In a letter sent out to parents, headteacher John Bayes has explained that Thurston Primary is moving key stage 2 (years 3-6) pupils onto home learning.
However, students in key stage 1 and early years will still be able to go into school.
Mr Bayes explained: "Over the weekend I have been informed of many positive lateral flow tests that took place within our school community, which affect key stage 2 classes.
"After great consideration a decision has been made to move pupils in key stage 2 to remote learning for the remainder of the term.
"The school building will be closed to those pupils.
"I understand the implications to families of such a decision but it is important to break the cycle of transmission so that families are not isolating over the Christmas break."
According to the letter, no cases have been reported in the early years, or years 1 and 2, and the school day will remain consistent for them.
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