Fibonacci In Nature: A Math Exploration For Kids

Fibonacci for kids

One of the coolest ways to show kids math in the real world is to introduce them to Fibonacci in nature!

Fibo-whaaat? you might ask.

The Fibonacci sequence is a series of numbers that follows a math pattern so simple that even a first grader can follow it. Here’s how it works…

Nature’s Secret Number Code

Take a look at the series below:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

To form the pattern, start by writing 1 and 1. Add them together to get 2. Add the last two numbers: 1+2=3.

Continue adding the previous two numbers to find the next number in the series.

These numbers make up the famed Fibonacci sequence: a group of numbers that mysteriously appear over and over again in nature. 

A man named Leonardo of Pisa, who lived in Italy in the middle ages, noticed that he kept coming across these numbers in the natural world.

This hidden code could be found in the numbers of petals on a flower, the structure of fruits and vegetables, the proportions of the human body, and even in the unique shape of spirals in nature.

Thanks to his observations and discoveries, we now call these Fibonacci numbers. (Fibonacci means “son of Bonaccio”–the name of Leonardo’s father.)

Let’s take a look at how these numbers appear in nature.

Fibonacci In Nature

One of the easiest ways to explore Fibonacci numbers is to count the petals on a flower. Very often there will be 5, 8, 13 , 21 or 34 petals–or a number very close to that.

Fibonacci in nature: flower petals

Sunflowers are particularly fascinating, as they show Fibonacci numbers in so many ways.

Fibonacci sunflower

Count the petals on a sunflower–there are many!–and you’ll most likely count exactly 21, 34 or 55 petals–nothing in between.

If you look closely at the center of a sunflower, you will see a spiral pattern. In fact, there are spirals in two directions.

If you have the patience to count the number of spirals, it will always be a Fibonacci number. Count the spirals in the other direction and it will be an adjacent Fibonacci number.

So if you count 34 spirals going to the right, you know that there will be either 21 or 55 spirals to the left.

Fibonacci Spirals

Other plants have this spiral characteristic as well.

Pine cones, pineapples, daisy centers, artichokes, and many succulents have a spiral pattern. If you look closely, you’ll see that the spiral pattern goes both directions.

Count the number of spirals and it will always be a Fibonacci number. Like the sunflower center, the number of spirals in the other direction will always be an adjacent Fibonacci number.

Fibonacci spirals in nature

Here’s another interesting thing about nature spirals…

Spirals in nature have a distinctive shape. They start out tightly coiled near the center, then unfurl more loosely as they grow.

Fibonacci spirals

These are called Fibonacci spirals, because (surprise, surprise) the spiral grows with the Fibonacci sequence.

Get a piece of graph paper and outline one of the squares. Do the same with another box right next to it.

Draw a box below these that are 2×2 squares. Next to that, a box that is 3×3 squares, then moving in a spiral shape, draw boxes that are 5×5 and 8×8, following the numbers in the Fibonacci sequence.

Each new box will be the width of the two previous boxes together.

Fibonacci nature spiral

Once you’ve drawn as many boxes as you can to fit on the page, you can draw a spiral as shown. It will look just like the spirals you find in nature.

Kids are often quite good at drawing a Fibonacci spiral on graph paper, sometimes taping new sheets to the sides to make their spirals even larger!

Fibonacci For Kids

The picture book Blockhead is the best way I’ve found to introduce Fibonacci to kids.

Blockhead: the life of Fibonacci

It’s an engaging read even for kids as young as kindergarten, as each page has hidden spirals and Fibonacci numbers that kids love to find.

It’s a magical experience for kids to explore real plants, flowers, starfish, and other natural objects that show Fibonacci numbers. And kids love to find the spiral shape in pinecones, pineapples, and flower centers.

girl with flower

If you’re not able to bring in actual objects, kids can find some beautiful images on Pinterest or in a Google search of “Fibonacci in nature”, “Fibonacci spirals”, or “Fibonacci flower petals”.

Pass out graph paper and invite kids to draw their own Fibonacci spirals. (Hint: Draw a few of your own first to get comfortable with it.)

Finally, take kids on a Fibonacci scavenger hunt. Your kids won’t forget it it, and you’ll be surprised at how many places they’ll find Fibonacci numbers!

Fibonacci in nature: holding flower

Here are some of my favorite Fibonacci resources for kids:

Adults who want to find out more about Fibonacci numbers (and yes, there is more!) can check out these great resources:

What are your thoughts about Fibonacci in nature? Share in the comments below! (If you liked this post, you’ll love Fractals In Nature as well!)

NOTE: Some links may be affiliate links. I only recommend products I have personally used, loved, and would buy again. 

nature math Fibonacci

6 Comments on “Fibonacci In Nature: A Math Exploration For Kids”

  1. Thank you very much for this information! It’s straight to the point with valid explanations plus awesome example photos! My students will definitely get excited about this topic!
    Thank you again!

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