The combination of mathematical and conceptual difficulties makes teaching quantum physics at secondary schools a precarious undertaking. With many of the conceptual difficulties being unavoidable, simplifying the mathematics becomes top priority. The particle/wave-in-a-box provides a teaching model which includes many aspects of serious quantum physics, while avoiding most of the mathematics. In a Dutch quantum physics project for secondary schools, this model was adopted to play a key role. Much to our surprise, we ran into many more applications than we originally expected. In many instances the model yields order of magnitude estimates, for instance of atomic and nuclear size, or qualitative insights, for instance about energy levels, molecular bonding and electron pressure. Moreover, either directly or with minor modifications, the particle-in-a-box model provides reasonable approximations of a range of phenomena, including the absorption spectra of organic pigments, the mass of the proton and the spectra of quantum dots.