Resumen
Inquiry and modelling are relevant processes of mathematical activity, and both are considered as important competencies for problem solving, since their subprocesses have a family resemblance that makes them mutually complementary and enriched. In this line, we report an investigation focused on the study of the synergies and relationships established between the inquiry and modelling processes emerging in a learning situation, based on a realistic and authentic archaeological context. To this end, we considered one theoretical cycle to explain each process, and then designed a learning situation contextualised in a realistic and authentic archaeological context which promoted the development of inquiry and modelling skills for its solving. Methodologically, we conducted a case study with students in a secondary school of Badalona (Catalonia, Spain), who solved the learning situation grouped into working teams. Through a thematic analysis, we identified the steps of both processes followed by the students when solving the learning situation, and thus we delved into the synergies and relationships established between inquiry and modelling processes. Finally, we reflect on how both processes mutually enrich when dealing with a problem-situation and propose an integrative cycle for the development of inquiry and modelling skills in the classroom.