A supervised exercise program that gets young children running and playing for an hour before school could make them happier and healthier, while also jibing with the needs and schedules of parents and school officials, according to a new study involving two dozen elementary and middle schools.

The results also caution, however, that the benefits may depend on how often children actually participate.

Physical activity among children in most of the developed world has been on a steep decline for decades. National exercise guidelines in the United States recommend that children and adolescents engage in at least an hour of exercise every day. But by most estimates, barely 20 percent of young people are that active, and many scarcely exercise at all. Meanwhile, rates of obesity among children as young as 2 hover at around 17 percent, according to the Centers for Disease Control and Prevention.

Understandably, many concerned experts have suggested a variety of physical-activity interventions, from more sports programs to the use of “active” video games that allow children to move without relinquishing their screens and joysticks.