Veronica Shand brought her children back to school early this year. Really, really early.

Just after 7 a.m. on Saturday — a full two days before students in Maryland’s largest school system go back to class — Shand and her brood became the first of thousands of families to line up for free backpacks outside the Montgomery County Public Schools headquarters in Rockville.

It would be nearly four hours before they’d be let into the auditorium, where Eastpacks, Trailmakers and JanSports were stacked 6 feet high in carts. But it would be worth it, Shand said, upon emerging from the giveaway with four children — each of them carrying a brand new school bag pre-loaded with pens, pencils, paper and other supplies.

“I’m a single mother of six — four still in school,” said Shand, a certified nursing assistant from Rockville. “I couldn’t afford to buy them all new backpacks. It’s just a real blessing to be able to get these for free.”

They were the first of 8,133 backpacks given away at Saturday’s back-to-school fair, and school officials said they could have given away thousands more if they’d had more donations.

Classes also start Monday in the D.C. school system, in several other Maryland counties and in Loudoun County.

On Saturday in Rockville, security scrambled to keep line-jumpers at bay as the queue stretched deep into the Montgomery College parking lot across the street. The clamor for freebies illuminated the striking level of need in an area generally known for its affluence.

“We’re a wealthy county, but we’re also a county with great needs,” Montgomery schools Superintendent Joshua P. Starr said.

About a third of the system’s estimated 149,000 students are eligible for free or reduced-price meals, an indicator of poverty. That means there are more poor kids in Montgomery schools than there are total students in some local school systems.

“This is the real Montgomery County,” Starr said, wearing jeans and a DayGlo orange T-shirt with “Ask MCPS” printed on it.

The Springbrook High School marching band had just performed the ESPN “SportsCenter” theme song near a face-painting tent. A Spanish-language hip-hop song by Wisin y Yandel blared in the direction of the giveaway line. There was a dance party on the other side of the parking lot, and there were free apples, free blood-pressure tests and booths giving away information about Saturday school and music classes and tutors and family services.

Last year’s back-to-school fair in Montgomery was canceled because of Hurricane Irene (which blew through the region just after the East Coast earthquake), so the system gave away 7,000 backpacks on the first day of school. There was a panic in 2010 when the ceiling in the central-office auditorium caught fire the day before the fair, but the 5,000 backpacks stored inside were unscathed.

System officials jokingly wondered if locusts might show up this year, but there were no disasters — other than not having enough backpacks, said Division of Family and Community Partnerships supervisor Denise Stultz.

“I hate running out,” Stultz said shortly before running out.

“A lot of families need our help,” she said, standing between massive carts filled with backpacks. She opened one, from the elementary-school side, and pulled out a package of supplies: composition book, 16 crayons, a dozen No. 2 pencils, a glue stick and a plastic box. “We got these for $9.61 each, including the backpack.”

Some of the 8,133 backpacks were bought and donated by church groups, but the majority were purchased with the $52,000 Stultz and her staff raised in the past year. In a perfect world, “where people realize just how much poverty there is in Montgomery County,” Stultz said she’d have a half-million dollars to buy 50,000 pre-loaded backpacks, which would be distributed to students in different locations.

But 8,133 was enough to cover Dawn Bowens, who got four free backpacks — and thanked everybody within earshot as she left the auditorium.

“I have two children of my own, and I take care of two others,” she said. “They do not want to go to school without a backpack. They want to be like everybody else; they don’t want to be pointed out for not having a backpack. But I only work part-time, and it would be a struggle, kind of hard, if I had to buy these. This really, really helps.”