The Atacama Large Millimeter/submillimeter Array (ALMA) radio telescope has commenced science observations of the Sun starting in late 2016. Since the Sun is much larger than the field of view of individual ALMA dishes, the ALMA interferometer is unable to measure the background level of solar emission when observing the solar disk. The absolute temperature scale is a critical measurement for much of ALMA solar science, including the understanding of energy transfer through the solar atmosphere, the properties of prominences, and the study of shock heating in the chromosphere. In order to provide an absolute temperature scale, ALMA solar observing will take advantage of the remarkable fast-scanning capabilities of the ALMA 12 m dishes to make single-dish maps of the full Sun. This article reports on the results of an extensive commissioning effort to optimize the mapping procedure, and it describes the nature of the resulting data. Amplitude calibration is discussed in detail: a path that uses the two loads in the ALMA calibration system as well as sky measurements is described and applied to commissioning data. Inspection of a large number of single-dish datasets shows significant variation in the resulting temperatures, and based on the temperature distributions, we derive quiet-Sun values at disk center of 7300 K at lambda = 3 mm and 5900 K at lambda = 1.3 mm. These values have statistical uncertainties of about 100 K, but systematic uncertainties in the temperature scale that may be significantly larger. Example images are presented from two periods with very different levels of solar activity. At a resolution of about 25 '', the 1.3 mm wavelength images show temperatures on the disk that vary over about a 2000 K range. Active regions and plages are among the hotter features, while a large sunspot umbra shows up as a depression, and filament channels are relatively cool. Prominences above the solar limb are a common feature of the single-dish images.