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“We don’t want to shut our gates, so to speak,” said Mrs. Cheh, a Democrat, citing the promising level of diversity at the school. “But even if we did, what I’m telling you is we don’t have enough capacity.”

Ms. Henderson and her staff are charged with examining these issues and how resources are doled out in relation to school size. Schools with lower enrollment do not receive enough to keep up with the program offerings of its larger counterparts.

She noted that Prince William County, Va., places 80,000 students in 90 schools, while the District spreads 47,000 students among 125 schools.

“I think what you see in our larger middle schools is the opportunity for more flexibility and variety in the offerings,” Ms. Henderson said.

Mr. Brown said he hopes to find swift solutions to these issues, because “every child should have access to a quality seat.”

“You see,” he said, “our students can’t wait any longer.”

Asked after the hearing to verify the statistics she cited, particularly the figures on eighth-grade suicides, Ms. Henderson replied, “That’s what the survey said.”

Schools officials later said the question was part of the Youth Risk Behavior Survey administered last year by the Office of the State Superintendent of Education and funded by the CDC.

The answers came in response to the question, “Have you ever triedto kill yourself?” in a wide-ranging survey of 1,686 randomly selected D.C. middle school students.

The results were consistent with what the survey has found in other cities in recent years. The 2009 report, for example, recorded the same answer from 10.5 percent of eighth-graders in Chicago and 9 percent in Miami-Dade County, Fla.