Tens of thousands of striking teachers and supporters marched in Los Angeles on Friday, as talks to end the crippling walkout offered hope of a settlement between the union and school district officials.
Some 30,000 teachers walked off the job on Monday, after two years of contract negotiations on salaries, class sizes and more staffing failed.
The strike is affecting about 500,000 students and has cost the district -- the second largest in the nation -- nearly $100 million in state funding, which is based on student attendance.
The Los Angeles teachers union and the school district went back to the negotiating table on Thursday and talks resumed on Friday and were expected to extend into the weekend.
"We should be aware that we've been at this for 21 months, and there are some very fundamental issues that there are key differences on," Alex Caputo-Pearl, president of the United Teachers Los Angeles Union, told reporters on Thursday.
"An agreement is not going to take shape overnight, it's not going to be a quick and easy process, but today, there's been good and hard work done on that."
The union has said that the main point of contention is not so much salaries but class sizes, which can be over 40, and the need for more support staff, including nurses.
It is also demanding that the district cap and regulate charter schools, which are publicly funded institutions that operate independently of the established state school system.
Such schools have proliferated in Los Angeles in recent years.
School officials insist they have offered the union the maximum possible and say the teachers' demands are unrealistic and would bankrupt the district.
"It's just math," district superintendent Austin Beutner, a former investment banker, told reporters earlier this week. "This is just math. It's not a values conversation.
"The experts have all said we do not have the ability to spend more than we're spending."
However the teachers union says the district could tap into $1.8 billion in reserves to meet their demands and has vowed the strike would continue until a satisfactory deal is reached.
"We are going to work relentlessly this weekend in negotiations," Caputo-Pearl told the rally in downtown Los Angeles Friday. "But we have to come back on Tuesday with our picket lines even stronger than this week."