In some cases, they punch time cards; in others, they scribble their names on a sign-in sheet.

They take their places in plastic chairs either grouped around tables or scattered haphazardly.

Some immediately pull out crossword puzzles or books. Some knit. Others hold golf-putting contests. One takes out his guitar and strums.

One day last week, another, wearing a leotard and tights, spread out on the floor and stretched before practicing ballet against a wall in a corner.

Nearby, gazing out a window, a man slowly fell asleep, his head in his hands.

It’s all in a day’s work on the city payroll.

For seven hours a day, five days a week, hundreds of Department of Education employees — who’ve been accused of wrongdoing ranging from buying a plant for a school against the principal’s wishes to inappropriately touching a student — do absolutely no work.

In an investigation inside the nine reassignment centers called “rubber rooms” where these employees are sent, The Post has learned that the number of salaried teachers sitting idly waiting for their cases to be heard has exploded to 757 this year — more than twice the number just two years ago — at a cost of about $40 million a year, based on the median teacher salary.

. . .

The Metropolitan Transportation Authority acknowledged yesterday that one BIG reason it wants a 25-cent bus and subway hike is because its vending machines can dispense only dollar coins and quarters.

MTA spokesman Jeremy Soffin defended the increase as fair and said upping it by a nickel or dime wouldn’t be enough.

“The limitations of technology would make a $2.10 fare extremely costly to implement and would provide a much poorer quality of service,” Soffin said.

. . .

Riders weren’t buying it.

“It’s an outrage,” said Anthony Thompson, a Queens engineer. “Our money is being spent because of a hardware defect?”

Recruiter Jisele Lazo, 22, of Queens, said: “It stinks. Why don’t they just leave it at $2? Why are they making it easier for the machines? There are far more commuters than machines.”

. . .

Soffin said smaller change would mean longer lines and riders being saddled with pockets full of silver.

He said the size of the fare hike was not unreasonable because the $2 base fair had remained steady since 2003.

A 25-cent jump would amount to a “cost-of-living” increase for the system, Soffin said.

A rider buying a single-ride ticket priced at $2.10 with a $5 bill would be carting away 11 quarters and three nickels, or 58 nickels, he pointed out.

The machines also would likely run out of change more quickly, have to be filled more often and likely need more frequent maintenance, he said.

“I go to buy some oil and then I come out and I said, ‘Where’s my car?'” she said.

As it turned out, Papalazalou’s car wasn’t stolen — it was towed for being illegally parked in one of the lot’s reserved spaces for employees.

Papalazalou said she was unaware that the section she parked in along the lot’s fence is for employees only. Following her mistake, she paid a fee of $162 to get her car back.

Now Papalazalou said she fears coming to the lot because of the tow trucks looming around the corner waiting to tow illegally parked cars, many of whose owners don’t know that they’re occupying reserved spots.

Marketing executive Barbara Young said she was charged $20 for a trip from Lexington Avenue and 34th Street to Penn Station, double the $10 fare she should have paid under the emergency flat rates imposed by Mayor Bloomberg for the duration of the two-day hackout.

“I took the cab anyway because I had a lot to carry,” she said.

One cabby charged a tourist $100 for a ride from Kennedy Airport to Midtown, more than three times the $30 he should have charged, according to a doorman at the Hotel Pennsylvania.

Marco Segall said that despite hailing several cabs, he could not find one willing to charge him the $15 fare he should have paid under the temporary zoning plan.

One driver even asked him how much he wanted to pay.

“How much am I supposed to pay?” he said. “They’re racking it up, and they know it.”

. . .

Alliance leader Bhairavi Desai said that by taking a stand, she will gain new members and more clout against the city.

Bus drivers, UPS deliverymen, cyclists and pedestrians all said the streets were so much easier to navigate with fewer taxis on the road that they wished the strike would continue.