Q. "My husband and I have a question that many working parents must face: How can we arrange a pleasant summer for our 13-year-old daughter in Fairfax County? She will start high school in the fall.

"We both work full time and can't take a leave of absence to be at home during the summer. Our daughter feels very strongly that she is too old for a babysitter and doesn't want to go to camp again or attend summer school.

"We can afford any reasonable approach to solving this problem."

A. Many 13-year-olds are tired of camp and most are too old for sitters. Yet everybody needs some kind of constraints to get the most of their day and feel productive. This is where self-esteem comes from: The more you do, the more esteem you get, and the more you get, the more you want to do.

This is not to say your daughter will be busy all the time. This is also a great age for sleep, for lolling, for imagining what it's like to be a grown-up--and often convincing yourself that you are. You can expect your daughter to revel in her new privacy, spending hours learning how to put on make-up, walking in high heels and trying her hair in new ways. (In contrast, boys wait a year or two and then use their time alone to flex their muscles in front of the mirror, to look for fuzz above their lips and read Playboy with a new longing.)

These are all perfectly normal pastimes, but there are many more hours in the day.

If your 13-year-old expects to be responsible for herself, you need to require her to act responsibly: to assume some duties in the household, including dinner once a week; to learn some new skills; to do something she's never done before; to read more than usual, so she won't feel as awkward in high school.

Your daughter also should get a job.

The trick is in the amount of time she works. At this age, and in this culture, a daily job is fun for 2 hours, a chore for 4, and overwhelming for any longer.

What kind of job? The kind she invents.

She can make a dandy sitter for the someone old enough to be fairly self-sufficient and young enough to think a 13 should be obeyed. A sitting service for several 8-year-olds works well, so long as she doesn't have a friend help: The young children would be forgotten while they visited.

She can be responsible for these children around a swimming pool--providing they can swim--or can handle two at the Smithsonian buildings or the zoo, if she's familiar with the subway system.(If she's not, it's definitely one of the skills she should learn this summer.)

Not all jobs will be paid; indeed, most will not be.

The tighter city, state and federal budgets are expected to cut many public services this summer, making them rely more on volunteers. To offer to read to children for an hour in the library, or to help in a day-care center would be a great help, if she can be expected on a regular basis. Even though your daughter won't be paid in money, she will be paid in experience and self-confidence, which will make her a better, more sought-after sitter.

If little children hold little interest, there are other options: to visit with old people in a home, to help package food for a Meals on Wheels program, to volunteer at a pet shop or animal shelter.

And then there are the elections. Candidates will be swarming around Fairfax County once again. Whether they're running for the school board or Congress, they will need help. To some teen-agers, nothing is more exciting than hanging around election headquarters. The work isn't glamorous, but running errands, copying position papers and stuffing envelopes are all appreciated and necessary.

Volunteering is a good introduction to the work ethic. The child who learns to value her work according to its quality, speed and usefulness always will judge her work by these measures, not by the money she makes.

And for new skills: Aside from learning the metropolitan area transportation system--by running all those family errands to get the suitcase fixed here, the blender there--both boys and girls need to learn independence by college. They need to know how to mend and sew, do their laundry and iron, cook, paint, patch plaster, do simple carpentry and type.

And then there is the computer. In 10 years people who can't use computers will be the illiterates of the job market. Although typing isn't required first, it does make it easier, since the keyboards are almost the same. Besides, the machines are a blast. The 12- and 13-year-olds who have access to computers are so intrigued that they are quick to learn programming too, which ought to take care of summer all by itself.

There will be hundreds of classes this summer, although the schedules aren't set yet. Besides your own county facilities, some of the best have been given by the Arlington County Career Center; Glen Echo (run by the National Parks Service); Smithsonian Associates; Friends of the National Zoo; the Capital Children's Musuem and the Corcoran. A short class once or twice a week is not the same as summer school.

If your daughter were to drift about she would spend more and more time with other young drifters, and all the temptations likely to be offered. The best-reared child finds it hard to say "no" at 13 to the same things she will dismiss rather easily at 16.

So long as your daughter has a schedule for about half of her time--and you know where she is, and with whom, all of the time--she will end the summer with a new self-confidence, and at a time when she needs it most.