North Carolina

NC.6.RP Ratio and Proportional Relationships

• Understand ratio concepts and use ratio reasoning to solve problems.

  • NC.6.RP.1 Understand the concept of a ratio and use ratio language to:

    • NC.6.RP.1.a Describe a ratio as a multiplicative relationship between two quantities.

    • NC.6.RP.1.b Model a ratio relationship using a variety of representations.

      • Write a ratio (6-R.1)
      • Write a ratio: word problems (6-R.3)

  • NC.6.RP.2 Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context.

    • Unit rates (6-R.9)
    • Ratios and rates: word problems (6-R.15)

  • NC.6.RP.3 Use ratio reasoning with equivalent whole-number ratios to solve real-world and mathematical problems by:

    • NC.6.RP.3.a Creating and using a table to compare ratios.

    • NC.6.RP.3.b Finding missing values in the tables.

      • Ratio tables (6-R.7)

    • NC.6.RP.3.c Using a unit ratio.

      • Unit rates (6-R.9)
      • Ratios and rates: word problems (6-R.15)

    • NC.6.RP.3.d Converting and manipulating measurements using given ratios.

      • Convert between customary and metric systems (6-T.9)

    • NC.6.RP.3.e Plotting the pairs of values on the coordinate plane.

  • NC.6.RP.4 Use ratio reasoning to solve real-world and mathematical problems with percents by:

    • NC.6.RP.4.a Understanding and finding a percent of a quantity as a ratio per 100.

      • Percents of numbers and money amounts (6-S.11)
      • Percents of numbers: word problems (6-S.12)
      • Percents of numbers: fractional and decimal percents (6-S.13)
      • Percents - calculate tax, tip, mark-up, and more (6-V.7)

    • NC.6.RP.4.b Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity.

    • NC.6.RP.4.c Finding the whole, given a part and the percent.

      • Find the total given a part and a percent (6-S.16)
      • Sale prices: find the original price (6-V.6)

NC.6.NS The Number System

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

  • NC.6.NS.1 Use visual models and common denominators to:

    • NC.6.NS.1.a Interpret and compute quotients of fractions.

      • Divide fractions (6-L.6)
      • Divide fractions and mixed numbers (6-L.9)

    • NC.6.NS.1.b Solve real-world and mathematical problems involving division of fractions.

      • Divide fractions by whole numbers in recipes (6-L.4)
      • Divide fractions and mixed numbers: word problems (6-L.10)

• Compute fluently with multi-digit numbers and find common factors and multiples.

  • NC.6.NS.2 Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context.

    • Division patterns with zeroes (6-C.2)
    • Divide numbers ending in zeroes: word problems (6-C.3)
    • Divide whole numbers - 2-digit divisors (6-C.5)
    • Divide whole numbers - 3-digit divisors (6-C.6)

  • NC.6.NS.3 Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals.

    • Add and subtract decimal numbers (6-G.1)
    • Add and subtract decimals: word problems (6-G.2)
    • Complete the decimal addition or subtraction sentence (6-G.3)
    • Maps with decimal distances (6-G.5)
    • Multiply decimals (6-H.3)
    • Divide decimals by whole numbers (6-H.5)
    • Divide decimals by whole numbers: word problems (6-H.6)
    • Multiply and divide decimals by powers of ten (6-H.7)
    • Division with decimal divisors (6-H.9)
    • Add, subtract, multiply, or divide two decimals (6-O.6)
    • Add, subtract, multiply, or divide two decimals: word problems (6-O.7)

  • NC.6.NS.4 Understand and use prime factorization and the relationships between factors to:

    • NC.6.NS.4.a Find the unique prime factorization for a whole number.

      • Prime factorization (6-E.6)
      • Prime factorization with exponents (6-E.7)

    • NC.6.NS.4.b Find the greatest common factor of two whole numbers less than or equal to 100.

      • Greatest common factor (6-E.8)
      • GCF and LCM: word problems (6-E.12)

    • NC.6.NS.4.c Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100.

    • NC.6.NS.4.d Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators.

      • Add and subtract fractions with unlike denominators (6-J.3)
      • Add and subtract fractions with unlike denominators: word problems (6-J.4)

• Apply and extend previous understandings of numbers to the system of rational numbers.

  • NC.6.NS.5 Understand and use rational numbers to:

    • NC.6.NS.5.a Describe quantities having opposite directions or values.

    • NC.6.NS.5.b Represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

      • Understanding integers (6-M.1)
      • Compare temperatures above and below zero (6-T.10)

    • NC.6.NS.5.c Understand the absolute value of a rational number as its distance from 0 on the number line to:

      • NC.6.NS.5.c.1 Interpret absolute value as magnitude for a positive or negative quantity in a real-world context.

        • Absolute value (6-M.6)

      • NC.6.NS.5.c.2 Distinguish comparisons of absolute value from statements about order.

        • Integer inequalities with absolute values (6-M.9)
        • Put rational numbers in order (6-P.5)
        • Absolute value of rational numbers (6-P.8)

  • NC.6.NS.6 Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane.

