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Two pupils were threatened by a girl who took a knife into Strood Academy.
The school, in Carnation Road, Strood, confirmed a pupil had made threats last week and a butter knife was subsequently confiscated.
She has since been excluded for five days.
The school said police were informed of the incident after it occurred and while the knife was mentioned as part of a threat it was at no point brandished.
A statement said: "Last week a female student was found to be in possession of a small butter knife in their bag.
"The knife in question was confiscated and the student issued with a five-day exclusion.
"It is alleged that the student in question had earlier made verbal threats to two other students where she mentioned the knife and because of this the matter has been referred to the police for further investigation.
"We have been in regular communication with the parents of the students affected to inform them of the actions we have taken and the proposed measures going forward to prevent any further incidents of this nature.
"As an academy we have a zero tolerance approach to this type of threatening behaviour and we will be working with all agencies to ensure that the matter is fully investigated and appropriate action taken."
Kent Police confirmed they were investigating a report of a student threatening another pupil at Strood Academy between 12pm and 1pm on October 1 2020.
A statement added: "At the time of the incident the matter was dealt with by the school and a knife was confiscated. Officers are carrying out enquiries into the circumstances surrounding the incident."