  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 $\sim 5\times10^{10}~\rm{M}_\odot$, 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.
