# Colorado State Math Standards

Instructor: Carrie Soucy
Colorado state math standards outline the mathematical skills and competencies students should master at different grade levels, from preschool through high school. Read on to learn about the structure and content of these standards.

## Overview of Math Standards in Colorado

Colorado has four main groups of math standards. For each, students are expected to master grade-appropriate concepts and be able to apply them to real-life scenarios. These expectations are articulated for each grade from preschool through grade 8, and in one 'high school' grouping for grades 9 through 12. All correlate with the Common Core State Standards and prepare students to possess twelve math Prepared Graduate Competencies that all Colorado high school students should have when they graduate.

### The Standards By Grade Level

The standards and grade-level skill expectations for each are outlined below, along with Study.com courses designed to help educators create and implement lessons that align with Colorado math standards. All courses are self-paced and available online 24/7.

#### Number Sense, Properties, and Operations

Grade Level Skills and Concepts Resources for Teachers
High School - Complex numbers, real numbers, imaginary numbers
- Quantitative reasoning
High School Math - Number and Quantity
Grade 8 - The correspondence of rational and irrational numbers in the real number system Math Grade 8 - The Number System
Grade 7 - Proportional reasoning
- Rational number algorithms
Math Grade 7 - The Number System
Grade 6 - Ratio and rates in expressing and comparing quantities
- Positive rational number algorithms
- Rational numbers in the real number system
Math Grade 6 - The Number System
Grade 5 - The decimal number system and the foundation of algorithms
- Multi-digit and decimal algorithms
- Adding and subtracting fractions using algorithms
-Multiplying and dividing fractions
Math for Kids*
Grade 4 - The decimal system to the hundredths place
- Comparing fractional parts
- Algorithms
Grade 3 - The whole number system and algorithms
- Modeling and representing parts of a whole
- The relationship between multiplication and division
Grade 2 - The whole number system through 1,000
- Subtracting and adding within 100
Grade 1 - The whole number system to and beyond 100
- Number relationships in addition and subtraction
Kindergarten - Whole numbers and quantity
- Foundations of addition and subtraction
Preschool - Counting and representing quantity

*For grades Preschool through 5. Also applicable for Data Analysis, Statistics, and Probability standards, below.

#### Patterns, Functions and Algebraic Structures

Grade Level Skills and Concepts Resources for Teachers
High School - Algebraic, graphical, and table representations of functions
- Using functions to model and solve quantitative relationships
- Representing expressions
- Equations, inequalities and systems of equations solutions
High School Algebra
Grade 8 - Linear functions models
- Linear equations and systems of equations
- Distinguishing linear and nonlinear functions
Math Grade 8- Functions
Grade 7 - Generating equivalent expressions
- Quantitative relationships
Math Grade 7 - Expressions and Equations
Grade 6 - Algebra to generalize arithmetic properties
- Variables
Math: Grade 6 - Expressions and Equations
Grade 5 - The basis of number patterns Algebra for Kids*
Grade 4 - Symbols to represent patterns and relationships

*For Grades 5 and 4

#### Data Analysis, Statistics, and Probability

Grade Level Skills and Concepts Resources for Teachers
High School - Summary statistics and visual displays to generate knowledge
- Statistical methods to answer specific questions
- Probability models and randomness
High School Statistics
Grade 8 - Two-variable summary statistics and visual displays Grade 8: Statistics and Probability
Grade 7 - Statistical examination of data
- Math models and probability
Grade 7: Statistics and Probability
Grade 5 - Interpreting data with visual displays *Math for Kids
Grade 4 - Representing data with visual displays
Grade 3 - Describing data with visual displays
Grade 2 - Constructing visual displays
Grade 1 - Visual displays to answer questions

*For Grades 1 - 5. Also applicable for Number Sense, Properties, and Operations standards, above.

#### Shape, Dimension, and Geometric Relationships

Grade Level Skills and Concepts Resources for Teachers
High School - Analyzing the transformation of numbers on a plane
- Concepts of similarity
- Using algebra to analyze and describe numbers on a plane
- Measuring and quantifying multi-dimensional objects
- Geometric modeling of objects
High School Geometry
Grade 8 - Defining congruence and similarity
- Comparing with direct and indirect measurement
Common Core Math Grade 8 - Geometry
Grade 7 - Geometric modeling of figures and relationships
- Differences between area, volume, and angle/linear measures
Math Grade 7 - Geometry
Grade 6 - Measuring and analyzing objects in space Math Grade 6 - Geometry
Grade 5 - Addition and multiplication in calculating volume
- Describing geometric figures
Geometry for Kids*
Grade 4 - Measuring objects and time
- Analyzing and describing geometric figures in the plane and in space
Grade 3 - Describing geometric figures
- Area and linear measurement
- Measuring the attributes of time and objects
Grade 2 - Using and describing shapes
- Measuring and quantifying objects
Grade 1 - Describing and creating shapes
- Uses of measurement
Kindergarten - Characteristics, position and creation of shapes
- Comparing and ordering through measurement
Preschool - Observing and describing shapes

*For Grades Preschool - 5

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