Math Overview

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