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.

 Beam to Moon (Ratios and Proportions)
 Part-to-part and Part-to-whole Ratios
 Proportions and Common Multipliers
 Road Trip (Problem Solving)

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

 Beam to Moon (Ratios and Proportions)
 Part-to-part and Part-to-whole Ratios
 Proportions and Common Multipliers

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

 Beam to Moon (Ratios and Proportions)
 Household Energy Usage
 Road Trip (Problem Solving)

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.

 Household Energy Usage
 Road Trip (Problem Solving)

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

 Unit Conversions

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

 Function Machines 2 (Functions, Tables, and Graphs)
 Points, Lines, and Equations
 Slope

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.

 Percent of Change
 Percents and Proportions
 Polling: Neighborhood

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.

 Dividing Fractions
 Dividing Mixed Numbers

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

 Dividing Fractions
 Dividing Mixed Numbers

(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.

 Adding Whole Numbers and Decimals (Base-10 Blocks)
 Multiplying Decimals (Area Model)
 Multiplying with Decimals
 Square Roots
 Subtracting Whole Numbers and Decimals (Base-10 Blocks)
 Sums and Differences with 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.

 Factor Trees (Factoring Numbers)
 Finding Factors with Area Models

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.

 Adding Fractions (Fraction Tiles)

(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.

 Adding and Subtracting Integers
 Adding on the Number Line
 Addition of Polynomials
 Integers, Opposites, and Absolute 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.

 Absolute Value with Linear Functions
 Integers, Opposites, and Absolute Values

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

 Integers, Opposites, and Absolute Values

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.

 Adding and Subtracting Integers
 Adding on the Number Line
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values

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

 Fraction Garden (Comparing Fractions)
 Modeling Decimals (Area and Grid Models)
 Modeling Fractions (Area Models)
 Rational Numbers, Opposites, and Absolute Values

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.

 City Tour (Coordinates)
 Elevator Operator (Line Graphs)
 Points in the Coordinate Plane
 Points, Lines, and Equations

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.

 Integers, Opposites, and Absolute Values

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.

 Points in the Coordinate Plane

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.

 Order of Operations

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.

 Using Algebraic Equations
 Using Algebraic Expressions

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.

 Compound Interest
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Using Algebraic Equations
 Using Algebraic Expressions

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

 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Solving Algebraic Equations II

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

 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

(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.

 Solving Equations on the Number Line
 Using Algebraic Equations
 Using Algebraic Expressions

(Framing Text): Reason about one variable inequalities.

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

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.

 Absolute Value Equations and Inequalities
 Linear Inequalities in Two Variables
 Solving Linear Inequalities in One Variable

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

 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Solving Linear Inequalities in One Variable

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.

 Area of Parallelograms
 Area of Triangles
 Fido's Flower Bed (Perimeter and Area)

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.

 Points in the Coordinate Plane

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.

 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

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.

 Polling: City
 Polling: Neighborhood
 Reaction Time 2 (Graphs and Statistics)

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.

 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)

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.

 Describing Data Using Statistics
 Mean, Median, and Mode
 Movie Reviewer (Mean and Median)
 Populations and Samples
 Reaction Time 2 (Graphs and Statistics)
 Sight vs. Sound Reactions
 Stem-and-Leaf Plots

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Movie Reviewer (Mean and Median)
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)
 Stem-and-Leaf Plots

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.

 Real-Time Histogram

(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.

 Box-and-Whisker Plots
 Histograms
 Mean, Median, and Mode
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)
 Real-Time Histogram
 Stem-and-Leaf Plots

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

 Mascot Election (Pictographs and Bar Graphs)
 Movie Reviewer (Mean and Median)
 Reaction Time 2 (Graphs and Statistics)

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.

 Reaction Time 1 (Graphs and Statistics)

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Movie Reviewer (Mean and Median)
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)
 Real-Time Histogram

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.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Movie Reviewer (Mean and Median)
 Polling: City
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)
 Real-Time Histogram
 Sight vs. Sound Reactions
 Stem-and-Leaf Plots

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

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Movie Reviewer (Mean and Median)
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)

Correlation last revised: 4/4/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.