers and the extradimensional robodog. Also, the ghost-mathematician was pretty special. Could we have it all? But how? Here’s the most recent cover sketch (back and front). What do you think?

In case your students want to draw their own versions of the Mathematician’s haunted house just like the book team did, John made a GeoGebra prototype (isometric) where you can turn the individual slabs around: https://www.geogebra.org/m/su6cuxzq

Author events

Grand Valley State University interviewed the authors for their alumni newsletter. Check it out!

If you’d like a live event with the authors for your class, math circle, or other community, contact us.

1. Future Book Club: A live online event on July 25 hosted by Math Kangaroo USA with Kara Shane Colley, the author of My Hundred Friends
2. Math Maker activity: Do you use pretend-play, stories, or improv to do math at home or with students?
3. Research Triangle, NC live math: August 12 indoor math playspace at Dix Park, Raleigh

Future Book Club news

Join us for a live and interactive online event for students in grades 3-5 this Saturday, July 25, at 1 p.m. EDT. Register to receive your link. (The event won’t be recorded.)

Meet Kara Shane Colley, the author of My Hundred Friends (Natural Math), a book about a cozy world where the mathematics of factors and multiples means friendship. Do you like comics, puzzles, and mathematical art? Then bring your pencil box and your imagination, and solve Math Kangaroo problems with the book’s creative, powerful techniques honed by math and engineering pros.

Math Kangaroo USA is dedicated to helping students love mathematics. It runs an annual international mathematics competition that inspires tens of thousands of students, and celebrates everyone who comes and gives it a try. The problems focus on critical thinking, logical reasoning, and creative problem-solving skills.

Math Maker Neighborhood

There are many lists of mathematical techniques floating around, with ideas like “Make your problem smaller” or “Work on your proof backwards, starting from the end.” What if we made a list like this with techniques inspired by storytelling? Do you immerse your group in history or cultural traditions while teaching math? Do you invite your students to imagine being two-dimensional characters? Do you use math fantasy books, cartoons, pretend-play, or improv? Please drop us an anecdote about your experience! We started our growing list of techniques at an improv workshop at Math Camp for Teachers (North Carolina) and a storytelling workshop at the Math Circles Institute (Indiana) this summer.

Math Circles Institute 2026: math makers taking over the world.

Research Triangle, NC events

On August 12, 2026 from 10 a.m to noon, join us in a beautiful (and air-conditioned!) pop-up math playspace at Dix Park chapel, Raleigh for puzzles, games, and art activities for ages 5 to 125 in the Math Maker Neighborhood series. The theme for August is Dividing and Uniting.

Can you split the map, guiding visitors to the closest ice cream stand in the park? Can a song win a popularity contest if fewer than half of the listeners prefer it? Why do both spies and artists love prime numbers? Come and play with the mathematics of dividing, fairly or otherwise. Featuring a take-home math kit for ages five and up inspired by game theory, operations research, and computer science.

Yes, we will play with gerrymandering, as you might have guessed – but we’ll only vote for broccoli vs. ice cream. We’ll also bring back the crowd favorites from our past themes, such as the giant Soma cube and the fluffy cord tangle puzzles.

Optional RSVP here.

If you’d like to volunteer, have a question, or want to talk about children learning mathematics, contact Natural Math.

Kids are natural storytellers because they are still open to the world of possibilities and imagination. How powerful it could be to encourage students to use their imagination when doing math, or even better, when playing with math.

Maria: The book campaign hit 100% – THANK YOU! The book is a go!

Kara: I’ve been beta reading middle grade and young adult manuscripts for two of my friends since 2015. Kerry Duff has stories pouring out of her. She has written several novels and published two short stories in Cricket, the children’s literary magazine. My favorite story of hers is called Granby, which focuses on a little girl left behind after the circus leaves town.

Kristin Burchell has a deft hand for writing enchanting historical fiction. She has several published novels. My favorite is The Witches of Proposal Rock, which takes place in 1660s New England, where magic is a force “to be feared and avoided.”

Kerry and Kristin’s writing feels to me like a beautiful magic. It amazes me how their sentences flow effortlessly and the pacing holds your attention while they build up complex characters and compelling plots. 

It feels easier to describe bad writing: clunky, overdone, and painful to read. 

