A concrete screeding device for screeding uncured concrete placed at a support surface includes a screed head having a floating platform, a grade setting device and a vibrating member. The screed head is configured to be positioned at a start of a screeding pass and placed at a surface of placed uncured concrete. A screed moving device is operable to pull the screed head along the surface of the placed uncured concrete. While the screed head is pulled along the surface of the placed uncured concrete and fully supported at the surface of the placed uncured concrete, the floating platform floats on the surface of the placed uncured concrete and the grade setting device adjusts relative to the floating platform to establish a graded surface of the placed uncured concrete at which the vibrating member will move over and along.