# Sierpinski Triangle

## Learn to draw a fractal triangle, and combine yours with others to make a bigger fractal triangle.

Ages:

Materials:
Printed out triangle template (page 2 of activity) 1 copy per student
Markers or crayons
Scissors

Time:
Approx 30-45 minutes

See the NM State Content Standards met by this Fractivity.

Print out and use page TWO of the worksheet for this fractivity. (Don’t give the kids page 1, or they’ll trace the triangle.) Orient the blank triangle template so the triangle points up. The dots are the midpoints of the edges, half way between the corners. Connect the dots as shown below to form a new triangle, pointing down. Color it in.

You are left now with three white triangles. Find the midpoints of each of these three triangles, connect them, and color in the resulting triangles (pointing down).

Each of the 3 triangles now turns into 3 smaller triangles, leaving 9 small white triangles.

Connect the midpoints of each of the 9 white triangles to form 27 smaller triangles, pointing downward. Color them in.

Continue this process if you wish, as long as you have patience.

Be as creative as you wish in coloring the triangles.

When you’re done, cut the big triangle out and write your name on the back.

Next, join your fractal triangle with 2 other fractal triangles to form a bigger triangle. Then add 2 more groups of 3 triangles to form a bigger triangle made of 9 triangles. If you’re doing this with your whole class, you can join 3 groups of 9 to make a giant triangle made of 27 individual triangles. If you want to continue, 3 classes could join all their 81 triangles into an even bigger one. And why stop there???

3'd graders at Apache Elementary School in Albuquerque

If you do this project with your class, please consider contributing your fractal triangles to our Giant Fractal Trianglethon Project to help make the world’s largest Sierpinski Triangle! On March 14, 2010, we built a 7th order fractal triangle, made of 2187 triangles. Help us reach the next level, and build one out of 6561 triangles!

10 Responses to “Sierpinski Triangle”
1. Karen Hanthorn-Rhodes says:

Thank you.

Karen

2. FractalMan says:

Please send any completed fractal triangles to:
Fractal Foundation,
2917 Campus Blvd NE
Albuquerque, NM 87106

Thanks!

3. joao a de lima says:

I have been working on HR and Leadership. I created recently a People Leadership Model based on Sierpinsky Triangle. I’m preparing to write a book which title is: “Fractal Leadership - People Management for Winning Companies”. Whatever you can have on this subject, don’t hesitate to send me in my email!!!
Tks and kind regards,
JAL

4. Anne says:

Actually, I was having a tough time understanding sierpinski triangle (by the way, I’m only 13), and thanks to your site, I have finally got it!
Thank you!

5. aileen says:

i loved this! at first i was soooo confused and then i was like “oooh i get it!”hahaha now it seems like nothing! FRACTALS ARE KEWLl!!

6. sherril says:

My students and I built a tetrahedron three years ago. It was over 6 feet tall. My kids had a blast. This was a year end activity.

7. Mark Johnson says:

My students recently completed a stage 9 sierpinski triangle. It is about 9 feet tall and contains 19,683 colored triangles (we colored the upwards-pointing triangles). We call it our Sierpinski Christmas tree.