Before I wrote My Hundred Friends, I tried to write a little story inspired by the series The Adventures of the Black Hand Gang by Hans Jurgen Press. As children, my brothers and I were obsessed with this book. As you read, you follow a group of children as they solve a mystery. You solve along with them by studying “purposefully busy” pages to find the clues.

 
I tried to write a story that had to be solved using clues hidden in a “purposefully busy” picture, called Cousins’ Campout. The writing of it felt forced. I had to work backwards to build the mystery, pulling the details aggressively from my brain, instead of my imagination offering ideas up. It’s a cute enough story, but I just don’t have the knack for this type of writing. 

My drawing for Cousins’ Campout

Over the years, I’ve heard people say, “Write what you know.” I think that is why My Hundred Friends is a good story. I know math. I know numbers.

Maria: One of my favorite loanwords is sprezzatura: the art of making something difficult look easy. Every writer has the kind of stories they know, love, and have worked out, stories they can craft with the magic feeling of flow and page-turning ease. Writing is still a complex endeavor, no matter what. Discovering what feels like your story doesn’t make writing simple, merely doable. And bearable when editing gets tough.

Kara: After my 48th birthday, the idea came to me that I am actually friends with the numbers, and I wondered if that could be the basis of a book. Immediately, I jumped to thinking about the numbers multiplicatively. I suppose that is because of the Fundamental Theorem of Arithmetic, which says that every integer greater than 1 can be factored into a product of primes in exactly one way (aside from rearranging the factors). When I first learned about the Fundamental Theorem of Arithmetic, the “fundamental” in its name stood out to me. That word felt like a link to mathematicians of the past, like they were telling me, “This is what’s important.” I started to make a page for each number, naming how I related to that number. For example, 7 days is one week. Since I was thinking of the numbers multiplicatively, it made sense to me to write their prime factorization in the bottom right corner. 

Things just started jumping out at me. Two was excited to see 2 ✕ 2 in the bottom right corner of the 4th page, so I drew Two yelling, “Look! It’s me and me again!” Then, it was as if I could see that scene once more on Page 8 (2 ✕ 2 ✕ 2), so I drew Two yelling, “Wow, it’s me and me and me!” I realized that these patterns had to happen every time there was a perfect square or a perfect cube, on and on. 

Multiplying by 11 is delightfully straightforward. I had the narrator point that out with a simple catchphrase, “It’s fun to multiply by 11,” on pages 22, 33, 44 and so on, while the characters added their own takes. Math was propelling the story forward. The number-characters’ excitement and playfulness gave them personality. I was off and writing! Unlike my attempt at a Black Hand Gang-inspired puzzle-mystery story, My Hundred Friends unfolded naturally. 

Maria: Another straightforward catchphrase: “Good writing is rewriting.” An author might rewrite their sentences in their mind while taking a walk, edit on paper with their special pen, or discuss the draft with trusted friends. The techniques and rituals are many, but by the time your prose feels smooth to read, it’s been polished with deep focus. What care and love sustain that focus and propel the story depends on the author. Fundamental Theorem of Arithmetic? Sure! Factoring as a relatable inspiration for art is more popular than you’d think.

1. Future Book Club news about three math fiction stories for elementary, middle school, and young adult readers.
2. Math Maker activities: two graph theory explorations with Juneteenth themes for your family or math circle, ages 5 to adult.
3. Research Triangle, NC live math: event series at Dix Park, Raleigh, a joint fundraiser with The Forge Initiative, and more.

Future Book Club news

Every Natural Math book is made together with hundreds of early readers, parents and teachers who test the materials with students, as well as backers joining the crowdfunding campaigns and spreading the word. Thank you, Future Book Club. You rock! Here is some news about our upcoming books.

My Hundred Friends by Kara Shane Colley is a highly illustrated book where numbers are people, and multiplication, division, and factors lead to friendships. (People ask this a lot, but don’t worry, the primes aren’t lonely in the story!) Children who like pretend-play, anyone who’s into cozy comics, and those who want solid pre-algebra foundations will love this fresh take on multiplicative reasoning. The book is being crowdfunded at Natural Math until the end of June. Check it out! See sample pages, meet the author, read geeky updates about writing mathematical fiction, and join the club.

