In conventional baffled fishways, fixed geometric elements are implemented to increase the flow depth, dissipate energy, and to create low-velocity zones facilitating the fish passage. However, fixed baffles might have a potential to generate excessive hydraulic resistance, structural loading, and debris retention, particularly during high flow conditions. In this study, a mathematical modeling and design framework is proposed for passively adaptive fishways, where hinged and spring-loaded baffles are applied at low-head weirs. Within this context, each baffle is modeled as a rigid body rotating about a horizontal hinge and restrained by an equivalent torsional spring. A quasi-static moment equilibrium is formulated by combining spring resistance, differential hydrostatic loading, velocity dependent hydrodynamic loading, and submerged weight. The resulting equilibrium baffle angle is coupled with a one-dimensional open channel model through an angle dependent projected blockage ratio as well as the local head loss coefficient, yielding various dimensionless parameters regarding the geometric and hydraulic conditions. The model revealed that the downstream rotation of the baffles are enhanced when the hydrodynamic loading increases. Also, compared to an equivalent rigid baffle, the local head loss coefficient was shown to reduce under the blockage-based loss formulation, demonstrating the potential of spring-loaded baffles to provide strong hydraulic modification during fish passage. The proposed framework provides a basis for subsequent validation through laboratory experiments and/or CFD simulations, particularly for calibration of the hydrodynamic moment and head loss coefficients. Prior to field implementation, site-specific optimization for the baffle geometry and debris tolerance should also be considered to ensure reliable operation under variable flow conditions.