“All right, guys, look at this one,” the teacher, David Witt, tells two fifth-grade girls. “Is this the smallest of all these?”

Mr. Witt, an elementary-school science teacher who is one of the instructors at a Fifth-Grade Preparatory Academy at P.S. 89 at Queens, walks the students through a problem they both got wrong on their final practice test before tomorrow’s citywide math test. After an explanation of place value, both girls point to the right number, 1.05.

“If you can get rid of a couple of wrong answers, if you guess, you have a 50% chance,” Mr. Witt tells his pupils. “It’s like flipping a coin.”

Last year at this time, chaos prevailed at the city’s public elementary schools. A few months before, Mayor Bloomberg’s policy to hold back failing third-graders had been approved by a policy board only after three members who opposed it were removed. Demonstrations were held outside City Hall and the neighboring Department of Education headquarters at Tweed Courthouse. There was talk about families protesting the new testing requirement by having children take sick days when the standardized math and English tests were given.

This year, fifth-graders as well as third-graders are being held to the mayor’s plan to end “social promotion,” the practice of letting struggling students advance so that they don’t fall a grade behind their contemporaries. But last year’s uproar surrounding the citywide testing has subsided. The deputy chancellor for teaching and learning, Carmen Farina, said she hasn’t received any frantic calls or reports of crises.

“We were so calm, I forgot it was test day here,” Ms. Farina said of last Tuesday, when the English Language Arts exam was administered to students in the third, fifth, and sixth grades. “I think we’re kind of getting used to this.”

Tomorrow, students throughout the city take the math exam. The tests’ results, to be announced in June, could determine whether fifth-graders and third-graders are promoted to the next grade or must repeat a year of school. The scores could also be crucial to Mr. Bloomberg as he prepares to convince voters that his education policies have started to improve the country’s largest school system.

Despite the import of the exams, the “at risk” students at P.S.89 on Saturday morning said they felt prepared.

“I think I’ll do good,” a 10-year-old, Karina Lopez, said. “I think there are going to be division problems, so I think I will know them.”

She said the skills she learned at the special weekend review sessions helped her on the English exam last week.

“It was hard,” she said. “But when I read the first passage, I looked back. … That was a strategy that I learned in Saturday school.”

She said she felt like she came up with the right answer after rereading the passage.

Another 10-year-old, Christopher Caceres, said he learned a new vocabulary at “Saturday academy.” He said the most important word he learned was “inference.”

“I thought it meant to guess an answer,” he said. “It really means to make a good guess.”

The English exam was tough, he said, but he’s ready for the math.

Karina and Christopher were among more than 100 fifth-graders who attended the last of 24 sessions of the academy this weekend at the Elmhurst elementary school. Thousands of fifth graders at more than 100 elementary schools throughout the city have been practicing math and reading skills at similar programs since October, as part of the mayor’s new plan to end the social promotion of fifth-graders.

Ms. Farina said the students at the Saturday sessions have been coached in specific literacy and math skills, as well as in test-taking strategy and test-taking stamina. She said classroom teachers have also been integrating helpful test taking skills, such as stamina and pacing, into everyday lessons, so all students are prepared for the exams. Plus, she said, this year for the first time, parents have come to schools for special sessions on how to help their children prepare for the standardized tests.

Once the scores are in, Ms. Farina said, the department will crunch the numbers to find out if the students who attended the Saturday sessions more regularly performed better on the exams.

“I’m hoping we’re getting a lot of bang for our buck,” she said.

Regional and school-level officials said initial indications look positive.

“We all feel better this year than we did last year in terms of growth,” the local instructional superintendent in charge of P.S. 89, Diane Kay, said. She said there has been a focus all year on “targeted intervention,” using assessments to find problem areas and then helping children improve those skills.

Region 4’s director of intervention services, Eva Chejfetz, said schools throughout Queens have been focusing on providing interventions, and then asking, “If this isn’t working, what might be better?”

The Region 4 supervisor of the Saturday program, Karen Marino, said the attendance rates, which hovered around 90%, are a testament to the program.

“Children are getting up on a Saturday to come to the program,” she said. ‘That’s an important indicator.”

The principal of P.S. 89, Casper Cacioppo, said it seems as though the fifth grade weekend sessions are paying off, and he predicted students’ scores would improve on the standardized tests.

A teacher at P.S. 89’s program, Suzanne Constant, said her students actually thanked her Saturday morning for preparing them for the English exam.

“I think it was a great program,” she said. “Overall, their confidence was boosted tremendously.”