EAST PALO ALTO — Toothaches or asthma can cloud the minds of children who are eager to learn, but a new private school started by Dr. Priscilla Chan and her husband, Facebook CEO Mark Zuckerberg, might be just what the doctor ordered.

In East Palo Alto, a city with minorities and families living in poverty near the wealthy enclaves of Silicon Valley, The Primary School opened its doors this year to 51 low-income preschool students. It boasts an innovative curriculum that addresses children’s health needs as part of their educational experience.

“There are so many ways a school can really help a child be in their optimal frame of mind to be successful in the classroom that are way more common than what we traditionally define as special needs,” said Chan, a pediatrician and CEO of the school, in an exclusive interview.

The Primary School’s current students are 4 or 5 years old, but it continues to recruit more students and teachers. It will add more grades every year until it’s fully built out to serve 700 families in East Palo Alto and Menlo Park’s Belle Haven neighborhood. By that time, it will have 450 students from preschool to eighth grade and 250 kids from birth to 2 years old.

The school provides a free education for its students, who are selected through a lottery.

Across the nation, a growing number of schools such as the Harlem Children’s Zone in New York and publicly funded “community schools” also bring in health and social services, education experts say. And while some of these schools have seen success, the cost per child typically is expensive. Not all low-income communities have the resources to make it work.

“We have a very fragmented system with different organizations and government offices that are responsible for different parts of the child, which means that the same child often slips through the cracks because no one thinks to check that the reason why they’re not doing well in school is they can’t see the blackboard,” said Deborah Stipek, a professor at the Stanford Graduate School of Education.

While the Primary School hasn’t disclosed how much it costs to run, some of its executives noted they’re leveraging help from community organizations and health care providers. The school said it isn’t ready to let a reporter visit a classroom or talk to parents and teachers, but its leaders shared some of the work they’ve been doing in its first school year.

Partnering with the Ravenswood Family Health Center, the Primary School’s teachers received training on how to spot and manage a child with asthma, one of the leading causes of school absenteeism, according to the Centers for Disease Control and Prevention.

At least one-fifth of the kids at The Primary School have a significant asthma condition, said Meredith Liu, the school’s president and chief operating officer.

“Our goal is to equip parents and teachers and people who work with kids every day to manage the health rather than building an expensive system on top of it,” Liu said.

Ravenswood dentists also stopped by to clean some students’ teeth as part of a project called “Virtual Dental Home.”

Parents of students at the school work with coaches and teachers to help write growth plans to measure and track a child’s health, education and social-emotional progress, such as having a healthy relationship with adults or knowing how to ask for assistance.

“We had some kids who were barely making eye contact when they came in and now they’re speaking,” Liu said. “And just the ability to have a friend seems like small things for us, but makes all the difference for these kids.”

Inside the classroom, kids learned about healthy eating and even pretended they were doctors in a clinic taking care of imaginary babies. Students start off the day in a community circle, and then split into smaller groups to discuss different topics, Chan said.

In one group, children discussed who lived in their community. One classroom decided insects lived in their community, so they drew pictures of bugs and studied them.

“It’s really an immersive experience led by the child’s interest,” said Chan, a former teacher.

The Ravenswood City School District, another one of The Primary School’s partners, is looking for what it can learn from the program to bring into its own public-school classrooms. Gloria Hernandez-Goff, the district’s superintendent, said she’s interested in working with the school to improve the professional development of the district’s teachers and provide students with more social-emotional support.

Research shows that investments in early childhood education, especially for low-income kids, pay off. A recent study co-authored by Nobel laureate James Heckman, a professor of economics at the University of Chicago and the director of the Center for the Economics of Human Development, found that high-quality birth-to-five programs for disadvantaged children deliver a 13 percent return on investment each year. That’s because when they grow into adults, they’re healthier, better educated and less likely to be incarcerated.

The Primary School is one of Chan’s and Zuckerberg’s most hands-on educational investments in the Bay Area. The couple in 2014 pledged to contribute $120 million to schools in low-income Bay Area communities.

In 2010, Zuckerberg and Chan donated $100 million to turn around public schools in Newark, New Jersey. But a book titled “The Prize,” by Dale Russakoff, characterized the work as a failure because large chunks of the money went to labor and contract costs, charter schools and consultants.

Citing concerns about student privacy, The Primary School declined to disclose its exact location, but noted it sits near the Ravenswood Family Health Center.

Creating a culture where parents, teachers and doctors communicate better with each other about a child’s needs doesn’t necessarily need to cost more, Chan said.

It’s one area that Dr. Ryan Padrez is focusing on as the school’s medical director.

A challenge for pediatricians is that they see families only when they reach out to them and make an appointment. But parents and teachers see a student every day, he said.

“Even in these first few months, we’re still really just uncovering what can be possible in regards to developing a new innovative model to really go beyond what can be achieved in the pediatric office.”