In 2003 the Brazilian government introduced Bolsa Família (Family Grant) Program (PBF), which intended to guarantee the overcoming of poverty and extreme poverty by a monthly transfer of income to the families in situation of vulnerability and poverty in the country. Currently, the program transfers a monthly resource to 14 million families, which in return must enroll their children between 6 and 17 years old in Elementary and Secondary Schools and ensure a school attendance up to 85 percent of students from 6 to 15 years, and 75 percent for students from 16 to 17, besides other conditionalities. This research aimed to understand some of the schools institutional and pedagogical features of Mato Grosso do Sul state, that present, simultaneously, two conditions: have systematically positive results in national assessments, and concentrate a significant number of beneficiary students from Bolsa Família Program (PBF). Therefore, this study adopted a qualitative approach. Initially, an index through a classic linear regression was calculated for the municipal and state public schools of Mato Grosso do Sul, which, after the controlling of students socioeconomic characteristics, the school social composition due to the concentration of students from PBF, average proficiency and distribution in the performance levels of Prova Brasil (Brazil assessment), identified 14 schools that stand out among more than 1,900 schools in the state. From these, fours schools were selected in two different municipalities. Those who presented better results, also analyzing issues related to equity, were investigated in loco in the pursuit of understanding what these schools do to minimize the weight of the students social background. Thus, the criteria of management, leadership, the school internal environment, pedagogical practice, family-school-PBF were investigated, through a field research, observing the school and the classroom, and using semi-structured interviews with directors, coordinators, teachers, students and beneficiary families of the selected municipalities and schools. The group of schools that participated in the research has in common the fact of having positive and more homogeneous results despite attending poor students and students in situations of social vulnerability. Apart from this more general characteristic, the whole of schools investigated deliberately contains a great diversity. In this group, there is rural and urban schools, municipal and state, located in big and small cities. This diversity responds to the interest in knowing, in addition to common characteristics to the four schools, a wide repertoire of factors and practices that promote efficacy and school equity in circumstances that present specific institutional, operational and spatial challenges. Among the characteristics that are present in the group of schools, the results of the research allow highlighting: i. management with pedagogical emphasis, exercised by the director, or delegated to the coordinators; ii. positive school environmet promoted by directors and expressed in satisfaction with the work of directors, coordinators, teachers and recognition of the work of the school team by families and students; iii. harmonious and respectful relationships with students; iv. emphasis on learning processes, with diversified activities; v. monitoring of teachers pedagogical work by coordinators; vi. institutional prestige of schools, promoted by high grades in the IDEB, school discipline and teaching and professionals quality; vii. family-school relationship, with parents who feel heard by the institutions, show interest in the school, and are aligned with the expectation of school team participation. The main difference between these schools is related as selective forms of student interaction, which typically contribute to the maintenance of educational and social inequalities.