In this work, we venture to show how careful use of a program for quantum chemical calculations (such as VASP) may enrich teaching in solid-state chemistry and how principles of thermodynamics contribute to a validation of phase diagrams and reaction pathways using the quasiternary system Li[subscript 2]O-Al[subscript 2]O[subscript 3]-SiO[subscript 2] as an example. We show how to calculate formation and reaction energies, we discuss the stability of compounds with respect to their decomposition by introducing the convex hull principle, and we compare the relative stability of polymorphs as well. In a final sum-up, we treat the problem of triangulation in ternary phase diagrams. We show how such a practical course can refer to earlier preparatory courses on thermodynamics, crystallography, and quantum chemistry, and how the results of different tasks distributed among several groups of students can merge to an overall picture and help to solve many problems in understanding solid-state chemistry.