Francenia E. Beech turned off the lights in her sixth grade classroom at 2:50 p.m. yesterday and left school. With that act she joined an estimated 75 percent of Alexandria's 740 public school teachers in the first work-to-rule job action in the city's history.

"I usually stay until 5 o'clock giving kids extra help or grading papers," Beech said. "But today instead of helping the five children who were having trouble dividing decimals, I'm going home."

Beech, 35, a teacher at Lyles Crouch Elementary School, and other Alexandria teachers yesterday began working the minimum time required by their contracts as many began a week-long protest of the School Board's proposal to increase their salaries by only 4 percent.

Pam Walkup, president of the Education Association of Alexandria, which represents most of the city's teachers, estimated all but one-fourth of the Alexandria teachers were participating in the job action. School Board Chairman Lou Cook said that despite the demonstration, she didn't believe the city would be able to meet the teachers' demands.

Wearing buttons yesterday with the slogan, "Teachers deserve a whole apple," printed over a skinny apple core, the teachers refused to correct papers, attend meetings and help students outside the normal class day. They say the protest is supposed to pressure the School Board to increase their 1985-86 salaries by 5 percent. For Beech, who is paid $25,900 based on her master's degree and nine years experience, the one percentage point difference means $259 a year.

"I get paid for working 35 hours, but I put in 60 hours a week," Beech said. "We're doing this so that they the School Board know that we do a lot of work."

On March 20, the School Board, with Lynwood G. Campbell Jr. absent, voted 5 to 3 to give teachers and the school's staffers a 4 percent salary increase. The City Council has to approve the school system's overall budget, but the School Board decides how to allocate that money.

Cook, who voted for the 4 percent increase, said she did so because she believes that the council would never approve enough money to allow for anything higher. In the proposed 1986 city budget, former city manager Douglas Harman recommended a $41.9 million operating budget for the school system based on a 3 percent teachers' salary increase.

Cook says in order to grant the teachers the 5 percent increase, the City Council would have to allocate an additional $434,000 when it approves the final budget on May 14. "If we give the teachers 5 percent with the money we have now we'll have to make deep cuts elsewhere," Cook said.

As part of the work-to-rule protest this week, many teachers said they plan to wear black tomorrow, the day of the next School Board meeting.