In several approaches to the quantum gravity, area variables appear fundamental. A key result from quantization à la Loop Quantum Gravity is that the quantum area operators have discrete spectra. In addition there are certain constraints between the area variables which allow for their consistent gluing. The discrete area spectra together with the constraints form Diophantine-like equations and therefore pose an interesting challenge for getting quantum gravitational dynamics. I will tell you how using ‘effective spin foam models’ we can address this challenge. The framework of the effective spin foam models can also be used to study other quantum gravity questions.