Kids can do both -- play and learn. But they do need to learn in ways that fit with what they were doing in school before summer, and what they will be doing in school when fall comes. That means some structure over the summer. I know a lot of parents don't want to hear it but they should look at the research -- there is a lot of research to show that kids DO lose learning over the summer if they do nothing. Look at "summer learning loss" on Wikipedia as a start.
It's lovely to think about the golden days of lazy summer and nothing but mud pies and fun under the sprinkler. But studying does not mean a child can't do those things too. They don't have to do full-on school every day. But they do need some work to keep up skills at a minimum.
Math is a muscle. Use it or lose it. Someone posted that if your son is doing fine in math, he doesn't need it over the summer but would only need it if he were struggling -- not true. He needs to practice those skills or they will get rusty. Same for reading and writing. Everyone will say, "Oh, well, yes, my kids read over the summer, that's part of the fun," but kids also need to do at least some minimal writing, and they should be reading books new to them, and books that challenge them at their next grade's reading level or above if possible.
Check your local library and bookstores; most have kids' summer reading programs where kids read X books over the summer and get rewards for it. As for math, frankly, that's a not-so-fun chore that must be done unless you want your kid to do catch-up in the fall; online sounds like a bore but if you can find a good math program in your area (and in Chicago I bet you can) that is fun, have him do it -- it does not have to be hours and hours. Our daughter does Mathnasium (no homework!) maybe three hours a week in summer at their facility. She also attends a writing "camp" that's one week, half days. That leaves a ton of time for fun and games. And she chooses to go-- she's 12 so we don't force her but she loves writing camp in particular. We go to museums a lot but we also do that during the school year because there are so many where we live.
You can do stuff at home if you prefer.
It's not about some future job years off, or about being competitive with other kids. It's about ensuring a child keeps up not only the content of learning but the discipline of learning. During the school year, kids require personal discipline to keep going and meet their deadlines. A three-month halt in that discipline just makes it that much harder to get back in the groove later.
I would bet that many parents who advocate "let them play all summer, no study, no academics" are parents of younger elementary kids. Once they have middle schoolers they just can't do that any more or their kids are going to lag at the start of school and feel so rusty -- both in terms of academics and in terms of discipline to get things done before they have their fun.
The kids who are at writing camp, or at math, or my daughter's friends who are doing other academically-related camps this summer, are kids who actually enjoy this stuff, maybe because they were always encouraged to enjoy it. Treating academics as some unpleasant chore to be confined to the school year and "escaped from" with glee over the summer sends a pretty bad message-- doesn't it?