We report progress towards realizing discrete time crystals using a BEC of potassium-39 atoms bouncing on an oscillating mirror. In the absence of interactions, each bouncing atom performs classical motion in which there are resonant islands in phase space located around periodic orbits whose periods match an integral multiple s of the driving period T of the mirror. If all the atoms are prepared in a single wave-packet, in the absence of interactions they tunnel to neighbouring wave-packets on a timescale determined by the driving amplitude and period of the oscillating mirror. In the presence of a sufficiently strong attractive interaction, the Floquet eigenstates of the periodic system become Schrödinger cat-like states, so that measurement of the position of just a single atom is sufficient to break the timetranslation symmetry and cause the system to collapse into one of the s wave-packets bouncing with period sT. Such a system allows dramatic breaking of discrete time translation symmetry where the symmetry-broken state evolves with a period typically s=40 times longer than the driving period and does not decay. This system provides also a suitable platform for demonstrating a wide range of condensed matter phenomena in the time domain.