We show how to extract S matrix elements for reactive scattering from just the real part of an evolving wave packet. A three-term recursion scheme allows the real part of a wave packet to be propagated without reference to its imaginary part, so S matrix elements can be calculated efficiently. Our approach can be applied not only to the usual time-dependent Schrodinger equation, but to a modified form with the Hamiltonian operator (H) over cap replaced by f((H) over cap), where f is chosen for convenience. One particular choice for f, a cos(-1) mapping, yields the Chebyshev iteration that has proved to be useful in several other recent studies. We show how reactive scattering can be studied by following time-dependent wave packets generated by this mapping. These ideas are illustrated through calculation of collinear H+H-2-->H-2+H and three-dimensional (J=0)D+H-2-->HD+D reactive scattering probabilities on the Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential energy surface.