Scaled momentum distributions for the strange hadrons K S0 and ∧/∧were measured in deep inelastic ep scattering with the ZEUS detector at HERA using an integrated luminosity of 330 pb -1. The evolution of these distributions with the photon virtuality, Q 2, was studied in the kinematic region 10 < Q 2 < 40000 GeV 2 and 0.001 < x < 0.75, where x is the Bjorken scaling variable. Clear scaling violations are observed. Predictions based on different approaches to fragmentation were compared to the measurements. Leading-logarithm parton-shower Monte Carlo calculations interfaced to the Lund string fragmentation model describe the data reasonably well in the whole range measured. Nextto-leading-order QCD calculations based on fragmentation functions, FFs, extracted from e +e - data alone, fail to describe the measurements. The calculations based on FFs extracted from a global analysis including e +e -, ep and pp data give an improved description. The measurements presented in this paper have the potential to further constrain the FFs of quarks, anti-quarks and gluons yielding K S0 and ∧/∧ strange hadrons. © SISSA 2012.