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Abstract: The Standard Model of Particles and Interactions (SM) describes our current understanding of the fundamental particles that make up matter and their interactions. However, there are still many questions which are not answered by the SM, such as the origin of dark matter and dark energy, which together make up 95% of the energy in the universe, but are not yet included in the SM. Various extensions to the SM predict the existence of new particles, some of which could be dark matter candidates. The SM can be tested with direct searches for as-yet-undiscovered particles, such as the Higgs boson, at colliders which explore the energy frontier such as the Large Hadron Collider (LHC). An alternative, yet complementary, approach is to search for physics beyond the SM by making extremely precise measurements of SM quantities, where deviations from predicted values would indicate the presence of new physics. Qweak and MOLLER comprise a program of measurements at Jefferson Lab which will test the SM by exploiting the property of parity-violation in the weak interaction. They will measure the parity-violating asymmetry in elastic electron-proton or electron-electron (Møller) scattering, respectively, anticipated as the world's most precise measurements of the weak mixing angle, sin^2 θ_W, away from the Z resonance. I will describe the experiments and their potential impact on the development of the New Standard Model.