As I prepare for the classroom, I’ve asked trusted colleagues what math resources I should be looking over. Almost without exception, they direct me to the Progressions Documents for the Common Core State Standards. If you are unfamiliar with these, they are narratives that describe the progression of topics across grades. They help explain why the standards are sequenced the way they are and offer pedagogical strategies and solutions to challenging areas of mathematics.
Helpfully, working with the Kahn Academy, Common Core author Dr. Bill McCallum has shared a series of videos describing specific progressions. Dr. McCallum walks viewers through the standards with reference to research, examples of math problems associated with domains and clusters, and anecdotes about authoring the standards themselves. You can view the videos through the links below.
Common Core Introduction
CCSS Fractions Part I
CCSS Fractions Part II
CCSS Place Value
CCSS Multiply and Dividing Negative Numbers
CCSS Algebra Grade 8
CCSS Statistics in Middle School
CCSS Negative Numbers
CCSS Expressions and Equations (Grades 5 trough 7)