Area
Determines the area of figures by tiling with whole unit squares
Data Representation
Represents data in bar graphs with multi-unit scales
Whole Numbers: Multiplication/Division
Multiplies basic facts
Whole Numbers: Represent and Solve Word Problems
Solves one-step equal-groups multiplication word problems, whole numbers with products within 100
Rates/Ratios/Proportions/Percents
Identifies ratios between two quantities not from the same whole
Spatial Concepts and Symmetry
Identifies and creates nets for pyramids
Area
Determines the area of figures by tiling with whole unit squares
Determines the area of figures composed of whole unit squares
Data Representation
Represents data in bar graphs with multi-unit scales
Problem Solving with Units
Solves one-step money word problems involving whole number addition or subtraction
Number Sentences/Equations/Equivalence
Determines unknown factors in multiplication equations with whole numbers and products within 100
Solves one-step linear equations with positive rational numbers
Whole Numbers: Multiplication/Division
Divides basic facts
Multiplies basic facts
Whole Numbers: Represent and Solve Word Problems
Solves one-step equal-groups division word problems, whole numbers within 100
Solves one-step equal-groups multiplication word problems, whole numbers with products within 100
Rates/Ratios/Proportions/Percents
Determines missing values in a table of equivalent ratios within a real‑world scenario
Identifies ratios between two quantities not from the same whole
Spatial Concepts and Symmetry
Identifies and creates nets for prisms
Identifies and creates nets for pyramids
Area
Determines the area of figures by tiling with whole unit squares
Determines the area of figures composed of whole unit squares
Represents the area of rectangles composed of whole unit squares using multiplication expressions or equations
Conversion of Units
Completes simple conversions of units of time
Data Representation
Represents data in bar graphs with multi-unit scales
Money
Determines the decimal value of a collection of coins and/or bills given as names
Perimeter/Circumference
Determines the perimeter of basic polygons with all sides labeled
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Problem Solving with Units
Solves one-step money word problems involving whole number addition or subtraction
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Time
Completes simple conversions of units of time
Knows relative sizes of units of time
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Number Sentences/Equations/Equivalence
Determines unknown factors in multiplication equations with whole numbers and products within 100
Determines whether a linear equation or inequality is true for a given value of the variable
Solves one-step linear equations with positive rational numbers
Translates between verbal and algebraic equations
Writes a one-step linear equation in one variable to represent a real-world or mathematical context
Numerical Expressions
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Properties and Relationships of Operations
Understands division as equal sharing
Understands the inverse relationship between multiplication and division
Whole Numbers: Multiplication/Division
Divides basic facts
Multiplies basic facts
Whole Numbers: Represent and Solve Word Problems
Represents one-step multiplicative-comparison word problems with expressions or equations, whole numbers
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step word problems involving the four operations with whole numbers
Solves one-step equal-groups division word problems, whole numbers within 100
Solves one-step equal-groups multiplication word problems, whole numbers with products within 100
Rates/Ratios/Proportions/Percents
Determines missing values in a table of equivalent ratios within a real‑world scenario
Identifies ratios between two quantities not from the same whole
Uses a given unit rate to solve a one-step real-world problem
Uses tables to represent real-world relationships described by a given unit rate
Coordinate Geometry
Interprets points with whole number coordinates in the first quadrant within the given context
Spatial Concepts and Symmetry
Identifies and creates nets for prisms
Identifies and creates nets for pyramids
Angle Measurement
Calculates unknown angle measures using the additive property of angles
Area
Determines the area of figures by tiling with whole unit squares
Determines the area of figures composed of whole unit squares
Represents the area of rectangles composed of whole unit squares using multiplication expressions or equations
Bivariate Data
Constructs scatter plots of bivariate data
Capacity
Knows relative sizes of customary units of capacity
Conversion of Units
Completes simple conversions of units of time
Data Analysis
Adds and subtracts to answer questions about bar graphs with multi-unit scales
Data Representation
Constructs scatter plots of bivariate data
Represents data in bar graphs with multi-unit scales
Represents data in line or dot plots with whole‑number scales
Represents data in pictographs with multi-unit scales
Length
Knows relative sizes of customary units of length
Money
Determines the decimal value of a collection of coins and/or bills given as names
Perimeter/Circumference
Determines the perimeter of basic polygons with all sides labeled
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Problem Solving with Units
Solves one-step money word problems involving whole number addition or subtraction
Solves one-step money word problems involving whole number multiplication or division
Solves one‑step capacity word problems involving whole-number addition or subtraction
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Time
Completes simple conversions of units of time
Knows relative sizes of units of time
Volume
Determines the volume of figures by counting unit cubes
Algebraic Expressions
Writes linear expressions in one variable to represent real-world or mathematical contexts
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Linear Functions
Graphs a linear function of the form y = mx given a simple scenario
Number Sentences/Equations/Equivalence
Determines unknown divisors in division equations with whole numbers and dividends within 100
Determines unknown factors in multiplication equations with whole numbers and products within 100
Determines whether a linear equation or inequality is true for a given value of the variable
Solves one-step linear equations with positive rational numbers
Translates between verbal and algebraic equations
Writes a one-step linear equation in one variable to represent a real-world or mathematical context
Numerical Expressions
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Properties and Relationships of Operations
Understands division as equal sharing
Understands multiplication as a comparison of sizes
Understands the inverse relationship between multiplication and division
Whole Numbers: Concepts/Properties
Identifies factors of numbers less than 100
Identifies multiples of single‑digit numbers
Whole Numbers: Multiplication/Division
Divides basic facts
Multiplies basic facts
Whole Numbers: Represent and Solve Word Problems
Represents one-step equal-groups multiplication and division word problems with models, whole numbers
Represents one-step equal-groups multiplication word problems with expressions or equations, whole numbers
Represents one-step multiplicative-comparison word problems with expressions or equations, whole numbers
Solves multi-step addition and subtraction word problems, whole numbers greater than 100
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step word problems involving the four operations with whole numbers
Solves one-step division word problems that require interpretation of remainders, whole numbers
Solves one-step equal-groups division word problems, whole numbers within 100
Solves one-step equal-groups multiplication word problems, whole numbers with products within 100
Solves one-step multiplicative-comparison word problems, whole-number products greater than 100
Solves one-step multiplicative-comparison word problems, whole-number products within 100
Linear Functions
Interprets the meaning of the point (1, r) on a graph of a real‑world proportional relationship
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Determines if the relationship between two quantities in a real‑world scenario is proportional given a table
Determines missing values in a table of equivalent ratios within a real‑world scenario
Identifies ratios between two quantities not from the same whole
Interprets the meaning of the point (x, y) on a graph of a real‑world proportional relationship
Represents a ratio in multiple forms
Solves real‑world and mathematical problems given a table representing equivalent ratios of quantities
Uses a given unit rate to solve a one-step real-world problem
Uses ratios of whole numbers to calculate unit rates
Uses tables to represent real-world relationships described by a given unit rate
Coordinate Geometry
Interprets points with whole number coordinates in the first quadrant within the given context
Identification and Classification of 2-D Shapes
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Recognizes examples of quadrilaterals
Points, Lines, Segments, Rays, and Angles
Identifies parallel lines
Identifies right angles
Spatial Concepts and Symmetry
Identifies and creates nets for prisms
Identifies and creates nets for pyramids
Angle Measurement
Calculates unknown angle measures using the additive property of angles
Identifies/estimates angle measures
Area
Determines the area of figures by tiling with whole unit squares
Determines the area of figures composed of whole unit squares
Determines the area of rectangles with whole-number sides, formula not provided
Explains the relationship between tiling a figure and multiplying side lengths to find the area
Represents the area of rectangles composed of whole unit squares using multiplication expressions or equations
Solves problems involving areas of rectangles within a real-world or mathematical context
Bivariate Data
Constructs scatter plots of bivariate data
Describes and interprets data in a scatter plot
Distinguishes between linear and nonlinear relationships in scatter plots
Capacity
Completes simple conversions of customary units of capacity
Conversion of Units
Completes simple conversions of customary units of capacity
Completes simple conversions of customary units of length
Completes simple conversions of customary units of weight
Completes simple conversions of units of time
Solves multi-step length word problems involving whole numbers and conversion of customary units
Data Analysis
Adds and subtracts to answer questions about bar graphs with multi-unit scales
Identifies the median, quartiles, extreme values, and outliers from a box plot
Reads and interprets data from line or dot plots with whole‑number scales
Data Representation
Constructs scatter plots of bivariate data
Represents data in bar graphs with multi-unit scales
Represents data in line or dot plots with whole‑number scales
Represents data in pictographs with multi-unit scales
Length
Completes simple conversions of customary units of length
Knows relative sizes of customary units of length
Knows relative sizes of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Identifies the median, quartiles, extreme values, and outliers from a box plot
Money
Determines the decimal value of a collection of coins and/or bills given as names
Solves money word problems involving decimals and coins and/or bills given as names
Solves money word problems involving decimals and coins and/or bills given as pictures
Perimeter/Circumference
Determines the perimeter of basic polygons in which not all sides are labeled
Determines the perimeter of basic polygons with all sides labeled
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Problem Solving with Units
Solves money word problems involving decimals and coins and/or bills given as names
Solves money word problems involving decimals and coins and/or bills given as pictures
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves one-step money word problems involving whole number addition or subtraction
Solves one‑step capacity word problems involving whole-number addition or subtraction
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Time
Completes simple conversions of units of time
Volume
Determines the volume of figures by counting unit cubes
Determines the volume of rectangular prisms, formula not provided
Identifies rectangular prisms composed of unit cubes that have the same volume as a given rectangular prism
Understands that a unit cube has sides of 1 unit in length and a volume of 1 cubic unit
Weight/Mass
Completes simple conversions of customary units of weight
Algebraic Expressions
Interprets equivalent linear expressions within a real-world context
Translates between verbal and algebraic expressions
Writes linear expressions in one variable to represent real-world or mathematical contexts
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Linear Functions
Compares the rate of change between two proportional relationships represented in different ways
Graphs a linear function of the form y = mx given a simple scenario
Number Sentences/Equations/Equivalence
Determines unknown dividend in division equations with whole numbers and dividends within 100
Determines unknown divisors in division equations with whole numbers and dividends within 100
Determines whether a linear equation or inequality is true for a given value of the variable
Represents division equations with whole numbers as part‑unknown multiplication equations
Solves one-step linear equations with negative rational numbers
Solves one-step linear equations with positive rational numbers
Translates between verbal and algebraic equations
Writes a one-step linear equation in one variable to represent a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Numerical Expressions
Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Properties and Relationships of Operations
Represents division equations with whole numbers as part‑unknown multiplication equations
Understands division as equal sharing
Understands multiplication as a comparison of sizes
Understands the inverse relationship between multiplication and division
Rate of Change/Slope
Compares the rate of change between two proportional relationships represented in different ways
Whole Numbers: Concepts/Properties
Identifies factors of numbers less than 100
Identifies multiples of single‑digit numbers
Whole Numbers: Multiplication/Division
Divides basic facts
Whole Numbers: Represent and Solve Word Problems
Represents multi-step addition and subtraction word problems with expressions or equations, whole numbers
Represents one-step equal-groups division word problems with expressions or equations, whole numbers
Represents one-step equal-groups multiplication word problems with expressions or equations, whole numbers
Represents one-step multiplicative-comparison word problems with expressions or equations, whole numbers
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step word problems involving the four operations with whole numbers
Solves one-step division word problems that require interpretation of remainders, whole numbers
Solves one-step equal-groups division word problems, whole numbers within 100
Solves one-step multiplicative-comparison word problems, whole-number products greater than 100
Solves one-step multiplicative-comparison word problems, whole-number products within 100
Conversion of Units
Converts units of length between the customary and the metric systems
Length
Converts units of length between the customary and the metric systems
Linear Functions
Interprets the meaning of the point (1, r) on a graph of a real‑world proportional relationship
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Determines if the relationship between two quantities in a real‑world scenario is proportional given a table
Determines missing values in a table of equivalent ratios within a real‑world scenario
Identifies ratios between two quantities not from the same whole
Identifies the part-to-whole ratio between two quantities
Interprets the meaning of the point (0, 0) on a graph of a real‑world proportional relationship
Interprets the meaning of the point (x, y) on a graph of a real‑world proportional relationship
Recognizes a ratio within a context
Solves one-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real‑world and mathematical problems given a table representing equivalent ratios of quantities
Uses a given unit rate to solve a one-step real-world problem
Uses ratios of whole numbers and decimals to calculate unit rates
Uses ratios of whole numbers and fractions to calculate unit rates
Uses ratios of whole numbers to calculate unit rates
Uses tables to represent real-world relationships described by a given ratio
Uses tables to represent real-world relationships described by a given unit rate
Rational Numbers: Solve Real-World and Mathematical Problems
Solves one-step percent problems within a real-world or mathematical context
Coordinate Geometry
Determines the coordinates of points in the first quadrant of a coordinate plane
Interprets points with whole number coordinates in the first quadrant within the given context
Plots the coordinates of points in the first quadrant of a coordinate plane
Identification and Classification of 2-D Shapes
Classifies 2-D shapes by properties, given pictures
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Identifies and names special triangles, such as acute, right, scalene, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., given pictures
Knows definitions of special triangles, such as acute, right, scalene, etc.
