Innovative time allocation and timetable organisation can support the aim of providing students with individualised learning opportunities and deeper engagement with learning. Traditionally, time within schools is maintained and distributed through Western approaches to administration and organisation, which are socially and culturally produced and often deeply ingrained in practice. The turn to Innovative Learning Environments (ILE) in a growing number of international jurisdictions provides schools the opportunity to develop alternate time allocation and timetable organisational practices. To address the question, which is the title of this article, we have taken the socio-material perspective that there is a dialectical interplay of space, time and the lived experience of teaching and learning. This article's question is derived from a larger qualitative New Zealand study of two schools; a secondary college, and a "junior college". Participants included senior leaders, teachers and students who have a lived experience of alternative organisational approaches in open plan, flexible learning environments. This study explored the relationships between temporal and curricular organisational practices, pedagogy, and learning environments, whilst critically examining the underlying priorities and values these altered systems imply. This study makes a valuable contribution to innovative learning environments research as few studies focus specifically on timetable structures in this field. In conclusion, our analysis of findings indicates that progressive alternatives can make a compelling alternative to traditional models of temporal organisation.