- Council of the Great City Schools
The Common Core State Standards in mathematics was built on narrative documents, called progressions, to describe the progressions of topics and concepts across a number of grade levels. These documents, available in draft form, are informed by research on children’s cognitive development and by the logical structure of mathematics.
K-5, Number and Operations in Base Ten – focuses on the development of number and the base ten number system.
Kindergarten, counting and cardinality; K-5, Operations and Algebraic Thinking – this progression deals with early counting and how “much is in a group (cardinality).” The progression illustrates the basic operations including the kinds of quantitative relationships they model, and the type of problems that can be solved.
3-5 Number and Operations – Fractions – this progression illustrates the concept of fractions from grade three to five. This progression explores the concept of fraction as number beginning with fractions on a number-line. The Fraction Progression online professional development module is based upon this progression.
K-5 Progression on Geometric Measurement and Data (measurement part) - focuses on measurement in developing a conceptual framework for connecting number and geometry.
K-5 Progression on Geometric Measurement (data part)- focuses on the work with data in Grades K-5 that lays the foundation for the future study of statistics and probability as well as serving to strengthen and apply what students learn about number.
K-6 Progression on Geometry – focuses on the development of geometry from kindergarten through grade six. The overview of the document indicates that the progression will address three categories essential to elementary geometry: geometric shapes and their attributes; decomposing and composing shapes; and spatial relations and spatial restructuring.
Grades 6-8 Progression on Statistics and Probability – builds on students’ knowledge of data analysis to include an emphasis on variability; students developing more precise descriptions of data distributions; students transitioning from analyzing data to production of data; students moving from working with univariate to bivariate data.
High School Statistics and Probability and Statistics – this progression illustrates how students build upon their knowledge of probability and statistics from grades 6-8. Modeling is emphasized in this progression.
High School Algebra - focuses on the study of algebra which occupies a large part of a student’s high school career. This document does not treat in detail all of the material studied in algebra. Instead, it provides general guidance about ways to treat the material, notes key connections among standards, points out cognitive difficulties and pedagogical solutions, and provides additional details about problematic areas in mathematics.
Grade 8, High School, Functions – focuses on showing how the concept of functions develops and continues beginning in grade eight. This includes explicit connections and distinctions between functions and algebra including equation solving.
K-5 Elaborations of the Practice Standards – provides a grade band elaboration with concrete examples about how the Common Core State Standards for Mathematical Practice look in kindergarten through grade five classrooms.
6-8 Elaborations of the Practice Standards – provides a grade band elaboration, including concrete examples, about how the Common Core State Standards for Mathematical Practice look in grades 6-8 classrooms.