Developing students' ability to think about systems, as opposed to isolated facts, is of central importance in much of science teaching. Prior work in this area has focused on students' recognition of the processes occurring within a system. Comparatively, little work has been done on how students organise the objects that are contained within the system. Understanding how objects are organised within a system structure can promote understanding of the processes relating to the objects and advance students' thinking about systems. A systematic literature review revealed different existing theoretical perspectives on object arrangement within systems. These perspectives were combined into a single framework, the Systems Object Framework (SOF), that can be used to characterise student ideas about object arrangements. The SOF was used to analyse object arrangements depicted by students in pre and post-concept maps that were collected as part of a study on a systems-based curriculum. This analysis provided support for the structure of the SOF and showed that the SOF allows for tracking of changes in students' representation of object arrangements. The SOF contributes to the field by proposing new questions to be investigated and providing a common analytical tool that permits greater consistency across future studies.