We present a new semi-empirical model for the dust continuum number counts of galaxies at 1.1 millimeter and 850 µm. Our approach couples an observationally motivated model for the stellar mass and SFR distribution of galaxies with empirical scaling relations to predict the dust continuum flux density of these galaxies. Without a need to tweak the IMF, the model reproduces the currently available observations of the 1.1 millimeter and 850 µm number counts, including the observed flattening in the 1.1 millimeter number counts below 0.3 mJy (González-López et al. 2020) and the number counts in discrete bins of different galaxy properties. Predictions of our work include : (1) the galaxies that dominate the number counts at flux densities below 1 mJy (3 mJy) at 1.1 millimeter (850 µm) have redshifts between z = 1 and z = 2, stellar masses of ∼ 5 × 10 10