Welcome to another year of exploring the beauty of math in the world around us. I am looking forward to sharing our family’s math activities with you. Bookmark this page and come back each month to find free printables, activities and ideas to take your math outside. All the downloads are free for you to use with your family but if you would like to share them with others please link back to this page. Let’s have fun and discover math in nature!
Table of Contents
February – Symmetry
The book of nature is a fine and large piece of tapestry rolled up, which we are not able to see all at once, but must be content to wait for the discovery of its beauty, and symmetry, little by little, as it gradually comes to be more and more unfolded, or displayed. ~Robert Boyle
Our math this month takes us outside to discover symmetry all around us. Grab a hat, put on your walking boots and let’s find math in nature.
Symmetry can be found if one shape is exactly the same when it is moved, rotated or flipped.
Reflected symmetry can be found when one side of the shape is the mirror image of the other side.
- Look for reflected symmetry in leaves, insects and flowers.
- Take photos or draw in your nature journal.
- Draw a line to show the ‘line of symmetry’.
- Collect a bag of leaves, take a small hand mirror and ‘reflect’ the image along the line of symmetry.
Symmetry can also be rotational. Rotational symmetry can be found when an object looks the same as it rotates around a center point. As we rotate, we count at how many points the shape is identical. This is known as the order of symmetry. Flowers are a great way to discover rotational symmetry.
- Cut paper snowflakes of flowers to show rotational symmetry.
- Count the order of symmetry in flowers.
- Study some of the great artists to find both reflected and rotational symmetry.
- Read about the famous mathematician, Emmy Nother.
You can download our A4 PDF symmetry poster pack here.
For more symmetry fun, you might like this art project.
If you have ever wondered if Galaxy’s are symmetrical, you might like this post I wrote awhile back.
Have fun finding math around you! I’d love to see how you explored symmetry this month, send me your photos to jo.mathinnature@gmail.com and I’ll add them to the activity gallery!
March – Spiral
The spiral in a snail’s shell is the same mathematically as the spiral in the Milky Way galaxy, and it’s also the same mathematically as the spirals in our DNA. It’s the same ratio that you’ll find in very basic music that transcends cultures all over the world. Joseph Gordon-Levitt
I have always been fascinated by shells. There is something mesmorising about finding a spiral wonder created by a creature! This month our challenge is to notice the spirals that can be found in nature!
There are both 2 dimensional and 3 dimensional spirals.
We are going to be looking at the types of 2 Dimensional patterns that are found in nature.
- Fibonacci spiral
- Archimedean spiral
- Fermat’s spiral
The Fibonacci spiral is a type of Logarithmic spiral. It can be found in shells, Romanesco broccoli, galaxies and ferns. As the spiral progresses its separation distance grows according to the golden ratio.
The Archimedean spiral can be found in the way a millipede curls itself, in a cabbage and even your fingerprint. It is different to the Logarithmic spiral in that it has a constant separation distance as it progresses.
The Fermat’s spiral can be seen in the intersecting curves of the sunflower, pineapple and pinecone.
Some ideas to investigate spirals this month
- Go on a nature walk and look for spirals in nature.
- Create a poster or scrapbook page showing spirals.
- Paint a picture of a snail or shell or pinecone.
- Cut paper spirals.
- Have fun using a spirograph set.
- Make a spiral nature mobile.
- Explore spirals in Art by looking at Gustav Klimt’s Expectation, Stolet Frieze and Freya’s Tears.
- Read ‘Master Fibonacci – The Man Who Changed Math’ by Shelley Allen
You can download our A4 PDF spiral poster pack here
For more information and learning ideas, The Smart Happy Project has a great post on spirals in nature.
A fun interactive Math Spiral Art creator can be found at Toy Theater.
My post on Mathematics in a Sea Shell has a free vocabulary booklet for you to download.
Have fun explore math this month. I’d love to see what you discover. Tag me on instagram or email your photos to jo.mathinnature@gmail.com
April – Angle
Even the dullest bird or face becomes interesting when you give it a good look in the wild/flesh. The way the shadow drops across the cheek, the light hits an eyebrow, etc… there are many more angles, positions etc. than you can ever imagine. My heart always makes a little jump when I see things in birds or faces that surprise me. Siegfried Woldhek
Do you still wonder when you look at the beautiful around you? Artists and Scientist have an ability to look closely and see what we tend to take for granted. All around us are incredible sights to take our breath away.
Part of what I hope to do with my kids is instill in them the ability to look closely and investigate the world around them. This month I’ve been focusing on finding angles around us. Seeing angles in the trees and leaves helps to ground the concepts that we will be studying in our math books. So, come along with us and take a look at angles!
You can download our inspiration poster here
Some ways to investigate angles
- Look at the tree branches and leaf veins, follow the lines to see angles.
- Take photos and highlight the angle, use a protractor to measure the angle.
- Make a poster or scrapbook page all about angles.
- Play eye spy, but with angles instead of colours.
- Look for angles in art.
- Extend the learning to triangles and learn from Pythagoras.
- Go on a angle treasure hunt with our worksheet.
You can find out about all the different angles at Math is Fun or you might like to try this Angles in Nature investigation by Nature Days.
This YouTube video will encourage you to see Angles around you.
Have fun explore math this month. I’d love to see what you discover. Tag me on instagram or email your photos to jo.mathinnature@gmail.com
May – Fractals
A fractal is a way of seeing infinity. Fractal geometry is not just a chapter of mathematics, but one that helps everyman to see the same world differently. Benoit Mandelbrot
A Fractal is a “self-similar” repeating pattern. We can see these patterns in ferns, shells, broccoli, rivers, trees, cyclones, lightening, crystal formation, lungs, neurons, the coastline…
I like how the Fractal Foundation describes fractals,
“A fractal is a picture that tells the story of the process that created it.”
They are also a reflection of the order and precision we see in the universe and point not only to the process of how they were created, but by whom they were created
I invite you to discover fractals with us this month!
You can download the inspiration poster here
For more information about fractals and ways to investigate them, The Fractal Foundation has a great Fractivities page and an educator’s guide on their What Are Fractals page.
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