This year, Jackie Xuereb is teaching her sixth grade math students how to add and subtract fractions with unlike denominators. But next year, new standards will call for students to know that information before they enter her class.

Xuereb, a sixth grade math teacher at Washington Heights Expeditionary Learning School, is among the city math teachers preparing to swap the state’s learning standards for the Common Core this fall. And like many, she is struggling to keep the two sets of standards straight as the new standards move some topics an entire grade-level earlier than in the past.

“A lot of what used to be sixth grade standards are now taught in fifth grade,” Xuereb said. “I feel that I’m going to have to be really mindful and cognizant of this in my planning for next year. The kids are going to have these huge gaps.”

New York City piloted the Common Core standards in 100 schools last year and asked all teachers to practice working with them this year. Next year, every teacher in every elementary and middle school will be expected to teach to the new standards, and state tests will be based on them. Department of Education officials have argued that a full-steam-ahead approach is required because moving slowly would deprive students of the Common Core’s long-overdue rigor.

But some say that this approach will pose a special challenge for math teachers, particularly in the middle school years, as students begin learning advanced concepts that build on each other sequentially. William Schmidt, an education professor at Michigan State University who has researched the effect of the Common Core on learning, said students who miss a lesson the first time around are at risk of missing the concept entirely.

“If it’s done really carefully it might work, but that would be my worry, that this would require fairly careful thought about how to do that across the grades so that what’s happening in one grade will line up with the next,” he said. “If they’re not ramping this up from first grade on in a logical fashion … then the transition to more advanced math will be horrendous, too.”

The city has offered some help. Two weeks ago it published suggestions for topics teachers might tackle after the state tests, the last aligned to the old standards. And officials recently urged principals to use unused snow days in June as planning days for teachers preparing for the next phase of the rollout, which will feature two Common Core-aligned units and exams aligned to the content of the standards.

But some teachers say they have had to wait too long for clear direction. Molly Elverson, a seventh-grade math teacher at M.S. 228 in the Bronx, said she anticipates many stumbling blocks next year as she reconciles the new curriculum expectations with the realities of what students come to class prepared to learn.

“Integers are in seventh grade in New York State, [but] for Common Core, in sixth grade. So when do we start?” said Eleverson. “It’s all the logistics of it, figuring out when am I going to incorporate this, when am I going to have the time? And when am I supposed to assume they have learned it all?”

Similar shifts abound. For example, the Common Core tells teachers to move their units on computation with fractions  backwards, to fifth grade, even though that unit is now typically introduced in sixth grade. It also moves some concepts forward a year — such as the Pythagorean Theorem, which is taught in seventh grade but will be taught in eighth in the future.

Elverson said she feels fortunate to be part of a small math department of just three teachers who talk frequently. They have met as a group to discuss the rollout and agree upon when to teach integers and other concepts. But Department of Education resources to aid their discussion have been slow to arrive.

Deputy Chancellor Shael Polakow-Suransky said the city has helped schools as much as it can, given that the state has not yet released a “final blueprint” for next year’s math expectations or offered sample Common Core-aligned test questions. For the 80 percent of city schools that are still using the math curriculum the city mandated in 2003, the Common Core is going to mean radical changes, he said.

“It’s true that this is going to be a change in terms of the topics that are taught and the number of topics. Planning for that is difficult given that we don’t know all the information at this stage,” he said.

Polakow-Suransky said the city would be delivering more guidance to schools as it learns more. “I don’t know if it will be as early as everyone wants it to be but it will be before the end of the school year,” he said, adding that the department would allocate funding so schools can pay for curriculum planning sessions, ideally over the summer.

Xeureb said she would welcome the additional resources but is worried about waiting too long for them.

“What I do during my summers is I plan. If they don’t have a curriculum, that’s what I’m going to do this summer. I’ll have to sit down and really start doing it myself in July,” she said. “I can’t just take something and print it out — if they have a curriculum on the internet, I’m going to edit and revise it myself based on who the students are, so it would be nice to have it now, while we’re still in school and can plan as a department more easily.”

Xuereb and the other math teachers at WHEELS will attend a training conference held by the National Council for Teaching Math this summer, and she also devoted some time this school year to preparing her students for concepts that have been moved from seventh grade to sixth.

Tacking Common Core topics onto their existing curriculum increased Xuereb’s workload, but in some ways it was no different from what she does every year to get her students to the same starting point after they arrive with widely varying math backgrounds.

Indeed, some students have always arrived in class in September without adequate preparation, a reality that Josh Thomases, the city’s deputy chief academic officer for instruction, said justifies the city’s speedy Common Core rollout.

“As long as I have been an educator, there have been complaints from schools kindergarten through college about how their students are unprepared,” he said. “This work becomes more challenging in the face of a push towards understanding what it is to have standards. In this city, you can find examples of schools that are figuring this out, with the same resources as other schools, in really exciting ways.”

New York State is rolling out the Common Core in full earlier than many other states, but teachers elsewhere are being asked to adopt the new standards with even less preparation than city teachers are getting, according to Schmidt — making teachers across the country in for a rocky transition, he said.

“Any time you shift — and this is a fairly radical shift — there is no simple, easy way to do this,” Schmidt said. “It’s going to be hard on the kids, hard on the teachers, and when the first set of tests come out it’s going to be a miserable set of results. It’s all part of the process, and this is simply the best chance we have to give our students a good mathematics education.”

Already, teachers say the approach of next year’s Common Core-aligned tests have already wreaked havoc on their students.  Xuereb and Elverson both said questions on this year’s sixth- and seventh- grade exams threw students for a loop by asking them to complete tasks that under the current standards they weren’t expected to know.

“My kids kind of had breakdowns in the classroom because they saw a lot of these questions this year that I had never taught them because it was Common Core,” she said. “I know I had prepped my kids to say there are some field questions for next year, but you could see the effect on my students. They were visibly upset. It made me feel like they lost confidence in me a little bit.”

To avoid test anxiety and smooth the transition, Ryan Hall said teachers at his school, Williamsburg Collegiate Charter School, opted to align all of this year’s lessons to Common Core math standards. That practice-run far exceeds the city’s one-unit mandate, and he said they hoped it would leave students better prepared for high school, where the curriculum expectations are also changing, though more slowly.

“It was tough this year because I had so much more material to cover,” Hall said. “I taught every eighth-grade math standard, I taught every eighth-grade Common Core standard, and I’m trying to teach every ninth-grade algebra Regents standard.”

But he said no amount of planning will be able to compensate for the scale of the changes.

“The transitional years are really confusing because the Common Core is designed assuming a certain knowledge that [students] are coming into the grade with,” Hall said. “It is going to be pretty complicated for the next couple years, to ask, ‘what have they been exposed to, and what gaps will we need to fill anyway?’”