Homeless and living on a Hawaii beach, Sarah Kanuha never imagined being able to provide preschool for her youngest daughter.

But on Thursday the mother of five watched 4-year-old Aulii Malia Kanuha receive a preschool diploma. Aulii was one of 35 students to graduate from Ka Pa‘a­lana Traveling Preschool, which educates about 700 homeless children each year.

Kanuha found out about the program last year while living at Keaau Beach Park on the Wai­anae Coast. The family has since moved to a shelter.

"Socially she has grown so much," she said. "They blossomed her into this social little butterfly."

Kanuha’s oldest child, now 18, received free preschool in Michigan. But when the family moved back to the islands, her three other children never got any preschool. Hawaii, one of the country’s most expensive places to live, is one of 10 states with no state-funded pre-kindergarten program, according to the National Institute for Early Education Research.

The Kanuha family is one of many in the country trying to raise children in the face of joblessness and homelessness. An annual survey released this week says 16.4 million children in the U.S. — nearly one-fourth — were living in poverty in 2011, more than a year after the Great Recession officially ended. That’s an increase of 3 million kids since 2005, according to the Annie E. Casey Foundation survey.

The report showed that nearly half of Hawaii’s children didn’t attend preschool from 2009 to 2011.

Gov. Neil Abercrombie this week signed a bill that expands the state’s existing Preschool Open Doors program to fund subsidies for 900 children. The more than $7 million package is seen as a step toward eventually providing state-funded public preschool but is less than half of what Abercrombie originally proposed. Thousands of kids will lose services when the state’s junior kindergarten program for late-born 4-year-olds expires in mid-2015.

Educating children at homeless shelters and tents on the beach, Ka Pa‘a­lana is funded mostly through federal programs, including the Administration for Native Americans.

Because Hawaii’s circumstances prevent many families from being able to afford preschool, Ka Pa‘a­lana Director Danny Goya wanted his school to provide quality learning. So he sought to be accredited by the National Association for Education of Young Children, which he calls the "crème de la crème of accreditation."

The association rejected his application when he first applied in 2007. It normally accredits programs with a permanent, physical center, so the preschool set up a tent at a shelter, complete with a playground that now meets the association’s standards.

Ninety-five percent of the preschool’s beach outreach families are Native Hawaiian, and the program strives to perpetuate Hawaiian culture. Teachers use the culture to teach skills, such as learning to count in English and Hawaiian. The graduation ceremony closed with a Hawaiian prayer, or pule, led by two graduates.

The preschool also incorporates parents and caregivers: Adults spend time with the kids for several hours, then spend the rest of the day receiving skills such as vocational training and GED preparation.

The classes have helped homeless single father Leo Dew with his two daughters, Leo­lani, 6, and Leo­momi, 5.

"We’re blessed to have this program," he said after watching Leo­momi graduate.