Tennessee Standards
Tennessee 6th Grade Math Standards
All 29 Tennessee math standards for 6th grade, each explained in plain English. The official wording is one click away under each one.
29 standards
Ratios and Proportional Relationships
3 standardsUnderstand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1
Explain what a ratio is, describe how two amounts relate using ratio words, and tell ratios apart from fractions, like 3 legs to every 1 stool.
Official wording
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Make a distinction between ratios and fractions. For example, the ratio of wings to beaks in a bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. Another example could be for every vote candidate A received, candidate C received nearly three votes.
6.RP.A.2
Find the unit rate in a ratio, like $24 for 6 tickets being $4 per ticket, and use per-each language, keeping to simple fractions.
Official wording
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0. 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. Also, we paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. (Expectations for unit rates in 6th grade are limited to non-complex fractions).
6.RP.A.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 a runner ran 10 miles in 90 minutes, running at that speed, how long will it take him to run 6 miles? How fast is he running in miles per hour?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 customary and metric measurement units (within the same system); manipulate and transform units appropriately when multiplying or dividing quantities.
The Number System
8 standardsApply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.A.1
Divide fractions by fractions, explain the answer with models or by checking with multiplication, and solve story problems like how many 1/4 cup scoops fit in 2/3 cup.
Official wording
Interpret and compute quotients of fractions, and solve real-world and mathematical problems involving division of fractions by fractions (e.g., connecting visual fraction models and equations to represent the problem is suggested). 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 times 8/9 is 2/3 ((a/b) ÷ (c/d) = ad/bc). Further example: How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? 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.B.2
Divide multi-digit numbers quickly and accurately using the standard long division method.
Official wording
Fluently divide multi-digit numbers using a standard algorithm.
6.NS.B.3
Compute with multi-digit decimals in all four operations using standard methods, connecting each method to earlier models of what it means.
Official wording
Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm and making connections to previous conceptual work with each operation.
6.NS.B.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.C.5
Use positive and negative numbers for opposite amounts, like degrees above and below zero or deposits and withdrawals, explain what 0 means, and show opposites adding to 0.
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 as well as describing situations in which opposite quantities can combine to make 0.
6.NS.C.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. For example, – (–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.C.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 –3º C > –7º C to express the fact that –3º C is warmer than –7º C.cUnderstand the absolute value of a rational number as its distance from 0 on the number line and distinguish comparisons of absolute value from statements about order in a real-world context. For example, an account balance of -24 dollars represents a greater debt than an account balance - 14 dollars because -24 is located to the left of -14 on the number line.
6.NS.C.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 and Equations
9 standardsApply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.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.A.2
Write expressions with numbers and variables, name their parts like terms, factors and coefficients, and evaluate them from formulas, including exponents, in the right order.
Official wording
Write, read, and evaluate expressions in which variables stand for numbers.aWrite expressions that record operations with numbers and with variables. 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).
6.EE.A.3
Use properties like the distributive property to write equivalent expressions, like turning 5 times the sum of 2 and x into 10 + 5x, without negative coefficients.
Official wording
Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent expressions. (The distributive property of multiplication over addition is prominent here. Negative coefficients are not an expectation at this grade level.) 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.A.4
Decide when two expressions are equivalent because they give the same value for any number put in, like 2a + 6a and 8a.
Official wording
Identify when expressions are equivalent (i.e., when the expressions name the same number regardless of which value is substituted into them). For example, the expression 5b + 3b is equivalent to (5 +3) b, which is equivalent to 8b.
Reason about and solve one-variable equations and inequalities.
6.EE.B.5
Explain that a solution makes an equation or inequality true, and test numbers from a given set by substituting them in.
Official wording
Understand that a solution to an equation or inequality is the value(s) that makes that statement true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.6
Write expressions with variables to solve problems, knowing a variable can stand for one unknown number or for any number in a set.
Official wording
Use variables to represent numbers and write expressions when solving real-world and mathematical problems; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.B.7
Write and solve one-step equations like x + 7 = 12 or 4x = 18 with nonnegative rational numbers to solve real-world and math problems.
Official wording
Solve real-world and mathematical problems by writing and solving one-step equations of the form x + p = q, px = q, x – p = q, and x/p = q for cases in which p, q, and x are all nonnegative rational numbers and p ≠ 0. (Complex fractions are not an expectation at this grade level.)
6.EE.B.8
Write and read inequalities like x > 5 or x ≤ 10 that describe a limit in a problem, know they have endless solutions, and show them on a number line.
Official wording
Interpret and write an inequality of the form x > c, x < c, x ≤ c, or x ≥ c which represents a condition or constraint in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of inequalities on number line diagrams.
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9
Use variables for two changing amounts, write an equation like y = 8x for the dependent one, and connect it to a graph and a table, like pay versus hours worked.
Official wording
Use variables to represent two quantities in a real-world problem that change in relationship to one another. For example, Susan is putting money in her savings account by depositing a set amount each week ($50). Represent her savings account balance with respect to the number of weekly deposits (s = 50w, illustrating the relationship between balance amount s and number of weeks w).aWrite an equation in the form of y = px where y, p, and x are all non-negative and p ≠ 0, to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.bAnalyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Geometry
4 standardsSolve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.1
Find areas of triangles, special quadrilaterals and other polygons by fitting them into rectangles or cutting them into triangles and simpler shapes, in real-world problems.
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; know and apply these techniques in the context of solving real-world and mathematical problems.
6.G.A.2
Find the volume of rectangular prisms with fraction edge lengths by packing small fraction cubes and with V = lwh or V = Bh, in real-world problems.
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 = lwh and V = Bh where B is the area of the base to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.G.A.3
Draw polygons on a coordinate grid from vertex points and use coordinates to find lengths of horizontal or vertical sides, like on a map or floor plan.
Official wording
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or horizontal segments only). Apply these techniques in the context of solving real-world and mathematical problems.
6.G.A.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 and Probability
5 standardsDevelop understanding of statistical variability.
6.SP.A.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.A.2
Explain that data from a statistical question has a distribution described by its center, using mean, median or mode, its range, 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 measures of center (mean, median, mode), measures of variation (range only), and overall shape.
6.SP.A.3
Explain that the mean, median or mode sums up a whole data set in one number, while a measure of variation tells in one number how spread out it is.
Official wording
Recognize that a measure of center (mean, median, mode) 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.B.4
Show one set of number data in a dot plot, box plot, pie chart or stem-and-leaf plot.
Official wording
Display a single set of numerical data using dot plots (line plots), box plots, pie charts and stem plots.
6.SP.B.5
Summarize data in context, giving the count, what was measured and its units, the median or mean and the range, any pattern, and why that center suits the shape.
Official wording
Summarize numerical 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.cGive quantitative measures of center (median and/or mean) and variability (range) as well as describing any overall pattern with reference to the context in which the data were gathered.dRelate the choice of measures of center to the shape of the data distribution and the context in which the data were gathered.
The official Tennessee documents
- Tennessee Mathematics Standards · adopted February 2021 · since 2023-24
Tennessee Academic Standards for Mathematics, Tennessee Department of Education, tn.gov/education.
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.