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Teachers will get a raise and families will no longer be required to pay $100-a-sport athletic fees next school year under a spending plan approved in the wee hours of Friday morning by the Fairfax County School Board.

The average student-to-teacher ratios will not change in the region’s largest school system, although the board did set aside $2.5 million to pay for more teachers in schools that otherwise would have untenably large class sizes.

The board debated for about five hours and considered more than dozen amendments before passing the $2.4 billion budget by a 7-5 vote. The budget, which takes effect in July, represents an 8 percent increase over this year’s spending, including millions of dollars in state-mandated changes to the public employee pension plan.

This post has been updated.

In the fall of 2009, Chris Shumway paid a visit to his old grade school in Vienna, Wolftrap Elementary.

He had been a student there in the 1970s, and then had grown up and gone off to New York to work on Wall Street. By 2009, he was managing his own multibillion-dollar hedge fund, Shumway Capital.

He visited Wolftrap with the idea of donating something to the school in honor of his third grade teacher, Candace Leyton, who died in 2003 at age 54 of breast cancer.

Wolftrap’s principal, Anita Blain, said she told Shumway that the school had established a beautiful courtyard. Would he like to donate a bench? Or perhaps a tree?

“He said, ‘I’m really thinking more substantial,’ ” Blain said, recalling the conversation.

“He said, ‘Do you need a building?’”

Blain swallowed her shock — “Things like that just don’t happen,” she exclaimed — and embraced the offer. And Monday at noon, Wolftrap will hold a groundbreaking ceremony for the Candace Leyton Innovation Learning Lab.

What first appeared to be a failed campaign to nab Justin Bieber as her prom date instead earned a Virginia high school senior and her sister invitations to one of the biggest awards shows of the year.

According to the Daily Press, Cady Elmer received the invitation to Sunday’s Billboard Music Awards in Las Vegas via a video message from Bieber himself. The video was broadcast Saturday night at her prom.

“I’m going to have a car waiting for you so you can come to the Billboard Awards with me tomorrow. That’s exciting right? I mean, do you think that’s exciting?” Bieber said in the video.

How would you fare on Virginia’s new and more difficult generation of state math tests?

The exams, which are being given across Northern Virginia this month, are designed to require critical thinking, not just memorization and arithmetic. Pass rates are expected to drop, perhaps steeply.

Test yourself below on questions from an older and easier version of the exam — the 2010 math Standards of Learning tests, released by the Virginia Department of Education and available online.

More than 50 teachers, parents, taxpayers and activists took advantage of an opportunity Tuesday to offer the Fairfax school board input on next year’s budget.

Some spoke in favor of benefits for parent liaisons, who translate language and culture for immigrant students and their families; expanded foreign language opportunities in elementary schools; and more money for adult education programs.

Others criticized the salaries of central-office administrators (which have grown faster than teachers' salaries, according to one group’s analysis) and the practice of farming out professional development and teacher training to consultants. (Fairfax will pay the Disney Co., for example, $50,000 to provide a leadership workshop for 50 employees, each of whom will receive Mickey graduation ears at the conclusion of of the training.)

And still others addressed the big issue that the school board will have to resolve before it finalizes the budget on May 24: employees’ pay and retirement benefits.

“It’s time to put your money where your mouth is,” South Lakes High School teacher Lauren Ashley Villa told the board Tuesday. “Otherwise, it’s patronizing to hear you on the air touting that FCPS has the best school teachers, absent of the tag line that you don’t pay them a third of what they are worth.”