Standard Course of Study

NC.8.NS.1: Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a non-repeating, non-terminating decimal.

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

NC.8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving:

Circumference and Area of Circles

Square Roots

NC.8.NS.2.a: Square roots and cube roots to the tenths.

Circumference and Area of Circles

Square Roots

NC.8.NS.2.b: π to the hundredths.

Circumference and Area of Circles

Square Roots

NC.8.EE.1: Develop and apply the properties of integer exponents to generate equivalent numerical expressions.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions II

NC.8.EE.2: Use square root and cube root symbols to:

Operations with Radical Expressions

Simplifying Radical Expressions

Square Roots

NC.8.EE.2.a: Represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number.

Operations with Radical Expressions

Simplifying Radical Expressions

Square Roots

NC.8.EE.2.b: Evaluate square roots of perfect squares and cube roots of perfect cubes for positive numbers less than or equal to 400.

Operations with Radical Expressions

Simplifying Radical Expressions

Square Roots

NC.8.EE.3: Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other.

Number Systems

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

NC.8.EE.4: Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both decimal and scientific notation are used.

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

NC.8.EE.7: Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations by Graphing Each Side

Solving Two-Step Equations

NC.8.EE.7.a: Recognize linear equations in one variable as having one solution, infinitely many solutions, or no solutions.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

Solving Two-Step Equations

NC.8.EE.7.b: Solve linear equations and inequalities including multi-step equations and inequalities with the same variable on both sides.

Compound Inequalities

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Two-Step Equations

Systems of Linear Inequalities (Slope-intercept form)

NC.8.EE.8: Analyze and solve a system of two linear equations in two variables in slope-intercept form.

NC.8.EE.8.a: Understand that solutions to a system of two linear equations correspond to the points of intersection of their graphs because the point of intersection satisfies both equations simultaneously.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

NC.8.EE.8.b: Solve real-world and mathematical problems leading to systems of linear equations by graphing the equations. Solve simple cases by inspection.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

NC.8.F.1: Understand that a function is a rule that assigns to each input exactly one output.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

NC.8.F.1.a: Recognize functions when graphed as the set of ordered pairs consisting of an input and exactly one corresponding output.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

NC.8.F.1.b: Recognize functions given a table of values or a set of ordered pairs.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Functions

Points, Lines, and Equations

NC.8.F.2: Compare properties of two linear functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Graphs of Polynomial Functions

Linear Functions

Quadratics in Polynomial Form

Slope-Intercept Form of a Line

NC.8.F.3: Identify linear functions from tables, equations, and graphs.

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

NC.8.F.4: Analyze functions that model linear relationships.

NC.8.F.4.a: Understand that a linear relationship can be generalized by 𝑦 = 𝑚𝑥 + 𝑏.

Arithmetic Sequences

Cat and Mouse (Modeling with Linear Systems)

Compound Interest

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Points, Lines, and Equations

Slope-Intercept Form of a Line

Translating and Scaling Functions

NC.8.F.4.b: Write an equation in slope-intercept form to model a linear relationship by determining the rate of change and the initial value, given at least two (x, y) values or a graph.

Arithmetic Sequences

Cat and Mouse (Modeling with Linear Systems)

Compound Interest

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Points, Lines, and Equations

Slope-Intercept Form of a Line

Translating and Scaling Functions

NC.8.F.4.c: Construct a graph of a linear relationship given an equation in slope-intercept form.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

NC.8.F.4.d: Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the slope and y-intercept of its graph or a table of values.

Absolute Value with Linear Functions

Arithmetic Sequences

Cat and Mouse (Modeling with Linear Systems)

Compound Interest

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Translating and Scaling Functions

NC.8.F.5: Qualitatively analyze the functional relationship between two quantities.

Arithmetic Sequences

Function Machines 3 (Functions and Problem Solving)

Graphs of Polynomial Functions

Linear Functions

Slope-Intercept Form of a Line

Translating and Scaling Functions

NC.8.F.5.a: Analyze a graph determining where the function is increasing or decreasing; linear or non-linear.

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Point-Slope Form of a Line

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

Slope-Intercept Form of a Line

Standard Form of a Line

Translating and Scaling Functions

NC.8.F.5.b: Sketch a graph that exhibits the qualitative features of a real-world function.

Arithmetic Sequences

Function Machines 3 (Functions and Problem Solving)

Graphs of Polynomial Functions

Linear Functions

Quadratics in Polynomial Form

Slope-Intercept Form of a Line

Translating and Scaling Functions

NC.8.G.2: Use transformations to define congruence.

NC.8.G.2.a: Verify experimentally the properties of rotations, reflections, and translations that create congruent figures.

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

NC.8.G.2.b: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

NC.8.G.2.c: Given two congruent figures, describe a sequence that exhibits the congruence between them.

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

NC.8.G.3: Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the x-axis and y-axis on two-dimensional figures using coordinates.

Dilations

Rock Art (Transformations)

Rotations, Reflections, and Translations

Translations

NC.8.G.4: Use transformations to define similarity.

NC.8.G.4.a: Verify experimentally the properties of dilations that create similar figures.

NC.8.G.4.b: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.

NC.8.G.4.c: Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

NC.8.G.5: Use informal arguments to analyze angle relationships.

Investigating Angle Theorems

Isosceles and Equilateral Triangles

Polygon Angle Sum

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

NC.8.G.5.a: Recognize relationships between interior and exterior angles of a triangle.

Investigating Angle Theorems

Isosceles and Equilateral Triangles

Polygon Angle Sum

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

NC.8.G.5.b: Recognize the relationships between the angles created when parallel lines are cut by a transversal.

Investigating Angle Theorems

Isosceles and Equilateral Triangles

Polygon Angle Sum

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

NC.8.G.5.c: Recognize the angle-angle criterion for similarity of triangles.

Isosceles and Equilateral Triangles

Polygon Angle Sum

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

NC.8.G.5.d: Solve real-world and mathematical problems involving angles.

Investigating Angle Theorems

Triangle Angle Sum

NC.8.G.6: Explain the Pythagorean Theorem and its converse.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Surface and Lateral Areas of Pyramids and Cones

NC.8.G.7: Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Surface and Lateral Areas of Pyramids and Cones

NC.8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Distance Formula

Pythagorean Theorem

NC.8.G.9: Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.

Prisms and Cylinders

Pyramids and Cones

NC.8.SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

NC.8.SP.2: Model the relationship between bivariate quantitative data to:

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

NC.8.SP.2.a: Informally fit a straight line for a scatter plot that suggests a linear association.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

NC.8.SP.2.b: Informally assess the model fit by judging the closeness of the data points to the line.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

NC.8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate quantitative data, interpreting the slope and y-intercept.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

NC.8.SP.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

NC.8.SP.4.a: Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

NC.8.SP.4.b: Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Correlation last revised: 9/16/2020

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