Under the policy, school districts across the state will have until this summer to craft their implementation plans and must begin enforcing them at the start of next school year.

The seven new schools are part of a multiyear flurry of openings that city officials hope will reinvigorate the system at a time of faltering enrollment.

A funding shortfall in the state budget forced New York City to freeze enrollment for a popular child care voucher program for low-income families.