Rigor
Rigor: in major topics pursue:
• conceptual understanding, • procedural skill and fluency, and • application with equal intensity. Rigorous courses must increase students’ depth of understanding and their ability to communicate this understanding. Rigor used to mean pushing content from higher levels down to lower grades. The Common Core redefines rigor to require that conceptual understanding, procedural skill and fluency, and application be approached with equal intensity, and includes the ability to access concepts from multiple perspectives and apply them to new situations. Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as singledigit multiplication so that they have access to more complex concepts and procedures. Application: The Standards call for students to use math flexibly for applications in problemsolving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.  from achievethecore.org 
The big shifts that the Common Core State Standards: Mathematics bring are increased focus, coherence, and rigor as the guiding principles for mathematics instruction and learning.
Rigor in the SFUSD CurriculumThe SFUSD Curriculum contains a balance of instruction in Conceptual Understanding, Procedural Skill and Fluency, and Application. The elements that build toward this include:

The University of Oregon's Dev Prakash Sinha speaks to the rigor of the Common Core State Standards for Mathematics in this piece.
"I find the Common Core State Standards in Mathematics to be more rigorous, in both senses of the word, than traditional frameworks such as the one in which I was taught. Consider for example the following question: why is 35 x 27 = 27 x 35? Of course I mean more generally "why is multiplication commutative?"...
Read more here.
"I find the Common Core State Standards in Mathematics to be more rigorous, in both senses of the word, than traditional frameworks such as the one in which I was taught. Consider for example the following question: why is 35 x 27 = 27 x 35? Of course I mean more generally "why is multiplication commutative?"...
Read more here.