Common Core State Standards
6th Grade Math Standards
All 29 Common Core math standards for 6th grade, grouped into domains and written in plain English. The official wording is one click away. 2 have free practice you can print today.
29 standards
Ratios & Proportional Relationships RP
3 standardsUnderstand ratio concepts and use ratio reasoning to solve problems.
6.RP.1
Compare two amounts with a ratio and say what it means, like 2 : 1 is 2 wings for every 1 beak.
Official wording
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
6.RP.2
Find the unit rate behind a ratio, like $75 for 15 hamburgers is $5 per hamburger.
Official wording
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
6.RP.3
Solve ratio, rate and percent problems with tables, tape diagrams and double number lines, including unit prices, constant speed and converting units.
Official wording
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.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 including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?cFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
The Number System NS
8 standardsApply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.1
Divide a fraction by a fraction and solve word problems about it, like how many 3/4-cup servings fit in 2/3 of a cup.
Official wording
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2
Divide multi-digit numbers with standard long division, quickly and accurately.
Official wording
Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3
Add, subtract, multiply and divide multi-digit decimals with the standard written method for each.
Official wording
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4
Find the greatest common factor of two numbers up to 100 and the least common multiple of two numbers up to 12, and rewrite a sum like 36 + 8 as 4 (9 + 2).
Official wording
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. 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. For example, express 36 + 8 as 4 (9 + 2)..
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.5
Use positive and negative numbers for opposites in real life, like temperature above and below zero or money earned and owed, and say 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 (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.6
Place positive and negative numbers on a number line, know that -(-3) = 3, and plot points with negative coordinates in all four quadrants.
Official wording
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the 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, e.g., -(-3) = 3, 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 diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
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 diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.bWrite, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer than -7 °C.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. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.dDistinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
6.NS.8
Solve problems by graphing points in all four quadrants and find the distance between two points that line up horizontally or vertically.
Official wording
Solve real-world and mathematical problems by graphing points in all four quadrants of the 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 EE
9 standardsApply and extend previous understandings of arithmetic to algebraic expressions.
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.
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. For example, express the calculation "Subtract y from 5" as 5 - y.bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.cEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.
6.EE.3
Use the properties of operations to rewrite an expression in an equivalent form, like 3 (2 + x) as 6 + 3x.
Official wording
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
6.EE.4
Tell when two expressions are equivalent because they always give the same value, like y + y + y and 3y.
Official wording
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..
Reason about and solve one-variable equations and inequalities.
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.
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.
6.EE.7
Solve real problems with one-step equations like x + 3 = 7 or 4x = 20, using positive whole numbers, fractions and decimals.
Official wording
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.8
Write an inequality like x > 5 for a real condition, know it has infinitely many solutions, and show them on a number line.
Official wording
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9
Write an equation for two quantities that change together, like d = 65t for distance and time, and show the relationship in a table and a graph.
Official wording
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as 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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Geometry G
4 standardsSolve real-world and mathematical problems involving area, surface area, and volume.
6.G.1
Find the area of triangles, quadrilaterals and other polygons by splitting them into rectangles and triangles.
Official wording
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6.G.2
Find the volume of a rectangular prism with fractional edge lengths, both by packing it with small cubes and with the formula V = l w h.
Official wording
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to 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 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.
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.
Statistics & Probability SP
5 standardsDevelop understanding of statistical variability.
6.SP.1
Tell a statistical question, one with varied answers like how old are the students in my school, from one with a single answer.
Official wording
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
6.SP.2
Describe a set of data by its center, its spread and its overall shape.
Official wording
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3
Know that a measure of center, like the mean or median, sums up a data set in one number, while a measure of spread tells how much the values vary.
Official wording
Recognize that a measure of center for a numerical 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
Show numerical data on a number line as a dot plot, histogram or box plot.
Official wording
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.5
Summarize a data set in its context, reporting how many values there are, what was measured, the mean or median, the spread and the overall shape.
Official wording
Summarize numerical data sets in relation to their context, such as by:aReporting the number of observations.bDescribing the nature of the attribute under investigation, including how it was measured and its units of measurement.cGiving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.dRelating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
6th Grade Practice
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6th Grade Math Standards: Questions
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The plain-English lines on this page are EMStudio’s own explanations, shown beside the official wording. They are not part of the standard.