The district made the decision Thursday to shut down schools for cleaning on Friday and Monday after learning of the possible exposure involving Franklin Elementary, John Muir Elementary and Santa Monica High.
"We are aware of a community member with children in our schools who was exposed to coronavirus," SMMUSD Superintendent Dr. Ben Drati said in a letter to parents.
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Drati added that schools experienced a "higher than normal absentee rate" on Thursday and were working to determine "if students are ill, with what type of illness, or if parents are keeping students home during the coronavirus pandemic."
School district officials are expected to make an announcement about next steps by Friday evening.
The district runs 10 elementary schools, two middle schools, three high schools, an adult high school and an alternative school. Although classes will be canceled, teachers and staff are expected to report to work.
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School districts throughout Southern California have already announced plans to temporarily close or shift to online instruction as part of nationwide efforts to contain the spread of COVID-19.
However, the Los Angeles Unified School District - the second largest in the country, which has already declared a state of emergency over novel coronavirus - remains open. LAUSD called an emergency school board meeting Friday morning to possibly discuss further action.
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City News Service contributed to this report.