The purpose of this study is to implement an a-didactical activity relating to the acquisition of the triangle inequality, prepared within the framework of the "Didactic Situations Theory" (TDS), and to report the experiences of the students during the implementation process. The study employs a case study method based on a qualitative approach. Six seventh-grade students in a middle-low socioeconomic secondary school in the Marmara Region of Türkiye participated in the study. The researchers prepared an adidactical activity in which students discovered triangle inequality. Data were collected through observation, video recording, and worksheets. A descriptive analysis was performed on the data obtained. As a result of the analysis, it was concluded that students completed the activity with the correct expressions by experiencing different phases of the a-didactical situation.