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:

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.

 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

(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.

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 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 and Solving Two-Step Equations
 Solving Algebraic Equations II
 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)

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.

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 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 3 (Functions and Problem Solving)
 Graphs of Polynomial Functions
 Linear Functions
 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.

 Points, Lines, and Equations
 Slope-Intercept Form of a Line

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
 Cat and Mouse (Modeling with Linear Systems)
 Compound Interest
 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

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

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

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

 Quadratics in Polynomial Form

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.

 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.

 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.

 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.

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

 Polygon Angle Sum
 Triangle Angle Sum

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

 Triangle Angle Sum

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

 Similar Figures
 Similarity in Right Triangles

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:

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

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.

 Histograms

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

 Histograms

Correlation last revised: 4/4/2018

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