Recognizes examples of quadrilaterals
Sorts shapes into categories based on attributes, given pictures
Understands the relationships among categories of shapes
Points, Lines, Segments, Rays, and Angles
Identifies acute or obtuse angles
Identifies parallel lines
Identifies points, lines, rays, line segments, and angles
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Similarity
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Spatial Concepts and Symmetry
Identifies and creates nets for prisms
Identifies and creates nets for pyramids
Volume
Determines the volume of rectangular prisms, given the formula
Angle Measurement
Calculates unknown angle measures using the additive property of angles
Identifies/estimates angle measures
Area
Determines side lengths given the area of rectangles
Determines the area of figures composed of whole and partial unit squares
Determines the area of rectangles with whole-number sides, formula not provided
Explains the relationship between tiling a figure and multiplying side lengths to find the area
Solves problems involving areas of rectangles within a real-world or mathematical context
Bivariate Data
Constructs scatter plots of bivariate data
Describes and interprets data in a scatter plot
Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships
Determines if two categorical variables are correlated with a causal relationship or correlated without a causal relationship
Determines relative frequencies in a two-way frequency table
Determines whether two quantitative variables have a positive linear, negative linear, or zero association
Capacity
Completes simple conversions of customary units of capacity
Conversion of Units
Completes simple conversions of customary units of capacity
Completes simple conversions of customary units of length
Completes simple conversions of customary units of weight
Completes simple conversions of units of time
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Data Analysis
Adds and subtracts to answer questions about bar graphs with multi-unit scales
Adds and subtracts to answer questions about pictographs with multi-unit scales
Compares the means and medians of related data sets from random samples represented in histograms
Identifies outliers in a data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Reads and interprets data from a histogram
Reads and interprets line or dot plots with fractional scales
Solves multi-step problems using data from bar graphs with multi-unit scales
Data Representation
Constructs scatter plots of bivariate data
Represents data in line or dot plots with fractional scales
Represents data in line or dot plots with whole‑number scales
Represents data in pictographs with multi-unit scales
Length
Completes simple conversions of customary units of length
Knows relative sizes of customary units of length
Knows relative sizes of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Compares the means and medians of related data sets from random samples represented in histograms
Determines the median of a data set that is ordered
Identifies the median, quartiles, extreme values, and outliers from a box plot
Interprets the median in the context of a data set
Money
Determines the decimal value of a collection of coins and/or bills given as names
Solves money word problems involving decimals and coins and/or bills given as pictures
Perimeter/Circumference
Determines side lengths given the perimeter of rectangles
Determines the perimeter of basic polygons in which not all sides are labeled
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Problem Solving with Units
Solves money word problems involving decimals and coins and/or bills given as pictures
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step money word problems involving whole numbers within 100
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Solves one-step money word problems involving whole number addition or subtraction
Solves one‑step capacity word problems involving whole-number addition or subtraction
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Time
Completes simple conversions of units of time
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Volume
Determines the missing dimension of a rectangular prism composed of unit cubes given the volume and other dimensions
Determines the volume of figures by counting unit cubes
Determines the volume of rectangular prisms, formula not provided
Identifies rectangular prisms composed of unit cubes that have the same volume as a given rectangular prism
Represents the volume of rectangular prisms composed of unit cubes, using multiplication expressions or equations
Understands that a unit cube has sides of 1 unit in length and a volume of 1 cubic unit
Weight/Mass
Completes simple conversions of customary units of weight
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Algebraic Expressions
Evaluates linear expressions at given values with variables involving positive rational numbers
Evaluates nonlinear expressions at given values with variables involving positive rational numbers
Generates equivalent linear expressions by combining like terms
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets equivalent linear expressions within a real-world context
Translates between verbal and algebraic expressions
Writes linear expressions in one variable to represent real-world or mathematical contexts
Exponents
Evaluates numbers with whole-number bases and whole-number exponents
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Linear Functions
Compares the rate of change between two proportional relationships represented in different ways
Graphs a linear function of the form y = mx given a simple scenario
Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions
Writes the equation of a line in the form y = mx given a table of values or two ordered pairs
Number Sentences/Equations/Equivalence
Determines the number of solutions of a linear equation in one variable given the corresponding equation in the form x=a, x=x, or a=b
Determines unknown dividend in division equations with whole numbers and dividends within 100
Determines whether a linear equation or inequality is true for a given value of the variable
Solves multi-step linear equations with positive and negative rational numbers
Solves one-step linear equations with negative rational numbers
Solves one-step linear equations with positive rational numbers
Writes a one-step linear equation in one variable to represent a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Numerical Expressions
Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers
Applies the order of operations, without grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
Applies the order of operations, without grouping symbols or whole-number exponents, to simplify numerical expressions involving positive rational numbers
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Properties and Relationships of Operations
Understands division as equal sharing
Understands multiplication as a comparison of sizes
Understands the inverse relationship between multiplication and division
Radicals
Evaluates the square root of a perfect square
Rate of Change/Slope
Compares the rate of change between two proportional relationships represented in different ways
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
System of Equations/Inequalities
Solves a system of linear equations graphically
Writes a system of linear equations to represent a real-world or mathematical context
Writes and solves a system of linear equations involving a real-world or mathematical context
Whole Numbers: Concepts/Properties
Identifies factors of numbers less than 100
Whole Numbers: Represent and Solve Word Problems
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step multiplication and division word problems with whole numbers
Solves multi-step word problems involving the four operations with whole numbers
Solves one-step division word problems that require interpretation of remainders, whole numbers
Solves one-step equal-groups division word problems, whole numbers within 100
Solves one-step multiplicative-comparison word problems, whole-number products greater than 100
Solves one-step multiplicative-comparison word problems, whole-number products within 100
Conversion of Units
Converts unit rates to solve real-world problems
Converts units of length between the customary and the metric systems
Solves real-world or mathematical problems involving conversions between the customary and metric systems, given a conversion factor
Length
Converts units of length between the customary and the metric systems
Linear Functions
Interprets the meaning of the point (1, r) on a graph of a real‑world proportional relationship
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rate of Change/Slope
Identifies the unit rate from the graph of a proportional relationship
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Compares ratios within a real-world context
Compares unit rates in real‑world scenarios described by a given ratio
Converts unit rates to solve real-world problems
Creates tables representing proportional relationships involving positive rational numbers
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Determines if the relationship between two quantities in a real‑world scenario is proportional given a table
Determines missing values in a table of equivalent ratios within a real‑world scenario
Identifies ratios between two quantities not from the same whole
Identifies the part-to-whole ratio between two quantities
Interprets the meaning of the point (0, 0) on a graph of a real‑world proportional relationship
Solves one-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real‑world and mathematical problems given a table representing equivalent ratios of quantities
Solves real‑world problems involving rates associated with a ratio
Uses a given unit rate to solve a multi-step real-world problem
Uses a given unit rate to solve a one-step real-world problem
Uses ratios of decimals to calculate unit rates
Uses ratios of whole numbers and decimals to calculate unit rates
Uses ratios of whole numbers and fractions to calculate unit rates
Uses ratios of whole numbers to calculate unit rates
Uses tables to represent real-world relationships described by a given ratio
Uses tables to represent real-world relationships described by a given unit rate
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Solves one-step percent problems within a real-world or mathematical context
Area
Determines the area of parallelograms, formula not provided
Determines the area of triangles, formula not provided
Circles
Uses properties of chords to solve problems involving circles
Coordinate Geometry
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the other vertices plotted on the coordinate plane
Determines the coordinates of points in the first quadrant of a coordinate plane
Interprets points with whole number coordinates in the first quadrant within the given context
Plots the coordinates of points in the first quadrant of a coordinate plane
Identification and Classification of 2-D Shapes
Classifies 2-D shapes by properties, given pictures
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Identifies and names special triangles, such as acute, right, scalene, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., without pictures given
Knows definitions of special triangles, such as acute, right, scalene, etc.
