Millions of students eligible for the school meals program don’t take them — and it’s not because they have plenty to eat.

It’s widely agreed that stigma and bureaucracy keep students from getting the nutrition they need for a productive day and a healthy life. Many schools have taken steps to remove those barriers — but not enough.

According to a 2015  report, just 61 percent of Maine students eligible for free and reduced price lunch participate in the program. For breakfast, the rate drops to 40 percent.

Compared to other states, that’s not bad. However, by any measure there are tens of thousands of kids who could use a meal but don’t get one, and national rankings matter little to students trying to learn on an empty stomach.

Fortunately, schools here and throughout the country have solved the puzzle.

The biggest piece is the Community Eligibility Provision, which allows high-poverty schools to offer free meals to every student regardless of income.  As a result, schools cut down on administrative costs, and students can accept free meals without outing themselves as poor to their peers. It has been used to great effect in school districts large and small, in Maine and around the country.

In fact, use of the Community Eligibility Provision is the common denominator between the states that are leading the way in school breakfast program participation, the younger and weaker of the school meal programs.

If school lunch participation is low, breakfast is even lower. In Maine, just 60 percent of the kids who take a free and reduced price lunch take a breakfast too, even though almost all schools that offer lunch also offer breakfast — and its benefits to student health and performance are clear.

In addition to using community eligibility, schools with high breakfast participation also follow what is known as the “breakfast after the bell” model.

With breakfast after the bell, the meal is served not before school — which can be difficult for students rushing to get to class on time — but either in the classroom or through a “grab and go” kiosk. Schools are also putting in place “second chance” breakfasts for later in the morning, because many older students aren’t hungry first thing in the morning.

West Virginia has used these strategies to become a leader in delivering school meals to a high-poverty population. New York City last year increased participation in its breakfast program by 5 percent by implementing community eligibility and breakfast after the bell.

In both cases, tens of thousands of students who would have gone hungry a few years ago now have a good meal available. Studies have shown that will make them better students, and improve the schools around them.

This session, Maine lawmakers will debate bills concerning breakfast after the bell as well as simplifying the school meals application process. Leaders at all levels should be pushing community eligibility wherever it is allowed.

Many Maine schools have already embraced these reforms and are on the right track. The rest need to catch up.