We present a new semi-empirical model for the dust continuum number counts of galaxies at 1.1 millimeter and 850 micron. 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 micron number counts, including the observed flattening in the 1.1 millimeter number counts below 0.3 mJy citep{Gonzalez2019numbercounts} 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 $mu$m) have redshifts between $z=1$ and $z=2$, stellar masses of $sim 5times10^{10}~rm{M}_odot$, and dust masses of $sim 10^{8}~rm{M}_odot$; (2) the flattening in the observed 1.1 millimeter number counts corresponds to the knee of the 1.1 millimeter luminosity function. A similar flattening is predicted for the number counts at 850 $mu$m; (3) the model reproduces the redshift distribution of current 1.1 millimeter detections; (4) to efficiently detect large numbers of galaxies through their dust continuum, future surveys should scan large areas once reaching a 1.1 millimeter flux density of 0.1 mJy rather than integrating to fainter fluxes. Our modeling framework also suggests that the amount of information on galaxy physics that can be extracted from the 1.1 millimeter and 850 $mu$m number counts is almost exhausted.
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