Upper elementary and middle-school students who want a story that’s a step beyond multiplication will enjoy Modultown! That book about characters who live by modulo arithmetic will be going to its backers a couple of weeks from now. After that, it will be available to the general public. Check out a sample chapter and fanart from the early readers! The authors, Drs. Sasha Fradkin and Allison Bishop, and the artist, Mark Gonyea, really delivered on the bonus puzzle booklet. It came out beautiful and mathematically enticing. Here’s a little sample:

For the high school crowd, we have a young adult graphic novel coming out later this summer, AL, Logical by the son and father team of Xavi Golden and Dr. John Golden. If you like math puzzles, ghosts, and the strange, you will love this fantasy story. Xavi is wrapping up a new cover, to be revealed soon. Meanwhile, John is running the revised math notes by a few colleagues for a final round of feedback. Thank you to all who helped! Here’s a rabbit hole/bonus definitions game from the Notes. Beware, this game looks mild, but it can spark hours of math debates in your class or around the kitchen table.

The mathematician is pretty picky about language, and some would say that is not unusual for mathematicians. Is everything either dead or alive? Is the mathematician dead or alive? Is the mathematician a ghost? Are ghosts dead or alive? Mathematicians often try to resolve questions like these by coming up with a good definition. That allows us to be precise. But first we have to agree on the definition! We usually make lists of things we want to fit the category and of things that don’t fit the category. For Alive and Not Alive, where would you put: people, dogs, trees, wood, seeds, ghosts, bacteria, viruses, cells? This can get pretty difficult. What might seem counterintuitive is that we want it to be difficult! Try to break your definition with difficult examples.

Math Maker activities

Grab these ready-to-use printouts for your family mathematics, the “M” part of your STEM event, or a math circle. This June, we partnered with Triangle Math Teachers’ Circle and Dix Park to develop two graph theory activities. They are accessible for anyone who can count to 10 (ages 5 and up), and celebrate Juneteenth themes.

• Topology vs. Geometry – Gee’s Bend Quilts
• Map and Graph Coloring

Research Triangle, NC math maker events, Summer-Fall 2026

Join these local events! Math Maker Neighborhood is a gathering of people and organizations. We aim to make all the subject areas of mathematics accessible to everyone. Our benchmark: 5-year-old children making their own creations using mathematical tools from these subject areas and sharing that know-how with friends. These events put joyful experiences in a bigger mathematical context. Do you have a math circle, math event, or want to add math to your community event? Let’s add your gathering to this list!

Photo: Math Makers @ Dix Park, June 2026

• June 17, July 1, and August 12, 10 a.m. to noon—Math Makers @ Dix Park, Raleigh—all ages—family math mini-festival with puzzles, games, and art activities in an indoor space, with a take-home math kit—free, optional RSVP, volunteers welcome.
• August-December, every other Saturday morning—UNC Chapel Hill Math Circle—multiple age bands—explorations and problem-solving—free, registration is required.
• September 19, 10 a.m. to 7 p.m. —Bugfest, NC Museum of Natural Sciences, Raleigh—all ages—largest indoor and outdoor STEM festival in the region—free, come and play, volunteers welcome.
• Fall, to be announced—NC State Mini-Fest and Math Circle, Raleigh—multiple age bands—large-group interactive lecture and festival puzzles, games, and art activities at the math department—optional RSVP.
• Fall 2026, weekly—Durham Academy Math Circle—grades 3-4 students—explorations, art, and problem-solving—for students at DA (see the school catalog).

NEW: The Forge Initiative open tech space in Apex and Natural Math are collaborating to start math circles and events at The Forge. Until the end of June, we are running a joint fundraiser with the local math friends. Check it out!

If you’d like to volunteer, have a question, or want to talk about children learning mathematics, contact Natural Math.

Kids are natural storytellers because they are still open to the world of possibilities and imagination. How powerful it could be to encourage students to use their imagination when doing math, or even better, when playing with math.

Maria: I’d like to start a conversation about timely and untimely math stories so we can get better at mathematical storytelling as parents, teachers, and organizers. But first, I’d like to invite you to join the crowdfunding campaign for My Hundred Friends book before June 27th and tell your friends and colleagues about it!

This could have been such a good story!

We understand, remember, share, and guide our experiences through stories. That’s how we comprehend the world as more than a pile of data points and collaborate as more than disjointed individuals. That’s why storytelling is a human universal in every culture ever.

