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It's important to integrate nature into the math classroom to reinforce to students that math is  indeed everywhere, especially in nature. I think the students today want concrete evidence of why we learn the things we do. Having proof, in nature, tells us that math is a very intricate part of our lives, not just figures that have no meaning. A great example that is not mentioned in our readings is butterflies. They are an excellent example of symmetry. We know that both sides of the butterfly are equal sizes and the same decore on each wing. I believe it is also that way for balance, so they can fly.

An activity I did with my FDK class was using objects in nature for sorting. I had the students collect as many leaves as they could find. Then, I said I ask the students how are you going to sort them. Will it be by size, colour or shape. They just loved idea with working with nature. The students either chose size or colour.  I really love when I can incorporate nature and math  together.

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I came across this and it peaked my interest (mainly due to the fact that my students have been counting, collecting, and eating acorns - totally another story but you get it).

I tend to incorporate art, math, and nature regularly in the classroom. Its, seamless and so easily transitioned!

Measurement in seasonal changes, sequential order of sticks and leaves, to the addition and subtraction of acorns!

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You might already be familiar with STEM material. STEM is a set of curricula that prioritizes lessons around Science, Technology, Engineering, and Mathematics. The acronym is STEM. STEM curriculum can offer a gateway into subject integration, hence the "math in nature" idea!

If you're new to STEM or would like a "refresh," check out our article here. We review the top three benefits of STEM-and why it matters.

In this article, we will offer ideas for educators to incorporate mathematics with science and nature connection.

Hint: it involves pinecones.

Nature and Puzzled Mathematicians

Leonardo de Pisa-not to be confused with Leonardo de Vinci or Leonardo DiCaprio-was a brilliant mathematician. He's better known by his nickname, Fibonacci.

Fibonacci noticed repeating patterns in nature. He wondered why these patterns occurred: a certain sequence of numbers kept appearing in nature. These patterns include the spiral of a seashell, the structure of a pinecone, the shape of hurricanes, and the density of a cabbage.

This spiral has a mathematic background: it follows a sequence of numbers, known today as the Fibonacci sequence. This spiral appears everywhere in nature-as well as in human design.

Fibonacci Spiral, photographed by Gerd Altmann. Note the spiral of a seashell. It starts with a 1×1 square, then an additional 1×1 square, then a 2×1 square, a 3×2 square, etc.

Was Fibonacci the first to notice this? No. Many East Indian mathematicians were studying this pattern-and well before Fibonacci. But Fibonacci gets most of the credit, largely because of his published book from the 13 th century.

What is the Fibonacci Sequence?

The Fibonacci sequence is simple. Beginning with 0 and 1, each following number is the sum of the previous two numbers. Next, when we express these numbers as squares with widths, the pattern of their sequence forms a spiral.

For example, when we start with the initial 0 and 1, we have:

In more detail, the 3 was found by adding the numbers before it (1 + 2). Later in the sequence, the 13 was found by adding the two sums before it (5 + 8).
Thus, the initial Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, and 21.
Again, when we visualize these numbers as squares with widths, the pattern forms a beautiful spiral. Fibonacci documented this mathematical spiral and published it in his 13th-century book.

Math in Nature: Fibonacci Numbers Discovery Kit

This hands-on kit invites learners of all ages to investigate patterns in nature, with a focus on the Fibonacci sequence.

Once introduced to this spiral pattern in nature, you may start noticing it everywhere. This kit is a powerful way to increase observation skills and apply math to "real-world" phenomena.

Need enough for a whole class? Good news! This "Math in Nature" lesson is also available as a class set.

Math in Nature: Fibonacci Numbers Discovery Kit.

Each kit contains female pine cones, pine spirals, male pine cones in a magnifying observation box, a heat-treated pine branch, a 3x magnifier, and an educational guide.

In this kit, participants mark pine cones. Then, they count and record the Fibonacci numbers that they find.

For additional information on how to teach the Fibonacci sequence with this kit, check out our YouTube clips, created specifically for this lesson.

Hidden Properties in Math and Nature

Mathematical patterns can be found throughout nature, but it requires a closer look. Behind the design of a spider's web to the spiral of a nautilus shell? Math. The spiral of a hurricane? Math. The number of petals on certain flowers? Math.

Once introduced to mathematical patterns in nature, explorers of all ages can begin to recognize these patterns. They can be found everywhere.

Fun fact: many flower petals follow a Fibonacci sequence.

For one extension to this lesson, consider an additional lesson with the Golden Ratio. The Fibonacci sequence is very close to the Golden Ratio and can be used as an introduction.

In short, the golden ratio is another mathematical pattern that appears in geometry, art, nature, and architecture.

For a "Math in Nature" series, we recommend that educators introduce these patterns with the Fibonacci kit, alongside the book Growing Patterns by Sarah Campbell. Her colorful book offers strong visuals and poetic text.

You could also offer a follow-up lesson on the Golden Ratio, and a take-home assignment to investigate patterns.

What Now?

Get exploring! Do you have a favorite pattern in nature? Have you found the Fibonacci sequence in nature? Are there any patterns that math does not explain?

And speaking of poetic text in Growing Patterns, did you know that math is everywhere in poetry too? Stay tuned for our next STEM article, "Math in Poetry."

Want more STEM curriculum ideas? Click here for our "Math in Poetry" article!

If this article was helpful for you, please share it with a friend! As always, feel free to leave a comment below. We'd love to hear from you.

