The Common Core in Maryland
Skills available for Maryland sixth-grade math standards
Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.
Show alignments for:
- Maryland College and Career-Ready Frameworks Maryland College and Career-Ready Frameworks
- Maryland College and Career-Ready Standards: Grade 6 Maryland College and Career-Ready Standards: Grade 6
- Maryland College and Career-Ready Standards: Mathematical Practices Maryland College and Career-Ready Standards: Mathematical Practices
Actions
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.a Knowledge of ratio as a comparison of any two quantities
-
6.RP.1.b Knowledge of a ratio is not always a comparison of part-to-whole; Can be part-to-part or whole-to-whole
-
-
6.RP.2 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.
-
6.RP.2.a Knowledge that a unit rate emphasizes finding an equivalent ratio with a denominator of 1.
-
-
6.RP.3 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.
-
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.
-
6.RP.3a.1 Knowledge of multiplicative recursive patterns
-
6.RP.3a.2 Ability to use multiplicative relationships to extend an initial ratio to equivalent ratios; When working backward, use the inverse operation (division).
-
6.RP.3a.3 Ability to recognize a linear relationship appears when the pairs are plotted on the coordinate plane
-
-
6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
-
6.RP.3b.1 Ability to use division to determine unit rate
-
-
6.RP.3c Find 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.
-
6.RP.3c.1 Ability to introduce percent as a special rate where a part is compared to a whole and the whole always has a value of 100
- Percents of numbers and money amounts (6-V.4)
- Percents of numbers: word problems (6-V.5)
- Percents of numbers: fractional and decimal percents (6-V.6)
- Find the total given a part and a percent (6-V.9)
- Which is the better coupon? (6-X.1)
- Sale prices (6-X.5)
- Sale prices: find the original price (6-X.6)
- Percents - calculate tax, tip, mark-up, and more (6-X.7)
-
6.RP.3c.2 Ability to solve problems using equivalent ratios.
-
-
6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
-
6.RP.3d.1 Ability to expand ratio reasoning to units of measurement
- Convert and compare customary units (6-W.3)
- Convert, compare, add, and subtract mixed customary units (6-W.4)
- Multiply and divide mixed customary units (6-W.5)
- Customary unit conversions involving fractions and mixed numbers (6-W.6)
- Convert and compare metric units (6-W.7)
- Convert between customary and metric systems (6-W.9)
- Unit prices with customary unit conversions (6-X.4)
-
-
-
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, e.g., by using visual fraction models and equations to represent the problem.
-
6.NS.1.a Ability to explore the concept that division breaks quantities into groups
-
6.NS.1.b Ability to emphasize that when dividing by a value that is less than one, the quotient is greater than the dividend
-
6.NS.1.c Ability to explore both the measurement concept and the partition concept of division of fractions
-
6.NS.1.d Ability to introduce the fact that the measurement concept uses repeated subtraction or equal groups.
-
6.NS.1.e Ability to explore the common denominator algorithm as a method of repeated subtraction.
-
6.NS.1.f Knowledge of partition concept focuses on "How much is one?"
-
6.NS.1.g Knowledge of algorithm a/b ÷ c/d = a/b x d/c = ad/bc (invert and multiply) is an extension of the partition concept.
- Divide whole numbers and unit fractions (6-M.3)
- Divide fractions by whole numbers in recipes (6-M.5)
- Divide fractions (6-M.7)
- Divide fractions and mixed numbers (6-M.10)
- Divide fractions and mixed numbers: word problems (6-M.12)
- Add, subtract, multiply, or divide two fractions (6-N.1)
- Add, subtract, multiply, or divide two fractions: word problems (6-N.2)
-
-
-
Compute fluently with multi-digit numbers and find common factors and multiples.
-
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
- Divisibility rules (6-C.1)
- Division patterns with zeros (6-C.2)
- Divide numbers ending in zeros: word problems (6-C.3)
- Estimate quotients (6-C.4)
- Divide whole numbers - 2-digit divisors (6-C.5)
- Divide whole numbers - 3-digit divisors (6-C.6)
- Add, subtract, multiply, or divide two whole numbers (6-E.1)
- Add, subtract, multiply, or divide two whole numbers: word problems (6-E.2)
-
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
- Add and subtract decimal numbers (6-H.1)
- Add and subtract decimals: word problems (6-H.2)
- Estimate sums and differences of decimals (6-H.5)
- Maps with decimal distances (6-H.6)
- Estimate products of decimal numbers (6-I.1)
- Multiply decimals (6-I.3)
- Inequalities with decimal multiplication (6-I.4)
- Divide decimals by whole numbers (6-I.5)
- Divide decimals by whole numbers: word problems (6-I.6)
- Multiply and divide decimals by powers of ten (6-I.7)
- Division with decimal divisors (6-I.9)
- Inequalities with decimal division (6-I.10)
- Add, subtract, multiply, or divide two decimals (6-J.1)
- Add, subtract, multiply, or divide two decimals: word problems (6-J.2)
-
6.NS.4 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.
-
6.NS.4.a Ability to build on student knowledge of and differentiate between factors and multiples
-
6.NS.4.b Ability to build on student knowledge of factor pairs of whole numbers
-
6.NS.4.c Ability to identify and differentiate between common factors and common multiples of 2 whole numbers
-
-
-
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 (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 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.
-
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, e.g., -(-3) = 3, 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.1 Ability to introduce and define coordinate plane terminology, including coordinate plane and quadrants I, II, III, and IV
-
-
6.NS.6c Find 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.6c.1 Ability to include positive and negative fractions and decimals
-
6.NS.6c.2 Ability to introduce a scale on number lines and axes for 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 diagram.