Comic by Loonar Baboon

Kara: Kids are natural storytellers because they are still open to the world of possibilities and imagination. I love the comic above by Loonar Baboon. The adult sees a messy room. The child sees a room full of lions, robots, and mountains. How can we use math storytelling to leverage a child’s imagination? And how can we use a child’s imagination to leverage math skill-building?

Maria told me about the book, The Children’s Machine by Seymour Papert. He says, “Fantasy has always been encouraged in good creative writing and art classes. Excluding it from science is a foolish neglect of an opportunity to develop bonding between children and science.” The same goes for math! We encourage students to use their imagination when writing stories or making art. How powerful it could be to encourage students to use their imagination when doing math, or even better, when playing with math. 

Maria: Like everything else we make, stories can be good but also ugly or bad, from an anecdote that elicits only a confused “Huh?” to hostile propaganda. It all depends on how, why, and when the story is told.

Mathematics is a culture and storytelling is a part of every culture. And so as math people, we tell math stories. One of the most popular math stories, Hotel Infinity, starts like this: Somewhere, there’s that hotel with rooms numbered 1, 2, 3,… and the rooms never end, just like the numbers. Every room is full, but a guest comes to the door. The manager messages everyone to move one room up, so the person from #1 goes to #2, from #2 to #3, and so on. Since there’s always the next number, every single person still has a room, including the new guest, who moves to #1! Yet they never have to build rooms. Adding one to infinity makes… the same infinity. ∞ + 1 = ∞

When would you share a story like this with people learning about infinities? I like to use it as an introduction to spark curiosity and make people giggle. That’s a great mood for math, and moreover, the story boosts mathematical reasoning. The hotel gives structure to the sheer weirdness, complexity, and abstraction of the infinite, turning it into something concrete and relatable: rooms. Children see rooms and move from room to room daily, so rooms are easy to imagine or pretend-play.

And that’s not all! Whenever our characters intrinsically enact our math, we activate the problem-solving technique called Smart Little People. The original technique imagines physical and chemical phenomena enacted by microscopic crowds to solve engineering problems. For example, if two parts must stick together and come apart as needed, imagine friction as people holding hands, then releasing, then holding again. That’s how Velcro could have been invented. In the hotel story, numbers are people. What is ∞ + 2? We imagine 2 as two guests, and if they come to the door, the manager can ask everyone to…

Prime factorization of 56; “My Hundred Friends” is entirely made of Smart Little People

…move two rooms up, so #1 goes to #3, #2 goes to #4, and the first two rooms welcome the new guests.

∞ + 2 = ∞

From the Arabian Nights to Star Trek, people like to keep telling stories set in the same imaginary world. When would you go back to the infinite hotel and tell more of the story? I like to do that to help students level up within a topic, pose a tough problem, or tackle a mind-bending idea. Can we multiply infinities, for example? If another infinite hotel in the next galaxy over goes out of business, can the manager move guests to make enough room for all? (Spoiler: yes, and ∞ × 2 = ∞.) In time, we can even use the story to navigate abstract proofs like, “The set of all rational numbers is countable.”

When would you tell a different and related math story, such as “Life on the Infinite Farm?” I like to do that separately, after a break, giving each story its own space and time, even if we do that on the same day like some sort of intense Barbenheimer experience.

Ask yourself: when would you NOT tell a math story? Here’s what I’ve tried, and tried, and it never worked. Even a beloved story or a reliable anecdote falls flat if I first tell it during exercises for fluency. Won’t a good story in the middle make a worksheet fun? Won’t students have more stamina if some new characters introduce a tedious computation? Nope!

When students have just explored a new topic? When they are first applying their fresh understanding to some exercises and problems? It’s both too late and too early to introduce new story-worlds. Too late because the imagery of the story might clash with new math images just formed in each student’s mind and derail everything. Too early because applying a fresh new math idea to a new context won’t work without fluency in the old context. That’s why children often feel that “story problems” are both boring and hard.

Kara: I know from 20 years of teaching math that story problems are nearly universally disliked and feared by students. Story problems are often contrived, confusing, and overly complicated.

I heard math educator Dan Meyer talking about breaking math problems into a grid. One parameter is real world vs. fake world, and the other parameter is real work vs. fake work. Too often, story problems fall into the “real world – fake work” box. The problems are realistic, but there’s not a lot of real math going on. Often, the students just need to plug the given numbers into a formula, and they’re done.

Maria: By the time your story has built up enough context and depth for real work to happen, you’ve probably used too much storytelling technique for the world to remain entirely real.

