Discovering Pi: A Multisensory Journey Through Circles, Nature & Art (early elementary focus)

 

Thank you to Susan Gerofsky for her suggestions and passion for art and mathematics. 

Discovering Pi: A Multisensory Journey Through Circles, Nature & Art.

We realized some of the text is blocked at times and have linked our slides below.

Slides for our presentation.

Origami and a wish

 I started this week’s activity thinking I might have a yet-to-be-discovered hidden talent. I had watched Uyen Nguyen use Miura-Ori folds to create fashion, and she made it look—if not easy—at least fascinating. Perhaps this was origami I could get behind. It seemed (foolish of me to think) easier than making paper cranes.

I was sure I could whip a few out and astonish my mathematically inclined teens, and maybe even entice my friend who cringes whenever the word math is spoken. I am always trying to show her mathematics in new ways, but I haven’t convinced her yet. Math attitudes are hard to shake.

Anyhow, I grabbed some copy paper and cut a couple of squares. I watched the first video, but some of the action was off screen and I didn’t quite understand how to finish after making the second set of triangular folds. I fiddled with it for a bit and eventually declared (to myself), “This must be the wrong kind of paper! It’s too soft, too crinkly, too hard to work with!”

I briefly looked at the other activities and considered giving them a try. Alas, it was the Miura-ori folds that had hold of me.

I watched the next video and gained some new insight. It was easier to see what was happening. Without a voice giving instructions, I noticed the details more carefully. Even so, it still didn’t seem to be coming together quite correctly. I paused to search for the correct square size for this type of folding and came across a website that appeared to be part of a course assignment. The author noted that folding the pattern by hand requires patience and practice (Woodruff, n.d.).

This immediately validated my feelings of intense frustration. Of course I couldn’t get this right the first time I tried. It’s actually quite finicky.

The experience reminded me that when students bump up against new mathematical concepts, they too may feel the urge to quit or need to step away for a moment. Learning something new—whether it’s origami or mathematics—often involves moments of confusion, persistence, and small breakthroughs along the way.

In the end, my Miura-Ori fold is far from perfect, but the process itself turned out to be the real lesson. What looked simple at first required patience, careful observation, and a willingness to try again after frustration. It reminded me that learning mathematics often unfolds in the same way. Students rarely master a new idea the first time they encounter it. They need time to struggle, notice patterns, adjust their thinking, and try again. Perhaps that is part of the quiet beauty of both origami and mathematics—the way persistence slowly transforms a flat sheet of confusion into something structured, surprising, and meaningful.

If there is a wish folded into this experience, it is that my students—and perhaps even my math-averse friend—might someday see mathematics the same way: not as something rigid or intimidating, but as something that rewards patience, curiosity, and the courage to keep unfolding an idea a little further.

Woodruff, S. (n.d.). Miura-ori folding instructions. Retrieved from http://www.stevenwoodruff.com

From the Drink of Doom to the Golden Ratio: Teaching Math You Can Taste

                                                     Image created with Canva AI.

In her article, Exploring Ratios and Sequences with Mathematically Layered Beverages, Andrea Johanna Hawksley explores how mathematical ideas such as fractions, integers, ratios, and density can be understood through the process of making beverages. She describes how simple ingredients like sugar and water can be used to experiment with ratios and observe how those relationships affect density. For example, mixtures with ratios such as three to five can be compared with others that use different amounts of sugar and liquid to determine which solution is more dense. When one mixture is poured into another, it quickly becomes clear whether the prediction about density was correct. If the liquids mix together, the densities are similar, but if one liquid remains layered on top of another, the difference in density becomes visible.

Hawksley also introduces the Fibonacci sequence as a way to design layered drinks. By carefully considering ratios and building the drink from the most dense layer to the least dense, it is possible to create distinct layers within the glass. As the ratios begin to approach the golden ratio, the drink itself becomes a physical representation of that mathematical relationship—suggesting that you could, in a sense, be “drinking the golden ratio.” Through these examples, Hawksley demonstrates how creating layered beverages can become a hands-on way to explore fractions, ratios, proportions, and mathematical sequences.

