Correction: An earlier version of this story inaccurately reported the school board’s June 26 vote on the Monday half-day issue. The story has been corrected.

The Fairfax County School Board is scheduled to vote Thursday on using $7.6 million to cover the estimated cost of extending Mondays from half a day of classes to a full day for elementary students in the coming school year.

School officials acknowledge that the cost amounts to millions of dollars more than they expected to spend on the policy change, the result of difficulties in getting a portion of the funds from the County Board of Supervisors.

The school board approved eliminating half-day Mondays in late June, which would give elementary students an extra 75 hours of classroom time during the school year. But negotiations between school administrators and county officials about how to fund that have been murky.

After the idea surfaced publicly in June, School Superintendent Karen Garza sat beside Sharon Bulova, chairman of the Board of Supervisors, at an orchestral concert at Luther Jackson Middle School on June 11. The two discussed the proposal to end half-day Mondays, Bulova said.

“I had explained at that concert that I would be happy to work with her,” Bulova (D) said in an interview, noting that she offered to help Garza find county funds to defray a portion of the costs.

The next evening, at a work session of the school board , Bulova discussed the proposal and her meeting with Garza, saying the full-day Mondays was “something that I would like for us to work together to see how we could make that happen and how we could make that a priority in funding.”

Supervisor Jeff C. McKay (D-Lee), seated next to her, offered to do the same.

“You will have my unwavering support to find a path to do it sooner rather than later,” McKay said. “I can’t think of a better use of resources than to do this.”

Also present was Pat Herrity (R-Springfield), who did not weigh in publicly. In an interview, Herrity said that although he supported the idea, he thought that it was a school system decision that the schools would fund without asking for more taxpayer money, especially since the school system had $38 million in unspent cash left over from the prior year’s budget.

“When you’ve got a $38 million surplus, it looks a little out of bounds to be coming back and asking for more money,” Herrity said.

At a June 16 meeting, School Board Chairman Ilryong Moon mentioned that he had spoken with Bulova, who reiterated her support for the idea.

Of the supervisors, Moon (At Large) said he felt “no doubt whatsoever that they are going to come through with some sort of support — financial support.”

On June 26, the school board approved extending Mondays by a 10-1 vote, with the dissenting vote cast by board member Kathy L. Smith (Sully). (Board member Tammy Derenak Kaufax was absent.) Several school board members mentioned what they described as a financial commitment from the supervisors.

“It gave me the confidence that we could afford to do this,” said school board member Daniel G. Storck (Mount Vernon).

The next week, on July 1, supervisors John W. Foust (D-Dranesville) and McKay presented a motion to the board to consider providing funds to the schools to cover the costs of extending Mondays. What is usually a routine vote became a heated discussion about the school system’s finances. Some supervisors said they were surprised to hear from school officials that the county had allocated money for the effort, because the board had not.

Supervisor Michael R. Frey (R-Sully) said school officials had not mentioned a need to end half-day Mondays during their lengthy budget negotiations.

“Never once — this was not something that came up,” Frey said, noting that he supported the merits of the measure. “The strategy is they got what they wanted and what they thought they could out of us. Now they are going to sneak in the back door.”

Supervisor Catherine M. Hudgins (D-Hunter Mill) said she also approved of the change but not the recent moves to get funding.

“This makes me feel that something has been slipped under the table,” Hudgins said. “To me, it’s not the way we should be doing business.”

Smyth said that the county does not use its own carryover funds on recurring expenses.

“If the schools are willing to look at their budget and come up with money for this, more power to them,” said Smyth (D-Providence). “But dump this on us at carryover for an ongoing expense is something that I don’t think is appropriate.”

Two weeks later, the news hit the school board at a work session as it was discussing how to spend the leftover $38 million.

“Have we found out now that the Board of Supervisors is not interested in funding our full-day Mondays?” asked Pat Hynes (Hunter Mill). “That was part of our consideration for passing this.”

Bulova, in an interview, blamed the confusion on a misunderstanding of county budget procedures.

“I’m the chair of the board, but I can’t allocate money on my own,” Bulova said. “It’s not a Sharon Bulova decision. As sympathetic and supportive as I am, this is something our board would need to vote on.”

Garza said in a written statement that she hopes supervisors will still fund the shift.

“The change to full day Mondays is a positive one for our students, our teachers, our families and for our county as a whole,” Garza wrote. “Because of overwhelming support in our community, I remain optimistic that our county leadership will provide funding for this important change.”