RALEIGH, N.C. — North Carolina’s Supreme Court is considering a case that could decide whether a pre-kindergarten academic program designed to boost the educational prospects of poor children must be expanded to enroll every needy 4-year-old, a move one estimate put at up to $300 million a year.

The state’s high court will hear from attorneys Tuesday in the latest chapter in a 19-year-old dispute brought by poor school districts in Hoke, Halifax, Robeson, Cumberland and Vance counties.