Sierpinski Triangle

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

Ages:
1’st - 8′th grades

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.

Download the Worksheet

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!