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Nature activities are literally my favourite. The possibilities are endless and kids absolutely love them because it's outside and hands-on. It's also so inclusive....for example, if you ask a student to use leaves to show an algebraic expression, they all have access to those authentic manipulatives right outside their home.

For the younger grades, even drawing numbers in sand helps with fine motor and number practice. Patterning with nature is so great because, again, it's hands-on and a visual representation of patterns. It allows for creativity and is very open-ended as students could make an AB pattern, ABA, ABC, ABBA, etc. It's their choice and, as the educator, it tells a lot about the student simply just by the pattern they chose to create.

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From the materials provided, obviously symmetry, and shapes (Spatial Sense) seen in flowers and wild-life. We have algebra/patterning which includes the Golden Ratio (Fib.Sequence) along with many others. Again, some not described in the video/content would be things like Maple Syrup production. If you were to determine how much sap you'd extract from a Maple Tree, would be determined by its size, and these calculations can be done to determine how many litres of sap you'd yield (I was literally doing this on the weekend).

I could use my maple syrup example with my students by posing a problem (Q. Would is be possible to collect enough sap for everyone in the class to have their own 1L bottle from the trees around the school?)

Kids would have to collect data (determine how many students, how many trees we have on the property that Maple Tree's. They'd research how to identify a Maple first lol. Then the kids would use measurement and computation skills to determine 'if one full size maple tree can produce 10 gallons per seasons, determine how much each student would receive?

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I found this fantastic website by Penny Whitehouse, a mom, who is trying to connect her kids more to nature.  These activities could certainly be used with a class.
https://mothernatured.com/nature-exploration/fun-ways-to-measure-nature/

I stumbled unto this and I love this website: https://www.gardeningknowhow.com/special/children/using-gardens-to-teach-math.htm

I have a friend, who planted multiple gardens with her grade 5/6 class in math class (raised garden boxes to keep the critters out). The class was able to eat the fruits of their labour at the end :)  The kids loved this project!!

And I found this website that lists the top 10 movies for math. I will admit that I have seen a few of these ;)

https://www.mathnasium.com/claytonladue/news/10-best-math-movies-for-middle-school-students

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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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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.

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I enjoy looking at the shapes in nature, or human created shapes that we use every day. It's good to use houses and buildings to talk about 3D shapes, 2D shapes, and angles. When I go outside, often the kids find that there are shapes within shapes, such as windows inside windows, on the side of a house can all be little squares inside squares inside a square. They find quickly that shapes can be placed together to create other shapes. (This is important when finding area of irregular shapes)

The roofs of houses are a good source of 3d shapes, angles, and a great source for investigating and understanding the nets of the shapes. I(f you have clear protractors, they can hold them up and find the angles of the roof lines.)

There are lots of Nature walk resources for math, science (habitats, structures)

Here is a document outlining some procedures we were asked to take while learning outdoors.

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https://www.ltl.org.uk/free-resources/?swoof=1&pa_subject=mathematics

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Outdoor learning ideas | Learning through Landscapes

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Hundreds of free lesson ideas and activities for every age and subject area - ideal for curriculum-led outdoor learning and Forest School.

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Hi all,

Thanks for sharing the great resources. I'll be using some of your ideas as well!

I teach a lot about measurement and estimation outside. My school yard is quite large. I find kids can estimate in cm and m, but have a hard time grasping how long a km is. Our yard is approximately 300 metres deep and similar width. A lot of kids estimated the distance across to be 1 or 2 kilometres. As soon as I referenced our track for track and field, a lot of kids clued in relating the 100m race to the full length of the field. Very cool to see the "lights" turn on.

I have also done nature walks where we count how many leaves are on a branch, then we estimate how many branches the tree has. We then make an estimate about how many leaves the whole tree has. We talk about how estimation isn't just a guess, you need to something to base your estimate off of.  (Sorry Lynn, longer than I thought)!

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Some great math concepts to teach in nature:

colour book: with a Colour Book, you can collect flowers and organize them by colour to create an awesome keepsake and collection that never really ends.

Ordering: Many times when flowers or trees are planted, they grow at different rates. Next time you see a few trees or flowers grouped together, ask your student to order them from youngest to oldest. Once they state an answer, ask them why they chose those plants in that order. Maybe they classified the flowers by size, stating that the smaller ones were younger. Maybe they chose the short fat tree to be the oldest. Getting your student to think through an answer brings in important reasoning skills that are needed for school everyday.

