At all elementary and middle schools and some high schools in the Houston Independent School District – 20 in all – every student begins the day with a free breakfast right in the classroom.

The result: fewer absences and discipline problems and an increase in math scores, according to the district’s former superintendent Terry Grier.

Houston, the nation’s seventh largest school district, where three out of four students live in poverty, also offers free lunch to all students at 186 schools, without requiring applications to qualify. The potential stigma of receiving a free meal is eliminated,...