NC.8.NS: The Number System

(Framing Text): Know that there are numbers that are not rational, and approximate them by rational numbers.

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: Expressions and Equations

(Framing Text): Work with radicals and integer exponents.

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

(Framing Text): Analyze and solve linear equations and inequalities.

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)

(Framing Text): Analyze and solve pairs of simultaneous linear equations.

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: Functions

(Framing Text): Define, evaluate, and compare functions.

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

(Framing Text): Use functions to model relationships between quantities.

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: Geometry

(Framing Text): Understand congruence and similarity using physical models, transparencies, or geometry software.

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.

Dilations
Similar Figures

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

Dilations
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.

Dilations
Similar Figures

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

Dilations
Similar Figures

(Framing Text): Analyze angle relationships.

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.

Investigating Angle Theorems
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

(Framing Text): Understand and apply the Pythagorean Theorem.

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

(Framing Text): Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

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: Statistics and Probability

(Framing Text): Investigate patterns of association in bivariate data.

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.

Histograms

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

Histograms

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

Histograms