K - Grade 2Grade 3 - 5Grade 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**

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