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STEM Series: Discovering Math in Nature - Acorn Naturalists

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You might already be familiar with STEM material. STEM is a set of curricula that prioritizes lessons around Science, Technology, Engineering, and Mathematics. The acronym is STEM. STEM curriculum can offer a gateway into subject integration, hence the "math in nature" idea! If you're new to STEM or would like a "refresh," check out our article here.

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One activity that I have done is to have students make a collection of found objects (sticks, stones, rocks, pinecones, etc) and they arrange the items in different ways. I take a photo of each of the collections and we use them in our Math talks for discussing "how many?"

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We turned a recent walk in the forest into a lesson on symmetry- such a fun, hands-on way for kids to learn math! We searched for symmetry outside and even created our own symmetry art using nature we had found on our walk!

Follow our Math for Kids Pinterest board!

Learning opportunities are everywhere you look. Even as you're taking a walk outside, you are surrounded by boundless possibilities! As our family took a short stroll in a nearby forest, we spotted all kinds of interesting shapes and patterns in nature. Since Lucy and I had recently been reading some books on symmetry, we thought it'd be fun to examine the natural objects and see if we could find any that were symmetric. (This post contains affiliate links.)

We took pictures of various items we found on the walk: leaves, sticks, tree stumps, and pinecones. We made guesses on if we thought they were symmetrical and talked about why. When we got home we printed out our photos onto paper to study them more closely.

From our previous readings, we learned about the various kinds of symmetry. We decided to focus on rotational symmetry (where an image can be rotated on a central point and still looks the same) and on reflection symmetry (where one half is a reflection of the other half.)

After printing out our photos, we got out a little mirror ( like this one ) and tested out each image. This leaf was a good example of reflection symmetry.

It took Lucy a few tries to find the line of symmetry for this group of leaves. She loved seeing all the different ways she could make image look in the mirror!

After testing the pictures with the mirror, we sorted them into three different categories: images that were not symmetrical, images that were examples of rotational symmetry, and images that were examples of reflection symmetry.

When we were done sorting the pictures, we stuck them up on our wall with poster putty . (Poster putty is my favorite material for hanging papers on the wall. Easy to remove and no damage to the walls!) Now we can add to it with examples we find on future walks!

We also thought it would be fun to make our own examples of symmetry with nature. Have you heard of sun sensitive paper ? You can place objects on the paper, and then expose the paper to light to create designs and artwork. We love creating with this!

We walked around the yard and collected some natural materials. Then we used the collected items to create a rotationally symmetric design. It was such a great way to use what Lucy had learned about symmetry to create art!

Children's Books About Symmetry

Seeing Symmetry by Loreen Leedy

What Is Symmetry in Nature? by Bobbie Kalman

Is It Symmetrical? by Nancy Allen

Find more STEM activities in our ebook! Learn more about it here, or buy it now here!

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Finding Symmetry in Nature (Outdoor Math Activity for Kids) - Buggy and Buddy

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My husband and I took a walk with the kids to our nearby forest and studied examples of symmetry in nature. It was such a fun hands-on math activity for kids! I'm so excited to share with you how we turned a recent walk in the forest into a lesson on symmetry for kids.

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Integrating nature in math allows students to see that we can describe nearly anything with numbers. Math becomes more meaningful and connected, and students can see how amazing and interesting our world is!

Sharing pictures of nature and talking about the patterns, shapes, symmetry, and numbers would be a simple activity to do a few times a week. It could be something to do for a few minutes to begin the day. After a while, the mathematical language and thinking might become more automatic for students. These photos came from TPT.

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This is an amazing site!

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Math in Nature: 5 Stunning Ways We See Math in the World

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Do you notice math in the natural world? Do your kids? Learn about and explore the beauty of math in nature and then get outside to see it for yourself.

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While diving into this neat idea for sharing the importance of math- I came across a great resource

Math in Nature - ways we see math in the world , a cool Free resource for posters which could be used in the school or in the classroom (from MATHGEEKMAMA site) it encourages kids to see that math really is all around us

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I found this video really interesting as an introduction for “math in nature.” It made me think about my everyday life and how it is everywhere around me. “Shape of flowers, leaves, fruits,” etc. Estimating, measuring, rounding, addition, subtraction, multiplication, division, etc can all be taught using leaves, fruits, etc.

Lesson Ideas:

Measuring – Take students on a nature walk (on or around school grounds) and have them bring a ruler and notebook. Students can measure different things they find (sticks, tree stumps, leaves, flowers, stones, etc). They can draw and record their findings in notebook (helpful for low learners, ESL students or students with difficulty printing words). Discuss comparisons between different sizes. Extension: have students convert measurements (centimetres, feet, meters), calculate how long it would be if you lined up all sticks, rocks, leaves, etc., end to end.

Finding Shapes- Take students on nature walk:

Point out shapes as you seem them

Make a list of shapes to look for before you embark on nature walk

Tally of the shapes you find and then count which shape appeared more in nature.

Create graphs to show results

Reasoning skills: compare sizes of shapes (bigger, longer)

Find diameter, radius and circumference of the circles

Find angles of triangles.

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This is a fabulous website if you are wanting lesson plans and activities linked to nature. It's an Ontario resource, and if you scroll down to page 23 it has a large index chart that lists the name of the activity, the target grade(s), the season to complete the activity in, and also what subject the activity/lesson covers. For example you could see that the lesson: Sorting Rules in Nature is found on page 44, it's aimed for K-6, best completed in fall/spring and covers science, math and language curriculum expectations.