Recognizes examples of quadrilaterals
Sorts shapes into categories based on attributes, given pictures
Understands the relationships among categories of shapes
Perimeter/Circumference
Determines the circumference of circles, formula not provided
Determines the circumference of circles, given the formula
Points, Lines, Segments, Rays, and Angles
Identifies acute or obtuse angles
Identifies parallel lines
Identifies points, lines, rays, line segments, and angles
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Determines scale factors in problems involving scale drawings, maps, and models
Relationships involving Lines, Angles, and Polygons
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Similarity
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Determines scale factors in problems involving scale drawings, maps, and models
Spatial Concepts and Symmetry
Identifies and creates nets for prisms
Identifies the cross-sections of 3-D shapes
Volume
Determines the volume of rectangular prisms, formula not provided
Determines the volume of rectangular prisms, given the formula
Angle Measurement
Calculates unknown angle measures using the additive property of angles
Identifies/estimates angle measures
Measures non-right angles using a protractor
Area
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Determines side lengths given the area of rectangles
Determines the area of figures composed of whole and partial unit squares
Determines the area of rectangles with whole-number sides, formula not provided
Explains the relationship between tiling a figure and multiplying side lengths to find the area
Identifies a unit square
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving the area of figures composed of whole unit squares
Bivariate Data
Analyzes linear trends in scatter plots to make predictions
Constructs scatter plots of bivariate data
Constructs two-way frequency tables
Describes and interprets data in a scatter plot
Describes and interprets outliers and clusters in a scatter plot
Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships
Determines if two categorical variables are correlated with a causal relationship or correlated without a causal relationship
Determines relative frequencies in a two-way frequency table
Determines whether two quantitative variables have a positive linear, negative linear, or zero association
Identifies a lurking variable to explain why correlation does not imply causation in a given situation
Capacity
Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units
Completes simple conversions of customary units of capacity
Conversion of Units
Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units
Completes complex conversions of customary units of length involving fractions, decimals, or more than two units
Completes simple conversions of customary units of capacity
Completes simple conversions of customary units of length
Completes simple conversions of customary units of weight
Completes simple conversions of units of time
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Data Analysis
Adds and subtracts to answer questions about bar graphs with multi-unit scales
Adds and subtracts to answer questions about pictographs with multi-unit scales
Compares the distributions of multiple data sets presented in line or dot plots, or histograms
Compares the means and medians of related data sets from random samples represented in histograms
Identifies outliers in a data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Reads and interprets line or dot plots with fractional scales
Solves word problems using data from line or dot plots with fractional scales
Data Representation
Constructs scatter plots of bivariate data
Constructs two-way frequency tables
Represents data in line or dot plots with fractional scales
Fractions: Represent and Solve Word Problems
Solves word problems using data from line or dot plots with fractional scales
Length
Completes complex conversions of customary units of length involving fractions, decimals, or more than two units
Completes simple conversions of customary units of length
Knows relative sizes of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Compares the means and medians of related data sets from random samples represented in histograms
Determines the mean of a data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Interprets the median in the context of a data set
Money
Determines the decimal value of a collection of coins and/or bills given as names
Perimeter/Circumference
Determines side lengths given the perimeter of rectangles
Determines the perimeter of basic polygons in which not all sides are labeled
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Problem Solving with Units
Solves multi-step length word problems involving whole numbers
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step money word problems involving whole numbers within 100
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Solves one-step weight/mass word problems involving whole number addition and subtraction
Solves one‑step capacity word problems involving whole-number addition or subtraction
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Solves problems involving rectangular prisms composed of unit cubes
Properties and Relationships of Operations
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Time
Completes simple conversions of units of time
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Volume
Determines the missing dimension of a rectangular prism composed of unit cubes given the volume and other dimensions
Determines the volume of figures by counting unit cubes
Determines the volume of rectangular prisms, formula not provided
Identifies rectangular prisms composed of unit cubes that have the same volume as a given rectangular prism
Recognizes situations which describe volume
Represents the volume of rectangular prisms composed of unit cubes, using multiplication expressions or equations
Represents the volume of rectangular prisms composed of unit cubes, using repeated addition expressions or equations
Solves problems involving rectangular prisms composed of unit cubes
Understands that a unit cube has sides of 1 unit in length and a volume of 1 cubic unit
Weight/Mass
Completes simple conversions of customary units of weight
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Algebraic Expressions
Evaluates linear expressions at given values with variables involving positive rational numbers
Evaluates nonlinear expressions at given values with variables involving positive rational numbers
Generates equivalent linear expressions by combining like terms
Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Generates equivalent linear expressions by using the associative, commutative, or distributive property
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets equivalent linear expressions within a real-world context
Interprets the coefficient and constant in a linear expression within the context of a real‑world relationship
Multiplies monomials
Translates between verbal and algebraic expressions
Writes linear expressions in one variable to represent real-world or mathematical contexts
Exponents
Evaluates numbers with whole-number bases and whole-number exponents
Represents a whole number as a power of a whole number
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Solves one-step linear inequalities with positive rational numbers
Solves two-step linear inequalities
Writes a linear inequality in two variables to represent a real-world or mathematical context
Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context
Writes a one-step linear inequality in one variable to represent a real-world or mathematical context
Writes a two-step linear inequality in one variable to represent a real-world or mathematical context
Writes an inequality in the form x > c or x < c to represent a real-world or mathematical context
Writes and solves a two‑step linear inequality in one variable involving a real‑world or mathematical context
Linear Functions
Compares the rate of change between two proportional relationships represented in different ways
Graphs a linear function of the form y = mx given a simple scenario
Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions
Understands that the slope is the same between any two points on a line
Writes an equation in the form y = x + c to represent the relationship between real-world quantities given a table of values
Writes the equation of a line in the form y = mx given a table of values or two ordered pairs
Number Sentences/Equations/Equivalence
Determines the number of solutions of a linear equation in one variable given the corresponding equation in the form x=a, x=x, or a=b
Determines whether a linear equation or inequality is true for a given value of the variable
Evaluates formulas or linear equations at given values for the variables
Solves cubic equations by taking cube roots
Solves multi-step linear equations with positive and negative rational numbers
Solves one-step linear equations with negative rational numbers
Solves one-step linear equations with positive rational numbers
Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
Solves quadratic equations in the form x² = c
Solves two-step linear equations with positive rational numbers
Writes a one-step linear equation in one variable to represent a real-world or mathematical context
Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Numerical Expressions
Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers
Applies the order of operations, with grouping symbols and whole-number exponents, to simplify numerical expressions involving both positive and negative rational numbers
Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
Applies the order of operations, without grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Polynomial Functions
Identifies the zeros of a polynomial function from a graph
Properties and Relationships of Operations
Understands division as equal sharing
Radicals
Evaluates the square root of a perfect square
Rate of Change/Slope
Compares the rate of change between two proportional relationships represented in different ways
Understands that the slope is the same between any two points on a line
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
Scientific Notation
Converts a number from scientific notation to standard form
Converts a number from standard form to scientific notation
Determines the relative magnitude of two numbers expressed in scientific notation
System of Equations/Inequalities
Solves a system of linear equations graphically
Writes a system of linear equations to represent a real-world or mathematical context
Writes and solves a system of linear equations involving a real-world or mathematical context
Whole Numbers: Concepts/Properties
Identifies factors of numbers less than 100
Identifies prime and composite numbers
Whole Numbers: Represent and Solve Word Problems
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step multiplication and division word problems with whole numbers
Solves multi-step word problems involving the four operations with whole numbers
Solves one-step division word problems that require interpretation of remainders, whole numbers
Solves one-step equal-groups division word problems, whole numbers within 100
Conversion of Units
Converts unit rates to solve real-world problems
Converts units of length between the customary and the metric systems
Solves real-world or mathematical problems involving conversions between the customary and metric systems, given a conversion factor
Solves real‑world or mathematical problems involving conversions within a measurement system using ratio reasoning, given a conversion factor
Length
Converts units of length between the customary and the metric systems
Linear Functions
Interprets the meaning of the point (1, r) on a graph of a real‑world proportional relationship
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rate of Change/Slope
Identifies the unit rate from the graph of a proportional relationship
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Compares ratios within a real-world context
Compares unit rates in graphs of proportional relationships within a real‑world context
Compares unit rates in real‑world scenarios described by a given ratio
Converts unit rates to solve real-world problems
Creates tables representing proportional relationships involving positive rational numbers
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Determines missing values in a table of equivalent ratios within a real‑world scenario
Determines the whole in a real-world percent problem given the part and the percent
Identifies ratios between two quantities not from the same whole
Identifies the part-to-whole ratio between two quantities
Solves multi-step percent problems within a real-world or mathematical context
Solves one-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real‑world and mathematical problems given a table representing equivalent ratios of quantities
Solves real‑world problems involving rates associated with a ratio
Uses a given unit rate to solve a multi-step real-world problem
Uses a given unit rate to solve a one-step real-world problem
Uses ratios of decimals to calculate unit rates
Uses ratios of whole numbers and decimals to calculate unit rates
Uses ratios of whole numbers and fractions to calculate unit rates
Uses ratios of whole numbers to calculate unit rates
Uses tables to represent real-world relationships described by a given ratio
Uses two given unit rates to solve a multi-step real-world problem
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Determines the whole in a real-world percent problem given the part and the percent
Solves multi-step percent problems within a real-world or mathematical context
Solves one-step percent problems within a real-world or mathematical context
Area
Describes the effect on area when dimensions of a rectangle are changed
Describes the effect on area when dimensions of a triangle are changed
Determines the area of figures composed of polygons
Determines the area of parallelograms, formula not provided
Determines the area of triangles, formula not provided
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Circles
Recognizes the relationship between tangent lines and radii
Understands that the ratio of the circumference to the diameter is the same for two circles
Uses properties of chords to solve problems involving circles
Coordinate Geometry
Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the other vertices plotted on the coordinate plane
Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint
Determines the coordinates of points in the first quadrant of a coordinate plane
Interprets points with whole number coordinates in the first quadrant within the given context
Plots the coordinates of points in the first quadrant of a coordinate plane
Identification and Classification of 2-D Shapes
Classifies 2-D shapes by properties, given pictures
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Identifies and names special triangles, such as acute, right, scalene, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., without pictures given
Knows definitions of special triangles, such as acute, right, scalene, etc.
Sorts shapes into a hierarchy, given pictures
Sorts shapes into categories based on attributes, given pictures
Understands the relationships among categories of shapes
Perimeter/Circumference
Determines the circumference of circles, formula not provided
Determines the circumference of circles, given the formula
Determines the radius or diameter given the circumference of a circle
Points, Lines, Segments, Rays, and Angles
Identifies parallel lines
Identifies perpendicular lines
Problem Solving with Units
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Applies the concept of density to solve problems involving area and volume
Relationships involving Lines, Angles, and Polygons
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Solves multi‑step problems by applying the properties of supplementary, complementary, and vertical angles
Similarity
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Understands that the ratio of the circumference to the diameter is the same for two circles
Spatial Concepts and Symmetry
Identifies and creates nets for prisms
Identifies the cross-sections of 3-D shapes
Volume
Determines the volume of pyramids, given the formula
Determines the volume of rectangular prisms, formula not provided
Determines the volume of rectangular prisms, given the formula
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Angle Measurement
Calculates and explains how to find unknown angle measures using the additive property of angles
Calculates unknown angle measures using the additive property of angles
Explains how to find unknown angle measures using the additive property of angles
Identifies/estimates angle measures
Knows the definition of an angle
Measures non-right angles using a protractor
Understands what the measure of an angle represents
Area
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Determines side lengths given the area of rectangles
Determines the area of figures composed of rectangles
Determines the area of rectangles with whole-number sides, formula not provided
Identifies a unit square
Solves problems involving areas of rectangles within a real-world or mathematical context
Bivariate Data
Analyzes linear trends in scatter plots to make predictions
Approximates the line of best fit on a scatter plot
Constructs scatter plots of bivariate data
Constructs two-way frequency tables
Describes and interprets data in a scatter plot
Describes and interprets outliers and clusters in a scatter plot
Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships
Determines relative frequencies in a two-way frequency table
Determines whether two quantitative variables have a positive linear, negative linear, or zero association
Interprets the meaning of the slope or y-intercept of a line of best fit or regression line
Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship
Uses a given equation of a line of best fit to make predictions
Capacity
Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Conversion of Units
Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units
Completes complex conversions of customary units of length involving fractions, decimals, or more than two units
Completes complex conversions of more than two units of time
Completes simple conversions of customary units of length
Completes simple conversions of customary units of weight
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Data Analysis
Adds and subtracts to answer questions about pictographs with multi-unit scales
Compares the distributions of multiple data sets presented in line or dot plots, or histograms
Compares the means and medians of related data sets from random samples represented in histograms
Compares the variability of related data sets from random samples presented in box plots
Identifies outliers in a data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Reads and interprets line or dot plots with fractional scales
Solves word problems using data from line or dot plots with fractional scales
Data Representation
Constructs scatter plots of bivariate data
Constructs two-way frequency tables
Represents data in histograms
Represents data in line or dot plots with fractional scales
Fractions: Represent and Solve Word Problems
Solves word problems using data from line or dot plots with fractional scales
Length
Completes complex conversions of customary units of length involving fractions, decimals, or more than two units
