  We quantize a flat FRW cosmology in the context of the $f(R)$ gravity by
Noether symmetry approach. We explicitly calculate the form of $f(R)$ for which
such symmetries exist. It is shown that the existence of a Noether symmetry
yields a general solution of the Wheeler-DeWitt equation where can be expressed
as a superposition of states of the form $e^{iS}$. In terms of Hartle
criterion, this type of wave function exhibits classical correlations, i.e. the
emergent of classical universe is expected due to the oscillating behavior of
the solutions of Wheeler-DeWitt equation. According to this interpretation we
also provide the Noether symmetric classical solutions of our $f(R)$
cosmological model.
