Mathematics
Coherence
Mathematical understanding requires a progression of learning. This means that conceptual understanding in math (the knowledge and skills we want students to learn) clearly builds within a grade level. More importantly, the learning progression continues beyond a grade level and the standards clearly show how that conceptual understanding builds from grade level to grade level. Therefore, coherence supports the focus. The standards are not separate events but an interrelated mathematical system.
math should make sense
Supporting Coherence in knowledge of the standards
Coherence Sorting Activity
Supporting coherence in instructional design
Modes of Representation

Problem Solving Structures

Problem Solving Posters
Instructional Strategy Videos

Sample Problems
Math PRogression Streams
Seven progression streams can be found that span the Kindergarten through 12th grade Common Core Standards.
1) Counting and Cardinality
2) Algebraic Thinking 3) Number & Quantity 4) Geometry 5) Functions 6) Statistics and Probability 7) High School Modeling 
Learning progressions, or building blocks, can also be found within each of the domains. These building blocks of skills can create a sequential instructional path to achieve coherence and conceptual understanding.
The authors of the Common Core have also drafted learning progressions that show skillbuilding across grade levels. These narrative documents provide instructional guidance to support coherence in learning math.
Every grade level contributes to students' understanding of algebraic concepts. This progression document indicates required foundational skills in Kindergarten through Eighth grade that facilitate students' abilities to engage with Algebraic content at the High School level.
Images of the progression work done by "our" Math Instructional Cadre Leaders:
An Additional Resource to Build Mental Math
Number Talks, Grades K5: Helping Children Build Mental Math and Computational Strategies by Sherry Parrish
ISBN13: 9781935099116
ISBN10: 1935099116
* New Edition* with Common Core Connections
ISBN13: 9781935099659
ISBN10: 1935099655