Flipped classroom (FC) pedagogical frameworks have recently gained considerable popularity, especially at secondary school levels. However, there are rich opportunities to explore FC at tertiary levels, but progress on the area requires instructors' attention to well-designed tasks for students' collaborative learning. Realistic Mathematics Education (RME) provides a foundation for the development of such tasks. This article advances research on the role of task design in a FC context by considering how RME heuristics may be developed to include the out-of-class phase, where students prepare for in-class work with videos. This adaption, named flipped RME classroom design, is explored through two realizations of such a design with a group of computer engineering students during their first year of studying compulsory mathematics. Thematic analysis of the classroom observations shows that students' modelling activity in-class is supported by the design of an out-of-class component in combination with teacher guidance of students' modelling activity.