Two of the homes targeted had boilers stripped out of them, according to a series of incidents revealed by South Yorkshire Police.
The homes were in Gaunt Drive and Spring Close Mount, both in Gleadless Valley.
Other homes have been broken into in Eastwood Road, Sharrow; Guest Road, Hunters Bar; Laverdene Avenue, Totley Rise; Abney Brook Drive, Meadowhead and Springwell Crescent, Beighton.
Officers are also investigating a number of burglaries at commercial premises, including a restaurant on London Road and a dental practice on Birley Moor Road.
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Anyone with information should call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.