Rigor: in major topics pursue: conceptual understanding, procedural skill and fluency, and application with equal intensity.
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.

Don’t Leave Out the Math: Phil Daro on Teaching
Using a series of examples, CCSS lead writer Phil Daro stresses the value of teaching mathematics in greater depth and avoiding “clutter” in the curriculum. 5min video.