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We quantize a flat FRW cosmology in the context of the $f(R)$ gravity byNoether symmetry approach. We explicitly calculate the form of $f(R)$ for whichsuch symmetries exist. It is shown that the existence of a Noether symmetryyields a general solution of the Wheeler-DeWitt equation where can be expressedas a superposition of states of the form $e^{iS}$. In terms of Hartlecriterion, this type of wave function exhibits classical correlations, i.e. theemergent of classical universe is expected due to the oscillating behavior ofthe solutions of Wheeler-DeWitt equation. According to this interpretation wealso provide the Noether symmetric classical solutions of our $f(R)$cosmological model.

Noether symmetric $f(R)$ quantum cosmology and its classical correlations