AKRON, Ohio (JTA) — During a High Holidays discussion about repentance in Sarah Greenblatt’s Jewish values class, not all the students are listening. One girl stares out the window at the azure sky. Another sits in the back doodling.

But a boy in the front row wearing a creased black skullcap sits transfixed, notebook open, pencil poised.

Why is reflection and repentance so important around Rosh Hashanah? Greenblatt asks. The boy’s hand shoots up.

“The Torah, and also the Bible, tells us how to live right, how to get right and how to stay right,” he says.

This might be a typical scene in any Jewish day school except for one thing: The boy isn’t Jewish.

Fifth-grader Seth Pope is one of 58 non-Jewish students at the Lippman School, Akron’s only Jewish day school.

Four years ago, the school — then known as the Jerome Lippman Jewish Community Day School — was teetering. Enrollment had tumbled to 63 students, 33 of them Jews, and it was unclear whether the school could survive in this Rust Belt city 40 miles south of Cleveland.

Like a number of day schools in Jewish communities with dwindling populations, Lippman for years had been accepting a few non-Jewish students, but without any modifications to the Jewish-focused curriculum.

With the 46-year-old school at a crisis point, however, board members decided some fundamental changes were necessary. They changed the school’s name, began marketing to non-Jews, and created a dual-track curriculum that offered a choice between Judaic studies and global studies.

The school quickly saw positive returns. Enrollment climbed, and not just among non-Jews. This year, the school has 101 students; 43 are Jewish.

“The fear was Jewish families would not want to participate,” said Sam Chestnut, head of the school. “In fact, we’ve seen the opposite.”

Lippman is one of more than a dozen Jewish day schools in North America that accept students from non-Jewish families. In many cases, their presence is relatively small, at 5 or 10 percent, but at some schools non-Jews comprise 50 percent or more of students.

For struggling schools, the issue often is survival. Non-Jewish students can be a lifeline, bringing in much-needed cash and helping schools with shrinking enrollment achieve critical mass. In other cases, schools accept non-Jews as a matter of principle.

“The move toward more schools opening up in this way has been driven by the pragmatics of declining Jewish demographics in certain cities,” said Marc Kramer, executive director of Ravsak, a networking organization for 130 Jewish community day schools.

Kramer said there has been a recent uptick in the number of nondenominational Jewish day schools that accept non-Jews. In a recent survey of 50 Ravsak schools, 18 reported accepting non-Jewish students.

At Arizona’s Tucson Hebrew Academy, head of school Arthur Yavelberg says the 20 non-Jews among the school’s 164 students have boosted his school’s viability.

“Between the money they bring in and accessing scholarship services, you’re talking about $200,000-plus per year,” Yavelberg said. “A lot of families are concerned about social interactions as their kids get into adolescence, so the sheer numbers [of non-Jewish students] can make the school more attractive to Jewish families because they know there’s a larger social circle available.”

In New Orleans, the local Jewish day school’s decision four years ago to market to non-Jews had the opposite result: The number of Jewish students plunged to 15 from about 50. Only 29 students overall remain.

“There are going to be some hard decisions that the board is going to have to make,” said Deb Marsh, director of admissions at the school, which a year ago changed its name from the New Orleans Jewish Day School to Community Day School. “Is the Jewish day school a viable long-term school?”

The success of opening a school to non-Jewish enrollment often hinges on proportion. A small percentage of non-Jewish students can help stabilize a struggling school. But if a certain threshold is passed, the non-Jewish presence can alter a school’s culture.

“At what point does a notable presence of gentile children dissuade Jewish families from sending their kids there?” Kramer said. “Some families enroll their children in Jewish day schools because they want their environment to be defined by Jewish classrooms, Jewish values, Jewish conversations on the playground. What happens when the conversation about what did you do this weekend includes did you go to church?”

Tehiyah Day School in El Cerrito, Calif., just north of Berkeley, has had non-Jewish students since its founding in 1979. Head of school Bathea James says the diversity of the 250-strong student body — about five percent of whom are not Jewish — reflects the school’s values.

“I don’t believe you should take non-Jewish students purely for financial reasons,” James told JTA. “If you believe it enhances the community of your school somehow, then I think you should do it. If we can expose the beauty of Judaism to more people in the community, why wouldn’t we?”

At Tehiyah, all students study the same curriculum. About 30 percent of the day is spent on Judaic subjects, Hebrew or prayer. Non-Jewish families are among those chairing an upcoming Sukkot dinner.

At Lippman in Akron, 65 percent of students are in the Jewish track, including more than two dozen non-Jews, and some Jews have chosen the global studies track. Even those in the global program study some Hebrew, thanks to non-Jewish parents who requested it.

Yarmulkes at Lippman are optional, except in Jewish studies classes. But a few non-Jewish boys don them even outside of Jewish class.

“They wear it because it feels like a positive expression here,” Chestnut said.

When it comes to prayer, which is mandatory in the Jewish track, balancing Lippman’s inclusive philosophy with Jewish law can be a bit tricky. If a non-Jewish student wants to be called to the Torah, for example, he might be partnered with a Jewish classmate.

In most cases, non-Jews find their way to the Jewish schools through word of mouth, drawn to them because their friends go there, the school’s academics are strong or area public schools are weak. Some see the Jewish environment as a way to give their kids a strong ethical background. Lippman is the rare Jewish school that actively markets to non-Jews through billboard, radio and newspaper advertising.

And while Chestnut concedes open enrollment is not right for every school, in Akron’s diminutive Jewish community, it was not a difficult call.

“The first question is: Is it better to have no school at all or a school that offers a Jewish curriculum during the day and yet has non-Jews?” he said. “For our school it was an easy one.”