Completes simple conversions of customary units of length
Knows relative sizes of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Compares the means and medians of related data sets from random samples represented in histograms
Compares the variability of related data sets from random samples presented in box plots
Determines the mean of a data set
Determines the median of a data set that is not ordered
Determines the range of a data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Interprets the median in the context of a data set
Perimeter/Circumference
Determines side lengths given the perimeter of rectangles
Determines the perimeter of basic polygons in which not all sides are labeled
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Points, Lines, Segments, Rays, and Angles
Knows the definition of an angle
Understands what the measure of an angle represents
Problem Solving with Units
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Solves one-step weight/mass word problems involving whole number multiplication and division
Solves one‑step capacity word problems involving whole-number addition or subtraction
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Solves problems involving rectangular prisms composed of unit cubes
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Properties and Relationships of Operations
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Time
Completes complex conversions of more than two units of time
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Volume
Determines possible dimensions for rectangular prisms given one dimension and the volume in unit cubes
Determines the missing dimension of a rectangular prism composed of unit cubes given the volume and other dimensions
Determines the volume of figures by counting unit cubes
Determines the volume of figures composed of rectangular prisms
Determines the volume of rectangular prisms, formula not provided
Identifies rectangular prisms composed of unit cubes that have the same volume as a given rectangular prism
Recognizes situations which describe volume
Represents the volume of rectangular prisms composed of unit cubes, using repeated addition expressions or equations
Solves problems involving rectangular prisms composed of unit cubes
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Understands how volume is measured
Understands that a unit cube has sides of 1 unit in length and a volume of 1 cubic unit
Weight/Mass
Completes simple conversions of customary units of weight
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Algebraic Expressions
Adds and subtracts polynomials
Evaluates linear expressions at given values with variables involving positive rational numbers
Evaluates nonlinear expressions at given values with variables involving positive rational numbers
Generates equivalent linear expressions by combining like terms
Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Generates equivalent linear expressions by using the associative, commutative, or distributive property
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets equivalent linear expressions within a real-world context
Interprets the coefficient and constant in a linear expression within the context of a real‑world relationship
Multiplies a polynomial by a monomial
Multiplies monomials
Multiplies two binomial expressions
Translates between verbal and algebraic expressions
Writes algebraic expressions from a mathematical description of its component parts, including sum, product, quotient, term, and coefficient
Writes linear expressions in one variable to represent real-world or mathematical contexts
Exponents
Evaluates numbers with negative integer bases and whole-number exponents
Represents a whole number as a power of a whole number
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Uses substitution to determine an unknown exponent in an equation
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Represents an inequality in the form x>c or x<c on a number line given a real-world or mathematical context
Solves one-step linear inequalities with negative rational numbers
Solves two-step linear inequalities
Writes a compound inequality to represent a real-world or mathematical context
Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context
Writes a one-step linear inequality in one variable to represent a real-world or mathematical context
Writes a quadratic inequality in one variable to represent a real‑world or mathematical context
Writes a two-step linear inequality in one variable to represent a real-world or mathematical context
Writes an inequality in the form x > c or x < c to represent a real-world or mathematical context
Writes an inequality in the form x>c or x<c to represent a set of real numbers shown on a number line
Writes and solves a one-step linear inequality in one variable involving a real-world or mathematical context
Writes and solves a two‑step linear inequality in one variable involving a real‑world or mathematical context
Linear Functions
Compares the rate of change between two proportional relationships represented in different ways
Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions
Understands that the slope is the same between any two points on a line
Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a simple scenario
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a graph
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a table of values or two ordered pairs
Writes an equation in the form y = x + c to represent the relationship between real-world quantities given a table of values
Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs
Writes the equation of a line in the form y = mx given a table of values or two ordered pairs
Number Sentences/Equations/Equivalence
Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision
Determines the number of solutions of a linear equation in one variable given the corresponding equation in the form x=a, x=x, or a=b
Determines whether a linear equation or inequality is true for a given value of the variable
Evaluates formulas or linear equations at given values for the variables
Identifies an ordered pair that is a solution to a two-variable equation
Solves cubic equations by taking cube roots
Solves multi-step linear equations with positive and negative rational numbers
Solves one-step linear equations with negative rational numbers
Solves one-step linear equations with positive rational numbers
Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
Solves quadratic equations in the form x² = c
Solves radical equations that lead to linear equations
Solves two-step linear equations with negative rational numbers
Solves two-step linear equations with positive rational numbers
Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
Writes a one-step linear equation in one variable to represent a real-world or mathematical context
Writes a two-step linear equation in one variable to represent a real-world or mathematical context
Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context
Writes and solves a one-step quadratic equation in the form x² = c involving a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Writes the equation of a vertical line given a graph
Numerical Expressions
Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers
Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Polynomial Functions
Identifies the zeros of a polynomial function from a graph
Radicals
Evaluates the square root of a perfect square
Rate of Change/Slope
Compares the rate of change between two proportional relationships represented in different ways
Understands that the slope is the same between any two points on a line
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
Scientific Notation
Converts a number from standard form to scientific notation
Determines the relative magnitude of two numbers expressed in scientific notation
Multiplies and divides numbers expressed in scientific notation
Solves real-world problems with numbers expressed in scientific notation
System of Equations/Inequalities
Identifies an ordered pair that is a solution to a system of linear inequalities
Solves a system of equations with one linear and one quadratic equation algebraically
Solves a system of linear equations algebraically
Solves a system of linear equations graphically
Writes a system of linear equations to represent a real-world or mathematical context
Writes a system of linear inequalities to represent a real-world or mathematical context
Writes and solves a system of linear equations involving a real-world or mathematical context
Whole Numbers: Represent and Solve Word Problems
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step multiplication and division word problems with whole numbers
Solves multi-step word problems involving the four operations with whole numbers
Solves one-step division word problems that require interpretation of remainders, whole numbers
Solves one-step equal-groups division word problems, whole numbers within 100
Conversion of Units
Converts unit rates to solve real-world problems
Converts units of length between the customary and the metric systems
Solves real-world or mathematical problems involving conversions between the customary and metric systems, given a conversion factor
Solves real‑world or mathematical problems involving conversions between the customary and metric systems, given a ratio equivalent to a conversion factor
Solves real‑world or mathematical problems involving conversions within a measurement system using ratio reasoning, given a conversion factor
Length
Converts units of length between the customary and the metric systems
Linear Functions
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rate of Change/Slope
Identifies the unit rate from the graph of a proportional relationship
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Compares ratios within a real-world context
Compares unit rates in graphs of proportional relationships within a real‑world context
Compares unit rates in real‑world scenarios described by a given ratio
Converts unit rates to solve real-world problems
Creates tables representing proportional relationships involving positive rational numbers
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Determines missing values in a table of equivalent ratios within a real‑world scenario
Determines the whole in a real-world percent problem given the part and the percent
Identifies the part-to-whole ratio between two quantities
Solves multi-step percent problems within a real-world or mathematical context
Solves one-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real‑world and mathematical problems given a table representing equivalent ratios of quantities
Solves real‑world problems involving rates associated with a ratio
Uses a given unit rate to solve a multi-step real-world problem
Uses a given unit rate to solve a one-step real-world problem
Uses ratios of decimals to calculate unit rates
Uses ratios of fractions to calculate unit rates
Uses ratios of whole numbers to calculate unit rates
Uses two given unit rates to solve a multi-step real-world problem
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Determines the whole in a real-world percent problem given the part and the percent
Solves multi-step percent problems within a real-world or mathematical context
Solves one-step percent problems within a real-world or mathematical context
Area
Describes the effect on area when dimensions of a rectangle are changed
Describes the effect on area when dimensions of a triangle are changed
Describes the effect on area when the radius or diameter of a circle is changed
Determines the area of circles, given the formula
Determines the area of figures composed of polygons
Determines the area of parallelograms, formula not provided
Determines the area of triangles, formula not provided
Determines the ratio between areas of scaled figures
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Circles
Solves problems involving inscribed angles on a diameter
Understands that the ratio of the circumference to the diameter is the same for two circles
Uses properties of chords to solve problems involving circles
Writes the equation of a circle given the center and radius
Conic Sections
Writes the equation of a circle given the center and radius
Coordinate Geometry
Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the other vertices plotted on the coordinate plane
Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint
Determines the coordinates of points in the first quadrant of a coordinate plane
Determines the coordinates of the midpoint of a line segment
Determines the perimeter or area of a rectangle given vertices with the same first or second coordinate
Identifies the type of quadrilateral given the coordinates of the vertices
Plots the coordinates of points in the first quadrant of a coordinate plane
Identification and Classification of 2-D Shapes
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Identifies and names special triangles, such as acute, right, scalene, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., without pictures given
Knows definitions of special triangles, such as acute, right, scalene, etc.
Sorts shapes into a hierarchy, given pictures
Sorts shapes into categories based on attributes, given pictures
Understands the relationships among categories of shapes
Identification and Classification of 3-D Shapes
Applies measurement and geometric properties of 3‑D shapes to model and solve problems within a real‑world context
Perimeter/Circumference
Determines the circumference of circles, formula not provided
Determines the circumference of circles, given the formula
Determines the radius or diameter given the circumference of a circle
Points, Lines, Segments, Rays, and Angles
Identifies perpendicular lines
Problem Solving with Units
Applies measurement and geometric properties of 3‑D shapes to model and solve problems within a real‑world context
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Applies the concept of density to solve problems involving area and volume
Determines scale factors in problems involving scale drawings of geometric figures
Relationships involving Lines, Angles, and Polygons
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Solves multi‑step problems by applying the properties of supplementary, complementary, and vertical angles
Similarity
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Determines scale factors in problems involving scale drawings of geometric figures
Understands that the ratio of the circumference to the diameter is the same for two circles
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the cross-sections of 3-D shapes
Surface Area
Determines the surface area of a prism given a net
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Volume
Determines the volume of cylinders, given the formula
Determines the volume of pyramids, formula not provided
Determines the volume of pyramids, given the formula
Determines the volume of rectangular prisms, formula not provided
Determines the volume of rectangular prisms, given the formula
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Angle Measurement
Knows the definition of an angle
Measures non-right angles using a protractor
Area
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Determines the area of figures composed of rectangles
Determines the area of rectangles given the perimeter
Determines the perimeter of rectangles given the area
Identifies a unit square
Represents the area of figures composed of rectangles using expressions or equations
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Analyzes linear trends in scatter plots to make predictions
Approximates the line of best fit on a scatter plot
Constructs scatter plots of bivariate data
Constructs two-way frequency tables
Describes and interprets data in a scatter plot
Describes and interprets outliers and clusters in a scatter plot
Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships
Determines relative frequencies in a two-way frequency table
Determines whether two quantitative variables have a positive linear, negative linear, or zero association
Interprets the meaning of the slope or y-intercept of a line of best fit or regression line
Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship
Uses a given equation of a line of best fit to make predictions
Capacity
Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Conversion of Units
Completes complex conversions of customary units of capacity involving fractions, decimals, or more than two units
Completes conversions of metric units of length
Completes simple conversions of customary units of weight
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi-step weight word problems involving whole numbers and conversion of customary units
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Data Analysis
Adds and subtracts to answer questions about pictographs with multi-unit scales
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Compares the distributions of multiple data sets presented in line or dot plots, or histograms
Compares the means and medians of related data sets from random samples represented in histograms
Compares the median and variability of related data sets from random samples presented in box plots
Compares two data sets based on measures of center or variability to answer a question
Determines a valid conclusion based on a comparison of multiple data sets with similar variabilities using measures of center and variability
Identifies the median, quartiles, extreme values, and outliers from a box plot
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Solves word problems using data from line or dot plots with fractional scales
Data Representation
Constructs scatter plots of bivariate data
Constructs two-way frequency tables
Represents data in histograms
Fractions: Represent and Solve Word Problems
Solves word problems using data from line or dot plots with fractional scales
Length
Completes conversions of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Compares the means and medians of related data sets from random samples represented in histograms
Compares the median and variability of related data sets from random samples presented in box plots
Determines a missing value in a data set when the mean is known
Determines a valid conclusion based on a comparison of multiple data sets with similar variabilities using measures of center and variability
Determines how the measures of center are affected with the addition or deletion of a data value, including outliers
Determines the mean of a data set
Determines the median of a data set that is not ordered
Determines the range of a data set
Explains why the mean and median differ in a single data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Interprets the median in the context of a data set
Perimeter/Circumference
Determines side lengths given the perimeter of rectangles
Determines the area of rectangles given the perimeter
Determines the perimeter of basic polygons in which not all sides are labeled
Determines the perimeter of complex figures in which not all sides are labeled
Determines the perimeter of rectangles given the area
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Points, Lines, Segments, Rays, and Angles
Knows the definition of an angle
Problem Solving with Units
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi-step weight word problems involving whole numbers and conversion of customary units
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Solves one-step time word problems involving multiplication or division
