The academic gaps between groups of students — the poor and the middle class, or black and Hispanic children and their white and Asian peers — often are examined in broad strokes, across a district or an entire city. But a new analysis from the Center for New York City Affairs at the New School takes a closer look by mapping the achievement gaps within each public elementary school in New York City. The results reveal the challenges of integrating students across the system, and of integrating under one roof.

The study is a snapshot that looks at student performance on a single test, the state math assessment given in 2016 to third through fifth graders. At each school, it looks at the race of the test takers and estimates their household income using census information about where they live.

The report illustrates how closely race, income and academic performance are tied in this city. Almost all students in the study with estimated household incomes below $30,000 were black or Hispanic, while students with household incomes above $80,000 were predominantly white. And the poorer students were, the lower they tended to score on the test, even when they went to the same school as wealthier children.

Take P.S. 8, the Robert Fulton school in Brooklyn Heights, which the Center for American Progress identified last year as having one of the richest Parent Teacher Associations in the country, and which has a relatively diverse student body. While 64 percent of its students passed the state math test in 2016, compared with 36 percent of students citywide, black students at the school were nearly a full proficiency level behind their white peers.