Common Core State Standards for Mathematics (9-12) Quick Reference Guide
CCSS Mathematics Standards for High School
Mathematics consists of two standards – standards for Mathematical Practice and
Mathematical Content standards.
For additional information the Common Core State Standards for mathematics may be found
at: http://www.k12.wa.us/CoreStandards/Mathematics/pubdocs/CCSSI_MathStandards.pdf
Standards for Mathematical Practice
Standards of mathematical practice describe ways students ought to engage with the subject matter as
they grow in mathematical maturity and expertise throughout elementary, middle and high school
years.
Mathematical practices need to be connected to mathematical content through mathematics
instruction.
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at
all levels should seek to develop in their students. These practices rest on important “processes and
proficiencies” with longstanding importance in mathematics education, as set by National Council of
Teachers of Math (NCTM) process standards and the National Research Council (NRC) strands of
mathematical proficiency.
Mathematical Practices
1
2
3
4
5
6
7
8
Make sense of problems and preserve in solving them
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
1/30/13
Standards for Mathematical Content
Mathematics Standards for High School




Specify the mathematics that all students should study to be college and career ready
Additional mathematics students should learn to take advanced courses such as
calculus, advanced statistics, or discrete mathematics is indicated by (+) symbol.
All standards without a (+) symbol should be in the common mathematics curriculum for
all college and career ready students.
High Schools standards are listed in conceptual categories: (NOTE: Conceptual
categories portray a coherent view of high school mathematics; student’s work with a
specific category crosses a number of traditional course boundaries, potentially up
through and including calculus.)
o Number and Quantity
o Algebra
o Functions
o Modeling (NOTE: Modeling is best interpreted in relation to other standards.
Making mathematical models is a Standard for Mathematical Practice, and
specific modeling standards appear throughout the high school standards
indicated by a star symbol (*). The star symbol sometimes appears on the
heading for a group of standards, in that case, it should be understood to apply
to all standards in that group.)
o Geometry
o Statistics and Probability
Number and Quantity Overview
The Real Number System (N-RN)
 Extend the properties of exponents to rational exponents
 Use properties of rational and irrational numbers
Quantities (N-Q)
 Reason quantitatively and use units to solve problems
The Complex Number System (N-CN)
 Perform arithmetic operations with complex numbers
 Represent complex numbers and their operations on the complex plane
 Use complex numbers in polynomial identities and equations
Vector and Matrix Quantities (N-VM)
 Represent and model with vector quantities
 Perform operations on vectors
 Perform operations on matrices and use matrices in application.
Algebra Overview
Seeing Structure in Expressions (A-SSE)
 Interpret the structure of expressions
 Write expressions in equivalent forms to solve problems
Arithmetic with Polynomials and Rational Expressions (A-APR)
 Perform arithmetic operations on polynomials
 Understand the relationship between zeros and factors of polynomials
 Use polynomial identities to solve problems
 Rewrite rational expressions
1/30/13
Creating Equations (A-CED)
 Create equations that describe numbers or relationships
Reasoning with Equations and Inequalities (A-REI)
 Understand solving equations as a process of reasoning and explain the reasoning
 Solve equations and inequalities in one variable
 Solve systems of equations
 Represent and solve equations and inequalities graphically
Function Overview
Interpreting Functions (F-IF)
 Understand the concept of a function and use function notation
 Interpret functions that arise in applications in terms of the context
 Analyze functions using different representations
Building Functions (F-BF)
 Build a function that models a relationship between two quantities
 Build new functions from existing functions
Linear, Quadratic, and Exponential Models (F-LE)
 Construct and compare linear, quadratic, and exponential models and solve problems
 Interpret expressions for functions in terms of the situation they model
Trigonometric Functions (F-TF)
 Extend the domain of trigonometric functions using the unit circle
 Model periodic phenomena with trigonometric
 Prove and apply trigonometric identities
Modeling Overview

Modeling is best interpreted not as a collection of isolated topics but rather in relation to other
standards. Making mathematical models is a Standard for Mathematical Practice, and specific
modeling standards appear thorough the standards indicated by a star symbol (*)
Geometry Overview
Congruence (G-CO)
 Experiment with transformation in the plane
 Understand congruence in terms of rigid motions
 Prove geometric theorems
 Make geometric constructions
Similarity, Right Triangles, and Trigonometry (G-SRT)
 Understand similarity in terms of similarity transformation
 Prove theorems involving similarity
 Define trigonometric ratios and solve problems involving right triangles
 Apply trigonometry to general triangles
Circles (G-C)
 Understand and apply theorems about circles
 Find arc lengths and areas of sectors of circles
Expressing Geometric Principles with Equations (G-GPE)
 Translate between the geometric description and the equation for a conic section
 Use coordinates to prove simple geometric theorems algebraically
Geometric Measurement and Dimension (G-GMD)
 Explain volume formulas and use them to solve problems
 Visualize relationships between two-dimensional and three-dimensional objects
Modeling with Geometry
 Apply geometric concepts in modeling situations
1/30/13
Statistics and Probability Overview
Interpreting Categorical and Quantitative Data (S-ID)
 Summarize, represent, and interpret data on a single count or measurement variable
 Summarize, represent, and interpret data on two categorical and quantitative variables
 Interpret linear models
Making Inferences and Justifying Conclusions (S-IC)
 Understand and evaluate random processes underlying statistical experiments
 Make inferences and justify conclusions from sample surveys, experiments and observational
studies
Conditional Probability and the Rules of Probability (S-CP)
 Understand independence and conditional probability and use them to interpret data
 Use the rules of probability to compute probabilities of compound events in a uniform
probability model
Using Probability to Make Decisions (S-MD)
 Calculate expected values and use them to solve problems
 Use probability to evaluate outcomes of decisions
1/30/13