Solves one‑step capacity word problems involving whole-number addition or subtraction
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Properties and Relationships of Operations
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Time
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Volume
Determines possible dimensions for rectangular prisms given one dimension and the volume in unit cubes
Determines the length, width, or height given the volume of a rectangular prism and two of the dimensions
Determines the missing dimension of a rectangular prism composed of unit cubes given the volume and other dimensions
Determines the volume of a rectangular prism given a net shown on a grid
Determines the volume of figures composed of rectangular prisms
Determines the volume of rectangular prisms, formula not provided
Identifies rectangular prisms composed of unit cubes that have the same volume as a given rectangular prism
Recognizes situations which describe volume
Represents the volume of rectangular prisms composed of unit cubes, using repeated addition expressions or equations
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Understands how volume is measured
Understands that a unit cube has sides of 1 unit in length and a volume of 1 cubic unit
Weight/Mass
Completes simple conversions of customary units of weight
Solves multi-step weight word problems involving whole numbers and conversion of customary units
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Algebraic Expressions
Adds and subtracts polynomials
Evaluates linear expressions at given values with variables involving positive rational numbers
Evaluates nonlinear expressions at given values with variables involving positive rational numbers
Factors polynomials using a difference of squares
Factors quadratic trinomials
Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Generates equivalent linear expressions by using the associative, commutative, or distributive property
Generates equivalent nonlinear expressions by combining like terms
Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets equivalent linear expressions within a real-world context
Interprets the coefficient and constant in a linear expression within the context of a real‑world relationship
Interprets the factors of a polynomial within the context of a real‑world relationship
Interprets the variable in a linear expression within the context of a real-world relationship
Multiplies a polynomial by a monomial
Multiplies monomials
Multiplies two binomial expressions
Simplifies rational expressions
Translates between verbal and algebraic expressions
Writes linear expressions in one variable to represent real-world or mathematical contexts
Exponents
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Uses substitution to determine an unknown exponent in an equation
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Represents an inequality in the form x>c or x<c on a number line given a real-world or mathematical context
Represents the solutions of a compound linear inequality on a number line
Represents the solutions of a one-step linear inequality on a number line
Represents the solutions of a two-step linear inequality on a number line
Solves multi-step linear inequalities
Solves one-step linear inequalities with negative rational numbers
Solves two-step linear inequalities
Writes a compound inequality to represent a real-world or mathematical context
Writes a compound inequality to represent a set of real numbers shown on a number line
Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context
Writes a multi-step rational inequality in one variable to represent a real-world or mathematical context
Writes a one-step linear inequality in one variable to represent a real-world or mathematical context
Writes a quadratic inequality in one variable to represent a real‑world or mathematical context
Writes a two-step linear inequality in one variable to represent a real-world or mathematical context
Writes an inequality in the form x > c or x < c to represent a real-world or mathematical context
Writes an inequality in the form x>c or x<c to represent a set of real numbers shown on a number line
Writes and solves a two‑step linear inequality in one variable involving a real‑world or mathematical context
Linear Functions
Calculates the slope of a line on a graph
Compares the rate of change between two proportional relationships represented in different ways
Determines the y-intercept of a line given two points on the line
Graphs the equation of a line in the form y = mx + b
Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions
Understands that the slope is the same between any two points on a line
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a graph
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a table of values or two ordered pairs
Writes an equation in the form y = x + c to represent the relationship between real-world quantities given a table of values
Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs
Writes the equation of a line in the form y = mx given a graph
Writes the equation of a line in the form y = mx given a table of values or two ordered pairs
Number Sentences/Equations/Equivalence
Applies the simple interest formula to solve for the interest rate, principal, or time invested
Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision
Determines whether a linear equation or inequality is true for a given value of the variable
Evaluates formulas or linear equations at given values for the variables
Identifies an ordered pair that is a solution to a two-variable equation
Solves literal equations for linear variables
Solves multi-step linear equations with positive and negative rational numbers
Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
Solves quadratic equations in the form x² = c
Solves radical equations that lead to a quadratic equation
Solves radical equations that lead to linear equations
Solves rational equations
Solves two-step linear equations with negative rational numbers
Solves two-step linear equations with positive rational numbers
Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
Writes a quadratic equation in one variable to represent a real-world or mathematical context
Writes an exponential equation in one variable to represent a real-world or mathematical context
Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context
Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context
Writes and solves a one-step quadratic equation in the form x² = c involving a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Writes the equation of a vertical line given a graph
Numerical Expressions
Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers
Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers
Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Polynomial Functions
Identifies the zeros of a polynomial function from a graph
Radicals
Evaluates the square root of a perfect square
Rate of Change/Slope
Calculates the slope of a line on a graph
Compares the rate of change between two proportional relationships represented in different ways
Understands that the slope is the same between any two points on a line
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
Scientific Notation
Approximates very large and very small quantities using scientific notation
Converts a number from standard form to scientific notation
Determines the relative magnitude of two numbers expressed in scientific notation
Multiplies and divides numbers expressed in scientific notation
Solves real-world problems with numbers expressed in scientific notation
System of Equations/Inequalities
Determines the number of solutions to a system of linear equations
Identifies an ordered pair that is a solution to a system of linear inequalities
Shows the steps to solve a system of linear equations using linear combinations
Solves a system of equations with one linear and one quadratic equation algebraically
Solves a system of linear equations algebraically
Writes a system of linear equations given a graph
Writes a system of linear equations to represent a real-world or mathematical context
Writes a system of linear inequalities to represent a real-world or mathematical context
Writes and solves a system of linear equations involving a real-world or mathematical context
Whole Numbers: Represent and Solve Word Problems
Solves multi-step addition and subtraction word problems, whole numbers within 100
Solves multi-step word problems involving the four operations with whole numbers
Conversion of Units
Converts unit rates to solve real-world problems
Converts units of length between the customary and the metric systems
Solves real-world or mathematical problems involving conversions between the customary and metric systems, given a conversion factor
Solves real‑world or mathematical problems involving conversions between the customary and metric systems, given a ratio equivalent to a conversion factor
Solves real‑world or mathematical problems involving conversions within a measurement system using ratio reasoning, given a conversion factor
Length
Converts units of length between the customary and the metric systems
Linear Functions
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rate of Change/Slope
Identifies the unit rate from the graph of a proportional relationship
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Compares ratios within a real-world context
Compares unit rates in real‑world scenarios described by a given ratio
Converts unit rates to solve real-world problems
Creates tables representing proportional relationships involving positive rational numbers
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Determines missing values in a table of equivalent ratios within a real‑world scenario
Identifies the part-to-whole ratio between two quantities
Solves multi-step percent problems within a real-world or mathematical context
Solves one-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real‑world problems involving percent error
Solves real‑world problems involving rates associated with a ratio
Uses a given unit rate to solve a multi-step real-world problem
Uses a given unit rate to solve a one-step real-world problem
Uses ratios of decimals to calculate unit rates
Uses ratios of fractions to calculate unit rates
Uses ratios of whole numbers to calculate unit rates
Uses two given unit rates to solve a multi-step real-world problem
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Solves multi-step percent problems within a real-world or mathematical context
Solves one-step percent problems within a real-world or mathematical context
Solves real‑world problems involving percent error
Area
Describes the effect on area when dimensions of a rectangle are changed
Describes the effect on area when dimensions of a triangle are changed
Describes the effect on area when the radius or diameter of a circle is changed
Determines the area of circles, formula not provided
Determines the area of figures composed of polygons
Determines the area of parallelograms, formula not provided
Determines the area of quarter circles, semicircles, or three‑quarter circles
Determines the area of trapezoids, formula not provided
Determines the area of triangles, formula not provided
Determines the circumference given the area of a circle
Determines the radius or diameter given the area of a circle
Determines the ratio between areas of scaled figures
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Circles
Explains why an inscribed angle in a semicircle is a right angle
Recognizes relationships among the measures of central angles, inscribed angles, and circumscribed angles
Solves problems involving inscribed angles on a diameter
Understands that the ratio of the circumference to the diameter is the same for two circles
Uses properties of central and inscribed angles to solve problems involving circles
Uses properties of chords to solve problems involving circles
Writes the equation of a circle given the center and radius
Conic Sections
Writes the equation of a circle given the center and radius
Coordinate Geometry
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the other vertices plotted on the coordinate plane
Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint
Determines the coordinates of points in the first quadrant of a coordinate plane
Determines the coordinates of the midpoint of a line segment
Determines the perimeter or area of a rectangle given vertices with the same first or second coordinate
Plots the coordinates of points in the first quadrant of a coordinate plane
Identification and Classification of 2-D Shapes
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., given pictures
Identifies properties of a 2‑D shape, such as right angles, parallel sides, etc., without pictures given
Sorts shapes into a hierarchy, given pictures
Sorts shapes into categories based on attributes, given pictures
Understands the relationships among categories of shapes
Identification and Classification of 3-D Shapes
Applies measurement and geometric properties of 3‑D shapes to model and solve problems within a real‑world context
Perimeter/Circumference
Determines the circumference given the area of a circle
Determines the circumference of circles, formula not provided
Determines the radius or diameter given the circumference of a circle
Points, Lines, Segments, Rays, and Angles
Identifies perpendicular lines
Problem Solving with Units
Applies measurement and geometric properties of 3‑D shapes to model and solve problems within a real‑world context
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Applies the concept of density to solve problems involving area and volume
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Solves multi‑step problems by applying the properties of supplementary, complementary, and vertical angles
Similarity
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Understands that the ratio of the circumference to the diameter is the same for two circles
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the cross-sections of 3-D shapes
Surface Area
Determines the surface area of a prism given a net
Determines the surface area of rectangular prisms or cubes, formula not provided
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Volume
Describes the effect on volume when dimensions of a rectangular prism are changed
Determines the radius or diameter of a sphere given the volume
Determines the volume of cylinders, formula not provided
Determines the volume of cylinders, given the formula
Determines the volume of pyramids, formula not provided
Determines the volume of pyramids, given the formula
Determines the volume of rectangular prisms, formula not provided
Determines the volume of spheres, given the formula
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height
Angle Measurement
Knows the definition of an angle
Area
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Determines the area of figures composed of rectangles
Determines the area of rectangles given the perimeter
Determines the perimeter of rectangles given the area
Solves area word problems involving whole numbers and tiling rectangles with non-unit squares
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Analyzes linear trends in scatter plots to make predictions
Approximates the line of best fit on a scatter plot
Compares two sets of bivariate data to draw conclusions
Describes and interprets outliers and clusters in a scatter plot
Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships
Determines relative frequencies in a two-way frequency table
Determines whether two quantitative variables have a positive linear, negative linear, or zero association
Determines whether two quantitative variables have a positive or negative nonlinear association
Estimates the slope of a line of best fit
Interprets the meaning of the slope or y-intercept of a line of best fit or regression line
Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship
Uses a given equation of a line of best fit to make predictions
Uses a given exponential equation fitted to data to make predictions
Capacity
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Conversion of Units
Completes conversions of metric units of length
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step mass word problems involving whole numbers and conversion of metric units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Data Analysis
Adds and subtracts to answer questions about pictographs with multi-unit scales
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Compares the distributions of multiple data sets presented in line or dot plots, or histograms
Compares the means and medians of related data sets from random samples represented in histograms
Compares the medians of related data sets from random samples represented numerically and in a line or dot plot
Compares two data sets based on measures of center or variability to answer a question
Determines a valid conclusion based on a comparison of multiple data sets with similar variabilities using measures of center and variability
Identifies the median, quartiles, extreme values, and outliers from a box plot
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Solves word problems using data from line or dot plots with fractional scales
Data Representation
Represents data in box plots
Represents data in histograms
Fractions: Represent and Solve Word Problems
Solves word problems using data from line or dot plots with fractional scales
Length
Completes conversions of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Compares the means and medians of related data sets from random samples represented in histograms
Compares the medians of related data sets from random samples represented numerically and in a line or dot plot
Determines a missing value in a data set when the mean is known
Determines a valid conclusion based on a comparison of multiple data sets with similar variabilities using measures of center and variability
Determines how the measures of center are affected with the addition or deletion of a data value, including outliers
Determines the mean of a data set
Determines the median of a data set that is not ordered
Determines the range of a data set
Explains why the mean and median differ in a single data set
Identifies the median, quartiles, extreme values, and outliers from a box plot
Interprets the median in the context of a data set
Perimeter/Circumference
Determines the area of rectangles given the perimeter
Determines the perimeter of rectangles given the area
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving perimeters of non-rectangular polygons within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Points, Lines, Segments, Rays, and Angles
Knows the definition of an angle
Populations/Random Processes
Identifies a statistical question
Problem Solving with Units
Solves area word problems involving whole numbers and tiling rectangles with non-unit squares
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi-step mass word problems involving whole numbers and conversion of metric units
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Solves problems involving areas of rectangles within a real-world or mathematical context
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving perimeters of non-rectangular polygons within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Properties and Relationships of Operations
Applies the distributive property of multiplication to find the area of rectangles with whole-number sides
Time
Solves multi-step time word problems involving conversion across seconds, minutes, hours, etc.
