Up to 20 teachers in total at Monks Park, Whitfield, Hengrove and Portway schools could be affected.
The council said it was a demographic issue and that teachers had to be allocated according to pupil numbers.
But the National Union of Teachers said it was the worst year it had known for redundancies and a problem that had been known about for several years.
Assistant Divisional Secretary Paulette North said: "We have got a problem with children going out of Bristol, 79 are going to South Gloucestershire and we've known about this problem for three years.
"Heads are making very difficult decisions, they do not want to dumb down and lessen the curriculum and make classes larger, which is what's going to happen if teachers lose jobs."
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~59~RS~)