SEATTLE — More than a dozen Washington school districts have added at least a school worth of students over the past two years.

Finding enough classrooms for those children is becoming a challenge.

The districts growing the fastest worry the problem will deepen as the Legislature makes good on its promise to require schools to shrink class sizes in kindergarten through third grade and to give every child access to free, all-day kindergarten.

An Associated Press analysis of Washington school enrollment data shows 136 school districts, out of 295, added students between the 2011-12 school year and the current academic year. Of those, 17 needed to add 400 or more desks during that two-year span. The average elementary school in Washington state has 430 students, according to the National Center for Education Statistics.

Two Snohomish County school districts, Northshore and Everett, ranked among the top 20 districts with the fastest growth. Northshore in Bothell was fifth, adding 822 students. Everett was 18th, adding 377 students. Two other county districts ranked among 10 districts losing the most students over the same period. Monroe was ranked fourth among the fastest shrinking districts, with an enrollment loss of 457, while Stanwood-Camano was ranked seventh with 317 fewer students.

The majority of Washington districts are shrinking or growing too slowly to need new classroom space, but the ones struggling with overcrowding say they aren’t getting the help they need from voters or the state of Washington.

The Pasco school district in central Washington grew by nearly 1,000 students over the past two school years. The district, which has 16,607 students this year, grew the equivalent of an elementary school in each year of the past decade, said John Morgan, the district’s assistant superintendent for operations.

“It’s just a tremendous challenge for us,” he said.

Although district officials hope expansion will slow, a recent demographic study predicted growth will speed up as the economy continues to improve.

After failing to pass a school construction levy in 2011, voters did approve a slimmed down request in February 2013. Pasco is in the process of building three new elementary schools and moving sixth-graders back to elementary school to ease severe overcrowding in middle schools.

Pasco’s population explosion is attributed to a housing construction boom, Morgan said. As state law permits, the district also charges an impact fee on new housing developments, which has helped lower the need for school bonds.

Since the district is near the bottom of the state’s list of assessed value to be taxed for schools, Pasco has struggled to keep up despite support from taxpayers and impact fees.

In a district with 14 elementary schools, three middle schools, two high schools and an alternative school, Pasco is using 196 portable classrooms. The new elementary schools they are building will be able to accommodate 750 students, which is well above the state and national average.

In addition to building large new schools and putting portables on every possible corner of school property, the district has explored year-round school and dividing students into two shifts. Morgan said neither idea was popular with parents.

The districts are doing their best to prepare for legislative action on kindergarten and class sizes, but Morgan isn’t sure how the schools that already have the maximum number of portables on campus will accommodate more students.

The Lake Washington School District in the suburbs of Kirkland, Redmond and Sammamish east of Seattle estimates that it would need 79 new classrooms to meet the Legislature’s plans for smaller classes in kindergarten through third grade. If all-day kindergarten is mandated at the same time, school officials believe they will need 108 more classrooms.

Those classrooms would come on top of the growing district’s existing need for more classroom space. The district had a $404 million bond measure on the April 22 ballot, but it appears to be failing. The bond would have built five schools and added on to another.

The district currently has 26,220 students, an increase of 825 since last year.

Lake Washington Superintendent Traci Pierce says the district typically asks voters to approve new construction bonds every eight years, but that plan wasn’t keeping up with demand.

“We’ve got some pretty significant overcrowding,” Pierce said, noting that one elementary is nearing 800 students with 10 portables on its campus.

Nearly half the school districts in the state have had at least three consecutive bond election failures since 1998 or have never had a bond issued in the past 15 years, according to a report from the Office of the Superintendent of Public Instruction.

The state helps districts pay for school buildings, on a sliding scale with the poorest districts getting the biggest percentage of their costs covered, but one of the requirements for state aid is a local bond issue.

Districts that can’t pass a bond lose twice because they also won’t get any state money.

A bipartisan proposal to use more lottery money for school construction failed to pass during the 2014 Legislature, but lawmakers believe the idea has enough support to get a hearing next year.

State. Rep. Drew MacEwen, R-Union, said the proposal includes a plan to stop requiring local bonds before districts can get state construction dollars.

The Democratic co-sponsor, State Rep. Hans Dunshee, D-Snohomish, believes lawmakers need to address both the need for more teachers and more classroom space if they want to answer the Supreme Court’s 2012 McCleary decision on state education spending.

The Supreme Court has estimated that lawmakers will need to find $700 million to pay for the extra classrooms.

Gordon Beck, director of school facilities and organization for OSPI, predicted that many districts would use portables to add classroom space for the new initiatives. The state has about 4,000 portables in use today, Beck said.

The North Thurston school district, north of Olympia, is using about 200 portables, but it recently passed its biggest bond measure ever and is building a new middle school and expanding other schools to add classroom space.

With about 14,600 students this year, the district grew by nearly a thousand students in the past two years.

District spokeswoman Courtney Schrieve doubts North Thurston or any other district will be able to find the room for more kids in all-day kindergarten and smaller classes in the younger grades.

“The state is going to have to help provide for that,” she said.