    • NC.6.NS.6.a On a number line:

      • NC.6.NS.6.a.1 Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself.

        • Integers on number lines (6-M.2)
        • Rational numbers: find the sign (6-P.11)

      • NC.6.NS.6.a.2 Find and position rational numbers on a horizontal or vertical number line.

        • Decimal number lines (6-F.8)
        • Integers on number lines (6-M.2)
        • Graph integers on horizontal and vertical number lines (6-M.3)

    • NC.6.NS.6.b On a coordinate plane:

      • NC.6.NS.6.b.1 Understand signs of numbers in ordered pairs as indicating locations in quadrants.

        • Objects on a coordinate plane (6-X.2)
        • Quadrants (6-X.4)

      • NC.6.NS.6.b.2 Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

      • NC.6.NS.6.b.3 Find and position pairs of rational numbers on a coordinate plane.

        • Graph points on a coordinate plane (6-X.3)

  • NC.6.NS.7 Understand ordering of rational numbers.

    • NC.6.NS.7.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

      • Compare integers (6-M.7)

    • NC.6.NS.7.b Write, interpret, and explain statements of order for rational numbers in real-world contexts.

      • Compare and order rational numbers using number lines (6-P.3)
      • Compare rational numbers (6-P.4)
      • Put rational numbers in order (6-P.5)
      • Compare and order rational numbers: word problems (6-P.6)
      • Compare temperatures above and below zero (6-T.10)

  • NC.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.

    • Coordinate planes as maps (6-X.6)
    • Distance between two points (6-X.7)
    • Follow directions on a coordinate plane (6-X.8)

  • NC.6.NS.9 Apply and extend previous understandings of addition and subtraction.

    • NC.6.NS.9.a Understand additive inverses when adding and subtracting integers.

      • NC.6.NS.9.a.1 Describe situations in which opposite quantities combine to make 0.

      • NC.6.NS.9.a.2 Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair.

      • NC.6.NS.9.a.3 Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference.

      • NC.6.NS.9.a.4 Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences.

        • Add integers using counters (6-N.1)
        • Subtract integers using counters (6-N.4)

NC.6.EE Expressions and Equations

• Apply and extend previous understandings of arithmetic to algebraic expressions.

  • NC.6.EE.1 Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents.

    • Write multiplication expressions using exponents (6-D.1)
    • Evaluate exponents (6-D.2)
    • Write powers of ten with exponents (6-D.3)
    • Find the missing exponent or base (6-D.4)
    • Exponents with decimal bases (6-D.5)
    • Exponents with fractional bases (6-D.6)
    • Evaluate numerical expressions involving whole numbers (6-O.4)
    • Evaluate numerical expressions involving decimals (6-O.8)
    • Evaluate numerical expressions involving fractions (6-O.11)

  • NC.6.EE.2 Write, read, and evaluate algebraic expressions.

    • NC.6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers.

      • Write variable expressions: one operation (6-Y.1)
      • Write variable expressions: two operations (6-Y.2)

    • NC.6.EE.2.b Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity.

      • Identify terms and coefficients (6-Y.8)
      • Sort factors of variable expressions (6-Y.9)

    • NC.6.EE.2.c Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems.

      • Convert between Celsius and Fahrenheit (6-T.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)

  • NC.6.EE.3 Apply the properties of operations to generate equivalent expressions without exponents.

    • Properties of addition (6-Y.11)
    • Properties of multiplication (6-Y.12)
    • Multiply using the distributive property (6-Y.14)
    • Factor variable expressions using the distributive property (6-Y.17)
    • Write equivalent expressions using properties (6-Y.19)

  • NC.6.EE.4 Identify when two expressions are equivalent and justify with mathematical reasoning.

    • Identify equivalent expressions using strip models (6-Y.10)
    • Identify equivalent expressions I (6-Y.21)
    • Identify equivalent expressions II (6-Y.22)

• Reason about and solve one-variable equations.

  • NC.6.EE.5 Use substitution to determine whether a given number in a specified set makes an equation true.

    • Does x satisfy an equation? (6-Z.1)
    • Which x satisfies an equation? (6-Z.2)

  • NC.6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

    • Write variable expressions: word problems (6-Y.3)

  • NC.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form:

    • NC.6.EE.7.a x + p = q in which p, q and x are all nonnegative rational numbers; and,

      • Model and solve equations using algebra tiles (6-Z.5)
      • Write and solve equations that represent diagrams (6-Z.7)
      • Solve one-step equations with whole numbers (6-Z.10)
      • Solve one-step multiplication and division equations with decimals and fractions (6-Z.12)
      • Solve one-step equations: word problems (6-Z.16)

    • NC.6.EE.7.b px = q for cases in which p, q and x are all nonnegative rational numbers.

