There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help students create visual and intuitive understandings of the issues of sampling, randomness and populations. The interweaving of concepts, combined with the technical skills, is intended to challenge teachers, students and researchers. Creating meaningful and deep learning experiences for students requires considerable teacher knowledge and skill, being able to weave together concepts with context and metacognitive thinking. In particular, it takes skill in helping students to draw out from diverse activities the central and connecting themes. At the end of the program the lead teacher said she had previously never thought of designing a unit around a key idea such as randomness or inference. Being able to use such big conceptual ideas as a theme for a unit provided a very valuable and interesting experience, certainly deepening her own experience of the nuances within the ideas and how to build more connective conceptual experiences for the students. For students who go on to study formal statistics, the hope is that the experiences with informal inference in memorable contexts such as the dolphin problem will provide a foundation for appreciating and understanding the formal statistics associated with t-tests and p-values. For those who do not go on to study formal statistics, it is hoped that they have gained an appreciation of randomness and its usefulness in decision-making, moving beyond seeing random only as haphazard.