We present a novel technique designed to calculate the detailed differential number flux signature (as a function of energy and time) of precipitating radiation-belt electrons, driven by a magnetospherically reflecting (MR) whistler wave, initiated by a single cloud-to-ground lightning discharge. Our model consists of several stages. First, we calculate the MR whistler wave characteristics at 1¿ latitude intervals along a given field-line. This is accomplished using an extensive ray tracing and interpolation algorithm involving ~120 million rays, and accounting for the effects of Landau damping, spatial, and temporal dispersion. We then use these wave characteristics to compute the pitch angle changes of resonant electrons by assuming that the interactions are linear, and independent between adjacent latitude and wave frequency bins. The pitch angle changes are transformed to precipitating flux using a novel convolution method and displayed as a function of particle energy and time at the feet of a given field line. We have calculated and compared the differential number flux signatures at the northern and southern feet of the L = 2.3 and L = 3 field lines, and found that precipitation onset and duration times increase with latitude (consistent with previous work). The precipitation consists of suprathermal Landau resonance electrons (E $lesssim$ 10 keV) which are intense but contribute little to the total energy flux, a flux gap (10 keV $lesssim$ E $lesssim$ 80 keV) corresponding to a change in coupling mechanism from Landau resonance to gyroresonance, and a series of precipitation swaths (E $gtrsim$ 80 keV) corresponding to gyroresonance interactions. The swaths result in periodic maxima in the precipitated energy flux, which correspond to the equatorial traversals of the underlying MR whistler wave energy. Global precipitation signatures were computed for a number of lightning discharge latitudes and are presented in a companion paper (Bortnik et al., 2006).