Set within a theatrical unfolding of global youth climate movements, this paper explores the role of digital media in staging new possibilities for climate change education and activism. We engage Deleuze's method of dramatisation to theorise how young people are using digital platforms to perform climate activism and construct new political subjectivities through affective investments. We develop these ideas by describing the process of co-developing a climate change education App with young people. This co-design process brought together elements of climate education, environmental science, speculative fiction, gaming, social media, and hacktivism as techniques for dramatising climate change through digital practices of fabulation. We argue that climate change is a complex philosophical problem that needs to be dramatised -- and that young people are currently using digital media to elaborate speculative performances of this problem through the cultivation of a minor politics.