This paper reports on the potential for engaging students in an activity that considers the interconnectedness of the five Big Ideas of Statistics in the context of conducting random trials. In the study, two classes of Year 6 students (aged 11-12 years) used "TinkerPlots" to determine the sample space of a "Mystery Spinner." Analysed for this paper were data collected from entries made in completed workbooks while engaged in the learning activity and responses to relevant questions in an end-of-year questionnaire from 27 students. The results indicated using an activity that included a probability model contributed to students working mathematically with percentages and frequencies and supported the development of intuitions about randomness and informal inference. This was promoted by students analysing the variation in the distribution of data and describing their expectations about an unknown sample space.