Finding shapes: You can simply point out the shapes as you see them or you can make a list of shapes to look for before you embark on your nature walk. You can keep a tally of the shapes you find then count which shape appeared more in nature. You can even create a graph showing the results. To help develop more reasoning skills, have them compare the sizes of the shapes. Talk about which is bigger and which is longer.

Measuring: Have your kids measure different things they find such as sticks, tree stumps, flowers and stones. They can draw and record their findings in a notebook. You can also have them discuss the comparisons between the different sizes. Want to make it even more complicated? Have the kids convert the measurements from inches to centimeters and feet to meters.

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A fun STEM activity I've done with students was having them plan and build a play-structure for our school playground. They would have to measure the area to determine the amount of space they had and how much space each piece of equipment would need based on their various sizes options.

They were also given a budget, each piece of equipment cost varied and they had to make sure they stayed in budget while creating the most fun friendly playground.

This isn't exactly using nature to show math but it was math in nature and they were SOOOO engaged - it was a hit!

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I enjoyed going through this article while learning about math in nature because it opened my eyes to some things I haven’t noticed in nature for math already.

I absolutely LOVE math in nature and I love taking my students outside into the “Real World” to find math. Their eyes light up when you show them how math can be found in places that they never thought to look.

Last year in my Grade 3 LTO I had the opportunity to have the students take part in an online session with a person who connected bees and coding together! Even I was amazed at how that connected. We then had a discussion of other animals and things in nature that can be seen as coding.

I have looked at Estimation outside and had them estimate how many birds were in a flock, or how many orange leaves were on the ground and then we counted them.

We have gone outside and picked up one random leaf each off the school field and talked about symmetry and whether we think our leaf is symmetrical.

I have had the students work in pairs and use things that they have found outside to create patterns, and then we did a gallery walk and looked at each others patterns.

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Mathematics is visible everywhere in nature, even where we are not expecting it. It can help explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend.

Even subjective emotions, like what we find beautiful, can have mathematic explanations.

"Maths is not only seen as beautiful-beauty is also mathematical," says Dr. Thomas Britz, a lecturer in UNSW Science's School of Mathematics & Statistics. "The two are intertwined."

Dr. Britz works in combinatorics, a field focused on complex counting and puzzle solving. While combinatorics sits within pure mathematics, Dr. Britz has always been drawn to the philosophical questions about mathematics.

He also finds beauty in the mathematical process.

"From a personal point of view, maths is just really fun to do. I've loved it ever since I was a little kid.

"Sometimes, the beauty and enjoyment of maths is in the concepts, or in the results, or in the explanations. Other times, it's the thought processes that make your mind turn in nice ways, the emotions that you get, or just working in the flow-like getting lost in a good book."

Here, Dr. Britz shares some of his favorite connections between maths and beauty.
1. Symmetry-but with a touch of surprise
In 2018, Dr. Britz gave a TEDx talk on the Mathematics of Emotion, where he used recent studies on maths and emotions to touch on how maths might help explain emotions, like beauty.

"Our brains reward us when we recognize patterns, whether this is seeing symmetry, organising parts of a whole, or puzzle-solving," he says.

"When we spot something deviating from a pattern-when there's a touch of the unexpected-our brains reward us once again. We feel delight and excitement."

For example, humans perceive symmetrical faces as beautiful. However, a feature that breaks up the symmetry in a small, interesting or surprising way-such as a beauty spot-adds to the beauty.

"This same idea can be seen in music," says Dr. Britz. "Patterned and ordered sounds with a touch of the unexpected can have added personality, charm and depth."

Many mathematical concepts exhibit a similar harmony between pattern and surprise, elegance and chaos, truth and mystery.

"The interwovenness of maths and beauty is itself beautiful to me," says Dr. Britz.
2. Fractals: infinite and ghostly
Fractals are self-referential patterns that repeat themselves, to some degree, on smaller scales. The closer you look, the more repetitions you will see-like the fronds and leaves of a fern.

"These repeating patterns are everywhere in nature," says Dr. Britz. "In snowflakes, river networks, flowers, trees, lightning strikes-even in our blood vessels."

Fractals in nature can often only replicate by several layers, but theoretic fractals can be infinite. Many computer-generated simulations have been created as models of infinite fractals.

"You can keep focusing on a fractal, but you'll never get to the end of it," says Dr. Britz.

"Fractals are infinitely deep. They are also infinitely ghostly.