Volume
Determines possible dimensions for rectangular prisms given one dimension and the volume in unit cubes
Determines the length, width, or height given the volume of a rectangular prism and two of the dimensions
Determines the missing dimension of a rectangular prism composed of unit cubes given the volume and other dimensions
Determines the volume of a rectangular prism given a net shown on a grid
Determines the volume of figures composed of rectangular prisms
Determines the volume of rectangular prisms, formula not provided
Recognizes situations which describe volume
Represents the volume of rectangular prisms composed of unit cubes, using repeated addition expressions or equations
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Understands that a unit cube has sides of 1 unit in length and a volume of 1 cubic unit
Weight/Mass
Solves multi-step mass word problems involving whole numbers and conversion of metric units
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Algebraic Expressions
Adds and subtracts polynomials
Factors polynomials using a difference of squares
Factors polynomials with a degree greater than 2 by identifying common monomial factors
Factors polynomials with a degree greater than 2 by identifying common monomial factors and factoring the resulting polynomial
Factors quadratic trinomials
Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Generates equivalent linear expressions by using the associative, commutative, or distributive property
Generates equivalent nonlinear expressions by combining like terms
Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets equivalent linear expressions within a real-world context
Interprets the constant in a quadratic expression within the context of a real-world relationship
Interprets the factors of a polynomial within the context of a real‑world relationship
Multiplies a polynomial by a monomial
Multiplies monomials
Multiplies polynomials
Multiplies two binomial expressions
Proves the square of a binomial identity using area models
Simplifies rational expressions
Translates between verbal and algebraic expressions
Writes a rational expression as a sum of a polynomial and a proper rational expression
Writes linear expressions in one variable to represent real-world or mathematical contexts
Exponential and Logarithmic Functions
Solves a real‑world problem involving an exponential relationship between quantities
Exponents
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Uses substitution to determine an unknown exponent in an equation
Geometric Proof/Logic/Inductive and Deductive Reasoning
Proves the square of a binomial identity using area models
Inequalities
Determines whether a linear equation or inequality is true for a given value of the variable
Represents the solutions of a compound linear inequality on a number line
Represents the solutions of a multistep linear inequality on a number line
Represents the solutions of a two-step linear inequality on a number line
Represents the solutions of a two-variable linear inequality on the coordinate plane
Solves compound linear inequalities
Solves multi-step linear inequalities
Solves one-step linear inequalities with negative rational numbers
Solves two-step linear inequalities
Writes a compound inequality to represent a real-world or mathematical context
Writes a compound inequality to represent a set of real numbers shown on a number line
Writes a quadratic inequality in one variable to represent a real‑world or mathematical context
Writes an inequality in the form x > c or x < c to represent a real-world or mathematical context
Writes and solves a two‑step linear inequality in one variable involving a real‑world or mathematical context
Linear Functions
Calculates the slope of a line given ordered pairs
Compares the rate of change between two proportional relationships represented in different ways
Understands that the slope is the same between any two points on a line
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a graph
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario
Writes the equation of a line in the form y = mx + b given a graph
Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs
Writes the equation of a line in the form y = mx + b given the slope and a point on the line
Number Sentences/Equations/Equivalence
Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision
Determines whether a linear equation or inequality is true for a given value of the variable
Evaluates formulas or linear equations at given values for the variables
Identifies an ordered pair that is a solution to a two-variable equation
Solves literal equations for linear variables
Solves multi-step linear equations with positive and negative rational numbers
Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
Solves quadratic equations in the form x² = c
Solves quadratic equations with complex solutions
Solves radical equations that lead to a quadratic equation
Solves radical equations that lead to linear equations
Solves rational equations
Understands the relationship between the points of intersection of the graphs of f(x) and g(x) and the solutions to the equation f(x) = g(x)
Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
Writes a quadratic equation in one variable to represent a real-world or mathematical context
Writes an exponential equation in one variable to represent a real-world or mathematical context
Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context
Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context
Writes and solves a one-step quadratic equation in the form x² = c involving a real-world or mathematical context
Writes and solves a one‑step cubic equation in the form x^3=c involving a real‑world or mathematical context
Writes and solves a rational equation in one variable involving a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Writes the equation of a vertical line given a graph
Numerical Expressions
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Represents descriptions of calculations with numerical expressions or equations that include parentheses
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Polynomial Functions
Applies the polynomial Remainder Theorem
Identifies the zeros of a polynomial function from a graph
Quadratic Functions
Writes a quadratic function given the zeros
Radicals
Evaluates the square root of a perfect square
Rate of Change/Slope
Calculates the slope of a line given ordered pairs
Compares the rate of change between two proportional relationships represented in different ways
Understands that the slope is the same between any two points on a line
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
Scientific Notation
Determines the relative magnitude of two numbers expressed in scientific notation
Multiplies and divides numbers expressed in scientific notation
Solves real-world problems with numbers expressed in scientific notation
System of Equations/Inequalities
Determines the number of solutions to a system of linear equations
Graphs a system of linear equations
Graphs a system of linear inequalities
Identifies an ordered pair that is a solution to a system of linear inequalities
Solves a system of equations with one linear and one quadratic equation algebraically
Solves a system of linear equations given a table
Writes a system of linear equations given a graph
Writes a system of linear equations to represent a real-world or mathematical context
Writes a system of linear inequalities to represent a real-world or mathematical context
Writes and solves a system of linear equations involving a real-world or mathematical context
Whole Numbers: Represent and Solve Word Problems
Solves multi-step addition and subtraction word problems, whole numbers within 100
Conversion of Units
Solves real-world or mathematical problems involving conversions between the customary and metric systems, given a conversion factor
Solves real‑world or mathematical problems involving conversions between the customary and metric systems, given a ratio equivalent to a conversion factor
Solves real‑world or mathematical problems involving conversions within a measurement system using ratio reasoning, given a conversion factor
Linear Functions
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rates/Ratios/Proportions/Percents
Calculates the unit rate from a table of a proportional relationship
Compares ratios within a real-world context
Creates tables representing proportional relationships involving positive rational numbers
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real-world problems involving percent or fractional increase
Solves real‑world problems involving percent error
Solves real‑world problems involving rates associated with a ratio
Uses a given unit rate to solve a multi-step real-world problem
Uses ratios of decimals to calculate unit rates
Uses ratios of fractions to calculate unit rates
Uses ratios of whole numbers to calculate unit rates
Uses two given unit rates to solve a multi-step real-world problem
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world problems involving percent or fractional increase
Solves real‑world problems involving percent error
Area
Describes the effect on area when dimensions of a rectangle are changed
Describes the effect on area when dimensions of a triangle are changed
Describes the effect on area when the radius or diameter of a circle is changed
Determines the area of circles, formula not provided
Determines the area of figures composed of polygons
Determines the area of figures composed of polygons and circles
Determines the area of quarter circles, semicircles, or three‑quarter circles
Determines the area of trapezoids, formula not provided
Determines the area of triangles, formula not provided
Determines the circumference given the area of a circle
Determines the ratio between areas of scaled figures
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Circles
Calculates the area of sectors given the measure of the central angle
Describes a series of transformations that show two given circles are similar on the coordinate plane
Determines the center and radius given the standard form of the equation
Explains why an inscribed angle in a semicircle is a right angle
Recognizes relationships among the measures of central angles, inscribed angles, and circumscribed angles
Solves problems involving inscribed angles on a diameter
Understands that the ratio of the circumference to the diameter is the same for two circles
Uses properties of central and inscribed angles to solve problems involving circles
Uses properties of chords to solve problems involving circles
Writes the equation of a circle given the center and radius
Conic Sections
Determines the center and radius given the standard form of the equation
Writes the equation of a circle given the center and radius
Coordinate Geometry
Determines the coordinates of missing vertices of geometric figures in the first quadrant given the other vertices plotted on the coordinate plane
Determines the coordinates of one endpoint of a line segment given the coordinates of the midpoint and the other endpoint
Determines the coordinates of points in the first quadrant of a coordinate plane
Determines the coordinates of the midpoint of a line segment
Determines the perimeter or area of a rectangle given vertices with the same first or second coordinate
Determines the slope of a line perpendicular to a given line
Uses coordinate geometry to justify the type of figure formed based on its properties, given a set of points
Uses slopes to identify perpendicular lines
Writes the equation of a line parallel to a given line
Writes the equation of a line parallel to a line that passes through a given point
Writes the equation of a line perpendicular to a given line
Writes the equation of a line perpendicular to a line that passes through a given point
Geometric Proof/Logic/Inductive and Deductive Reasoning
Describes a series of transformations that show two given circles are similar on the coordinate plane
Identification and Classification of 2-D Shapes
Describes a set of shapes based on attributes, given pictures
Describes shapes using multiple categories based on attributes, given pictures
Sorts shapes into a hierarchy, given pictures
Understands the relationships among categories of shapes
Perimeter/Circumference
Determines the circumference given the area of a circle
Determines the circumference of circles, formula not provided
Problem Solving with Units
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Solves problems involving surface areas of prisms within a real-world or mathematical context
Solves problems involving volumes of 3-D figures composed of cones, cylinders, and spheres within a real-world or mathematical context
Solves problems involving volumes of cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Applies the concept of density to solve problems involving area and volume
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Uses coordinate geometry to justify the type of figure formed based on its properties, given a set of points
Similarity
Applies scale factors to solve problems involving scale drawings of geometric figures
Applies scale factors to solve problems involving scale drawings, maps, and models
Understands that the ratio of the circumference to the diameter is the same for two circles
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the 3-D shape created when a 2-D shape is rotated around an axis
Identifies the cross-sections of 3-D shapes
Surface Area
Determines the surface area of a prism given a net
Determines the surface area of rectangular prisms or cubes, formula not provided
Determines the surface area of triangular prisms, formula not provided
Solves problems involving surface areas of prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Volume
Describes the effect on volume when dimensions of a rectangular prism are changed
Determines a base length given the volume and height of a rectangular pyramid
Determines the radius or diameter of a cylinder given the volume and height
Determines the radius or diameter of a sphere given the volume
Determines the volume of cylinders, formula not provided
Determines the volume of pyramids, formula not provided
Determines the volume of pyramids, given the formula
Determines the volume of rectangular prisms, formula not provided
Solves problems involving volumes of 3-D figures composed of cones, cylinders, and spheres within a real-world or mathematical context
Solves problems involving volumes of cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height
Uses geometric modeling as a method to solve real-world problems with given physical or cost requirements
Area
Determines the perimeter of rectangles given the area
Solves area word problems involving whole numbers and tiling rectangles with non-unit squares
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Analyzes linear trends in scatter plots to make predictions
Approximates the line of best fit on a scatter plot
Describes and interprets outliers and clusters in a scatter plot
Determines relative frequencies in a two-way frequency table
Determines whether two quantitative variables have a positive linear, negative linear, or zero association
Estimates the slope of a line of best fit
Interprets the meaning of the slope or y-intercept of a line of best fit or regression line
Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship
Uses a given quadratic equation fitted to data to make predictions
Capacity
Completes conversions of metric units of capacity
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Conversion of Units
Completes conversions of metric units of capacity
Completes conversions of metric units of length
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Data Analysis
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Compares the distributions of multiple data sets presented in line or dot plots, or histograms
Compares two data sets based on measures of center or variability to answer a question
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Solves word problems using data from line or dot plots with fractional scales
Data Representation
Represents data in box plots
Represents data in histograms
Fractions: Represent and Solve Word Problems
Solves word problems using data from line or dot plots with fractional scales
Length
Completes conversions of metric units of length
Solves multi-step length word problems involving whole numbers and conversion of customary units
Measures of Center and Spread (Variability)
Compares the measures of center of two data sets after the addition or deletion of data values, including outliers
