We explore 11-12-year-old students' emerging ideas of models and modelling as they engage in a data-modelling task involving inquiry based on data obtained from an experiment. We report on a design-based study in which students identified what and how to measure, decided how to structure and represent data, and made inferences and predictions based on data. Our focus was on the following: (1) the nature of the student-generated models and (2) how students evaluated the models. Data from written work generated by groups and transcripts of interviews were analysed using progressive focusing. The results showed that groups constructed models of actual data by paying attention to various aspects of distributions. We found a tendency to use differing criteria for evaluating the success of models. This data modelling process also fostered students' making sense of key ideas, tools and procedures in statistics that are usually treated in isolation and without context in school mathematics. In particular, we identified how some students appeared to gain insights into how a 'good' statistical model might incorporate some properties that are invariant when the simulation is repeated for small and large sample sizes (signal) and other properties that are not sustained in the same way (noise).