"You might have a whole page full of fractals, but the total area that you've drawn is still zero, because it's just a bunch of infinite lines."
3. Pi: an unknowable truth
Pi (or 'π') is a number often first learned in high school geometry. In simplest terms, it is a number slightly more than 3.

Pi is mostly used when dealing with circles, such as calculating the circumference of a circle using only its diameter. The rule is that, for any circle, the distance around the edge is roughly 3.14 times the distance across the center of the circle.

But Pi is a lot more than this.

"When you look into other aspects of nature, you will suddenly find Pi everywhere," says Dr. Britz. "Not only is it linked to every circle, but Pi sometimes pops up in formulas that have nothing to do with circles, like in probability and calculus."

Despite being the most famous number (International Pi Day is held annually on 14 March, 3.14 in American dating), there is a lot of mystery around it.

"We know a lot about Pi, but we really don't know anything about Pi," says Dr. Britz.

"There's a beauty about it-a beautiful dichotomy or tension."

Pi is infinite and, by definition, unknowable. No pattern has yet been identified in its decimal points. It's understood that any combination of numbers, like your phone number or birthday, will appear in Pi somewhere (you can search this via an online lookup tool of the first 200 million digits).

We currently know 50 trillion digits of Pi, a record broken earlier this year. But, as we cannot calculate the exact value of Pi, we can never completely calculate the circumference or area of a circle-although we can get close.

"What's going on here?" says Dr. Britz. "What is it about this strange number that somehow ties all the circles of the world together?

"There's some underlying truth to Pi, but we don't understand it. This mystique makes it all the more beautiful."
4. A golden and ancient ratio
The Golden Ratio (or 'ϕ') is perhaps the most popular mathematical theorem for beauty. It's considered the most aesthetically pleasing way to proportion an object.

The ratio can be shortened, roughly, to 1.618. When presented geometrically, the ratio creates the Golden Rectangle or the Golden Spiral.

"Throughout history, the ratio was treated as a benchmark for the ideal form, whether in architecture, artwork, or the human body," says Dr. Britz. "It was called the "Divine Proportion."

"Many famous artworks, including those by Leonardo da Vinci, were based on this ratio."

The Golden Spiral is frequently used today, especially in art, design and photography. The center of the spiral can help artists frame image focal points in aesthetically pleasing ways.
5. A paradox closer to magic
The unknowable nature of maths can make it seem closer to magic.

A famous geometrical theorem called the Banach-Tarski paradox says that if you have a ball in 3-D space and split it into a few specific pieces, there is a way to reassemble the parts so that you create two balls.

"This is already interesting, but it gets even weirder," says Dr. Britz.

"When the two new balls are created, they will both be the same size as the first ball."

Mathematically speaking, this theorem works-it is possible to reassemble the pieces in a way that doubles the balls.

"You can't do this in real life," says Dr. Britz. "But you can do it mathematically.

"That's sort of magic. That is magic."

Fractals, the Banach-Tarski paradox and Pi are just the surface of the mathematical concepts he finds beauty in.

"To experience many beautiful parts of maths, you need a lot of background knowledge," says Dr. Britz. "You need a lot of basic-and often very boring-training. It's a bit like doing a million push ups before playing a sport.

"But it is worth it. I hope that more people get to the fun bit of maths. There is so much more beauty to uncover."

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The mystique of mathematics: 5 beautiful math phenomena

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Mathematics is visible everywhere in nature, even where we are not expecting it. It can help explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend. Even subjective emotions, like what we find beautiful, can have mathematic explanations.

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Symmetry in Nature.

This can be a very informative and interesting lesson carried out by engaging in a nature walk.

Paper folding is one activity used in the class to teach symmetry.

Linked with Reflection.

Can be integrated with Art.

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Maths - Symmetry in nature - Animation - English

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Here is a link that I found very informative and a book that I use in the classroom that promotes outdoor learning in mathematics with many wonderful lesson ideas.

Estimate everything outside!

Number: having a guess before counting the flock of birds flying overhead – we count ten birds and then use this to count the rest in chunks of ten.

Money: evaluating whether we have enough money to buy something we need.

Distance: estimating how far away the end of
the playing field is.

Volume: thinking about the volume of water in one bucket or watering can compared to another.

Weight and mass: wondering how much food the birds will eat at a bird table.

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Learning with Nature: Inspiring the Next Systems-Thinkers | Jamie Byron | TEDxWalthamED