Click image for enlargement. Illustration by David Stroud.

By Memorial Day, summer vacation is alluringly close but not quite in grasp. Children salivate at the thought of boundless free time.

By Labor Day, lots of same are more than glad to have rejoined their friends again in a regimented classroom.

Wise parents have ways to stave off summer boredom beyond opening the wallet -- repeatedly -- to pay for expensive, prepackaged excursions to museums, malls, arcades or amusement parks.

Consider putting the children's brains to work -- not at hard labor, but at brainstorming a fun backyard children's event, and then holding it.

Backyard circus? Or how about a pet show, talent show or swimming-pool Olympics? Whatever the project may be, the youngsters get to think it up, "sell" it to their parents, plan it out, set it up , talk it up -- to recruit other kids as participants or customers -- and, finally, pull it off.

The beauty of this stratagem is that it will consume a lot of unstructured free time. We're only half kidding.

It will definitely take hours. But another formidable beauty is the notion that by producing a for-kids event, your children will integrate lots of worthwhile intellectual skills in the process.

Las Vegas educator William Speer calls it "a child's version of systems engineering."

That's a fancy way to say that children who are involved from start to finish in carrying out an event will use the following skills: imaginative pooling of ideas, problem identification, problem solving, reasoning, and communication -- both to win parental permission and to devise invitations or advertising fliers. They will also have to logically sequence their steps of preparation. They will have to take and delegate responsibility, which may in turn require negotiation skills.

Speer is a professor of curriculum and instruction at the University of Nevada, Las Vegas. He is also a director of the Center for Mathematics and Science Education at UNLV.

Not to mention, the young impresarios will also use math skills to price the supplies they need to buy, to measure dimensions of props or craft items, or optimistically, count and divide any proceeds.

Buy supplies? You weren't thinking that because you didn't have to shell out for Circus Circus that this would be free?

Not a chance. Permitting the offspring to hold a fun event may or may not cost money, but it will cost some parental time, Speer guarantees. And yet, parents will have to do a balancing act.

On the one hand they will need to help the child or children pick a do-able event. Las Vegas mother Becki Breed recalled how three summers ago, daughter Bethany, then 8, wanted to hold a play with friends to raise money for the needy.

"I thought of a play, because I was good at acting," said Bethany, now 11, who is home schooled.

Becki, however, pointed out it might be hard to get children together for enough rehearsals, since the date Bethany had picked for her fund-raiser was less than two weeks away. Together, parent and child modified the concept to a talent show, so participants could practice on their own. Bethany found another advantage to the revised scheme. Each child could do what he or she was good at.

Her show was a wild success. She ended up with seven children who sang, danced, did gymnastics, played guitar, recited a poem or explained a science project from school.

About six families turned out.

Bethany raised about $20, due to the extremely low cost of admission, which she donated to her church.

On the other hand, if the kids say, "Hey, let's put on a show," parents need to restrain themselves from micromanaging, Speers adds.

"Parents can't let them just run wild with the ideas. But frankly the reverse is true, you can't handcuff them, either," Speer warns. If parents "provide too much direction or too much information," children won't take ownership of the project.

Once the generations agree on a basic concept, parents need to monitor from afar, according to Speer. But "it does require 'touch points,' " he says, by which he means interim checks so parents can monitor the children's progress, and troubleshoot as needed.

The feeling of mastery that comes from completing a difficult, many-element project simply fills a person's sails, Bethany Breed agrees. Not only did her acting talent put on a show, they also cooperated to jointly make a dinner for adult guests before the show. Everybody got to strut in the limelight, and the proceeds when to a worthwhile cause. "It was a little stressful," she concludes. "It was pretty fun."