When Denver Public Schools counselor Patricia Vaughan noticed a third-grader leaving the building with a bulging backpack, she asked him what was inside.

She was stunned to see that the bag was full of food for him and his family. The youngster, who was the best tetherball player on the playground, had been letting other children win in return for food from their lunches.

"He very proudly exhibited all the food he had negotiated for at the lunch table," she said. "I didn't realize that there was this kind of need, and that kids were addressing it on their own. I felt glad that he was resilient enough to come up with a solution to take food home to his family."

The conversation with the boy made Vaughan realize that many of the children who receive free and reduced-cost breakfasts and lunches at school during the week went hungry on weekends and during school holidays. She began looking for a way to ensure that the children had food when they weren't in school. Vaughan soon discovered that food banks, social service agencies and schools around the country were facing the same issue. The popular solution: Backpack food programs, where students take a backpack full of enough shelf-stable food to eat over the weekend.

The programs have sprung up around the country as officials discover the need, said Karrie Denniston, vice president of Feeding America, a leading domestic hunger-relief charity.

"It's such a presenting need across the nation," she said. "It's really a very hidden epidemic."

Demand for the program increases every year, she said. In 2010, the organization supplied 5.8 million backpacks, up from 2.1 million in 2008.

When Vaughan started her school's program in the fall of 2009, she provided food for 30 backpacks. This year, she anticipates sending food home with more than 350 kids.

Often school personnel realize the problem after noticing other trends like an increase in discipline problems on Fridays, as children realize they will likely go without meals for two days, or more Monday morning visits to the school clinic, where kids go because a lack of food has made them tired or dizzy.

The programs operate fairly simply. Volunteers pack the backpacks full of groceries like granola bars, easy-to-prepare canned or boxed food, apple sauce, peanut butter and jelly, juice boxes, canned fruit and vegetables and oatmeal. Some programs provide fresh fruit and vegetables. Once the bags are packed, children take them home over the weekend and return the backpacks on Monday.

The cost of filling a backpack ranges from $2 to $8 a week depending on how much food is donated and whether the program is big enough to buy in bulk.

"It's such a simple solution," Denniston said. "It's so easy to love this program."

The program also helps children academically, said Stan Curtis, founder of the Louisville, Ky.-based Blessings in a Backpack.

"Children learn best when all their basic needs are meet," said Curtis, whose organization provided more than 37,000 kids with weekly backpacks of food last year.

Principals routinely tell him that test scores, attendance and behavior improve after the program has begun, he said.

At Lowry Elementary School in Denver, teachers have noticed a lot of positive changes since the program began, Vaughan said.

"It puts them on a level playing field with every other kid," she said. "Their belly is full, and they can all start from the same spot."

Before her children started bringing food home from the school, Janice Wright often had to visit the food bank at the end of the month in order to feed the family.

"The kids always have something to eat," the Denver resident said. "They love it."

Helping families offer their children nutritious meals during the weekend also helps build a sense of community at the school, said Dollie Cottrill, principal at Price's Fork Elementary School in Blacksburg, Va.

"We're always looking for ways to help our children and families - especially in the last few years with the down economy," she said.

Children stop by the nurse's office and grab their backpacks on their way home on Friday afternoons. The pick-up is very subtle so that other children in the building don't realize what's happening, Cottrill said.

"It's a privacy issue," she said. "We respect that this might not be something you want to advertise."

The program, which is organized by nearby St. Michael Lutheran Church, has garnered support from local universities, businesses and civic organizations, said the Rev. John Wertz.

"Folks have been amazingly generous," he said. "The idea of hungry children stirs something in people's hearts."