One idea that stood out to me while reading this article was how something as simple as making a drink can become a way to experience mathematical relationships in a tangible and visual way.

This article also brought up a wonderful memory from when I was a B.Ed. student. One of my cohort members created an amazing lesson on density that he called the “Drink of Doom!” It combined a dramatic story about what this mysterious drink might do if someone drank it with a visually stunning layered mixture that allowed students to see density in action. If I recall correctly, he even ended the demonstration by adding baking powder to the drink, which reacted with vinegar and caused it to dramatically erupt.

Moments like this are a good reminder that visual experiences that surprise us or capture our attention can be powerful teaching tools. They act as the hook that draws students in, especially those who may be reluctant or unsure about mathematics. Yet it often feels like those hooks get forgotten as we move from lesson to lesson and year to year. (And somehow, decade to decade—oy, I cannot believe I have been teaching for decades now.)

Reading this article also made me wonder how an activity like this could work practically in a classroom. A demonstration might be interesting, but it would likely be far more meaningful if students could experiment with the densities and ratios themselves. When would an activity like this be most impactful? Would it work best as a culminating experience, or as an exploration during a unit? I would love to see curriculum include more opportunities like this.

It also makes me wonder if I could create some of these opportunities myself. Perhaps I could look through the curriculum we currently use, Math Up, and see where activities like this might fit within each unit. Or perhaps I could start small—adding something like this to just one unit each term, as suggested earlier in the course, and slowly building a collection of experiences where students can see and feel mathematics in action.

When did you last surprise your students with mathematics — and when did mathematics last surprise you?

Where in your current curriculum do you think an activity like this could fit, and would you use it as an introduction, exploration, or culminating experience?

Draft link for final project

Draft of final project: Pi Lessons for Third Grade

Pi Lessons for Third Grade

Birthday Cake and Fib Poems: Family Time

This week's theme of mathematical poetry was like a breath of fresh air. As I read through the poetic offerings in the Bridges 2021 Fib Collection, I felt a genuine sense of lightness. It was something I really needed — there has been a lot of heaviness around me lately, and that weight found its way quietly into my first two attempts at Fib poems:

Sleep

Sleep

Now

Sleep now

Rest your head

Wide awake all night

Exhaustion is my companion

The List

Work

to

Complete

to do list calling my name now

the book will have to wait again

Looking at the poems, I can see how the Fib form did something interesting — it gave shape to feelings I hadn't quite articulated. The constraint became a container for expressing the stress I've been living with lately. Despite the to-do lists and the sleeplessness, the evening had other plans.

I have two teen boys, aged 15 and 16, and part of our family ritual is sharing snippets from our day. Usually we get short answers; on a good night, details and some back-and-forth. Tonight I was excited to share what I'd learned about Fib poems. My 16-year-old surprised me by admitting he didn't know what the Fibonacci sequence was — this despite being in Pre-Calc 12! After a quick introduction to the sequence and the form, what followed was a full Fib poem writing contest, with the winner earning the right to choose what I would make for the next dessert. We happened to be eating leftover birthday cake, so the theme chose itself.

Cake

bunt

Cake

Amazing

Tastes so heavenly

Absolutely delectable

-Cameron McClellan

Untitled

Cake

Yum

Why not!

Eat it all

Chow down on frosting

It’s not just for birthdays is it?

-Ty McClellan

Throwback Request

Cake

Sweet

Sugar

Birthday boy

Request is honoured

The cake a frosted snake shape

-Kristie McClellan

My 16-year-old served as judge (declining to write, in true teenage fashion). After the verdict was rendered, my husband and I kept going — we'd caught the bug. As Sarah Glaz notes in her introduction to the collection, "Fib writing is addictive" (p. 469), and I think she's right. There's something about the interplay of constraint and rhythm that keeps pulling you back for another attempt. We chose travel as our next theme:

Where the Money Goes

Planes

Trains

Moving

Got to go!

