  We apply the rotation-invariant Green's function method (RGM) to study the
spin $S=1/2$ Heisenberg model on a one-dimensional sawtooth lattice, which has
two nonequivalent sites in the unit cell. We check the RGM predictions for
observable quantities by comparison with the exact-diagonalization and
finite-temperature-Lanczos calculations. We discuss the thermodynamic and
dynamic properties of this model in relation to the mineral atacamite
Cu$_2$Cl(OH)$_3$ complementing the RGM outcomes by results of other approaches.
