What can Sierpinski's Triangle do in New High School classrooms?

Abstract

The purpose of this paper is to report the experience of the first author, as a Mathematics teacher, in carrying out activities involving the construction of the Sierpinski Triangle in classes of the 2nd year of high school in a
public school. The motivation to carry out the activity arose from the discipline Topics in Geometry and Measurements,
at EMAC, and the need to discuss geometric sequences and progressions. During the classes, the students constructed
the Sierpinski Triangle, which is a fractal in which each iteration contains proportional and smaller copies of the initial triangle, aiming at the discussion of possible relationships existing in the figure. As a result, the use of measurements stands out, as some students had difficulty using the ruler for decimal measurements. In addition, the issue of legitimacy was observed, as the students felt the need for the teacher's approval regarding the aesthetics of the figure produced, and found interesting the investigations involving the proportion between the measurements of the sides of the triangles and the formalization of the number of triangles produced at each iteration by means of a geometric progression. In the work as a teacher, it is understood that these activities enhance the teaching of Mathematics and attract greater interest from students, favoring discussions about geometry, measurements and progressions.