The number of students who scored high enough to qualify for New York City’s gifted and talented programs rose this year, the Education Department said on Thursday. But the neighborhoods in which those children live continued along a familiar pattern: In wealthy districts, more children take the tests, and score well on them, than in districts where families are poor.

In an effort to make the programs available to more students, the department also announced that new gifted and talented programs would open next school year in four districts that do not currently have them, beginning at the third-grade level.

Those are Districts 7 and 12, in the Bronx, and Districts 16 and 23, in Brooklyn. With the new programs in place, every district in the city will have a gifted program, the department said.