In this work, we investigated through a case study the pedagogical discourse of the upper secondary school teacher when introducing the derivative concept. The subject was selected considering her experience and expertise in the field of mathematics education. Eleven class sessions were audio and video recorded, and three of them were transcribed verbatim for analysis. The theoretical framework used in the analysis was the sociocultural theory of commognition (Sfard, 2008). Specifically, we focused on identifying one of the properties of discourse, routines, which are repetitive patterns that can be inferred by observing the rest of the properties (i.e., word use, visual mediators, and narratives). Thus, some subtypes of explanation and motivation routines that complement those appearing in the work by Viirman (2015) were identified and classified: exemplification, use of personified language, use of paraphrases and synonyms, promotion of autonomy in learning, variation, outline, location, linking concepts and reference to difficulty. Likewise, we distinguished among them which are more typical of the transition stage to university than of previous courses and vice versa, as well as which of them can be used by teachers to help students to be successful in their transition to university.