Next Generation Learning Standards: Grade 6
Skills available for New York Grade 6 math standards
Domain
Print skill plan
6.RP
Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship.
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems.
6.RP.3a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Equivalent ratios
Ratio tables
Plot on the coordinate plane
Compare ratios
6.RP.3a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Equivalent ratios
Ratio tables
Plot on the coordinate plane
Compare ratios
6.RP.3b: Solve unit rate problems.
Unit rates
Unit pricing
Constant speed
6.RP.3b: Solve unit rate problems.
Unit rates
Unit pricing
Constant speed
6.RP.3c: Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent.
Represent percentages
Convert between percents, fractions, and decimals
Solve percent problems with models
Find a percent of a number
Find what percent one number is of another
Find the whole
Solve percent problems
6.RP.3c: Find a percent of a quantity as a rate per 100. Solve problems that involve finding the whole given a part and the percent, and finding a part of a whole given the percent.
Represent percentages
Convert between percents, fractions, and decimals
Solve percent problems with models
Find a percent of a number
Find what percent one number is of another
Find the whole
Solve percent problems
6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
6.RP.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
6.NS
The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
Divide fractions
Word problems
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
Divide fractions
Word problems
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2 Fluently divide multi-digit numbers using a standard algorithm.
6.NS.2 Fluently divide multi-digit numbers using a standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.
Addition and subtraction
Multiplication and division
Mixed operations
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.
Addition and subtraction
Multiplication and division
Mixed operations
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor other than 1. Find the least common multiple of two whole numbers less than or equal to 12.
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor other than 1. Find the least common multiple of two whole numbers less than or equal to 12.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.6 Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.
6.NS.6 Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.
6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself, and that 0 is its own opposite.
6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself, and that 0 is its own opposite.
6.NS.6b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
6.NS.6b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line. Find and position pairs of integers and other rational numbers on a coordinate plane.
Number lines
Coordinate plane
6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line. Find and position pairs of integers and other rational numbers on a coordinate plane.
Number lines
Coordinate plane
6.NS.7 Understand ordering and absolute value of rational numbers.
6.NS.7 Understand ordering and absolute value of rational numbers.
6.NS.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line.
6.NS.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line.
6.NS.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts.
6.NS.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts.
6.NS.7c: Understand the absolute value of a rational number as its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
6.NS.7c: Understand the absolute value of a rational number as its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
6.NS.7d: Distinguish comparisons of absolute value from statements about order.
6.NS.7d: Distinguish comparisons of absolute value from statements about order.
6.NS.8 Solve real-world and mathematical problems by graphing points on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
6.NS.8 Solve real-world and mathematical problems by graphing points on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Positive and negative numbers
  • •
    Coming soon: Checkpoint: The coordinate plane
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Positive and negative numbers
  • •
    Coming soon: Checkpoint: The coordinate plane
6.EE
Expressions, Equations, and Inequalities
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
Write expressions
Evaluate expressions
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
Write expressions
Evaluate expressions
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers.
6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers.
6.EE.2b: Identify parts of an expression using mathematical terms (term, coefficient, sum, difference, product, factor, and quotient); view one or more parts of an expression as a single entity.
6.EE.2b: Identify parts of an expression using mathematical terms (term, coefficient, sum, difference, product, factor, and quotient); view one or more parts of an expression as a single entity.
6.EE.2c: Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order (Order of Operations).
Order of operations
Evaluate variable expressions
Real-world formulas
6.EE.2c: Evaluate expressions given specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order (Order of Operations).
Order of operations
Evaluate variable expressions
Real-world formulas
6.EE.3 Apply the properties of operations to generate equivalent expressions.
6.EE.3 Apply the properties of operations to generate equivalent expressions.
6.EE.4 Identify when two expressions are equivalent.
6.EE.4 Identify when two expressions are equivalent.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Reason about and solve one-variable equations and inequalities.
