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# Math Overview

- Pre-Kindergarten
- Kindergarten
- Grade 1
- Grade 2
- Grade 3
- Grade 4
- Grade 5
- Grade 6
- Grade 7
- Grade 8
- Geometry Overview
- Algebra 1 Overview
- Algebra 2 Overview

## Counting & Cardinality

- Know number names and the counting sequence
- Count to tell the number of objects
- Compare numbers

## Operations & Algebraic Thinking

- Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from

## Measurement & Data

- Describe and compare measurable attributes
- Classify objects and count the number of objects in each category
- Work with money

## Geometry

- Identify and describe shapes (squares, circles, triangles, rectangles)
- Analyze, compare, create, and compose shapes

## Counting & Cardinality

- Know number names and the count sequence
- Count to tell the number of objects
- Compare numbers

## Operations & Algebraic Thinking

- Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from

## Number & Operations in Base Ten

- Work with numbers 11 to 19 to gain foundations for place value

## Measurement & Data

- Describe and compare measurable attributes
- Classify objects and count the number of objects in each category

## Geometry

- Identify and describe shapes:
- Circles
- Cones
- Cubes
- Cylinders
- Hexagons
- Rectangles
- Spheres
- Squares
- Triangles

- Analyze, compare, create, and compose shapes

## Operations & Algebraic Thinking

- Represent and solve problems involving addition and subtraction
- Understand and apply properties of operations and the relationship between addition and subtraction
- Add and subtract within 20
- Work with addition and subtraction equations

## Number & Operations in Base Ten

- Extend the counting sequence
- Understand place value
- Use place value understanding and properties of operations to add and subtract

## Measurement & Data

- Measure lengths indirectly and by iterating length units
- Tell and write time
- Represent and interpret data
- Work with money

## Geometry

- Reason with shapes and their attributes

## Operations & Algebraic Thinking

- Represent and solve problems involving addition and subtraction
- Add and subtract within 20
- Work with equal groups of objects to gain foundations for multiplication

## Number & Operations in Base Ten

- Understand place value
- Use place value understanding and properties of operations to add and subtract

## Measurement & Data

- Measure and estimate lengths in standard units
- Relate addition and subtraction to length
- Work with time and money
- Represent and interpret data

## Geometry

- Reason with shapes and their attributes

## Operations & 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

## Number & Operations in Base Ten

- Use place value understanding and properties of operations to perform multi-digit arithmetic

## Number & Operations-Fractions

- Develop understanding of fractions as numbers

## Measurement & 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

## Operations & Algebraic Thinking

- Use the four operations with whole numbers to solve problems
- Gain familiarity with factors and multiples
- Generate and analyze patterns

## Number & Operations in Base Ten

- Generalize place value understanding for multi-digit whole numbers
- Use place value understanding and properties of operations to perform multi-digit arithmetic

## Number & Operations-Fractions

- Extend understanding of fraction equivalence and ordering
- Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
- Understand decimal notation for fractions, and compare decimal fractions

## Measurement & Data

- Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
- Represent and interpret data
- Geometric measurement: Understand concepts of angle and measure angles

## Geometry

- Draw and identify lines and angles, and classify shapes by properties of their lines and angles

## Operations & Algebraic Thinking

- Write and interpret numerical expressions
- Analyze patterns and relationships

## Number & Operations in Base Ten

- Understand the place value system
- Perform operations with multi-digit whole numbers and with decimals to hundredths

## Number & Operations-Fractions

- 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
- The Number System
- Gain familiarity with concepts of positive and negative integers

## Measurement & Data

- Convert like measurement units within a given measurement system
- Represent and interpret data
- Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition

## Geometry

- Graph points on the coordinate plane to solve real-world and mathematical problems
- Classify two-dimensional figures into categories based on their properties

## Ratios & 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
- Compute fluently with multi-digit numbers and find common factors and multiples
- Apply and extend previous understandings of numbers to the system of rational numbers

