Kay Frazier knows her grandson, a third-grader, struggles in reading. That’s why she has always signed him up for summer school in the District, figuring he needs the extra help.

But this year, for the first time, D.C. public schools’ summer program is enrolling students by invitation only. And Frazier’s grandson wasn’t invited.

School officials told Frazier that he is too far behind, she said.

The District’s summer program for elementary- and middle-school students used to be open to everyone on a first-come, first-served basis. Officials have reconfigured the program to target lagging readers, a strategy meant to maximize limited resources and reach students who are likely to benefit the most from the five-week program.

But there’s a trade-off: The new summer program is not designed to meet the intensive needs of students who are most profoundly below grade level. That leaves out Frazier’s grandson and hundreds of other struggling D.C. children.

“Because of the numbers of struggling students that we have, from just below grade level to many years below grade level, there are always going to be students who need support who aren’t going to be able to get it from this program,” said Dan Gordon, the school system’s deputy chief for academic programming. “We’re not at the point where we can run summer school for everyone.”

Volumes of research have shown that summertime learning matters, especially for poor children. With less access to enriching out-of-school experiences, poor children tend to lose more academic ground than their middle-class peers during the languid summer months, exacerbating the achievement gap with every passing year.

That so-called summer slide is part of a broader literacy problem in the District. Fewer than half of D.C. children are proficient in reading, according to standardized tests, and more than a third of all city residents are functionally illiterate, according to a 2007 report.

Some charter schools have lengthened their academic years or adopted year-round calendars to stop the summer slide. And several D.C. public schools run their own summer programs, paying for them out of the school budget or with the help of grants.

But the school system doesn’t have the resources to offer summer help to every child who needs it, Gordon said. The school system’s central office is spending about $2.4 million this year — or about one-third of 1 percent of its $800 million budget — on summer programs for general-education students in kindergarten through 12th grade. In 2012, those programs served 3,750 students, according to budget documents submitted to the council.

Invitation-only admission helps concentrate those scarce resources on students who truly need extra help, Gordon said. Officials selected students who scored within a certain range on reading assessments, a tactic meant to identify those most likely to benefit from summer programs.

Some struggling readers, particularly in middle school, were not invited because they scored too high. But many students were excluded because they scored too low. Those students are so far behind that they need more intensive help — such as one-on-one instruction — than the summer program is designed to provide, Gordon said.

“We felt like it was really important to invite students to the program who could benefit most from the program we could offer,” he said.

Frazier said she doesn’t see the sense in excluding children who are struggling the most.

“They’re telling kids who really, really need the help, ‘Forget you, you’re on your own,’ ” said Frazier, a Ward 7 resident who serves as her grandson’s guardian.

“He’s already behind,” she said. “This will put him further behind.”

There are about 10,700 struggling readers in kindergarten through eighth grade, according to the reading assessments that officials used to flag summer school candidates. Officials invited about 7,700 of those students and have enough space to enroll about 2,700. If those children don’t fill the available seats, the school system might invite more students.

Some of the struggling readers who did not receive a summer school invitation might have disabilities, Gordon said. They will be eligible for a special-education summer program that last year served about 1,000 students.

Others will have a chance to enroll in summer camps that community-based organizations operate in school buildings. Last year, those programs served about 3,000 children.

But details about those camps aren’t yet available to parents, and Frazier is concerned that they wouldn’t offer the kind of robust academic help that her grandson needs.

She said parents she knows are not aware of the invitation-only policy because the school system did not send a letter explaining the change. School officials said they did not explain the change in a letter because they didn’t want to confuse parents in case the program doesn’t fill up and they can invite more students.

Frazier learned of the new policy only when her granddaughter, a second-grader, received an invitation.

“Enrolling in Summer School is one of the best things you can do to help your child succeed,” the invitation said. “Students who do not participate in enriching summer programs lose ground over the summer.”

The warning galled Frazier. She knows both her grandchildren need summer lessons to keep from falling further behind, but she doesn’t know how to get that help for her grandson now that public summer school isn’t an option.

A private, academics-focused program at a nearby church would cost nearly $1,000 for the summer, more than she can afford. She figures that although she’s not a trained teacher, she might end up tutoring the boy at home.

“I have to do something,” Frazier said. “I can’t let him sit here all summer.”