Q. " Help! I am a working mother of a 13-year-old and summer is coming," writes an Arlington parent.

"The county-run summer program is out this year -- my daughter is too old. Volunteering for the Red Cross, or anything else, for that matter, is out -- my daughter is too young.

"Private camps cost about $150 a week and that type program is good only for a brief time during the summer.

"Is there anything short of leaving a young teen-ager at home by herself (and who knows what else)? What do other parents suggest for this forgotten age group?"

A. You're right; this is a forgotten age, and yes, a lot of things can happen to a Thirteen left at home alone.

Your daughter probably would be fine on her own, although bored, but it would put her under pressure to rely only on herself for 40-plus hours a week.

Nevertheless, 13 is the time to let go.

You've been letting go a little more ever since she was born, but now you have to let go faster. It's a matter of balancing her need for independence against your need for peace of mind.

More than anything else, a Thirteen needs to feel self-sufficient, and particularly to get around on her own. That's why she needs a dozen things to do during the summer, but not in the same place.

When her days are chopped into pieces -- a patch of time spent here; another few hours there -- the days are filled with anticipation and she learns to be responsible for herself and to govern her time.

You can have your daughter bring a friend and a picnic to your office once a week, eat lunch with them outdoors, send them to a museum or to a movie and have them back by quitting time. Or have her meet you with a picnic at the end of the day, and you go together to some free mall concert or activity.

And yes, you will be edgy when she is bopping aound alone on the subway, but your child needs practice to grow up. If you keep her too young too long, one day she's going to try more than she can handle.

There should be some time at home to read and play with makeup, and some to meet extra, satisfying responsibilities, like growing a patch of lettuce and tomatoes and cooking one dinner a week. It's important for any child to feel needed, but particularly at this age.

The rest of the time is spent getting as many new experiences as she can through diversified work and play and classes.

Every candidate in November needs some help now: collating, stapling, stuffing campaign literature into envelopes.

The Special Olympics needs help. Have your daughter call Jean Severy, the volunteer director, at 244-1910, to be a hugger (to hug the winners at the finish line); to hold the tapes; to give awards; to keep score and to help the entrants get from one place to another.

The classes that sound best to us are in your own Arlington, but they're sponsored by the school system, rather than the recreation department.

The career Center, 816 S. Walter Reed Dr., is having a number of substantive classes for motivated teenagers who live anywhere in the metropolitan area. They offer the only science courses we've heard about that aren't remedial: courses in botany, biology and veterinary science -- and they also will have TV production; computer programming; photography; graphics; commercial art; automechanics; speedreading.

Each class costs $40 and runs from 8 to noon, three days a week for three weeks, with the first session starting July 1 and the second, July 22. Anyone living in Arlington gets free school bus pick-up to Wakefield-Lee High School, with a shuttle between the high school and the center and back again. And Wakefield-Lee, like all Arlington high schools, has a swimming pool.

If your daughter is interested in art, the Corcoran School of Art has two four-week sessions, three hours a day and four days a week, for $150.

In drama, Catholic University has its fine, four-week course June 30-July 25, Monday through Friday, 9-2, and longer if your daughter is in one of the weekly productions. Cost: $300 with another $210, plus meals, if you want her to live there.

There also is the Arena's Living Stage, the improvisational theater starting June 23 for three hours twice a week for five weeks, at a cost of $200. Glen Echo will offer eight photography lessons four times a week, for three hours each, from June 23-July 3. Cost: $79, plus film and paper

The Smithsonian Associates have two-hour classes for a week, starting either July 14 or July 21. They are in photography, calligraphy, cartooning, and acting, among other, and most cost between $30-$40.

As long as you're willing for you daughter to be adventurous, this summer could be her best.