Glioblastoma (GBM) is the most common and lethal brain tumour, with a median overall survival of only 12-18 months. Resistance to temozolomide (TMZ), the only drug approved for GBM treatment, is one of the main causes of this dismal prognosis, and the main obstacle to develop new succesful treatments. Despite intense efforts, the mechanisms of TMZ resistance remain poorly understood. In this line, mathematical models are useful tools to gain insights into the underlying mechanisms, being able to isolate phenomena and test new hypotheses. We present a continuum mathematical framework for modelling cellular adaptation and phenotypic plasticity. The phenotypic state of cells is modelled as an internal variable which is modified by environmental factors such as TMZ exposure and in turn affects cell behaviour, in this case leading to drug resistance. After a model selection procedure, we obtain a calibrated model able to reproduce the acquisition of TMZ resistance in treated GBM spheroids. The results allow to define some treatment guidelines for overcoming the in vitro resistance. Moreover, the potential of the model for determining the adaptation mechanism as well as to differentiate between the sensitive and resistant cell populations is highlighted.