-
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.1 Ability to develop conceptual understanding to go beyond "absolute value always is positive".
-
-
6.NS.7d Distinguish comparisons of absolute value from statements about order.
-
6.NS.7d.1 Ability to develop understanding within real-world contexts
-
-
-
6.NS.8 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.
-
6.EE Expressions and Equations
-
Apply and extend previous understandings of arithmetic to algebraic expressions.
-
6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.
-
6.EE.1.a Ability to develop understanding of a whole-number exponent as shorthand for repeated multiplication of a number times itself
- Write multiplication expressions using exponents (6-D.1)
- Evaluate powers with whole number bases (6-D.2)
- Find the missing exponent or base (6-D.4)
- Evaluate powers with decimal bases (6-D.5)
- Evaluate powers with fractional bases (6-D.6)
- Evaluate powers with whole number, decimal, and fractional bases (6-D.7)
-
6.EE.1.b Ability to introduce squares and cubes first because they can be represented geometrically
-
6.EE.1.c Ability to extend understanding of order of operations to include exponents
-
-
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.1 Ability to define what a variable is
-
6.EE.2a.2 Knowledge that there are multiple ways to read the same expression
-
-
6.EE.2b Identify 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.
-
6.EE.2b.1 Ability to introduce and define coefficient and term
-
6.EE.2b.2 Ability to read expressions aloud to explore the concept of quantities
-
-
6.EE.2c Evaluate 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).
- Evaluate numerical expressions involving whole numbers (6-E.7)
- Convert between Celsius and Fahrenheit (6-W.11)
- Evaluate variable expressions with whole numbers (6-Y.4)
- Evaluate multi-variable expressions (6-Y.5)
- Evaluate variable expressions with decimals, fractions, and mixed numbers (6-Y.6)
- Complete a table for a two-variable relationship (6-CC.8)
-
-
6.EE.3 Apply the properties of operations to generate equivalent expressions.
-
6.EE.3.a Ability to use properties of operations to simplify expressions, therefore producing equivalent expressions
-
-
6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
-
-
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.
- Does x satisfy an equation? (6-AA.1)
- Which x satisfies an equation? (6-AA.2)
- Solve one-step equations with whole numbers (6-AA.10)
- Solve one-step multiplication and division equations with decimals and fractions (6-AA.12)
- Solve one-step equations: word problems (6-AA.17)
- Solutions to inequalities (6-BB.1)
- Solve one-step inequalities (6-BB.5)
-
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 and px = q for cases in which p, q and x are all nonnegative rational numbers.
-
6.EE.7.a Ability to reinforce that solving equations is finding values of the variable that make the equation true
-
6.EE.7.b Ability to develop conceptual understanding of inverse operations
-
6.EE.7.c Ability to develop an understanding of how to apply properties of equality
-
6.EE.7.d Knowledge of preserving equivalence as you solve equations
-
-
6.EE.8 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.
-
6.EE.8.a Ability to develop conceptual understanding of representing solutions to inequalities on a number line diagram
-
6.EE.8.b Knowledge of ≤ and ≥
-
6.EE.8.c Knowledge of symbolic components of the graph of an inequality; Specifically, open circle vs. closed circle, direction of shading
-
6.EE.8.d Knowledge that an open circle represents a value that is NOT actually part of the solution set
-
6.EE.8.e Knowledge that solutions x>c or x
-
-
-
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; 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.
-
6.EE.9.a Ability to differentiate between independent and dependent variables
-
6.EE.9.b Knowledge of the relationship between the two variables
-
6.EE.9.c Knowledge of terminology associated with graphing ordered pairs
-
6.EE.9.d Ability to write an equation based on a graph or a table
-
-
6.G Geometry
-
Solve real-world and mathematical problems involving area, surface area, and volume.
-
6.G.1 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.1.a Ability to combine triangles to create rectangles
-
6.G.1.b Ability to partition quadrilaterals and polygons into all triangles or a combination of triangles and rectangles/squares
-
6.G.1.c Knowledge of the base and height of a right triangle are the length and width of a rectangle to discover the formula A = bh/2
-
-
6.G.2 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 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.SP Statistics and Probability
-
Develop understanding of statistical variability.
-
6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
-
6.SP.1.a Ability to introduce and develop statistical reasoning
-
6.SP.1.b Ability to determine the difference between a statistical question and a non-statistical question
-
-
6.SP.2 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.2.a Ability to develop conceptual understanding of the characteristics of a data set
-
6.SP.2.b Ability to develop an understanding of outliers
-
-
6.SP.3 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.
-
6.SP.3.a Knowledge of median and mean as measures of center
-
6.SP.3.b Knowledge of range as a measure of variation
-
6.SP.3.c Ability to look at a set of data and estimate the measures of center
-
-
-
Summarize and describe distributions.
-
6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
-
6.SP.4.a Ability to recognize that a dot plot is a line plot
-
6.SP.4.b Ability to recognize that a box plot is a box-and-whisker plot
-
-
6.SP.5 Summarize numerical data sets in relation to their context, such as by:
-
6.SP.5a Reporting the number of observations.
-
6.SP.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
-
6.SP.5b.1 Knowledge of conceptual understanding of statistical interpretation, focusing on the context of data sets
-
-
6.SP.5c Giving 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.
-
6.SP.5c.1 Ability to identify data that are outliers and understand how they affect the measures of central tendency
-
-
6.SP.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
-
-