Determines a missing value in a data set when the mean is known
Determines how the measures of center are affected with the addition or deletion of a data value, including outliers
Determines the mean of a data set
Determines the range of a data set
Interprets the median in the context of a data set
Perimeter/Circumference
Determines the perimeter of rectangles given the area
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Populations/Random Processes
Identifies a statistical question
Problem Solving with Units
Solves area word problems involving whole numbers and tiling rectangles with non-unit squares
Solves multi-step capacity word problems involving whole numbers and conversion of customary units
Solves multi-step length word problems involving whole numbers
Solves multi-step length word problems involving whole numbers and conversion of customary units
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving perimeters of rectangles within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Volume
Determines the missing dimension of a rectangular prism composed of unit cubes given the volume and other dimensions
Determines the volume of figures composed of rectangular prisms
Recognizes situations which describe volume
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Weight/Mass
Solves multi‑step weight word problems involving decimals or fractions and conversion of customary units
Algebraic Expressions
Factors algebraic expressions by grouping
Factors polynomials with a degree greater than 2 by identifying common monomial factors
Factors polynomials with a degree greater than 2 by identifying common monomial factors and factoring the resulting polynomial
Factors quadratic trinomials
Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Identifies equivalent exponential expressions
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets equivalent linear expressions within a real-world context
Interprets the base in an exponential expression within the context of a real‑world relationship
Interprets the factors of a polynomial within the context of a real‑world relationship
Multiplies monomials
Multiplies polynomials
Simplifies rational expressions
Squares binomial expressions
Translates between verbal and algebraic expressions
Uses properties of exponents to simplify algebraic expressions involving whole-number exponents
Writes a rational expression as a sum of a polynomial and a proper rational expression
Writes linear expressions in one variable to represent real-world or mathematical contexts
Exponential and Logarithmic Functions
Solves a real‑world problem involving an exponential relationship between quantities
Exponents
Uses properties of exponents to simplify algebraic expressions involving whole-number exponents
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Geometric Proof/Logic/Inductive and Deductive Reasoning
Justifies the steps in solving a linear equation
Inequalities
Represents the solutions of a compound linear inequality on a number line
Represents the solutions of a multistep linear inequality on a number line
Represents the solutions of a two-variable linear inequality on the coordinate plane
Solves compound linear inequalities
Solves multi-step linear inequalities
Writes a quadratic inequality in one variable to represent a real‑world or mathematical context
Writes an exponential inequality in one variable to represent a real-world or mathematical context
Writes and solves a two‑step linear inequality in one variable involving a real‑world or mathematical context
Linear Functions
Graphs the equation of a line in the form y = mx
Understands that the slope is the same between any two points on a line
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario
Writes the equation of a line in standard form given a table of values or two ordered pairs
Writes the equation of a line in standard form given the slope and y-intercept
Writes the equation of a line in the form ax + by + c = 0 given a graph
Number Sentences/Equations/Equivalence
Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision
Determines the quadratic equation that is used to solve a given rational equation
Identifies an ordered pair that is a solution to a two-variable equation
Justifies the steps in solving a linear equation
Solves literal equations for linear variables
Solves quadratic equations in one variable by completing the square
Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
Solves quadratic equations with complex solutions
Solves radical equations that lead to a quadratic equation
Solves radical equations that lead to linear equations
Solves rational equations
Understands the relationship between the points of intersection of the graphs of f(x) and g(x) and the solutions to the equation f(x) = g(x)
Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
Writes a quadratic equation in one variable to represent a real-world or mathematical context
Writes an exponential equation in one variable to represent a real-world or mathematical context
Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context
Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context
Writes and solves a rational equation in one variable involving a real-world or mathematical context
Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context
Numerical Expressions
Evaluates numerical expressions involving multiple operations with whole numbers and parentheses
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Uses properties of exponents to simplify numerical expressions involving whole-number exponents only
Polynomial Functions
Applies the polynomial Remainder Theorem
Determines a missing coefficient of a polynomial function given an x-intercept
Factors polynomial functions to determine zeros
Identifies the zeros of a polynomial function from a graph
Quadratic Functions
Determines the zeros of a quadratic function by factoring
Understands the relationship between the zeros of a function and the x-intercepts of the graph of the function
Writes a quadratic function given the zeros
Rate of Change/Slope
Understands that the slope is the same between any two points on a line
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
Scientific Notation
Adds and subtracts numbers expressed in scientific notation
Determines the relative magnitude of two numbers expressed in scientific notation
Multiplies and divides numbers expressed in scientific notation
Solves real-world problems with numbers expressed in scientific notation
System of Equations/Inequalities
Determines the number of solutions to a system of linear equations
Graphs a system of linear inequalities
Solves a system of equations with one linear and one quadratic equation algebraically
Solves a system of linear equations given a table
Writes a system of linear equations given a graph
Writes a system of linear equations to represent a real-world context involving rates and distances
Writes a system of linear inequalities given a graph
Writes a system of linear inequalities to represent a real-world or mathematical context
Writes and solves a system of linear equations involving a real-world or mathematical context
Conversion of Units
Solves real-world or mathematical problems involving conversions between the customary and metric systems, given a conversion factor
Solves real‑world or mathematical problems involving conversions within a measurement system using ratio reasoning, given a conversion factor
Linear Functions
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rates/Ratios/Proportions/Percents
Creates tables representing proportional relationships involving positive rational numbers
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world and mathematical problems using ratios or proportional reasoning
Solves real-world problems involving percent or fractional increase
Solves real‑world problems involving percent error
Solves real‑world problems involving rates associated with a ratio
Uses a given unit rate to solve a multi-step real-world problem
Uses ratios of decimals to calculate unit rates
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world problems involving percent or fractional increase
Solves real‑world problems involving percent error
Area
Describes the effect on area when the circumference of a circle is changed
Describes the effect on area when the radius or diameter of a circle is changed
Determines the area of circles, formula not provided
Determines the area of figures composed of polygons and circles
Determines the circumference given the area of a circle
Determines the ratio between areas of scaled figures
Solves problems involving areas of circles within a real-world or mathematical context
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Circles
Calculates arc lengths
Calculates the area of a circle given the measure of the central angle and the area of a sector
Calculates the area of sectors given the measure of the central angle
Calculates the central angle of a sector given the area of the sector
Describes a series of transformations that show two given circles are similar on the coordinate plane
Explains why an inscribed angle in a semicircle is a right angle
Recognizes relationships among the measures of central angles, inscribed angles, and circumscribed angles
Solves problems involving angles of inscribed quadrilaterals
Solves problems involving inscribed angles on a diameter
Understands that the ratio of the circumference to the diameter is the same for two circles
Uses properties of central and inscribed angles to solve problems involving circles
Uses properties of chords to solve problems involving circles
Writes the equation of a circle given a graph
Writes the equation of a circle given the center and a point on the circle
Writes the equation of a circle given the center and radius
Conic Sections
Writes the equation of a circle given a graph
Writes the equation of a circle given the center and a point on the circle
Writes the equation of a circle given the center and radius
Coordinate Geometry
Determines the area of a rectangle given the coordinates of the vertices
Determines the coordinates of the midpoint of a line segment
Determines the perimeter of a rectangle given the coordinates of the vertices
Determines the perimeter of a triangle given the coordinates of the vertices
Determines the slope of a line perpendicular to a given line
Determines the slope of a line perpendicular to a line that passes through two given points
Uses coordinate geometry to justify the type of figure formed based on its properties, given a set of points
Writes the equation of a line perpendicular to a given line
Writes the equation of a line perpendicular to a line that passes through a given point
Geometric Proof/Logic/Inductive and Deductive Reasoning
Describes a series of transformations that show two given circles are similar on the coordinate plane
Identification and Classification of 2-D Shapes
Describes a set of shapes based on attributes, given pictures
Understands the relationships among categories of shapes
Perimeter/Circumference
Describes the effect on area when the circumference of a circle is changed
Determines the circumference given the area of a circle
Solves problems involving perimeters of quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Problem Solving with Units
Solves problems involving areas of circles within a real-world or mathematical context
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving perimeters of quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Solves problems involving surface areas of prisms within a real-world or mathematical context
Solves problems involving volumes of cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings, maps, and models
Applies the concept of density to solve problems involving area and volume
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Uses coordinate geometry to justify the type of figure formed based on its properties, given a set of points
Similarity
Applies scale factors to solve problems involving scale drawings, maps, and models
Understands that the ratio of the circumference to the diameter is the same for two circles
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the 3-D shape created when a 2-D shape is rotated around an axis
Identifies the cross-sections of 3-D shapes
Surface Area
Determines the surface area of a prism given a net
Solves problems involving surface areas of prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Volume
Describes the effect on volume when dimensions of a cylinder are changed
Describes the effect on volume when dimensions of a rectangular prism are changed
Describes the effect on volume when dimensions of a sphere are changed
Determines a base length given the volume and height of a rectangular pyramid
Determines the radius or diameter of a sphere given the volume
Determines the volume of cones, formula not provided
Determines the volume of cylinders, formula not provided
Determines the volume of pyramids, formula not provided
Determines the volume of pyramids, given the formula
Solves problems involving volumes of cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height
Uses geometric modeling as a method to solve real-world problems with given physical or cost requirements
Area
Solves area word problems involving whole numbers and tiling rectangles with non-unit squares
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Analyzes linear trends in scatter plots to make predictions
Approximates the equation of the line of best fit
Describes and interprets outliers and clusters in a scatter plot
Determines relative frequencies in a two-way frequency table
Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a real-world context
Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a scatter plot
Interprets the meaning of the slope or y-intercept of a line of best fit or regression line
Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship
Data Analysis
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Compares the distributions of multiple data sets presented in line or dot plots, or histograms
Compares two data sets based on measures of center or variability to answer a question
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Recognizes data distributions that could be fit to a normal distribution curve
Solves word problems using data from line or dot plots with fractional scales
Data Representation
Represents data in box plots
Fractions: Represent and Solve Word Problems
Solves word problems using data from line or dot plots with fractional scales
Measures of Center and Spread (Variability)
Compares the measures of center of two data sets after the addition or deletion of data values, including outliers
Determines a missing value in a data set when the mean is known
Determines the mean of a data set
Determines the range of a data set
Interprets the median in the context of a data set
Perimeter/Circumference
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Populations/Random Processes
Identifies a statistical question
Problem Solving with Units
Solves area word problems involving whole numbers and tiling rectangles with non-unit squares
Solves problems involving both area and perimeter of rectangles within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Volume
Recognizes situations which describe volume
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Algebraic Expressions
Factors algebraic expressions by grouping
Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms
Identifies equivalent exponential expressions
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets the base in an exponential expression within the context of a real‑world relationship
Multiplies polynomials
Rewrites a polynomial to interpret factors of the polynomial within the context of a real-world relationship, given in standard form
Simplifies rational expressions
Translates between verbal and algebraic expressions
Writes a rational expression as a sum of a polynomial and a proper rational expression
Exponential and Logarithmic Functions
Writes an equivalent form of an exponential expression to reveal the initial value and the exponential rate of growth or decay within a real‑world context
Exponents
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Geometric Proof/Logic/Inductive and Deductive Reasoning
Justifies the steps in solving a linear equation
Inequalities
Represents a compound inequality on a number line given a real-world or mathematical context
Linear Functions
Understands that the slope is the same between any two points on a line
Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario
Writes the equation of a line in standard form given a table of values or two ordered pairs
