An experiment in which the fission of uranium-238 upon bombardment with neutrons is demonstrated in the context of an undergraduate lab course. The occurrence of fission is shown by means of gamma spectroscopy which reveals the presence of the fission product strontium-92. In addition, we also investigate the reaction in which plutonium-239 is formed after neutron activation of the uranium, with neptunium-239 as an intermediary step. From the gamma spectra, it is found that both reactions are demonstrated with a significance of more than 5 σ. For the fission reaction, a cross section of (2.8 ± 1.4) × 10 - 2 barn is inferred.