John,
One of the first things teachers and principals do to see a radical difference at recess is to identify and support student leaders.
There's just no downside and a whole lot of positives:
Younger kids get more coaching and help with games—and older students take responsibility for the playground, honing leadership skills.
Older students with different strengths, or those who struggle academically, may find the playground is an opportunity to shine—they just need an adult to trust in them.
And younger kids, who may not want to "tattle," can often feel more comfortable asking for help or confiding in an older student first, rather than finding an adult to mediate.
Think about assigning these roles to get older students more involved (or share this list with fellow recess staff who manage the older kids):