U.S. News and World Report has published an online article titled "A Guide to Common Core", dated March 4, 2014 and authored by Amy Golod.

Among the "Myths and Facts", the article strives to quell concern that the standards are "one size fits all" and do not support the gifted:

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But as the introduction to the English Language Arts standards points out, teachers still have the flexibility and responsibility to customize instruction depending on their students’ abilities. “The Standards set grade-specific standards but do not define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations,” the introduction reads .
However the link to the source document does not substantiate the claim but rather leads to a Page Not Found error message. The CCSS website remains in a state of flux.

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A misconception which arose early in the development of the standards was that “Common Core would mean a uniform and standard set of instruction that would negate the need for gifted and talent programs, which is obviously not true,” says Michael Casserly, executive director of the Council of the Great City Schools, a national coalition of urban public school systems.
Unfortunately the article does not provide supporting statements within the CCSS. Considering that the CCSS website has been subject to frequent changes, some may say that the CCSS website could easily contain one or more statements acknowledging gifted learners.

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“The Common Core is about raising the bottom half,” says Common Core Development Team member Bauerlein.
Some may say this statement of focus on the bottom half reinforces rather than negates a belief that CCSS may provide further benign neglect for students who've mastered the prescribed standards early and are eager to learn something new.