ABSTRACT We have performed high-sensitivity mapping observations of several complex organic molecules around Sagittarius B2 with the ARO 12 m telescope at 3 mm wavelength. Based on their spatial distribution, molecules can be classified as either ‘extended’, those detected not only in Sgr B2(N) and Sgr B2(M), or ‘compact’, those only detected toward or near Sgr B2(N) and Sgr B2(M). The ‘extended’ molecules include glycolaldehyde (CH2OHCHO), methyl formate (CH3OCHO), formic acid (t-HCOOH), ethanol (C2H5OH) and methyl amine (CH3NH2), while the ‘compact’ molecules include dimethyl ether (CH3OCH3), ethyl cyanide (C2H5CN), and amino acetonitrile (H2NCH2CN). These ‘compact’ molecules are likely produced under strong UV radiation, while the ‘extended’ molecules are likely formed at low temperatures, via gas-phase or grain-surface reactions. The spatial distribution of ‘warm’ CH2OHCHO at 89 GHz differs from the spatial distribution of ‘cold’ CH2OHCHO observed at 13 GHz. We found evidence for an overabundance of CH2OHCHO compared to that expected from the gas-phase model, which indicates that grain-surface reactions are necessary to explain the origin of CH2OHCHO in Sagittarius B2. Grain-surface reactions are also needed to explain the correlation between the abundances of ‘cold’ CH2OHCHO and C2H5OH. These results demonstrate the importance of grain-surface chemistry in the production of complex organic molecules.