In its 30 or so years existence the Material Point Method (MPM) has proved to be outstanding in solving challenging modeling problems in engineering and in animation. The theoretical background and thus a measure of confidence in the method continues to improve but is still lacking somewhat. A starting point for MPM theory is that the GIMP method of Bardenhagen and Kober was described in part as a Petrov-Galerkin method. There are two parts to this description of MPM. The first is the Eulerian mapping from particles to grid and the second is the mapping back of grid-advanced variables to the particles in defining a Lagrange integration of particles and their velocities, accelerations, stresses and deformation gradients. The use of a finite element approaches for both these parts of MPM may be used to clarify and provide insight into many aspects of MPM such as mass-lumping , the grid crossing error and linearity preservation, as well as allowing existing results and finite element error theory to be applied. Finally, this approach also allows recent error estimation procedures to be positioned within the same framework. The theoretical insights obtained by this approach are illustrated with a number of experiments that show the underlying GIMP interpolation accuracy, and how this accuracy translates into observed results. The results obtained show the importance of using the linearity preservation approach and error estimation in both improving the accuracy of MPM and showing what that accuracy is for a range of problems.