SEATTLE — The city opened more of its community centers Monday to help Seattle parents who were scrambling for child care as a teacher strike entered its fourth day. Several of the centers quickly filled, forcing them to turn families away.

Seattle Parks and Recreation spokesman David Takami said 21 community centers were taking care of some 2,000 children in kindergarten through sixth grade at no cost, and that number is rising. Many of the centers are at capacity, and the effort is costing the city about $21,000 a day, he said.

“It’s pretty much been an early-morning mad dash for kids to get into camp,” said Jason Busbee, a front-desk coordinator at the Queen Anne Community Center.

Busbee described the atmosphere as “one big party,” with volunteers helping oversee activities that included kickball, foosball and lawn darts. The center even ordered bouncy houses.

The strike, over issues that include pay raises and the length of the school day, has delayed the start of the public school year for about 53,000 students. The school district canceled classes for a fifth day Tuesday.

District bargainers were reviewing the latest proposal presented by the Seattle Education Association, Seattle Public Schools spokeswoman Stacy Howard told reporters Monday.

Meanwhile, the Seattle City Council passed a resolution designating this week “Seattle Educators Week” in support of the union and the striking teachers.

Councilwoman Kshama Sawant said if the union wins it will be a huge step forward for students and educators, but it would also resonate outside of Seattle.

“A victory for the union is also a victory for education across the country. It shows that if we organize and remain united, we can resist attacks on public education,” she said.

Many teachers in Washington state’s largest school district say they have gone six years without a cost-of-living raise, making it difficult to live in Seattle, where expenses have been rising in part from the influx of highly paid tech workers.