So much to explore

See the world so full of wonders

-Kristie McClellan

Escape

Go

Far

Go near

Life is great away

You see something new everyday

-Ty McClellan

What strikes me, reflecting on the whole evening, is how quickly the form became a vehicle for genuine expression — for my heaviness, for my family's silliness, for our shared love of adventure. The mathematical structure didn't get in the way of feeling; it seemed to invite it. I find myself wondering: is there something about the Fibonacci sequence's closeness to natural growth patterns — the golden ratio, the spiral — that makes it feel instinctively satisfying as a poetic form? And for our students, who might arrive in math class certain that mathematics has nothing to do with their inner lives, could an experience like this — writing a Fib poem about something they actually care about — begin to shift that story?

Poetry in the Glade: Bridges 2021 Fib Collection. (2022). Journal of Humanistic Mathematics, 12(1), 467–500. https://doi.org/10.5642/jhummath.202201.35

Four Teachers/For Teachers

In this 2019 interview conducted by Sarah Glaz for the Journal of Mathematics and the Arts, poet and mathematician JoAnne Growney reflects on her journey navigating both disciplines. Growney, who earned a PhD in mathematics before completing an MFA in Creative Writing, discusses how her rural upbringing, formative teachers, and guiding philosophy that "everything connects" shaped her as a mathematical poet. The interview is interwoven with ten of her poems and touches on her blog Intersections – Poetry with Mathematics, her advocacy for women in STEM, and her belief that poetry and mathematics are not opposing ways of seeing the world, but deeply interconnected ones.

This was a genuinely delightful read. Growney's poems are threaded throughout the article, inviting pauses to reflect on meaning and moments of whimsy. I'll focus on the two stops that stayed with me most.

The poem "Four Teachers" (subtitled "The Ones I Best Remember") describes four very different educators. In the interview, Growney recalls a high school English teacher who would walk into class and say, "Guess what I watched on television last night?" — and then share something she'd learned from a TV show. The lesson Growney draws is simple: you can learn from everything. What struck me is how quietly powerful that model of teaching is. That teacher wasn't delivering a formal lesson on curiosity — she was living it out loud. It made me pause and ask myself: am I bringing that same energy into my classroom, or just delivering content? Honestly, it depends on the day. But my favourite moments are when I get to share some of my learning with my students. Demonstrating my role as a learner is something I hope I model for my students often.

The same poem also describes a professor that Growney actively disliked as the professor was demanding, error-prone on the blackboard, and exacting about writing perfect mathematical English. In the interview, she explains that this woman was "very important" to her, because it was in her class that she first began linking language and mathematics together. This thought hit me fairly hard because we tend to focus on the positive role models, mentors, and teachers that influence us. However, Growney makes a compelling argument that some of the important people in our lives are not necessarily those we liked. It reminds me that we can learn from all people, even if there are parts of them we seem to bristle against.

Throughout the interview, I kept returning to one question: what actually makes a poem mathematical? Growney's answer, as I understand it, isn't really about equations or numbers. Her ideal, she says, is a poem that uses mathematical terminology correctly — so that a reader who knows the math finds additional depth, while a reader who doesn't still finds a work of art. The poem about Hedy Lamarr, built around the concept of "perfect numbers," does exactly this. And the title "Four Teachers" kept pulling at me as a second reading too — "for teachers" — as though the poem were addressed outward as well as backward. Whether or not that's intentional, it enacts what Growney describes: language operating on more than one level at once. That, more than any formula, seems to be what makes a poem mathematical.

Can you think of a teacher — one you may not have liked or appreciated at the time — who you now recognize as having had a real impact on you? What did they do that mattered, even if it didn't feel that way then?

Glaz, S. (2019). Artist interview: JoAnne Growney. Journal of Mathematics and the Arts, 13(3), 243–260. https://doi.org/10.1080/17513472.2018.1532869