Diagram by Dan Meyer

Meyer encourages math teachers to pose problems in the “fake world – real work” box. His example below is “Pick any number you want. Multiply it by 40 and add 200. What questions could we ask about all our numbers?”

Okay, I pick 1:

40(1)+200 = 240

Next, I pick 10:

40(10)+200 = 600

What questions could we ask? 

Hmm, will the result always be even? Will the results always be positive? Will the results always be a whole number? Do the results lie on a certain line? 

Maria: I read world-building books like My Hundred Friends to unlock powerful new ideas like factors and multiples for children who’ve never done that math before. I also read My Hundred Friends as a complementary and separate experience with children who study or have studied multiplication, to reach new depth and build new connections. But I try not to be like, “What, factoring 60 makes you cry? Here, now numbers have faces, and 2 is a nice shade of pink, go go go!” 

Kara: Ever since I’ve heard this analysis, I felt more liberated to move towards the “fake world – real work” box. I built My Hundred Friends in that box: it’s a cozy world that takes place in a math scrapbook where cheeky little number-characters romp around. There’s a lot of math going on, but the math results naturally from the context of the imaginary world in the story. The number-characters and I happily play with factors, multiples, and primes, and the story invites readers to do the same.

I like how it’s funny and learnful.
Elizabeth, 4th grade reader

Maria: In My Hundred Friends by Kara Shane Colley, the math of factors and multiples is friendship. It’s a cozy little world, inviting readers to play and explore. From April 27 to June 27, head to My Hundred Friends crowdfunding campaign to preorder hardcover copies for your family or group, reserve your complimentary PDF, and support mathematical storytelling!

Kara: While editing the book, I spent several afternoons reading early drafts of My Hundred Friends with a Montessori class of 4th, 5th, and 6th graders. The teacher gave me a corner of the room and set me up with pairs of students.

I greeted the children and explained, “I’m writing a book and I’d like your feedback on it. I’d like you to read it and tell me what you like, what you don’t like, what’s confusing. I’ve illustrated the book so far, but I am not going to be the actual illustrator.” I handed them my sketchbook, and they turned to page 1.

In the first few pages, the children noticed right away how excited the numbers are to see themselves in the other numbers. On page 4 in the bottom right corner was 4’s prime factorization, 2 ✕ 2, with Two exclaiming, “Look! It’s me and me again.” On page 8 in the bottom right corner was 8’s prime factorization, 2 ✕ 2 ✕ 2, with Two doing excited cartwheels and exclaiming, “Wow, it’s me! And me! And me!”

Quoting Two’s line, Beck, a 4th grade reader, said, “‘It’s me!’ I’ve never seen a book like that.”

The numbers being numbers have inherent, repetitive structure just bursting to come out. The children turned the page from page 8 to page 9. In the bottom right corner, they saw 9’s prime factorization, 3 ✕ 3. The children chuckled to themselves when they saw Three exclaim, “Look! It’s me and me again.”

And it wasn’t very long before the children reached page 16, where they saw 16’s prime factorization, 2 ✕ 2 ✕ 2 ✕ 2. They smiled and laughed again. Helen, a 6th grade reader, told me, “I like 2. He’s always there!” Theo, another 6th grade reader, remarked, “I like the patterns in the book. I feel rewarded.”

Maria: Humans are social creatures, and big areas of our brains are devoted to people and relationships. Our imaginations spark playful bonds with characters and toys. What if we could use all that social reasoning to boost our mathematical power? Yet merely adding a face and limbs to a number won’t give it enough life for a good story or game. My favorite authors create their number-characters and storylines with deep care for each number’s mathematical behavior. In beloved books like The Cat in Numberland and shows like Numberblocks, numbers are persons, and everyday adventures spring from their mathematical personalities.

Kara: The children also liked the connections to daily life. When they reached page 13 with its connections to bagels, 4th grade readers Beck and Elizabeth became animated, telling me that the bagel should be “tastier-looking” and that I should “toast it and color it.” Based on this feedback, the bagel did become tastier as I made edits to the book. (I can’t wait to see illustrator Coley Nielsen’s bagel! Yum!)

The children interacted with the drawings in ways that I didn’t expect, reaching out to grab the bagel or tracing the path of a jumping number-character. They touched the pages, brushing their hands over the number-characters, almost like they were petting them. Theo said, “Your drawings are so cute, so sweet!”

