[Breaking news update at 12:54 p.m. ET]
The United Teachers Los Angeles union and the Los Angeles Unified School District have reached a tentative deal that will get teachers back into their classrooms right away, Mayor Eric Garcetti said Tuesday.
The deal was struck after a marathon 21-hour negotiating session that ended Tuesday morning, the mayor said.
More than 30,000 educators have been on strike for six school days, demanding smaller class sizes, higher salaries, and more staff.
If the union ratifies a contract today, teachers on strike will return to their classrooms Wednesday.
[Previous story, published at 11:43 a.m. ET]
(CNN) -- They may get an "A" for effort, but after 21 hours of negotiations, the Los Angeles Unified School district and the local teachers' union are still stuck in a stalemate.
So for the sixth school day in a row, about 30,000 educators are on strike Tuesday, demanding smaller class sizes, higher teacher salaries and more school nurses and counselors.
"We work with students every day who face trauma and face hardship," Garfield High School teacher Erika Huerta said. "So we're doing this as a life passion to improve our community. And we all reminded each other that we're powerful enough for another week if we have to."
Marathon negotiations between the United Teachers Los Angeles union and LAUSD stretched from Monday morning to Tuesday morning, said Mayor Eric Garcetti, who's helping facilitate the talks.
All sides want the strike to end now. But while the union wants the school district to pony up more money to meet its demands, LAUSD says its $1.8 billion in reserves is already earmarked for education spending during this three-year budget cycle.
So it's still not clear when 600,000 students -- who are still expected to go to school during the strike -- will see their regular teachers again.
But there's a shred of good news: "We are making progress," UTLA said. "No more details can be given since the parties have agreed to confidentiality."
Firefighters join the fight
On Tuesday, they got a big boost from members of the International Association of Firefighters, who are in Los Angeles for a conference this week.
"We stand with LA teachers," read signs held by dozens of firefighters as they rallied during a parade Tuesday morning.
Some chanted "fighting for justice" as they rode atop a fire truck. A sign posted on the front of the red truck said "#RedForEd" -- a familiar slogan from the wave of recent nationwide teachers' strikes .
This strike is costing $125 million ... and counting
While teachers are demanding millions more dollars in school funding, their strike has already cost the school district more than $125 million .
That's because the state of California funds schools based on daily attendance, and the number of students going to school has plunged during the strike.
Some parents say they're purposefully keeping their kids out of school in hopes that the money drain suffered by the district will lead to a resolution more quickly.
But so far, no one's budging. So the mayor has been trying to mediate the dueling sides.
"We've been working tirelessly to reach an agreement & have made tremendous progress with 5 days & 50+ hours of negotiation," Garcetti tweeted. "I am optimistic that we have the momentum to take the final steps toward bringing teachers & young people back to classrooms."