Systems and methods for constructing concrete foundations are provided which allow for rapid and high-precision placement and alignment of anchor bolts across large distances. A frame system is constructed outside of an excavation and then suspended, using supports, over an excavation. The frame system can include a frame having one or more templates for anchor bolts, a form suspended from the frame, and a mat and cage assembly tied to the frame. The frame system can be aligned in proper position and the anchor bolts placed in the frame system before the concrete is placed. In this way, the anchor bolts can be cast in place as the footing is placed.