## Expressions & 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 & Probability

- Develop understanding of statistical variability
- Summarize and describe distributions

## Ratios & Proportional Relationships

- Analyze proportional relationships and use them to solve real-world and mathematical problems

## The Number System

- Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

## Expressions & Equations

- Use properties of operations to generate equivalent expressions
- Solve real-life and mathematical problems using numerical and algebraic expressions and equations

## Geometry

- Draw, construct and describe geometrical figures and describe the relationships between them
- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

## Statistics & Probability

- Use random sampling to draw inferences about a population
- Draw informal comparative inferences about two populations
- Investigate chance processes and develop, use, and evaluate probability models

## The Number System

- Know that there are numbers that are not rational, and approximate them by rational numbers

## Expressions & Equations

- Work with radicals and integer exponents
- Understand the connections between proportional relationships, lines, and linear equations
- Analyze and solve linear equations and pairs of simultaneous linear equations

## Functions

- Define, evaluate, and compare functions
- Use functions to model relationships between quantities

## Geometry

- Understand congruence and similarity using physical models, transparencies, or geometry software
- Understand and apply the Pythagorean Theorem
- Solve real-world and mathematical problems involving volume of cylinders, cones and spheres

## Statistics & Probability

- Investigate patterns of association in bivariate data

## Number & Quantity

### Quantities

- Reason quantitatively and use units to solve problems

## Geometry

### Congruence

- Experiment with transformations in the plane
- Understand congruence in terms of rigid motions
- Prove geometric theorems
- Make geometric constructions

### Similarity, Right Triangles & Trigonometry

- Understand similarity in terms of 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 area 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 & 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

## Statistics & Probability

### Conditional Probability & 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

- Use probability to evaluate outcomes of decisions

## Number & Quantity

### The Real Number System

- Extend the properties of exponents to rational exponents
- Use properties of rational and irrational numbers

### Quantities

- Reason quantitatively and use units to solve problems

## Algebra

### Seeing Structure in Expressions

- Interpret the structure of expressions
- Write expressions in equivalent forms to solve problems

### Arithmetic with Polynomials & Rational Expressions

- Perform arithmetic operations on polynomials

### Creating Equations

- Create equations that describe numbers or relationships

### Reasoning with Equations & 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

### 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 & Exponential Models

- Interpret expressions for functions in terms of the situation they model

## Statistics & Probability

### Interpreting Categorical & 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

## Number & Quantity

### The Complex Number System

- Perform arithmetic operations with complex numbers
- Use complex numbers in polynomial identities and equations

### Vector & Matrix Quantities

- Represent and model with vector quantities
- Perform operations on matrices and use matrices in applications

## Algebra

### Seeing Structure in Expressions

- Interpret the structure of expressions
- Write expressions in equivalent forms to solve problems

### Arithmetic with Polynomials & Rational Expressions

- Perform arithmetic operations on polynomials
- Understand the relationship between zeros and factors of polynomials
- Use polynomial identities to solve problems
- Rewrite rational expressions

### Creating Equations

- Create equations that describe numbers or relationships

### Reasoning with Equations & Inequalities

- Understand solving equations as a process of reasoning and explain the reasoning
- Represent and solve equations and inequalities graphically

## Functions

### Interpreting Functions

- 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 & Exponential Models

- Construct and compare linear, quadratic, and exponential models and solve problems

### Trigonometric Functions

- Extend the domain of trigonometric functions using the unit circle
- Model periodic phenomena with trigonometric functions
- Prove and apply trigonometric identities

## Statistics & Probability

### Interpreting Categorical & Quantitative Data

- Summarize, represent and interpret data on a single count or measurement variable

### Making Inferences & Justifying Conclusions

- Understand and evaluate random processes underlying statistical experiments
- Make inferences and justify conclusions from sample surveys, experiments and observational studies

### Using Probability to Make Decisions

- Use probability to evaluate outcomes of decisions