A variation of the method of invariant imbedding can be applied to a class of particle transport problems for which the average energy of a particle can be closely correlated to the number of collisions it has undergone in the course of transport through a scattering medium. A method for calculating emergent n'th scattered particle currents from scattering media developed that combines an orders-of-scattering formulation with the invariant imbedding method. The final expressions obtained for these currents assume the form of coupled integral recursion relations expressing the interdependence of the currents of the various scattering orders Extensive numerical results are presented, along with comparisons obtained by other techniques arising from the implementation of these recursion relations. Various cases of neutron and electron scattering, both isotropic and anisotropic, are considered.