23 October 4:00 am
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Written by Katie Hale

This is an article from’s newest e-magazine. The magazine is chocked full of great information-perfect for teaching preschool math–calculus.

Often as homeschool parents we face the day when our children simply don’t like the subject we are teaching them. While this occurs in every classroom at some point, we strive to make it a non-issue in our home education classes. Mathematics is one of the most frequently complained about subjects, but I have found that incorporating different everyday things, especially nature into our classroom, alleviates the distaste for math.

Learning How To Teach Fractal Math Using Nature is something you can use in early grades as well as with your high school students. Not only do students of all ages enjoy the exploring nature aspect of these lessons, but they gain a new found appreciation for mathematics and how it helps our world function on a daily basis.


What Is A Fractal? A fractal is a naturally existing repeating pattern that displays endlessly at every scale. They can grow continually larger to infinity in repeating shapes. This natural phenomenon is a mathematical set that is great for showing how math multiplies equally at nearly every level.

Why Teach With Fractals? When kids are staring at geometric shapes they can quickly become bored and not understand how it applies to their daily lives. By taking a spin to look at naturally occurring fractals which are another part of mathematics similar to geometry, you can bring math full circle in their lives. By showing them how a shape can repeat in nature you are showing them how math applies to their daily lives.

How To Teach Fractal Math:

Look At Natural Occurrences Around Your Home:

  • Rivers, tributaries, coastlines. These all have repeating shapes and lengths. If you measure at different intervals, you will always find similarities in how they branch off, how they grow and where they lead.
  • Snowflakes. One of the first holiday crafts we teach our kids to make is a great example of fractal math. As we fold and snip pieces of paper we see that the shapes are repeating themselves throughout the structure of a snowflake. Those who have been given the chance to study actual snowflakes through a microscope can tell you how fractal math applies to every single miniscule flake.
  • Frost On Glass. This is a great way to have kids study the shapes and patterns of fractals up close. In winter months you can often see frost on glass that is fractal in nature. Get up close and have your students point out the patterns as they repeat.
  • Leaves From Trees And Plants. The most commonly occurring fractal we see on a daily basis is that of trees and leaves. Ferns are a wonderful example to look at to find fractal patterns, but many other varieties provide great study opportunities.
  • Broccoli and Cauliflower. Open up the veggie bin and let the kids take a look at that head of cauliflower they are complaining about eating. Seeing the fractal patterns in their foods will possibly make it more appealing as a meal.

Teaching about fractal math doesn’t have to be complicated or difficult. As you travel for vacations or leisure look at your maps for fractals in river beds, mountain formations and other scenery. Go on nature hikes together to find fractal leaves and trees. Plant a garden and grow vegetables that show fractal patterns. No matter where you choose to have your classroom, teaching fractal math using nature can be a great addition to your curriculum this year.

Here is some additional information you might find interesting—



Katie Hale is a homeschooling mom, freelance writer and author aspiring to make every piece of the world a classroom. You can find more from her at her site You Brew My Tea (

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