Hanging Sierpinski’s Triangles


The entire community at Mission Hill Middle School is focused on a, well, mission: demystify, celebrate and embrace math. For twenty minutes every day, the entire school stops to engage in Morning Math. Using the school’s innovative MHTV in-classroom broadcast system, students, teachers and staff are led in a math activity by a rotating cast of math teachers. From word problems to number stumpers to origami, students exercise their math muscles in a creative response to the performance requirements of the federal No Child Left Behind mandate.

In a recent Morning Math session, students learned about fractals in general, and the Sierpinski triangle in particular.traingletocrop.jpg Beginning with an equilateral triangle, students were asked to locate the midpoints of each of the three sides and draw lines connecting them, thus forming four similar triangles within the original. Then imagining the center triangle being ‘punched out’, continue the same process with the remaining three triangles, and so on. The steps were repeated, extending the pattern to four iterations (a potentially infinite process). The lesson included the mathematical concepts behind the fractal and the visual impact of the resulting pattern.

Mission Hill math teacher Beto Byram was inspired to gather the work of students school-wide and form them into two trianglescale.jpgmega-triangles, 11 feet on each side. “I’m really impressed with the outcome of the project,” said Mr. Byram. “It’s a great example of showing students a prime characteristic of fractals: self-similarity or each smaller part a duplicate of the larger whole. This was truly a collective effort – 162 student-created triangles were used. Libby Fogel was an indispensable assistant in getting all the parts ready; Jessica Pappas, Alyssa Rodriguez and Bianca Zambrano assembled the massive final pieces.”

Making the entire experience a true community effort, PTA President Bill Kiff enlisted the help of his pals at the Santa Cruz Fire Department. Dressed in their full gear, they brought in their big ladders to hang the students’ work.