Rudy Nguyen, 10, is homeless.

Last week, he was sleeping on the floor at a San Francisco drop-in homeless shelter with his parents and 3-year-old brother Danny. Thin mats kept them off hard linoleum.

In the last two months, he spent three nights at a bus shelter and a week on the streets, sleeping on his parents' laps in a park.

Yet every morning, Rudy Nguyen takes two Muni buses to San Francisco's Spring Valley elementary school, where the fourth-grader is expected to be ready to read, write and multiply numbers - like every other kid in school.

Rudy is among a growing number of San Francisco schoolchildren in homeless families who too often come to class cold, hungry and sleep-deprived, making learning difficult if not impossible.

"If you're not fed, if you're not warm, if you're not sleeping ... you can't turn that off and focus on double-digit multiplication," said Jessica Chiarchiaro, Rudy's fourth-grade teacher.

In the city's public schools, there are 2,200 homeless children, some in shelters, others in cars, or on couches, or in long-term hotel rooms. That's 400 more homeless children than a year ago.

They are among the most difficult children to teach, educators say, because their unstable lives often lead to frequent absences or tardiness, lethargy, health issues and behavioral outbursts.

Doing homework can be tough without a kitchen table.

And yet in the spring, these homeless children will take the same standardized test as students in Hillsborough, Piedmont and Beverly Hills where every physical and academic need is met - their heated bedrooms full of books, computers and educational toys, their kitchens stocked with food.

"We're being held accountable for these kids scoring a certain percentage correct on a standardized test," Chiarchiaro said of the homeless schoolchildren. "I wish public schools had more resources so we can help them."

Homeless students typically post scores below or far below grade level on those tests, landing at the opposite end of the achievement gap from kids with greater advantages.

Late for school

One recent morning, Rudy's parents, Sophorn "Julie" Sung and Tung Nguyen, juggled a bag of clothes, jackets and Rudy's 3-year-old brother, Danny, as they left the Oshun drop-in shelter in the Mission District. They weren't allowed to leave anything at the shelter for the day, so they headed to a local storage facility.

Rudy and his family waited outside until 8 a.m. when the storage gates opened. At Rudy's school, breakfast was being served.

Rudy hadn't eaten yet.

The family came to San Francisco from Dallas in September after Rudy's unemployed father believed he had a good-paying job in shipping and receiving waiting for him. The job didn't pan out.

They had sold everything to come to California, except for the few belongings in the storage locker.

"Oh, he's going to be late again," Sung said as she stashed the clothes for the day.

School was just starting when Rudy arrived 45 minutes later. He had been delayed because the 49 Mission Muni bus he and his family hoped to catch pulled away as they crossed the street. They caught the next bus.

On the way to school, Rudy didn't talk much.

"Mom, I'm hungry and cold," he said as he walked up the final hill toward Spring Valley elementary school.

His mom didn't respond.

2,200 homeless students

The 2,200 homeless students in the San Francisco Unified School District compose about 4 percent of enrollment. They live in single-resident occupancy hotels, long- or short-term shelters or in apartments with one or more other families, sleeping on couches or floors. Some are on the streets, but that's rare.

The trend mirrors an increase in the number of homeless families in San Francisco, where a record 267 families last week were on a wait list for one of 59 rooms in city-funded shelters, triple the number in previous years. Rudy's family is on the list and has an estimated seven-month wait for one of those rooms. Getting into one of the rooms would allow the four of them to stay put for several months.

The school district offers a range of services to support homeless students, including free bus passes, tutoring, counseling and free school supplies like uniforms and backpacks.

Cost of services grows

But this year, district officials are worried.

The services for homeless students will cost an estimated $480,000, about $110,000 more than last year, said spokeswoman Gentle Blythe.

Federal funding will cover only $275,000 of that, with the district responsible for the shortfall.

The Muni passes alone will cost $300,000.

Yet providing transportation and other support is critical for these students, school officials said.

At Fairmount Elementary School, there are 20 homeless children enrolled this year. That's 1 out of every 18 of the school's students, or one or two per classroom on average.

Elizabeth Torres, the school's parent liaison who helps families navigate the bureaucracy of school and social services, sees homelessness reflected in a variety of ways.

"If they're in shelters or bunched up, behavioral issues come into play," she said. "They feel isolated or angry because they're in the situation."

And some kids physically manifest it, with stomach pains, for example, a symptom of depression, she said.

"I've had children from these families that have been very clingy because they don't have that consistency of where they'll be sleeping," she said.

Because of low test scores, the school has received extra district funding for a parent liaison, a nurse, a psychologist and a social worker.

Without those positions, serving the homeless children's needs would be impossible, Torres said.

It would be that much harder to get the children to learn.

"It's really not their fault," said Fairmount first-grade teacher Laura Spender-Davies. "It's very heartbreaking."

As Rudy walked in the door at Spring Valley the morning he missed the bus, a staff member stopped and had a quiet conversation with him and then brought Rudy breakfast from the kitchen: milk, cereal, animal crackers and a banana. He ate by himself in the cafeteria.

By the time he got to class, he was more than 10 minutes late.

Classmates were sitting on a rug talking about the similarities and differences between two books by the same author. Rudy joined them, but over the next 15 minutes, he never raised his hand. He glanced at the clock, picked at a scab on his hand and occasionally looked up at his teacher.

School is hard, he had said earlier. "I like math, but it's hard."

Back at his desk, Rudy shuffled through his notebooks, picking up one then another.

Despite being at the school for more than a month, he wasn't sure which one was his reading journal. He needed to have a book out.

"Remember you have your books in your desk?" his teacher, Chiarchiaro, whispered to him, helping pull out the materials.

Feel like outsiders

Many homeless children show up at a school midyear, well after routines are established and classmates are comfortable with their social circles and schedules.

Students like Rudy miss out on the community building that happens in those first weeks. Their names are missing from artwork or other projects stapled to bulletin boards, Chiarchiaro said.

They never feel like they belong, she said. "They have this lost sense about them."

Unlike Fairmount, Rudy's school doesn't qualify for a parent liaison, someone to help families enroll in the site's food pantry, for example.

And teachers aren't always privy to each child's situation, so they try to gauge needs with simple questions, Spencer-Davies said.

Did you sleep well? Did you have a good breakfast?

It also helps to be aware of what homelessness means, she said.

For example, students shouldn't be asked to map their bedrooms, say for a lesson on proportions.

"Some kids don't have bedrooms," Spencer-Davies said.

'It's pretty bad'

In the meantime, Rudy doesn't tell his classmates he's homeless. He's afraid they will shun him.

He rarely smiles, but when he does, his dimples show.

When asked what it means to be homeless, he didn't mention the cold, or the cramped shelter or the "weird" nights he spent sleeping in a park.

His answer was simpler.

"Well, it's pretty bad, 'cause you don't have money, or a house or food. Pretty much, um, I think, that's it."