This math problem is of the type that students in third grade should expect to see on this year's Common Core-aligned state tests, according to state education officials.

Educators have gotten a few hints into what new, more challenging state exams could look like this spring. To help them prepare more, city officials are encouraging them to review old exams and new sample questions side by side to see exactly what has changed.

While teachers waited for the state to release examples of how they are re-imagining the yearly exams to line up with new, Common Core curriculum standards, city officials offered their own comparison guide. The guide took the form of a slideshow, with examples of Common Core-aligned math and English tasks developed by city officials, and an explanation of how they compared to old lessons.

And when the state’s only batch of sample test questions came out in late June, city officials prepared another comparison, but with official questions and 2010 exam questions. They presented the comparison to principals in June at an annual conference for school leaders, and then gave it to reporters earlier this month.

The comparisons, officials said, show that students can expect to read more challenging texts and see more multi-step math problems and word problems that reflect real-world scenarios.

They include a set of algebra problems for third- and sixth-graders from 2010, followed by comprable problems from a 2013 sample test. One new question, for example, asks sixth-graders to consider a clothing store offering a 30 percent discount on its wares. In three parts, students must not only find the reduced price of several items, but also figure out what an item would cost with an additional discount, or without a discount at all. The comparison question from 2010 is a word problem with just one step, asking students to divide two numbers.

The comparison also show an English language arts text from 2010 and a possible 2013 text, along with several questions that ask eighth-grade students to respond to what they’ve read. The 2013 sample, from Helen Keller’s autobiography, asks students to close-read and explain two ways that Keller’s relationship with language changed in the passage. The 2010 questions are based on “Rufus,” a simplified version of a Kansas newspaper columnist’s chronicle of his dog. They ask students to draw just one example of the main character’s intelligence from the passage and then explain the non-literal use of the word “lost” in its opening.

Information about what this year’s state tests, the first aligned to the Common Core, will look like has come out in dribs and drabs, even as city and state officials have warned educators and parents to expect lower scores.

But more clues are coming next week. State officials plan to brief reporters on changes to the state’s assessment system, field tests, how questions are being developed, and how the tests link to the Common Core.

During a recent presentation to reporters on the new standards, the city Department of Education’s chief academic officer, Shael Polakow-Suransky, said the math questions were not necessarily more difficult, but would be more likely to test students’ ability to solve problems that require multiple steps and apply what they’ve learned in unfamiliar ways.

Nancy Gannon, director of the city’s Office for Academic Quality, said in a phone interview that multi-step math problems also require students to develop and exercise “soft skills” the Common Core is meant to foster, such as the willingness to try harder when an answer isn’t obvious.

“One piece of the Common Core is around building resilience and the capacity for kids to continue trying, persevering in the work,” she said. “It’s not just about computation, it’s about being able to carry a problem through. Hopefully we’ll get a better sense of how well they understand the concepts behind the problem … and where kids are falling off.”

According to the comparisons the city distributed, the state’s sample literature questions draw from texts with a much higher lexile (a unit of measuring the difficulty level of a text) than the 2010 eighth-grade ELA exam. Gannon said she expected to see reading passages’ difficulty rise across the board: In the past, she said, the texts have been so easy that quizzing students about them could not tell whether the students were on grade level, only if they were far behind.

“Our understanding of what is an appropriate text right now is significantly lower than what we’re moving toward,” she said. “For kids said to be reading on grade level last year, as we move to a more rigorous text it will look like their reading level dropped. It will look like kids are sinking when they’re actually not.”

There’s only one real way to guard against sharply falling scores, Gannon said.

“What does the test prep look like for that? It looks like kids reading a lot of complex texts and writing a lot of essays,” she said. “We think the kind of readiness that this requires is actually great instruction.”

The city’s document comparing 2010 test questions and the state’s 2013 sample questions is below.