Maria: Why do we care so deeply about children touching their mathematics? Because that physical play develops excellent habits of mind. Children learn to order numbers in space to hunt for complex patterns. They use visual structures like graphs and tables to solve problems, or read data from clever diagrams such as factor trees in My Hundred Friends. Our society is full of complex number patterns and data. Early, happy familiarity with organizing numbers in space helps every child.

Kara: I usually spent about 15 minutes with one pair of children, and then the next pair of children came to my corner. Many pairs just read the book straight through, starting at page 1 and going forward. One pair of children, Theo and Pascale, reached page 24 and noticed that the number-character Twenty-Four had one strip of brown at the bottom. Pascale, a 4th grade reader, asked, “What’s brown?” She paused and then wondered, “ Is it 12?” as they flipped back to page 12. Pascale guessed, “6?” as they flipped back to page 6. “No, it’s 3!” she exclaimed as they landed on page 3.

They were on to something! They had picked up some sort of pattern with the colors. From that point forward, Theo and Pascale started reading with an eye towards what was going on with the colors. I didn’t explain the role of colors in the book; they were having fun trying to figure it out. I held myself back, asking a few open-ended questions, like “What do you notice?” or “What do you see?” 

This was such an exciting moment for me. I had created a world where kids were exploring and asking themselves math questions. They were playing with the number-characters, playing with math. At the end of our session together, Elizabeth remarked, “I like how it’s funny and learnful.” That felt like high praise! 

If you have a child, a classroom, or a fondness for cozy math, I invite you to come explore My Hundred Friends. What number connections might your child make? How might your student pretend-play with their favorite number-characters? 

“The chalkboard appeared when Two wanted to draw on it.”

Maria: In My Hundred Friends by Kara Shane Colley, the math of factors and multiples is friendship. It’s a cozy little world, inviting readers to play and explore. From April 27 to June 27, head to My Hundred Friends crowdfunding campaign to preorder hardcover copies for your family or group, reserve your complimentary PDF, and support math joy for all!

Evolution of the cover

Kara: In making drafts of the cover, you can see that some aspects of the cover stayed the same. On every draft, there are number-characters hanging from the title, sitting on the title, running up a path, and cheeky number Seven trying to get our attention!

It was my publisher Maria’s idea that the number-characters should be doing math on the cover. In the illustrator Coley Nielsen’s cover, you can see Two building a cubic model with blocks, Fifty-Five playing tag with their factors, and Seventeen proudly displaying their factor rainbow.

Maria: It is said that sci-fi isn’t about the future and fantasy isn’t about magic: it’s all about our life, here and now. Where does math come from? We make mathematics as we live our lives, create, and discover together. Kara and the number-characters built such a friendly village with their mathematics! Imagine that. Let’s go!

Evolution of page 9

Kara: Collaborating with Coley has been exhilarating. The process of working with her helped me develop some ideas that weren’t totally fleshed out in my head. As you can see in the early draft, I originally thought of the pages of the story as loose leaf paper with a horizontal line at the top of the page and holes punched down the left side. As you can see on the second draft, the horizontal line at the top remained but the hole punches were gone. As we prepared to send over the second draft for Coley to draw her version, I realized that the whole book was like a math journal; it was a scrapbook that I made of my hundred friends. Because it was a scrapbook, I asked Coley to draw graph paper and make it look like it was taped onto the page.

Maria: Our numbers, our math – is it out there, hiding in plain sight all around us, to be discovered? Or does mathematics come alive by our creativity, the same way pretend-play toys or fiction characters do? The readers can see Kara’s and Coley’s art either way.

Evolution of page 12

Kara: Another evolution of the world occurred as Coley began to draw drafts of page 12. In my mind, I was the one writing “12 is one dozen” and I was the one who drew the egg carton. Coley drew a couple of versions of the egg carton for us and that made me realize that I didn’t want a totally realistic egg carton. I wanted a rough “sketch-like” version of the egg carton.

On the other hand, the chalkboard at the bottom was part of the imaginary number-character world. I didn’t draw the chalkboard. The number-characters came to play in the math scrapbook, and the chalkboard appeared when Two wanted to draw on it.

Come check out My Hundred Friends. The book is a kind, welcoming math gathering. We invite you to come, hang out, and meet a few new friends.

