This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process that involves several steps: the explication of a learning goal, the formulation of hypotheses on students' learning, the design of specific learning activities. The study provides a case study of how model eliciting activities that start from rich context problems could play a central role to support emergent modelling. This result can be attributed to a combination of several factors: the choice of a rich context problem that stimulated students to elaborate formal mathematical concepts mathematising their informal solving strategies, and the use of a suitable artefact, that presented mathematics as a means of interpreting and understanding reality.