SPOKANE, Wash. — Two weeks before graduation last spring, Lori Wyborney, the principal at John R. Rogers High School, and her three assistant principals gathered around a table covered with papers and Popeyes takeout. On a screen facing them was a list of three dozen students who administrators believed could succeed in an Advanced Placement class. But the students were not yet scheduled to take one in the fall.

The principals looked at each student’s profile, which included the student’s answers to districtwide survey questions about what worried them about A.P. classes, what subjects interested them and which adults in the building they trusted. Wyborney, concentrating as she sat with her elbows on the table and one hand absent-mindedly raised to her mouth, kept up a running commentary. “Boy, she’s not taking much next year,” she said of a student before placing her in A.P. digital photography. Of another: “He’s looking at a four-year college. He has got to get into A.P. English.”

Over and over, she declared, “I’m on it” as she scribbled the names of students to whom she planned to propose scheduling changes.

The meeting was part of a broad effort across the district to decrease the gap between the number of students from high-income families and low-income families who go to college. In Spokane, 48 percent of graduates in 2014 who received free or reduced-price lunch — a typical indicator of poverty — went on to higher education the next year, compared with 65 percent of those who didn’t receive subsidized meals, according to state data. Nationally, 52 percent of low-income high school graduates immediately enrolled in college that year, compared with 81 percent of high-income students.