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Math Overview
- Pre-Kindergarten
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- 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