For the first time in a decade, city education officials have selected new math and reading curricula for the school system — a move that significantly changes what students in elementary and middle schools will be taught.

The change was prompted by the introduction of a more challenging set of state standards, known as the Common Core, which calls for students to read more nonfiction texts in English and to focus on fewer topics — but in greater depth — in math.

Principals are being given several months to select from a number of curricula created over the last year by five vendors, including Pearson, the firm that produces the state’s high-stakes exams in grades 3 through 8.

Education officials are also recommending an English curriculum available for free on the state Education Department Web site. They said the state’s free math curriculum wasn’t ready in time.

Schools may stick with their current offerings, but will get specific warnings about how each curriculum falls short of the new standards, officials said.

The cost of switching to new books and materials is expected to be roughly $56 million this coming year, assuming that 70 percent of the schools opt in.

Oddly, students are to be given math and reading tests aligned with the Common Core in April and May — even though the corresponding curricula won’t be introduced in schools until September.

It’s one of the reasons educators are predicting that test scores will nose-dive this spring.