Math is often introduced through numbers on a page, but long before students open a textbook, the natural world is already filled with patterns, measurements, shapes, angles, distances, ratios, and change. A sunflower keeps count in its spirals. A tree casts a shadow that helps us estimate its height. A butterfly carries symmetry on its wings. A set of animal tracks gives us distance, direction, and clues about movement.

Math is everywhere, and sometimes students need to step outside to see it.

SUNFLOWER → SPIRALS → PATTERNS → FIBONACCI NUMBERS

When students study the center of a sunflower or the scales of a pinecone, they begin to notice that nature is not arranged randomly. Spirals repeat. Patterns overlap. Numbers begin to describe something students can hold, observe, and investigate.

A lesson about Fibonacci numbers becomes more understandable when students can slowly turn a pinecone in their hands and count the spirals moving in two different directions. They are not only completing a math problem. They are using mathematics to understand how something grows.

TREE → SHADOW → ANGLE → HEIGHT

A tall tree can become a trigonometry problem. Students can measure its shadow, compare it with another known measurement, examine the angle of the sun, and estimate the tree’s height without ever climbing it.

That experience changes the purpose of the math. Students are no longer calculating because a set of directions told them to do it. They are calculating because they want to know how tall the tree is.

This kind of learning leaves room for mistakes, repeated measurements, new strategies, and conversations between students. It also gives them a reason to care about whether their answer makes sense.

BUTTERFLY → REFLECTION → SYMMETRY → DESIGN

Butterfly wings, leaves, flowers, spiderwebs, snowflakes, and even some animal tracks give students opportunities to explore symmetry and geometry. They can identify lines of symmetry, compare shapes, sketch reflections, and look for places where a natural object does not match perfectly.

Those small differences matter. Nature gives students a more honest picture of mathematics because patterns can be clear without being flawless. Students learn to look closely, describe what they notice, and support their thinking with evidence.

ROCKS → SORTING → RATIOS → DATA

A small collection of river rocks can become a lesson in classification, ratios, proportions, graphing, mean, median, mode, and range. Students might sort rocks by size, color, texture, shape, or material. Two groups can study the same collection and organize it in completely different ways.

That opens the door to meaningful mathematical conversations. Which categories were useful? How many rocks belonged in each group? What fraction of the collection was smooth? What was the most common size? How could the data be displayed so another person could understand it?

ANIMAL TRACKS → DISTANCE → DIRECTION → MOVEMENT

Tracks tell stories through measurement. Students can measure the distance between prints, compare stride lengths, look for changes in direction, and estimate how an animal may have been moving.

A set of tracks also reminds students that numbers do not exist alone. Distance connects with habitat. Direction connects with food, water, shelter, and safety. Mathematics becomes one tool students can use to interpret the story left behind.

OBSERVE → MEASURE → COMPARE → WONDER

Our Math in Nature collection was created to help educators bring these experiences to students. The lessons explore tree-height trigonometry, sunflower spirals, mean, median and mode with leaves, geometry in stone, biodiversity percentages, snowflake fractals, wind direction, seed dispersal, shadows, animal tracks, symmetry, river-rock ratios, graphing, Fibonacci patterns, river curves, prairie sampling, and more.

Each lesson begins with something students can notice in the world around them. Many of the investigations can take place in a schoolyard, on a sidewalk, near a window, in a neighborhood park, or with a small collection of natural objects brought into the classroom.

Students do not need access to a national park to begin. They need time to look, permission to wonder, and a reason to use mathematics to make sense of what they find.

SEE IT → SOLVE IT → LIVE IT → LOVE IT

At Expeditions in Education, we believe classrooms have no walls. Taking math outside does not mean leaving academic learning behind. It gives students a place to apply what they are learning and helps them understand why those skills matter.

A child who struggles with numbers on a worksheet may recognize a pattern in a flower. A student who hesitates to participate in the classroom may become the careful observer who notices a difference in animal tracks. Another may discover that measuring, mapping, sorting, and graphing are ways to tell the story of a place.

The next math lesson may already be waiting beneath a tree, beside a puddle, inside a pinecone, or along the edge of the playground.

Follow the arrows. Measure what you find. Let nature show your students where the math has been hiding.

EXPLORE THE FREE LESSONS → MATH IN NATURE

All Expeditions in Education resources are free for educators to use with proper credit. Please keep the organization’s name and logos on the materials and link back to expeditionsineducation.org when sharing them.

​Six years ago today—September 7, 2020—we officially launched Expeditions in Education.

I remember how excited we were to finally share this new adventure with the world. We had two challenges ready to go on our website, a lot of ideas, and no way of knowing exactly where the journey would take us.