Big thanks and a bonus tier at Modultown! crowdfunding

Thanks to six score backers, our next children’s puzzle-adventure story, Modultown! by Dr. Sasha Fradkin and Dr. Allison Bishop, reached its funding target on Kickstarter and made the “Projects We Love” list. Yay! It’s so heartening to know that people care about math stories. You can help us get this Creative Commons book into the hands of even more children and unlock bonus puzzles by contributing to the campaign by December 1. (If you are reading this after December 1, pre-order the book at NaturalMath.com/Modultown.)

Head to the campaign page to check out the funny video with student fanart, meet the quirky, many-handed Moduli, and grab an awesome zoo-themed scavenger hunt and other author tour materials for your family or math circle.

The authors say:

Math Storytelling? Why?

By personifying math through relatable characters in magical worlds, we show kids that math is alive and much more than a formula on a page. Mathematics is a language describing human phenomena and a canvas for creativity.

Just like the stories we love, many great inventions of mathematics start with a desire to express something in our world or to create fantastic worlds of our own. We believe that math and stories are complementary tools for building human understanding, transferring knowledge, and ingraining concepts in memory. We believe that every child has a math story to tell.

Quintessa the fifteen-handed Modultown resident says:

On the one hand, you may have children who will enjoy this book.

On the second hand, you support creative approaches to math education.

On the third hand, you just like puzzles.

On the fourth hand, you want to learn what modular arithmetic really is.

On the fifth hand, you read Funville and were sad when it ended.

On the sixth hand…

Read more at kickstarter.com/projects/naturalmath/modultown-a-math-inspired-childrens-book.

Future Book Club volunteer opportunities

If you are reading this, you probably value reading. And math. Reading math? Reading about math? All of the above! That’s why I want to tell you about our Future Book Club.

The Future Book Club is like a book club, but for upcoming books. Club members work with authors as math makers, helping them shape and edit future books. This is a unique volunteer opportunity for teens, children, parents, and anyone passionate about mathematical writing. Besides helping out a great cause and learning the ropes of writing and editing, this comes with our big thanks and volunteer hour certificates from the Natural Math Alliance, a 501(c)(3) nonprofit.

What’s in the works? Something for everyone! Here are three examples of what the Future Book Club is currently working on:

• My Hundred Friends, a cozy-core children’s comic book about friendship and factorization. “One is every character’s favorite, like the Dalai Lama of the numbers” – Kara Colley, author and character.
• Roots: It Starts with a Story, an upper elementary and middle school resource for those who might have struggled but will thrive with math as a language first and a pattern second.
• AL, Logical!, a graphic novel that’s like a high school math circle, but in a haunted, multidimensional mansion where a lonely, brave artist finds the restless ghost of a mathematician, and then…

We also started a small pilot project for mentoring child authors to connect with like-minded math makers and find their audiences.

Contact Dr. Maria @ Natural Math to learn more about joining the Future Book Club.

https://naturalmath.com/contact-us/

Math Maker Moments

Building and sharing Dragon Nests (paper models of hyperbolic saddle points)
E3 Black STEAM Career Fair, Hargraves Community Center, Durham, North Carolina
November 15, 2025

Some math activities are so rich in mathematical connections, inspirations, and energy! If mathematical routines were people, Growing Patterns would be a pillar of the community. Growing Patterns routine connects several key ideas in computer science, algebra, geometry, and beyond. Moreover, all that is doable at the pre-algebra level; you’ll be essentially learning algebraic reasoning from scratch. Here’s what we did over the hours of the project, in a nutshell:

1. Admired Fawn Nguyen’s (last name is pronounced “win”) whimsical collection of hundreds of growing patterns at VisualPatterns.org and decided to add to it!
2. Made our own visual growing patterns using graph paper, colored pens, and wooden cubes.
3. Using spreadsheets, scripted recursive formulas for a few starter number sequences: counting numbers, even numbers, odd numbers, and alternating numbers (1, -1, 1, -1…).
4. Scripted recursive formulas for the three patterns we’d like to add to the collection.
5. Wrote stories explaining the three patterns.
6. Scripted closed formulas for n-th entries in the three patterns.
7. Looked at the corresponding functions using a grapher (Desmos).

