K - Year 2Year 3 - 5Year 6 - 8Number and QuantityAlgebraFunctionsGeometryStatistics & Probability
Counting and Cardinality
- Know number names and the count sequence.
- Count to tell the number of objects.
- Compare numbers.
Operations and Algebraic Thinking
- Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
- Add and subtract within 20.
- Work with equal groups of objects to gain foundations for multiplication.
Number and Operations in Base Ten
- Work with numbers 11-19 to gain foundations for place value.
- Use place value understanding and properties of operations to add and subtract.
Measurement and Data
- Describe and compare measurable attributes.
- Classify objects and count the number of objects in each category.
- Measure and estimate lengths in standard units.
- Relate addition and subtraction to length.
- Work with time and money.
- Represent and interpret data.
Geometry
- Identify and describe shapes.
- Analyze, compare, create, and compose shapes.
- Reason with shapes and their attributes.
Operations and Algebraic Thinking
- Represent and solve problems involving multiplication and division.
- Understand properties of multiplication and the relationship between multiplication and division.
- Multiply and divide within 100.
- Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- Write and interpret numerical expressions.
- Analyze patterns and relationships.
Number and Operations in Base Ten
- Use place value understanding and properties of operations to perform multi-digit arithmetic.
- Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations - Fractions
- Develop understanding of fractions as numbers.
- Use equivalent fractions as a strategy to add and subtract fractions.
- Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
- Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.
- Represent and interpret data.
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
- Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Geometry
- Reason with shapes and their attributes.
- Graph points on the coordinate plane to solve real-world and mathematical problems.
- Classify two-dimensional figures into categories based on their properties.
Ratios and Proportional Relationships
- Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
- Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- Multiply and divide multi-digit numbers and find common factors and multiples.
- Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
- Apply and extend previous understandings of arithmetic to algebraic expressions.
- Reason about and solve one-variable equations and inequalities.
- Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
- Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
- Develop understanding of statistical variability.
- Summarize and describe distributions.
Functions
- Define, evaluate, and compare functions.
- Use functions to model relationships between quantities.
The Real Number System
- Extend the properties of exponents to rational exponents
- Use properties of rational and irrational numbers.
Functions
- Reason quantitatively and use units to solve problems
The Complex Number System
- 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
- Represent and model with vector quantities.
- Perform operations on vectors.
- Perform operations on matrices and use matrices in applications.
Seeing Structure in Expressions
- Interpret the structure of expressions
- Write expressions in equivalent forms to solve problems
Arithmetic with Polynomials and Rational Functions
- Perform arithmetic operations on polynomials
- Understand the relationship between zeros and factors of polynomials
- Use polynomial identities to solve problems
- Rewrite rational functions
Reasoning with Equations and Inequalities
- 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
Functions
- Create equations that describe numbers or relationships
Interpreting Functions
- 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
- Build a function that models a relationship between two quantities
- Build new functions from existing functions
Linear, Quadratic, and Exponential Models
- Construct and compare linear and exponential models and solve problems
- Interpret expressions for functions in terms of the situation they model
Trigonometric Functions
- Extend the domain of trigonometric functions using the unit circle
- Model periodic phenomena with trigonometric functions
- Prove and apply trigonometric identities
Congruence
- Experiment with transformations in the plane
- Understand congruence in terms of rigid motions
- Prove geometric theorems
- Make geometric constructions
Similarity, Right Triangles, and Trigonometry
- Understand similarity in terms of similarity transformations
- Prove theorems involving similarity
- Define trigonometric ratios and solve problems involving right triangles
- Apply trigonometry to general triangles
Circles
- Understand and apply theorems about circles
- Find arc lengths and areas of sectors of circles
Expressing Geometric Properties with Equations
- Translate between the geometric description and the equation for a conic section
- Use coordinates to prove simple geometric theorems algebraically
Geometric Measurement and Dimension
- 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
Making Inferences and Justifying Conclusions
- Understand and evaluate random processes underlying statistical experiments
- Make inferences and justify conclusions from sample surveys, experiments and observational studies
Interpreting Categorical and Quantitative Data
- 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
Conditional Probability and the Rules of Probability
- 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
- Calculate expected values and use them to solve problems
- Use probability to evaluate outcomes of decisions