Number Sentences/Equations/Equivalence
Justifies the steps in solving a linear equation
Solves literal equations for nonlinear variables
Solves quadratic equations in one variable by completing the square
Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method
Solves quadratic equations with complex solutions
Solves rational equations
Understands the relationship between the points of intersection of the graphs of f(x) and g(x) and the solutions to the equation f(x) = g(x)
Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
Writes a quadratic equation in one variable to represent a real-world or mathematical context
Writes an exponential equation in one variable to represent a real-world or mathematical context
Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context
Writes and solves a rational equation in one variable involving a real-world or mathematical context
Numerical Expressions
Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero
Polynomial Functions
Applies the polynomial Remainder Theorem
Factors polynomial functions to determine zeros
Quadratic Functions
Converts a quadratic equation from standard form to vertex form to reveal the vertex of the corresponding parabola
Determines the zeros of a quadratic function by factoring
Writes a quadratic function given the zeros
Rate of Change/Slope
Understands that the slope is the same between any two points on a line
Rational Numbers: Solve Real-World and Mathematical Problems
Solves real-world problems using appropriate problem-solving strategies and evaluates the reasonableness of the solutions
Scientific Notation
Determines the relative magnitude of two numbers expressed in scientific notation
Multiplies and divides numbers expressed in scientific notation
System of Equations/Inequalities
Determines the number of solutions to a system of linear equations
Solves a system of equations with one linear and one quadratic equation algebraically
Solves a system of linear equations given a table
Writes a system of linear inequalities given a graph
Linear Functions
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rates/Ratios/Proportions/Percents
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world problems involving percent or fractional increase
Solves real‑world problems involving percent error
Writes an equation in the form y = mx to represent a real‑world proportional relationship for a given ratio
Rational Numbers: Solve Real-World and Mathematical Problems
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world problems involving percent or fractional increase
Solves real‑world problems involving percent error
Area
Determines the area of circles, formula not provided
Determines the area of figures composed of polygons and circles
Determines the circumference given the area of a circle
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Circles
Calculates arc lengths
Calculates the area of sectors given the measure of the central angle
Describes a series of transformations that show two given circles are similar on the coordinate plane
Determines the center and radius of a circle given the general form of the equation
Determines whether a point lies on a circle given the center and radius
Explains why an inscribed angle in a semicircle is a right angle
Graphs a circle given the equation
Justifies relationships between the arc length, radius, and central angle measured in radians
Proves properties of angles involving quadrilaterals inscribed in a circle
Recognizes relationships among the measures of central angles, inscribed angles, and circumscribed angles
Solves problems involving inscribed angles on a diameter
Uses properties of central and inscribed angles to solve problems involving circles
Uses properties of chords to solve problems involving circles
Writes the equation of a circle given a graph
Writes the equation of a circle given the center and a point on the circle
Writes the equation of a circle given the center and radius
Conic Sections
Determines the center and radius of a circle given the general form of the equation
Determines whether a point lies on a circle given the center and radius
Graphs a circle given the equation
Writes the equation of a circle given a graph
Writes the equation of a circle given the center and a point on the circle
Writes the equation of a circle given the center and radius
Writes the equation of a parabola given the focus and vertex
Coordinate Geometry
Uses coordinate geometry to justify the type of figure formed based on its properties, given a set of points
Writes the equation of a line perpendicular to a line that passes through a given point
Geometric Proof/Logic/Inductive and Deductive Reasoning
Describes a series of transformations that show two given circles are similar on the coordinate plane
Justifies relationships between the arc length, radius, and central angle measured in radians
Proves properties of angles involving quadrilaterals inscribed in a circle
Identification and Classification of 2-D Shapes
Understands the relationships among categories of shapes
Perimeter/Circumference
Determines the circumference given the area of a circle
Solves problems involving perimeters of quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Problem Solving with Units
Solves problems involving areas of figures composed of polygons within a real-world or mathematical context
Solves problems involving perimeters of quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Solves problems involving volumes of cones within a real-world or mathematical context
Solves problems involving volumes of cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings, maps, and models
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Calculates unknown angle measures using the properties of complementary, supplementary, and vertical angles
Uses coordinate geometry to justify the type of figure formed based on its properties, given a set of points
Similarity
Applies scale factors to solve problems involving scale drawings, maps, and models
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the 3-D shape created when a 2-D shape is rotated around an axis
Identifies the cross-sections of 3-D shapes
Surface Area
Determines the surface area of a prism given a net
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Volume
Determines the radius or diameter of a sphere given the volume
Determines the volume of cones, formula not provided
Determines the volume of cylinders, formula not provided
Determines the volume of pyramids, formula not provided
Determines the volume of spheres, formula not provided
Solves problems involving the volumes of cones and cylinders within a real-world or mathematical context
Solves problems involving volumes of cones within a real-world or mathematical context
Solves problems involving volumes of cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses geometric modeling as a method to solve real-world problems with given physical or cost requirements
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Determines relative frequencies in a two-way frequency table
Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a real-world context
Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a scatter plot
Data Analysis
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Compares two data sets based on measures of center or variability to answer a question
Interprets the measures of center or variability given data presented in box plots
Reads and interprets data from a box plot
Reads and interprets data from a histogram
Recognizes data distributions that could be fit to a normal distribution curve
Measures of Center and Spread (Variability)
Compares the measures of center of two data sets after the addition or deletion of data values, including outliers
Compares the variability of related data sets from random samples using the mean absolute deviation
Determines a missing value in a data set when the mean is known
Determines the range of a data set
Interprets the measures of center or variability given data presented in box plots
Interprets the median in the context of a data set
Populations/Random Processes
Identifies a statistical question
Problem Solving with Units
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Volume
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Algebraic Expressions
Factors algebraic expressions by grouping
Identifies equivalent exponential expressions
Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient
Interprets a quadratic expression within the context of a real‑world relationship
Interprets the base in an exponential expression within the context of a real‑world relationship
Writes a rational expression as a sum of a polynomial and a proper rational expression
Exponential and Logarithmic Functions
Writes an equivalent form of an exponential expression to reveal the initial value and the exponential rate of growth or decay within a real‑world context
Geometric Proof/Logic/Inductive and Deductive Reasoning
Justifies the steps in solving a linear equation
Linear Functions
Writes the equation of a line in standard form given a table of values or two ordered pairs
Number Sentences/Equations/Equivalence
Determines the quadratic equation that is used to solve a given radical equation
Justifies the steps in solving a linear equation
Solves literal equations for nonlinear variables
Solves quadratic equations in one variable by completing the square
Solves quadratic equations with complex solutions
Understands the relationship between the points of intersection of the graphs of f(x) and g(x) and the solutions to the equation f(x) = g(x)
Writes a multi-step linear equation in one variable to represent a real-world or mathematical context
Writes and solves a rational equation in one variable involving a real-world or mathematical context
Polynomial Functions
Identifies the factors of a polynomial function from a graph
Quadratic Functions
Converts a quadratic equation from standard form to vertex form to reveal the vertex of the corresponding parabola
Determines the maximum or minimum value of a quadratic function by completing the square
Rates/Ratios/Proportions/Percents
Determines if the relationship between two quantities in a real‑world scenario is proportional by creating a table
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world problems involving percent or fractional increase
Rational Numbers: Solve Real-World and Mathematical Problems
Solves multi-step percent problems within a real-world or mathematical context
Solves real-world problems involving percent or fractional increase
Area
Determines the area of figures composed of polygons and circles
Circles
Describes a series of transformations that show two given circles are similar on the coordinate plane
Describes properties of quadrilaterals inscribed in a circle
Determines the center and radius of a circle given the general form of the equation
Determines whether a point lies on a circle given the center and radius
Justifies relationships between the arc length, radius, and central angle measured in radians
Proves properties of angles involving quadrilaterals inscribed in a circle
Recognizes relationships among the measures of central angles, inscribed angles, and circumscribed angles
Uses properties of central and inscribed angles to solve problems involving circles
Uses properties of chords to solve problems involving circles
Writes the equation of a circle given a graph
Writes the equation of a circle given the center and radius
Conic Sections
Determines the center and radius of a circle given the general form of the equation
Determines whether a point lies on a circle given the center and radius
Writes the equation of a circle given a graph
Writes the equation of a circle given the center and radius
Writes the equation of a parabola given the focus and vertex
Geometric Proof/Logic/Inductive and Deductive Reasoning
Describes a series of transformations that show two given circles are similar on the coordinate plane
Justifies relationships between the arc length, radius, and central angle measured in radians
Proves properties of angles involving quadrilaterals inscribed in a circle
Perimeter/Circumference
Solves problems involving perimeters of quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Problem Solving with Units
Solves problems involving perimeters of quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings, maps, and models
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Similarity
Applies scale factors to solve problems involving scale drawings, maps, and models
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the 3-D shape created when a 2-D shape is rotated around an axis
Identifies the cross-sections of 3-D shapes
Surface Area
Uses the net of a prism to solve surface area problems within a real-world or mathematical context
Volume
Determines the radius or diameter of a sphere given the volume
Determines the volume of spheres, formula not provided
Solves problems involving the volumes of cones and cylinders within a real-world or mathematical context
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Uses geometric modeling as a method to solve real-world problems with given physical or cost requirements
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Data Analysis
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Reads and interprets data from a box plot
Recognizes data distributions that could be fit to a normal distribution curve
Measures of Center and Spread (Variability)
Interprets the median in the context of a data set
Populations/Random Processes
Identifies a statistical question
Problem Solving with Units
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Volume
Solves problems involving volumes of rectangular prisms within a real-world or mathematical context
Geometric Proof/Logic/Inductive and Deductive Reasoning
Justifies the steps in solving a linear equation
Number Sentences/Equations/Equivalence
Justifies the steps in solving a linear equation
Solves literal equations for nonlinear variables
Solves quadratic equations in one variable by completing the square
Writes and solves a rational equation in one variable involving a real-world or mathematical context
Polynomial Functions
Identifies the factors of a polynomial function from a graph
Quadratic Functions
Determines the maximum or minimum value of a quadratic function by completing the square
Circles
Describes a series of transformations that show two given circles are similar on the coordinate plane
Describes properties of quadrilaterals inscribed in a circle
Determines whether a point lies on a circle given the center and radius
Proves properties of angles involving quadrilaterals inscribed in a circle
Recognizes relationships among the measures of central angles, inscribed angles, and circumscribed angles
Uses properties of central and inscribed angles to solve problems involving circles
Uses properties of chords to solve problems involving circles
Conic Sections
Determines whether a point lies on a circle given the center and radius
Writes the equation of a parabola given the focus and directrix
Geometric Proof/Logic/Inductive and Deductive Reasoning
Describes a series of transformations that show two given circles are similar on the coordinate plane
Proves properties of angles involving quadrilaterals inscribed in a circle
Rates/Ratios/Proportions/Percents
Applies scale factors to solve problems involving scale drawings, maps, and models
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Similarity
Applies scale factors to solve problems involving scale drawings, maps, and models
Spatial Concepts and Symmetry
Identifies 3-D shapes using cross-sections
Identifies the cross-sections of 3-D shapes
Volume
Uses geometric modeling as a method to solve real-world problems with given physical or cost requirements
Bivariate Data
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Data Analysis
Analyzes data in a two‑way frequency table to determine whether there is a positive, a negative, or no association between two categorical variables
Recognizes data distributions that could be fit to a normal distribution curve
Geometric Proof/Logic/Inductive and Deductive Reasoning
Justifies the steps in solving a linear equation
Number Sentences/Equations/Equivalence
Justifies the steps in solving a linear equation
Relationships involving Lines, Angles, and Polygons
Applies the Triangle Inequality Theorem
Spatial Concepts and Symmetry
Identifies the cross-sections of 3-D shapes
Volume
Uses geometric modeling as a method to solve real-world problems with given physical or cost requirements
Spatial Concepts and Symmetry
Identifies the cross-sections of 3-D shapes