In this paper we present a report of an experience with a qualitative character, which aimed to examine the use of different activities through a didactic sequence for teaching non-Euclidean geometry, in particular Spherical and Hyperbolic. To this end, we conducted a participatory research with 14 students of the 2nd year of High School in a public school of Tijucas, Santa Catarina. The research relied upon the Theory of Meaningful Learning by Ausubel. The research was divided into three phases: in the first one, a pretest was applied, in the second moment, it occurred the implementation of the didactic sequence, and finally a post-test was applied. The results show that, after the didactic sequence, most students were able to assimilate, differentiate and reconcile concepts of Euclidean, Spherical and Hyperbolic Geometry. For it still is a new subject in school databanks, there were students who remained with a Euclidean positioning facing a non-Euclidean problem. [ABSTRACT FROM AUTHOR]