6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x – p = q; px = q; and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
Solve equations
Real-world problems
6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x – p = q; px = q; and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
Solve equations
Real-world problems
6.EE.8 Write an inequality of the form x > c, x ≥ c, x ≤ c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line.
6.EE.8 Write an inequality of the form x > c, x ≥ c, x ≤ c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. Given a verbal context and an equation, identify the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Independent and dependent variables
Find values
Make and interpret graphs
Write equations
6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. Given a verbal context and an equation, identify the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Independent and dependent variables
Find values
Make and interpret graphs
Write equations
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Two-variable relationships
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Two-variable relationships
6.G
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.1 Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.
Triangles
Quadrilaterals
Compound figures
Word problems
6.G.1 Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems.
Triangles
Quadrilaterals
Compound figures
Word problems
6.G.2 Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.G.2 Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
6.G.5 Use area and volume models to explain perfect squares and perfect cubes.
6.G.5 Use area and volume models to explain perfect squares and perfect cubes.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Area of polygons
  • •
    Coming soon: Checkpoint: Surface area and volume
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Area of polygons
  • •
    Coming soon: Checkpoint: Surface area and volume
6.SP
Statistics and Probability
Develop understanding of statistical variability.
6.SP.1a Recognize that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers.
6.SP.1a Recognize that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers.
6.SP.1b Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
6.SP.1b Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
6.SP.1c Understand that the method and sample size used to collect data for a particular question is intended to reduce the difference between a population and a sample taken from the population so valid inferences can be drawn about the population. Generate multiple samples (or simulated samples) of the same size to recognize the variation in estimates or predictions.
6.SP.1c Understand that the method and sample size used to collect data for a particular question is intended to reduce the difference between a population and a sample taken from the population so valid inferences can be drawn about the population. Generate multiple samples (or simulated samples) of the same size to recognize the variation in estimates or predictions.
6.SP.2 Understand that a set of quantitative data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.2 Understand that a set of quantitative data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3 Recognize that a measure of center for a quantitative data set summarizes all of its values with a single number while a measure of variation describes how its values vary with a single number.
6.SP.3 Recognize that a measure of center for a quantitative data set summarizes all of its values with a single number while a measure of variation describes how its values vary with a single number.
Summarize and describe distributions.
6.SP.4 Display quantitative data in plots on a number line, including dot plots and histograms.
6.SP.4 Display quantitative data in plots on a number line, including dot plots and histograms.
6.SP.5 Summarize quantitative data sets in relation to their context.
6.SP.5 Summarize quantitative data sets in relation to their context.
6.SP.5a: Report the number of observations.
6.SP.5a: Report the number of observations.
6.SP.5b: Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.
6.SP.5b: Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.
6.SP.5c: Calculate range and measures of center, as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Measures of center and variability
Outliers
6.SP.5c: Calculate range and measures of center, as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Measures of center and variability
Outliers
6.SP.5d: Relate the range and the choice of measures of center to the shape of the data distribution and the context in which the data were gathered.
6.SP.5d: Relate the range and the choice of measures of center to the shape of the data distribution and the context in which the data were gathered.
Investigate chance processes and develop, use, and evaluate probability models.
6.SP.6 Understand that the probability of a chance event is a number between 0 and 1 inclusive, that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
6.SP.6 Understand that the probability of a chance event is a number between 0 and 1 inclusive, that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
6.SP.7 Approximate the probability of a simple event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
6.SP.7 Approximate the probability of a simple event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
6.SP.8 Develop a probability model and use it to find probabilities of simple events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
6.SP.8 Develop a probability model and use it to find probabilities of simple events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
6.SP.8a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events.
6.SP.8a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events.
6.SP.8b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
6.SP.8b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Samples of a population
  • •
    Coming soon: Checkpoint: Statistical questions and numerical data
  • •
    Coming soon: Checkpoint: Theoretical and experimental probability
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Samples of a population
  • •
    Coming soon: Checkpoint: Statistical questions and numerical data
  • •
    Coming soon: Checkpoint: Theoretical and experimental probability