# Math progressions documents

These documents describe the progressions of mathematical topics on which the Common Core State Standards in Mathematics were built. They explain how mathematical ideas develop across a number of grade levels and and are informed both by research on children's cognitive development and by the logical structure of mathematics. They can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics.

## Included Resources

This is the home page for Progressions Documents for the Common Core Math Standards

Overview of the organization of the Common Core State Standards for Mathematics, and how the Standards are informed by the structure of mathematics as well as three areas of educational research: large-scale comparative studies, research on children’s learning trajectories, and other research on cognition and learning. This introduction outlines how the Standards have been shaped by each of these influences, describes the organization of the Standards, discusses how traditional topics have been reconceptualized to fit that organization, and describes terms used in the Standards and the Progressions

This progression discusses the most important goals for elementary geometry according to three categories: Geometric shapes, their components (e.g., sides, angles, faces), their properties, and their categorization based on those properties; Composing and decomposing geometric shapes; Spatial relations and spatial structuring.

This progression concerns Measurement and Data standards related to geometric measurement. The remaining Measurement and Data standards are discussed in the K–3 Categorical Data and Grades 2–5 Measurement Data Progressions.

These progressions concern Measurement and Data standards related to data. Other Measurement and Data standards are discussed in the Geometric Measurement Progression.

This progression describes how students develop an understanding of the base-ten number system and how students’ work in the base-ten system is intertwined with their work on counting and cardinality, and with the meanings and properties.

This progression describes how students develop an understanding of fractions and their properties and how this work deepens and extends their understandings of numbers and operations .

This progression describes how students develop an understanding of statistics and probability in Grades 6-8, and how this understanding builds on and deepens the knowledge and experiences in data analysis developed in earlier grades (see K-3 Categorical Data Progression and Grades 2-5 Measurement Progression)

This progression describes how students in Grades 6–8 build on their extensive experience in K–5 working with the properties of operations in the context of operations with whole numbers, decimals and fractions and start to use properties of operations to manipulate algebraic expressions and produce different but equivalent expressions for different purposes.

This progression describes how students in Grades 6–8 extend their conception of numbers to understand the rational numbers as a number systems, and then in high school to irrational and complex numbers. The progression also describes how this understanding is built on two important concepts which have developed throughout K–5. The first is the representation of whole numbers and fractions as points on the number line, and the second is a firm understanding of the properties of operations on whole numbers and fractions.

This progression describes how the study of ratios and proportional relationships extends students’ work in measurement and in multiplication and division in the elementary grades, and how ratios and proportional relationships are foundational for further study in mathematics and science and useful in everyday life.

This progression describes coherence of the Algebra standards in high school including their relationship to the Functions category. It does not describe in detail all of the material studied, rather it gives some general guidance about ways to treat the material and ways to tie it together. It notes key connections among standards, points out cognitive difficulties and pedagogical solutions, and gives more detail on particularly knotty areas of the mathematics.

This progression describes how the Functions standards develop in Grade 8 through high school. It also describes connections to Algebra, Modeling, geometric transformations, and how students begin to gain experience with functions in Grades K-7.

This progression describes how Modeling is central to mathematics, and how students learn Modeling and use it to apply and learn mathematics. It also explains the connections between Modeling and the content and practice standards, describes features and examples of mathematical models and how they are used and explains the modeling process.

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