The common core state standards outline what students should understand and be able to do in their study of mathematics. One trademark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. Mathematical understanding and procedural skills are equally important, and both are assess-able using mathematical tasks of sufficient richness.

Schools have a choice of choosing two pathways for mathematics based on the common core standards. At the high school level, the standards are organized by conceptual category*(number & quantity, algebra, functions, geometry, modeling and probability & statistics),* showing the body of knowledge students should learn in each category to be college and career ready, and to be prepared to study more advanced mathematics.

The *Framework *provides a context for implementing the *California Common Core State Standards for Mathematics* (PDF; 3MB), which were first adopted by California in 2010, and then modified in 2013. Standards describe what students should know and be able to do in each subject in each grade. Frameworks provide guidance for implementing the standards. Common Core is a state-led effort adopted by 45 states, so that all children—no matter where they come from or where they live—will receive a world-class education that is consistent from school to school and state to state.

The State Board of Education today approved the new *Mathematics Framework for California Public Schools on November 6, 2013, *which provides instructional guidance for teachers and administrators. The *Framework *provides grade-level explanations and examples of the standards for mathematics practice and content, integrating mathematical thinking and conceptual understanding with procedural skills and application.

“The Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve is meant to guide teachers in curriculum development and instruction as they work to ensure that all students meet or exceed the CA CCSSM. The framework also provides educators and developers of instructional materials with a context for implementing the standards. Building on the standards, the framework addresses how all students in California public schools can best meet those standards. California’s mathematics framework is available online and, as such, will remain a “living” document that will be updated regularly.” (CDE, 2015)