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“Many people believe that if they went to D.C. public schools, their child is a legacy,” Ms. Arlotto said. “I’ve had people tell me that.”

Mary Lord, a Ward 2 member of the D.C. State Board of Education, said the chairman’s bill is a “strong first step toward strengthening the District’s already strong residency verification requirements.”

The law could be bolstered by quarterly reports on students’ residency status, increased signs on the requirements at schools and an examination of best practices in other states, she said.

Without tighter enforcement, Ms. Arlotto is worried children will grow up and realize they told lies during their early years in school.

“It’s unfortunate,” she said, “that parents expect their kids to deceive people.”