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Math 6+ CCSS 2010 1.1

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Learning Continuum - Math 6+ CCSS 2010 1.1

RIT 151-160

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • Area

    • Determines the area of figures by tiling with whole unit squares

  • Data Representation

    • Represents data in bar graphs with multi-unit scales

RIT 161-170

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • Rates/Ratios/Proportions/Percents

    • Identifies ratios between two quantities not from the same whole

Geometry

Geometric Measurement and Relationships

  • Spatial Concepts and Symmetry

    • Identifies and creates nets for pyramids

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 171-180

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • Spatial Concepts and Symmetry

    • Identifies and creates nets for prisms

    • Identifies and creates nets for pyramids

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 181-190

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 191-200

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 201-210

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 211-220

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 221-230

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 231-240

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 241-250

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 251-260

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 261-270

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 271-280

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 281-290

Operations and Algebraic Thinking

Expressions and Equations

  • 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

The Real and Complex Number Systems

Ratios and Proportional Relationships

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 291-300

Operations and Algebraic Thinking

Expressions and Equations

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

Statistics and Probability

Interpreting Categorical and Quantitative Data

  • 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

RIT 301-310

Operations and Algebraic Thinking

Expressions and Equations

  • 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

Geometry

Geometric Measurement and Relationships

  • 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

RIT 311-320

Geometry

Geometric Measurement and Relationships

  • Spatial Concepts and Symmetry

    • Identifies the cross-sections of 3-D shapes

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