We have obtained extensive photometric observations of the polluted white dwarf WD 1145+017 which has been reported to be transited by at least one, and perhaps several, large asteroids with dust emission. Observation sessions on 37 nights spanning 2015 November to 2016 January with small to modest size telescopes have detected 237 significant dips in flux. Periodograms reveal a significant periodicity of 4.5004 h consistent with the dominant ('A') period detected with K2. The folded light curve shows an hour-long depression in flux with a mean depth of nearly 10 per cent. This depression is, in turn, comprised of a series of shorter and sometimes deeper dips which would be unresolvable with K2. We also find numerous dips in flux at other orbital phases. Nearly all of the dips associated with this activity appear to drift systematically in phase with respect to the 'A' period by about 2.5 min d super( -1) with a dispersion of ~0.5 min d super( -1), corresponding to a mean drift period of 4.4928 h. We are able to track ~15 discrete drifting features. The 'B'-'F' periods found with K2 are not detected, but we would not necessarily have expected to see them. We explain the drifting motion as due to smaller fragmented bodies that break off from the asteroid and go into a slightly smaller orbit. In this interpretation, we can use the drift rate to determine the mass of the asteroid, which we find to be ...10 super( 23) g, or about 1/10th the mass of Ceres. (ProQuest: ... denotes formulae/symbols omitted.)