Mrs. Baker, played by the irrepressible 10-year-old local pop diva Samantha Cassidy, wants a baby and Mr. Baker, the similarly pre-teened Oliver Carson, does not. (On alternate days last weekend these characters were performed by Danielle Hopkins and Jesse Dawson.) Mr. Baker wants a big fat, gingerbread cookie to eat. They fight/sing about it: “Food feeds all your problems unless your problems are food.”

Sugar Rush, a new musical play presented as Theatre by Kids for Kids at the Katharine Cornell in Vineyard Haven, premiered last weekend in two evening and two daytime performances, all of it under the celebrated aegis of IMP.

The story takes place, at least judging by the costumes supervised by Donna Swift (and with a lot of help, we can imagine, from the parents of this all-kids cast and crew), in that happy part of the Middle Ages when everyone had a time-honored job to do and an outfit to do it in, maybe even two so that one could be in the wash bucket while the other was being worn.

Fairy godmothers were rampant in those heady days, and in Sugar Rush a fairy almost immediately appears (Raven McCormack in Cast One on Friday night and Saturday morning and Alley Estrella in Cast Two on Saturday night and Sunday afternoon) to grant both the Bakers their separate wishes with the sweep of a pink-puff wand: Mrs. Baker gets a real live baby boy but he happens to be made of, as the Gingerbread Boy himself expresses it, “The most delicious ginger bread.” So Mr. Baker has an enormous cookie at hand, but his paternal instincts keep him from chowing down on his own kid.

Third-grader Emily Mello plays the G-B in the second cast and another third-grader, Nina Moore, in Cast One — and they are truly cute and feisty and delicious enough to eat, which is what most of the villagers are desirous to do. But here’s where the old nursery jingle kicks in, “Run, run, as fast as you can, you can’t catch me, I’m the Gingerbread Man!”

A trio of red-robed ascetics named Sage, Basil and Rosemary weigh in on how no one should eat anything because everything’s bad for you (except for maybe sage, basil and rosemary). They actually gag on the word “gluten.” Sage is played and sung by Tessa Whitaker, with the back up in Cast One of Alex Habekost and Meghan Sonia and in Cast Two with Hailey Meader and Mackenzie Condon.

The other pivotal parts are played by Sally Caron (One) and Harold Lawry (Two) as Miss Glaze, who’d love to stop the Gingerbread Man in his road-runner tracks by glazing him for her gingerbread museum. Sydney Johnson in both casts plays the Fitness Fox, with a slick solo number convincing all that eating the cutie-pie Gingerbread Boy would be a bad choice since sugar upsets your system in seven ways to Sunday. He himself, because he’s a fox, makes off with the human cookie and gives in to an extravagant craving for sugar. He staggers back to the bakery with an upset tummy. Once again the fairy godmother saves the day.

The musical was created by IMP founder and director Donna Swift, along with her writing partner, Ross Mihalko (he resides in North Carolina but they communicate by Skype.) The duo’s musical partner is Brian Weiland, who grew up in Bourne but now teaches music at the Oak Bluffs School. In his bio he says he can “play any instrument you don’t have to blow through.” For the production of Sugar Rush, he performed on piano and guitar, accompanied by his sixth-grade son, Liam, on bass guitar.

Ms. Swift started her improvisation group, IMP, in 2002, and the evening productions of Sugar Rush featured a number of cast members strutting their improv stuff. Ms. Swift says, “There are over 250 improvisation games out there, and these kids learn to take one of these themes and run with it.”

Other cast members include Katherine Morse, Opal Wortman, Jack Creighton, Alexander Nagle, Victoria Scott, Anne Culbert, Thomas Hopkins, Tripp Hopkins, Tyler Edwards, Tianna Rambonga, Kate LaPlume, Patrick Dutton, Julia Crocker, Anne Culbert, Sarah Felix, Megan Delphous, Harold Lawry, and Summer Cardoza.

Clearly Ms. Swift respects the talents of her students enough to give them all a chance to shine.

A few more nods must go to the excellent production staff, again all minors: assistant director and stage manager Della Burke; production manager Mariah MacKenzie; stage crew, the IMPers Ashley Girard, Mariah MacKenzie, Chris Pitt, Aaron Wilson, Clare Boland, Amy Fligor and Carter D’Angelo.

Upcoming IMP events will start with a new session of after-school improv classes on Feb. 2; Feb. 5 is IMP Camp Day at the Space; Feb. 19 ushers in Story Theater at the Space. For details, see the web site imp4kids.com.