A screeding machine includes a base unit positionable at framework that defines a concrete structure and a screed head assembly movably mounted at the base via an extendable and retractable mechanism. The screed head assembly includes a grade establishing member, a vibrating member, and elevation actuators for adjusting elevation of the screed head assembly. The screed head assembly is positioned at a screeding location via extension of the extendable and retractable mechanism and is movable over the uncured concrete in a screeding direction via retraction of the extendable and retractable mechanism. Adjustable wings disposed at and in front of the grade establishing member in the screeding direction are movable along the grade establishing member. When one of the ends of the screed head assembly is positioned at a frame portion, the wing at that end of the screed head assembly is moved to position the wing at the frame portion.