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New York Standards

New York 6th Grade Math Standards

All 35 New York math standards for 6th grade, each explained in plain English. The official wording is one click away under each one.

35 standards

Ratios and Proportional Relationships

3 standards
Understand ratio concepts and use ratio reasoning to solve problems.
NY-6.RP.1
Explain what a ratio is and describe one in words, like there are 3 cats for every 2 dogs at the shelter.
Official wording
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
NY-6.RP.2
Find the unit rate that goes with a ratio and describe it in words, like 4 cups of flour for 2 cakes meaning 2 cups per cake.
Official wording
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. Note: Expectations for unit rates in this grade are limited to non-complex fractions.
NY-6.RP.3
Solve ratio and rate problems with tables of equivalent ratios, graphs, unit rates, percents of a quantity, and unit conversions, like finding 30% of 80.
Official wording
Use ratio and rate reasoning to solve real-world and mathematical problems.aMake 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.bSolve unit rate problems.cFind 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.dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

The Number System

8 standards
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
NY-6.NS.1
Divide fractions by fractions, explain what the quotient means, and solve word problems, like how many 1/2-cup servings are in 3/4 cup of yogurt.
Official wording
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
Compute fluently with multi-digit numbers and find common factors and multiples.
NY-6.NS.2
Divide multi-digit numbers quickly and accurately using a standard written method, like long division of 7,452 by 36.
Official wording
Fluently divide multi-digit numbers using a standard algorithm.
NY-6.NS.3
Add, subtract, multiply, and divide multi-digit decimals quickly and accurately using a standard written method for each, like 12.6 × 0.35.
Official wording
Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.
NY-6.NS.4
Find the greatest common factor of numbers up to 100 and the least common multiple of numbers up to 12, and factor sums, like 36 + 8 as 4 times the sum of 9 and 2.
Official wording
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.
Apply and extend previous understandings of numbers to the system of rational numbers.
NY-6.NS.5
Use positive and negative numbers for opposite amounts, like temperatures above and below zero or deposits and withdrawals, and explain what 0 means in each case.
Official wording
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.
NY-6.NS.6
Place integers and other rational numbers on number lines and coordinate grids, see opposites as mirror points around 0, and use signs to find a point's quadrant.
Official wording
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.aRecognize 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.bUnderstand 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.cFind 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.
NY-6.NS.7
Order positive and negative numbers, like -3 is warmer than -7, and read absolute value as distance from 0, so a balance of -30 is a debt of 30.
Official wording
Understand ordering and absolute value of rational numbers.aInterpret statements of inequality as statements about the relative position of two numbers on a number line.bWrite, interpret, and explain statements of order for rational numbers in real-world contexts.cUnderstand 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.dDistinguish comparisons of absolute value from statements about order.
Common Core 6.NS.7
NY-6.NS.8
Solve problems by graphing points in all four quadrants, using coordinates and absolute value to find the distance between points that share an x or y value.
Official wording
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.

Expressions, Equations, and Inequalities

9 standards
Apply and extend previous understandings of arithmetic to algebraic expressions.
NY-6.EE.1
Write and work out expressions with whole-number exponents, like 5³ = 125.
Official wording
Write and evaluate numerical expressions involving whole-number exponents.
Common Core 6.EE.1
NY-6.EE.2
Write and work out expressions with letters standing for numbers, like 5 - y, name their parts (terms, factors, coefficients) and follow the order of operations.
Official wording
Write, read, and evaluate expressions in which letters stand for numbers.aWrite expressions that record operations with numbers and with letters standing for numbers.bIdentify 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.cEvaluate 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).
Common Core 6.EE.2
NY-6.EE.3
Use number properties to write equivalent expressions, like writing 3 times the sum 2 + x as 6 + 3x, or combining y + y + y into 3y.
Official wording
Apply the properties of operations to generate equivalent expressions.
NY-6.EE.4
Tell when two expressions are equivalent, meaning they give the same value for any number put in, like y + y + y and 3y.
Official wording
Identify when two expressions are equivalent.
Reason about and solve one-variable equations and inequalities.
NY-6.EE.5
Check whether a given number makes an equation or inequality true by substituting it in.
Official wording
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.
Common Core 6.EE.5
NY-6.EE.6
Use a letter for an unknown or changing number when writing an expression for a real problem.
Official wording
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.
Common Core 6.EE.6
NY-6.EE.7
Write and solve one-step equations like x + 5 = 12, 4x = 28, or x/3 = 6 to answer real-world problems, using numbers that are zero or positive.
Official wording
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.
NY-6.EE.8
Write an inequality like x > 4 or x ≤ 10 to describe a limit in a real situation, know it has endless solutions, and graph them on a number line.
Official wording
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.
Represent and analyze quantitative relationships between dependent and independent variables.
NY-6.EE.9
Use two variables for quantities that change together, like distance and time, pick out which one depends on the other, and connect the equation to tables and graphs.
Official wording
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.

