Theories of gravity other than general relativity ( GR ) can explain the observed cosmic acceleration without a cosmological constant . One such class of theories of gravity is f ( R ) . Metric f ( R ) theories have been proven to be equivalent to Brans-Dicke ( BD ) scalar-tensor gravity without a kinetic term ( \omega = 0 ) . Using this equivalence and a 3+1 decomposition of the theory it has been shown that metric f ( R ) gravity admits a well-posed initial value problem . However , it has not been proven that the 3+1 evolution equations of metric f ( R ) gravity preserve the ( hamiltonian and momentum ) constraints . In this paper we show that this is indeed the case . In addition , we show that the mathematical form of the constraint propagation equations in BD-equilavent f ( R ) gravity and in f ( R ) gravity in both the Jordan and Einstein frames , is exactly the same as in the standard ADM 3+1 decomposition of GR . Finally , we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f ( R ) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation . We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f ( R ) models .