  Every cosmology lecturer these days is confronted with teaching the modern
cosmological standard model $\Lambda$CDM, and there are many approaches to do
this. However, the danger is imminent that it is presented to students as
something set into stone, merely to be accepted as a fact based on the plenty
of evidences we have. This is even more critical, given that the standard model
of cosmology confronts us with entities not yet fully understood, namely a
cosmological constant $\Lambda$ and cold dark matter. In this article, we
report on an advanced cosmology course exercise, conducted in computer lab,
which was conceived as a means to have students experience first-hand why the
$\Lambda$CDM model has become so prevalent in the interpretation of modern
cosmological data. To this end, we focused on the cosmic microwave background
radiation (CMB) and calculated theoretical temperature and matter power
spectra, using the modern Boltzmann code CLASS. By comparing and analyzing the
outcome for $\Lambda$CDM, as well as for three other exotic cosmological
models, the students were able to grasp the impact of cosmological parameters
on CMB observables, and also to understand some of the complicated CMB physics
in a direct way. Our chosen examples are not exhaustive and can be easily
modified or expanded, so we express the hope that this article will serve as a
valuable resource for interested students and lecturers.