Today, those first two challenges have grown into hundreds of lessons, videos, activities, publications, design challenges, virtual experiences, and classroom resources. We have traveled to extraordinary places, worked alongside wonderful educators and park rangers, and helped students discover that learning can begin with something as simple as noticing, wondering, and asking a question.

What began as an idea has become a community—and that community continues to remind us why this work matters.

To celebrate our anniversary, we have created a new FREE companion guide for Fat Bear Week, which begins September 22. Fat Bear Week: Feeding Curiosity gives educators ten fun ways to connect the bears of Katmai with observation, math, ecosystems, engineering, evidence, and student wonder. It also includes a student sheet for every activity, classroom voting materials, and links to the official Explore.org and National Park Service resources.

Download the FREE companion guide here:

https://drive.google.com/file/d/1sNVsFYQxK9jf7iitcaquqjCCD3sCYT5e/view?usp=sharing

Six years later, we are still learning, still creating, and still believing that the world becomes a classroom when we give students permission to be curious.

Thank you to every educator, ranger, partner, supporter, family member, and friend who has helped Expeditions in Education grow from two challenges into more than we ever imagined possible. We could not have taken this expedition without you.

Happy anniversary to Expeditions in Education—and here’s to whatever adventure comes next.

Even while I am on vacation, I still find myself thinking like an educator. Every place we visit holds a story, and I want to share ways teachers can bring some of those stories back to their students.

While visiting the Anne Frank House, I kept thinking about the chestnut tree Anne could see from the attic window.

During more than two years of hiding, Anne often looked outside at the tree, the sky, and the birds. In a life filled with fear and confinement, nature gave her a glimpse of freedom, beauty, and hope. The tree reminded her that a world still existed beyond those walls—a world hatred could not completely take away.

Anne wrote about how nature helped her feel less alone and less afraid. Her words remind us that nature is more than a beautiful backdrop. It can be a refuge, a source of courage, and a quiet reminder that life continues—even during the darkest moments.

The original chestnut tree fell in 2010, but saplings grown from it now live in places around the world. In that way, Anne’s tree continues to grow, carrying her story and reminding each of us to notice beauty, protect hope, speak out against hatred, and never forget what can happen when evil is allowed to prevail.

More than 80 years later, we still need Anne’s courage. We still need her hope. And perhaps we still need the reminder she found outside that attic window: even in darkness, keep looking toward the light.

Inspired by Anne’s connection to the natural world, I created 30 nature prompts for our educators to use with their students. These prompts can open the door to observation, writing, art, reflection, history, and meaningful conversations about hope, freedom, courage, prejudice, and our responsibility to stand up for others.

The official Anne Frank House also offers online and 3D experiences that allow students to explore the Secret Annex and learn more about Anne’s life from anywhere:
https://www.annefrank.org/en/museum/web-and-digital/

Request an online guided school visit

• 30 Nature Prompts Inspired by Anne Frank’s Chestnut Tree
• Look through a window. What part of nature catches your attention first? Why?
• If you looked at the same tree every day, what changes would you begin to notice?
• Draw or describe a tree that makes you feel peaceful.
• What do you think Anne may have felt when she looked at the chestnut tree?
• Find something in nature that reminds you to have hope. Explain your choice.
• Write a journal entry about the sky as if you could see it only through one window.
• How can watching birds help someone feel connected to the world beyond a room?
• Choose one natural object—a leaf, stone, flower, feather, or seed. What message might it carry?
• Write a letter to Anne telling her about a tree or natural place that is important to you.
• Imagine that Anne’s chestnut tree could speak. What might it have said to her?
• Describe a time when being outside helped you feel calmer or happier.
• What can a tree teach us about standing strong during difficult times?
• Observe one tree for five minutes. Record everything you see, hear, and wonder.
• Draw the view from your favorite window. Include every part of nature you can see.
• Complete this sentence: “When I spend time in nature, I feel…”
• How does the natural world remind us that life continues?
• Write a poem titled “Outside the Window.”
• Imagine receiving a sapling from Anne’s chestnut tree. Where would you plant it, and why?
• Design a small garden that could give people hope during difficult times.
• Find an example of nature growing in an unexpected place. What does it teach you about perseverance?
• Compare a tree in winter with the same tree in spring. How might its changes represent hope?
• Write about a bird flying past Anne’s window. Where might it have been going, and what might Anne have imagined?
• Choose a color from nature that represents courage. Explain your choice.
• Create a nature symbol for freedom. It could be a plant, animal, weather pattern, or landscape.
• What is something beautiful in nature that people often overlook?
• Sit quietly outdoors for three minutes. What sounds make you feel connected to the world?
• Write a message of hope that could be placed beside a tree for someone else to discover.
• Anne’s tree lives on through saplings planted around the world. How can one small living thing carry a much larger story?
• What can we do to make sure stories like Anne’s continue to be remembered?
• Finish this thought: “Even in darkness, nature reminds us…”