The drawings, stories, functions, formulas, and scripts are all different representations of the same infinite, growing sequences. They help us understand the mathematical nature of the sequence and express its growth in a single closed formula. That formula, for us, evokes many geometric, algebraic, and computer-science connections, kind of like e=mc^2 packs a vast amount of physics for those who know how to derive it.

A Very Long Pool

A very long pool is my pattern, where the water is some blue squares(or opposite), the Rim is the green squares making an equal shell around the water(or opposite once again), and the stairs is the singular green square on the right side of the pool. The “very long pool” is essentially a pool that grows by the second, making it (technically) infinite or just very long.

The number of squares and recursive formulas for the water, rim, stairs, and the total space of the pool:

Closed formula for the Nth total space: N*6+4.

Heart

Growing emotions is one of my patterns, it is a heart that continually grows forever or infinitly. The yellow squares inside is the inner heart, where it beats and grows in size, and the purple squares outside is the outer heart, that protects the inner heart from dangers. Given that is grows infinitly, it isn’t strong enough to be on it’s own, and is very sensitive(emotional) and prone to damage. Together they grow and grow to the point where there is no stopping point.

The number of squares and recursive formulas for the inner heart, the outer heart, and the total number of squares:

Closed formula for the Nth total space, outer heart: N*4+6; inner heart 2*N^2+4*N-3.

Road to… Nothing

The road to nothing is my pattern, where there is a road, a very long road, or you could just say, infinite. Most patterns go infinite if there is no stopping point, so does this pattern. This road leads to, you guessed it, nothing… If there is no stopping it, there is no end which means it leads to nothing. It may come across one or two things, but it doesn’t stop going, it leads no one, once again. It has no purpose, it is useless you may call it, it has no emotions, unlike the growing emotions pattern, so it has no feelings, so say whatever you want to it, as it won’t even respond. But anyways, the yellow part is some holes in the road, and the purple is some stepping pads that make up the road.

The number of squares and recursive formulas for the green parts, pink parts, and total squares in the road:

Note that in this example, the closed formula for the total number of squares in the road to nothing is quite easy. But alternating recursive patterns by color took some doing, the way we did them!

Closed formula for the Nth total bricks in the road: N*3.

Our partner Alliance of Indigenous Math Circles organized two summer camps this June. The first was at the beautiful and impressively curated California Indian Museum and Cultural Center in Santa Rosa. The second was at the Navajo Preparatory School, a high-quality academic and outreach hub at Farmington, NM.

The camps included a math festival, a problem-solving game called Math Wrangle, many deep-dive math sessions on topics from cryptography to mathematics of braids, and of course a lot of cultural activities. We will share more materials as we organize them for publication. Meanwhile, here are photos from the camps and two art projects for you, which we created with Pomo and Navajo people.

A weaver’s hands.

Donna Fernandez, director of AIMC, and campers. “It doesn’t matter what tribe on the planet you are from; you all still made baskets. Everyone already has a basket in them and I’m just helping them to bring it out.” —Pomo basket weaver Corine Pearce.

A camper with her stick-and-bean game, exploring probability.

James Taylor, leader of Math Amigos, with the campers playing tic-tac-toe on a torus to explore the game of Set. “I learned that mathematical engagement has a “shape.” When a group of participants is thoroughly “hooked” by a problem, it is as if the center of the table they circle becomes a black hole, drawing them in, arching their backs as if in a deep huddle. When I see that shape, I know that students are hooked, so I stand back to give them space to let joyful mathematics progress.” Klein, B. (2019). Math unbounded: A transcultural experiment.

Another familiar shape of collaborative mathematics: a big math circle by Navajo hogan house (see below).

Desert sunset.

Math friends sharing a solstice. The optics of our camera caught the rays of the rising sun perfectly aligning with the walls of this Great Kiva, a Puebloans building from about 1000 years ago.

The Navajo are Indigenous people of the Southwestern United States. Explore hogans, traditional Navajo dwellings known for their sturdy, sustainable, and comfortable designs. Learn to construct geometric shapes with hogan builders’ tools. Part 1 compares tools and axioms of different geometries. Part 2 focuses on the Navajo geometry. Click these links to download the materials.

The Pomo are Indigenous Californians. They are world-famous for their basket art. You can find gorgeous Pomo baskets in many major museums. They are also used for practical purposes in modern households. In this set of activities, you can learn about fractals and fractal dimensions using designs from Pomo artists. Click the link to download the materials.