A screeding machine for screeding uncured concrete placed within framework to form a concrete structure, the screeding machine comprising: a base unit positionable at framework that defines the concrete structure to be formed; a screed head assembly movably mounted at the base unit via an extendable and retractable mechanism, wherein the screed head assembly comprises (i) a grade establishing member, (ii) a vibrating member, and (iii) adjustable wings disposed at and in front of the grade establishing member in a screeding direction, and wherein the adjustable wings are movable along the grade establishing member via respective actuators; elevation actuators operable to adjust elevation of the screed head assembly responsive at least in part to elevation sensors that sense elevation of respective ends of the screed head assembly; a control system, wherein the control system, responsive to signals from the elevation sensors, controls the elevation actuators to set the grade of the uncured concrete; wherein the screed head assembly is positionable at a screeding location within the framework via extension of the extendable and retractable mechanism and is movable over the uncured concrete in the screeding direction from the screeding location via retraction of the extendable and retractable mechanism; wherein, when one of the ends of the screed head assembly is positioned at a frame portion that defines part of the concrete structure being formed, the wing at that end of the screed head assembly is moved via actuation of the respective actuator to position the wing at the frame portion to limit excess concrete in front of the grade establishing member in the screeding direction from flowing over the frame portion when the screed head assembly is moved in the screeding direction; and characterized in that the control system operates in a float mode when the sensor control is turned off and the screed head assembly is positioned at the frame portion allowing the screed to float or rest on said frame portion as the screed head is moved along to screed the concrete, and operates in a sensor control mode, responsive to the elevation sensor, when the screed head assembly is positioned at a location where no frame portion is present to maintain the screed head at the desired or appropriate or set grade. a base unit positionable at framework that defines the concrete structure to be formed; a screed head assembly movably mounted at the base unit via an extendable and retractable mechanism, wherein the screed head assembly comprises (i) a grade establishing member, (ii) a vibrating member, and (iii) adjustable wings disposed at and in front of the grade establishing member in a screeding direction, and wherein the adjustable wings are movable along the grade establishing member via respective actuators; elevation actuators operable to adjust elevation of the screed head assembly responsive at least in part to elevation sensors that sense elevation of respective ends of the screed head assembly; a control system, wherein the control system, responsive to signals from the elevation sensors, controls the elevation actuators to set the grade of the uncured concrete; wherein the screed head assembly is positionable at a screeding location within the framework via extension of the extendable and retractable mechanism and is movable over the uncured concrete in the screeding direction from the screeding location via retraction of the extendable and retractable mechanism; wherein, when one of the ends of the screed head assembly is positioned at a frame portion that defines part of the concrete structure being formed, the wing at that end of the screed head assembly is moved via actuation of the respective actuator to position the wing at the frame portion to limit excess concrete in front of the grade establishing member in the screeding direction from flowing over the frame portion when the screed head assembly is moved in the screeding direction; and characterized in that the control system operates in a float mode when the sensor control is turned off and the screed head assembly is positioned at the frame portion allowing the screed to float or rest on said frame portion as the screed head is moved along to screed the concrete, and operates in a sensor control mode, responsive to the elevation sensor, when the screed head assembly is positioned at a location where no frame portion is present to maintain the screed head at the desired or appropriate or set grade.