Cosmic ray count rates with a set of portable Geiger counters were measured at different altitudes on the way to a mountain top and aboard an aircraft, between sea level and cruise altitude. Basic measurements may constitute an educational activity even with high school teams. For the understanding of the results obtained, simulations of extensive air showers induced by high-energy primary protons in the atmosphere were also carried out, involving undergraduate and graduate teaching levels. (Contains 5 footnotes and 7 figures.)