Geometry

5 standards
Solve real-world and mathematical problems involving area, surface area, and volume.
NY-6.G.1
Find the area of triangles, trapezoids, and other polygons by rearranging them into rectangles or cutting them into triangles, like a trapezoid split into two triangles.
Official wording
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.
NY-6.G.2
Find the volume of box-shaped prisms with fraction edge lengths in real-world problems, like a 1/2 by 3/4 by 2 inch box holding 3/4 cubic inch.
Official wording
Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
NY-6.G.3
Draw polygons from the coordinates of their corners and use the coordinates to find side lengths.
Official wording
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.
Common Core 6.G.3
NY-6.G.4
Unfold a 3D shape into a net of rectangles and triangles and use the net to find its surface area.
Official wording
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.
Common Core 6.G.4
NY-6.G.5
Use squares and cubes built from unit pieces to show why numbers like 9 = 3² and 27 = 3³ are perfect squares and perfect cubes.
Official wording
Use area and volume models to explain perfect squares and perfect cubes.

Statistics and Probability

10 standards
Develop understanding of statistical variability.
NY-6.SP.1a
Tell a statistical question, which expects a range of answers, from a single-answer one, like how tall students in the class are versus how tall I am.
Official wording
Recognize that a statistical question is one that anticipates variability in the data related to the question and accounts for it in the answers.
NY-6.SP.1b
Explain that a sample can tell us about a whole population only when it truly represents that population, like surveying students from every grade.
Official wording
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.
NY-6.SP.1c
Explain how the way data is collected and the sample size help a sample match its population, and take several same-size samples to see how estimates vary.
Official wording
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.
NY-6.SP.2
Describe a set of data collected for a statistical question by its center, its spread, and the overall shape of its graph.
Official wording
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.
NY-6.SP.3
Explain that a measure of center sums up all the data with one number, while a measure of variation uses one number to show how spread out the data are.
Official wording
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.
NY-6.SP.4
Show numerical data on a number line with dot plots and histograms, like a dot plot of pets per family or a histogram of test scores.
Official wording
Display quantitative data in plots on a number line, including dot plots, and histograms.
NY-6.SP.5
Summarize a data set in context by reporting how many values there are, what was measured and in what units, the range and center, and any pattern or unusual values.
Official wording
Summarize quantitative data sets in relation to their context.aReport the number of observations.bDescribe the nature of the attribute under investigation, including how it was measured and its units of measurement.cCalculate 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.dRelate 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.
NY-6.SP.6
Explain that a probability is a number from 0 to 1 showing how likely an event is, where near 0 is unlikely, about 1/2 is even, and near 1 is likely.
Official wording
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.
NY-6.SP.7
Estimate a probability by running a chance process many times and tracking results, like flipping a cup 100 times, and predict outcomes from a known probability.
Official wording
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.
NY-6.SP.8
Build probability models, either with equal chances for every outcome or from observed data, find probabilities with them, and explain gaps between model and results.
Official wording
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.aDevelop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events.bDevelop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

The official New York documents

New York State Next Generation Mathematics Learning Standards, Copyright 2017, New York State Education Department, used with permission.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.