Here is some food for thought. Children who consistently eat lunch at school are more likely to score better on standardized tests, according to a study out of India, one of the biggest and longest running studies looking at the effect of school lunch on academic performance.
Researchers studied over 200,000 rural households in India as a public free lunch program was rolled out over time. They found that kids with up to five years of midday meals had reading scores 18 percent higher than kids who were offered school lunches for less than a year. They also scored better on math tests.
The quality of the school lunch matters. A recent study out of California found that when school-age children were offered more nutritious food for lunch, the students scored better on end-of-the-year tests.