      • Model and solve equations using algebra tiles (6-Z.5)
      • Write and solve equations that represent diagrams (6-Z.7)
      • Solve one-step equations with whole numbers (6-Z.10)
      • Solve one-step multiplication and division equations with decimals and fractions (6-Z.12)
      • Solve one-step equations: word problems (6-Z.16)

• Reason about one variable inequalities.

  • NC.6.EE.8 Reason about inequalities by:

    • NC.6.EE.8.a Using substitution to determine whether a given number in a specified set makes an inequality true.

      • Solutions to inequalities (6-AA.1)

    • NC.6.EE.8.b Writing an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.

      • Write inequalities from number lines (6-AA.3)

    • NC.6.EE.8.c Recognizing that inequalities of the form x > c or x < c have infinitely many solutions.

      • Solutions to inequalities (6-AA.1)

    • NC.6.EE.8.d Representing solutions of inequalities on number line diagrams.

      • Graph inequalities on number lines (6-AA.2)

• Represent and analyze quantitative relationships between dependent and independent variables.

  • NC.6.EE.9 Represent and analyze quantitative relationships by:

    • NC.6.EE.9.a Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another.

      • Write an equation from a graph using a table (6-BB.3)
      • Identify independent and dependent variables: word problems (6-BB.4)
      • Solve word problems by finding two-variable equations (6-BB.7)
      • Write a two-variable equation (6-BB.10)

    • NC.6.EE.9.b Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).

      • Find a value using two-variable equations (6-BB.5)
      • Find a value using two-variable equations: word problems (6-BB.6)
      • Complete a table for a two-variable relationship (6-BB.8)
      • Identify the graph of an equation (6-BB.11)
      • Graph a two-variable equation (6-BB.13)
      • Interpret a graph: word problems (6-BB.14)

NC.6.G Geometry

• Solve real-world and mathematical problems involving area, surface area, and volume.

  • NC.6.G.1 Create geometric models to solve real-world and mathematical problems to:

    • NC.6.G.1.a Find the area of triangles by composing into rectangles and decomposing into right triangles.

    • NC.6.G.1.b Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles.

      • Area of compound figures (6-FF.11)
      • Area of compound figures with triangles (6-FF.12)

  • NC.6.G.2 Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems.

  • NC.6.G.3 Use the coordinate plane to solve real-world and mathematical problems by:

    • NC.6.G.3.a Drawing polygons in the coordinate plane given coordinates for the vertices.

      • Graph triangles and quadrilaterals (6-CC.8)

    • NC.6.G.3.b Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.

      • Distance between two points (6-X.7)

  • NC.6.G.4 Represent right prisms and right pyramids 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.

    • Nets of three-dimensional figures (6-EE.3)
    • Surface area of cubes and rectangular prisms (6-FF.21)
    • Surface area of triangular prisms (6-FF.23)
    • Surface area of pyramids (6-FF.24)

NC.6.SP Statistics and Probability

• Develop understanding of statistical variability.

  • NC.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.

    • Identify statistical questions (6-HH.1)

  • NC.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.

    • Create line plots (6-GG.4)
    • Interpret stem-and-leaf plots (6-GG.21)
    • Create stem-and-leaf plots (6-GG.22)
    • Box plots (6-GG.23)
    • Calculate quartiles and interquartile range (6-HH.7)
    • Describe distributions in line plots (6-HH.11)

  • NC.6.SP.3 Understand that both a measure of center and a description of variability should be considered when describing a numerical data set.

    • NC.6.SP.3.a Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set.

      • NC.6.SP.3.a.1 Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set.

        • Calculate mean, median, mode, and range (6-HH.2)
        • Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)
        • Mean, median, mode, and range: find the missing number (6-HH.4)

      • NC.6.SP.3.a.2 Understand the median as a measure of center that is the numerical middle of an ordered data set.

        • Calculate mean, median, mode, and range (6-HH.2)
        • Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)
        • Mean, median, mode, and range: find the missing number (6-HH.4)

    • NC.6.SP.3.b Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads.

• Summarize and describe distributions.

  • NC.6.SP.4 Display numerical data in plots on a number line.

    • NC.6.SP.4.a Use dot plots, histograms, and box plots to represent data.

      • Create line plots (6-GG.4)
      • Create and interpret line plots with fractions (6-GG.5)
      • Create histograms (6-GG.15)
      • Box plots (6-GG.23)

    • NC.6.SP.4.b Compare the attributes of different representations of the same data.

  • NC.6.SP.5 Summarize numerical data sets in relation to their context.

    • NC.6.SP.5.a Describe the collected data by:

      • NC.6.SP.5.a.1 Reporting the number of observations in dot plots and histograms.

        • Interpret line plots (6-GG.3)
        • Interpret histograms (6-GG.14)

      • NC.6.SP.5.a.2 Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement.

        • Identify representative, random, and biased samples (6-HH.12)

    • NC.6.SP.5.b Analyze center and variability by:

      • NC.6.SP.5.b.1 Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations.

        • Calculate mean, median, mode, and range (6-HH.2)
        • Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)

      • NC.6.SP.5.b.2 Justifying the appropriate choice of measures of center using the shape of the data distribution.