Sierpinski’s Triangle

close up photo of green fern leaf
Photo by Tausif Hossain on

What do ferns, snowflakes, seashells and broccoli have in common? They are all fractals, of course! Fractals are fascinating and they are a great way to add some spice to your exponential functions unit. Have I told you how much I love exponential functions lately? I have a ton of exponential functions resources in my TpT store. In the Exponential Functions Stations Resource, I have a Sierpinski’s Triangle activity. What a great way to mix Art, Geometry and Algebra! The Sierpinski Triangle is an example of a fractal and an exponential function. I love the fact that so many real life objects can be examined through fractals and exponential functions.sierp-det Recently, I turned my Sierpinski Triangle activity into a google slides activity. I added some videos and an interactive fractal web page. I’d like to share this with my followers because I think that you will find it interesting and engaging for your students.

Young students can explore the Sierpinski triangle as well. Any math class that discusses triangles or patterns, could enjoy this activity. Change the google slides to fit your needs.

There’s more than one pattern that can be explored. In the pictures above, you could count shaded triangles each time to get, 1, 3, 9, 27, 81…  or count the unshaded triangles to get 0, 1, 4, 13, 40… which is increasing each time by 1, then 3, then 9 and so forth which is related to the first pattern. You can discuss area and perimeter of the inside triangles and see what patterns may occur! Mind Boggling! 

Another fun activity involving Sierpinski’s triangle is to build a 3-dimensional one. If you have a die cut machine at your school with a triangle pattern, you can make enough for each student in your classroom and get them to connect them in such a way to produce the pattern over and over and make it larger and larger. Google: Sierpinski’s Triangle in 3-D and look at the images. It’s very cool!

Are you ready to receive my Sierpinski’s Triangle Google Slides Activity? Click here and make a copy! Enjoy and please consider following my blog as well as my TpT store so you can continue to receive math activities similar to this one.




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30 year educator.

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