Caitlyn, 17, smiles with surprise at how readily the rhyme rolls off her tongue. Her grandmother Helen used to recite it to teach her stitches to crochet when she was 5 years old: “In the front door, out the back, through the window, and off comes Jack.”

Caitlyn fondly remembers the after-school hours she spent in her grandma’s quilting shop, where Grandma would get her started on a project and then gently coach her on the technique of crocheting, knitting, and later sewing as they worked in tandem.

“I love the bond that we created by crocheting and knitting,” she says. “As I got older, it became, and still is, a way that we connect. No words are needed. It’s just our quiet time of companionship interrupted by my occasional need for help untangling a knot or advice on getting past a challenging part of the pattern.”

What better metaphor for bridging the generation gap.

But before you call up a Norman Rockwell image of a gray-haired, bespectacled woman knitting in a rocking chair, needlecrafts of today are not your old-fashioned ball of yarn. Granny squares are a thing of the past.

“Knitting has been coming in and out of popularity for decades,” says Debbie Stoller, author of The New York Times bestsellers Stitch ‘n Bitch: The Knitter’s Handbook (Workman) and Stitch ‘n Bitch Crochet: The Happy Hooker (Workman). She is a self-proclaimed woman on a mission to “take back the knit.”

Stoller comes from a long line of crafty women like her maternal grandmother, who knit socks for all 15 members, 30 feet, in her family.

In 2000, Stoller started a New York City Stitch ‘n Bitch group (an open forum for anyone, male or female, interested in learning to knit) and she suddenly noticed people knitting everywhere: “coffee shops, lunch lines, movies, even in bars.

Some of these women were pierced, dyed, and tattooed. Others were fashion-forward, trendy types. Still others were of the crunchy-granola variety. And plenty of them could not be categorized at all,” she says in the introduction to Stitch ‘n Bitch.

Knitting today is hip as well as nostalgic and timeless — a truly equal-opportunity hobby. Crafty grandmas are but a small part of a legion of knitters (53 million strong according to the Craft Yarn Council of America) engaged in a fresh and seemingly lasting revival of knitting and crocheting.

The new knitters include retirees, housewives, movie stars, and counterculture hipsters. Some knit simply for the love of it; others wield their needles in a feminist statement to honor an undervalued women’s art form. Young knitters often embrace handicrafts in rebellion against a mass-produced, technology-saturated world.

Motivations aside, knitting is the perfect activity to share with your grandchildren. Assure them they’ll be in good company with crafters Julia Roberts, Cameron Diaz, Sarah Jessica Parker, and Hilary Swank.

If you’ve never hooked a stitch, invite your grandchildren to learn with you at a class or with a kit or book. Do simple projects like potholders or scarves, or make more adventurous items like monkey-faced backpacks, skull-and-crossbones ski hats, and heart-emblazoned string bikinis. There is a project for everyone.

Kits make great introductions to knitting and crocheting. The Craft Yarn Council of America is an excellent online resource for getting started as well. You can find needles, hooks, and projects made especially for kids at specialty yarn stores.

Here are a few age-specific knitting and crocheting tips and resources:

For ages 3 and older:

Stoller recommends providing younger children with some colorful yarns, lacing grids, and safe plastic tools to explore and play with hooking projects. You can make your own lacing toys by cutting out simple shapes — teddy bears, hearts, stars — from felt or foam sheets and use a hole punch to a create a simple pattern for toddlers to lace through.

For ages 5 and older:

Finger knitting is perfect for children in this age group since it requires no needles or hooks — just yarn and practice. Finger knitting produces a long, thin strip of stockinette stitch that they can use to make scarves, ties, belts, or they can make wraps or even blankets when they combine strips or braid strips for the larger pieces.

Finger Knitting 2 (Heian) by Suzuki Katsino includes illustrations and easy instructions. You can also find illustrated, step-by-step guides online.

For ages 7 and older:

There are many great, all-inclusive kits for kids in this age range. Some to try are: The Here Knitty Knitty Knit Kit from The Land of Nod, which comes in a charming wicker basket and includes simple instructions, child-friendly wooden needles, and 100 yards of rainbow acrylic yarn. Potholders and Other Loopy Projects (Klutz) by Barbara Kane is an all-in-one kit for kids 6 and older.

For ages 10 and older:

Crochet: Learn to Crochet Six Great Projects (Klutz) and Knitting: Learn to Knit Six Great Projects (Klutz), both by Anne Akers Johnson, are all-in-one kits for making fun projects including a purse, a hat, and a chic scarf. Books to try include Knitting for Dummies (For Dummies) by Pam Allen, Tracy Barr, and Shannon Okey, Crocheting for Dummies (For Dummies) by Karen Manthey and Susan Brittain, Stitch ‘N Bitch: The Knitter’s Handbook, and Stitch ‘N Bitch Crochet: The Happy Hooker, both by Debbie Stoller.

Mary, crochet coach to 9-year-old granddaughter Julia, puts it best, “Julia and I love shopping for yarns, picking out colors ,and just seeing what happens.” Most recently, their collaboration has yielded a plum and sage-green hourglass-shape baby blanket for Julia’s first cousin Una.

“I love the way it turned out, even if it’s not square,” giggles Julia.

Roll with it — just one of the many lessons held in a ball of yarn and some quality time spent with grandma.