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It’s a Monday morning at Willow Ridge Elementary School, and a group of 4-year-olds are learning how caterpillars turn into butterflies.

The pre-kindergarten students are sitting cross-legged on the floor and they’re shouting out names for their metamorphosing bugs: Power Ranger. Cocoon Worm. Shaky. Shark.

Everyone has a hand in the air with an idea. A few minutes later, the children let loose for their “silly” dance. Bounce. Freeze. Giggle.

Behind all the fun, educators say, is important classroom time that lets some young students catch up with their peers before they enter kindergarten, and state lawmakers want to see more 4-year-olds in pre-K for longer hours.

“It’s not all just play time and babysitting,” said Michael Baumann, Sweet Home’s assistant superintendent for human resources and planning. “They’re doing a lot of word recognition. They’re doing a lot of fine and gross motor skill development. They’re really working very closely in language and communication.”

The Sweet Home pre-kindergarteners are among nearly 7,000 in Erie and Niagara counties who go to school each day. Some, like those in Sweet Home, attend pre-K at their local elementary schools. Others attend district programs at area preschools. For now, almost all of them attend for just a few hours a day in pre-K slots limited by space and funding.

A new wave of state funding that will be available for full-day pre-K programs during the 2014-15 school year could open up new opportunities for the state’s youngest public-school students.

But how state lawmakers chose to disburse the $340 million across the state has raised concerns that it will primarily benefit New York City, where a political debate between Mayor Bill de Blasio and Gov. Andrew M. Cuomo culminated in a deal in which $300 million of the funds were earmarked for New York City.

The rest of the state’s nearly 700 school districts must compete for a piece of the remaining $40 million in 2014-15 if they want to expand their pre-K programs.

“Let’s put it this way,” said Rick Timbs, executive director of the Statewide School Finance Consortium, which advocates for more equitable school funding on behalf of more than 400 school districts across the state. “New York City has about half the kids, but they got 87 percent of the money. So you start saying to yourself right off the bat, ‘Wait a minute. What’s that all about?’ ”

Some Board of Regents members expressed a similar concern about the funding distribution at a meeting last month.

While many parents in Erie County suburbs choose to hold off on sending their children to school until kindergarten, some districts, which face some of the same challenges as urban districts like Buffalo, feel they need to be able to offer full-day pre-K.

“People debate, should a 4-year-old go to school all day? Certain kids need that environment to kind of catch up,” said Cheektowaga Central Schools Superintendent Dennis Kane.

At Cheektowaga Central, where more than half of the children are eligible for free or reduced lunch, the school district offers four half-day classes at Union East Elementary and another half-day class through Mary Queen of Angels School. Cheektowaga Central gets about $280,000 in state funding for its prekindergarten program, The district has estimated it would cost about that much to expand the program to full-day.

“In terms of giving those kids a fair share when it comes to their development and being truly prepared when they get to kindergarten, we have a lot of the same needs,” Kane said. “And we would hope that we can be looked upon as favorably as they are.”

Other districts don’t have an immediate plan to expand to full-day pre-kindergarten, despite the potential for new funding. At Sweet Home, the district offers about 144 slots for half-day pre-kindergarten and gets about 125 applications each year.

“We’re not at capacity yet,” Baumann said. “So we’re really not anticipating it having a lot of impact on us.”

email: djgee@buffnews.com