### NC.6.RP: Ratio and Proportional Relationships

#### (Framing Text): 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.

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

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

NC.6.RP.3.c: Using a unit ratio.

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

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.

### NC.6.NS: The Number System

#### (Framing Text): 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.

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

#### (Framing Text): Compute fluently with multi-digit numbers and find common factors and multiples.

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.

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.

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.

#### (Framing Text): 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.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.

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

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.

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

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

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

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.

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.

### NC.6.EE: Expressions and Equations

#### (Framing Text): 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.

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.

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.

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

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

#### (Framing Text): Reason about and solve one-variable equations.

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

#### (Framing Text): Reason about one variable inequalities.

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.

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

### NC.6.G: Geometry

#### (Framing Text): 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.b: Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles.

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.

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.

### NC.6.SP: Statistics and Probability

#### (Framing Text): 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.

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.

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.

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

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.

#### (Framing Text): 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.

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.

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

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.

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

Correlation last revised: 1/22/2020

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