NC--Standard Course of Study

(Framing Text): Use complex numbers in polynomial identities and equations.

NC.M3.N-CN.9: Use the Fundamental Theorem of Algebra to determine the number and potential types of solutions for polynomial functions.

Polynomials and Linear Factors

(Framing Text): Interpret the structure of expressions.

NC.M3.A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

NC.M3.A-SSE.1a: Identify and interpret parts of a piecewise, absolute value, polynomial, exponential and rational expressions including terms, factors, coefficients, and exponents.

Compound Interest

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

NC.M3.A-SSE.1b: Interpret expressions composed of multiple parts by viewing one or more of their parts as a single entity to give meaning in terms of a context.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Translating and Scaling Functions

Using Algebraic Expressions

NC.M3.A-SSE.2: Use the structure of an expression to identify ways to write equivalent expressions.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Simplifying Trigonometric Expressions

Solving Algebraic Equations II

Using Algebraic Expressions

(Framing Text): Understand the relationship between zeros and factors of polynomials.

NC.M3.A-APR.2: Understand and apply the Remainder Theorem.

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

NC.M3.A-APR.3: Understand the relationship among factors of a polynomial expression, the solutions of a polynomial equation and the zeros of a polynomial function.

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

(Framing Text): Create equations that describe numbers or relationships.

NC.M3.A-CED.1: Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Compound Interest

Exploring Linear Inequalities in One Variable

Geometric Sequences

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Quadratic Inequalities

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

NC.M3.A-CED.2: Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities.

Absolute Value Equations and Inequalities

Circles

Compound Interest

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

Solving Equations on the Number Line

Standard Form of a Line

Using Algebraic Equations

NC.M3.A-CED.3: Create systems of equations and/or inequalities to model situations in context.

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

(Framing Text): Understand solving equations as a process of reasoning and explain the reasoning.

NC.M3.A-REI.1: Justify a solution method for equations and explain each step of the solving process using mathematical reasoning.

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Formulas for any Variable

Solving Two-Step Equations

NC.M3.A-REI.2: Solve and interpret one variable rational equations arising from a context, and explain how extraneous solutions may be produced.

(Framing Text): Represent and solve equations and inequalities graphically.

NC.M3.A-REI.11: Extend an understanding that the 𝑥-coordinates of the points where the graphs of two equations 𝑦=𝑓(𝑥) and 𝑦=𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥)=𝑔(𝑥) and approximate solutions using a graphing technology or successive approximations with a table of values.

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Standard Form of a Line

(Framing Text): Understand the concept of a function and use function notation.

NC.M3.F-IF.1: Extend the concept of a function by recognizing that trigonometric ratios are functions of angle measure.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

NC.M3.F-IF.2: Use function notation to evaluate piecewise defined functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions

Translating and Scaling Functions

(Framing Text): Interpret functions that arise in applications in terms of the context.

NC.M3.F-IF.4: Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities to include periodicity and discontinuities.

Absolute Value with Linear Functions

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

(Framing Text): Analyze functions using different representations.

NC.M3.F-IF.7: Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; relative maximums and minimums; symmetries; end behavior; period; and discontinuities.

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Quadratics in Factored Form

Rational Functions

Translating and Scaling Functions

NC.M3.F-IF.9: Compare key features of two functions using different representations by comparing properties of two different functions, each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

Quadratics in Vertex Form

(Framing Text): Build a function that models a relationship between two quantities.

NC.M3.F-BF.1: Write a function that describes a relationship between two quantities.

NC.M3.F-BF.1a: Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table).

Compound Interest

Exponential Functions

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

NC.M3.F-BF.1b: Build a new function, in terms of a context, by combining standard function types using arithmetic operations.

Addition and Subtraction of Functions

(Framing Text): Build new functions from existing functions.

NC.M3.F-BF.3: Extend an understanding of the effects on the graphical and tabular representations of a function when replacing 𝑓(𝑥) with 𝑘•𝑓(𝑥), 𝑓(𝑥)+𝑘, 𝑓(𝑥+𝑘) to include 𝑓(𝑘•𝑥) for specific values of 𝑘 (both positive and negative).

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

NC.M3.F-BF.4: Find an inverse function.

NC.M3.F-BF.4a: Understand the inverse relationship between exponential and logarithmic, quadratic and square root, and linear to linear functions and use this relationship to solve problems using tables, graphs, and equations.

NC.M3.F-BF.4b: Determine if an inverse function exists by analyzing tables, graphs, and equations.

NC.M3.F-BF.4c: If an inverse function exists for a linear, quadratic and/or exponential function, 𝑓, represent the inverse function, 𝑓⁻ยน, with a table, graph, or equation and use it to solve problems in terms of a context.

(Framing Text): Construct and compare linear and exponential models and solve problems.

NC.M3.F-LE.3: Compare the end behavior of functions using their rates of change over intervals of the same length to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a polynomial function.

Compound Interest

Introduction to Exponential Functions

NC.M3.F-LE.4: Use logarithms to express the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝑑 where 𝑎, 𝑐, and 𝑑 are numbers and evaluate the logarithm using technology.

Compound Interest

Logarithmic Functions

(Framing Text): Extend the domain of trigonometric functions using the unit circle.

NC.M3.F-TF.2: Build an understanding of trigonometric functions by using tables, graphs and technology to represent the cosine and sine functions.

NC.M3.F-TF.2a: Interpret the sine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its y coordinate.

Cosine Function

Sine Function

Translating and Scaling Sine and Cosine Functions

NC.M3.F-TF.2b: Interpret the cosine function as the relationship between the radian measure of an angle formed by the horizontal axis and a terminal ray on the unit circle and its x coordinate.

Cosine Function

Sine Function

Translating and Scaling Sine and Cosine Functions

(Framing Text): Model periodic phenomena with trigonometric functions.

NC.M3.F-TF.5: Use technology to investigate the parameters, 𝑎, 𝑏, and ℎ of a sine function, 𝑓(𝑥)=𝑎 • 𝑠𝑖𝑛(𝑏 • 𝑥)+ℎ, to represent periodic phenomena and interpret key features in terms of a context.

Translating and Scaling Sine and Cosine Functions

(Framing Text): Prove geometric theorems.

NC.M3.G-CO.10: Verify experimentally properties of the centers of triangles (centroid, incenter, and circumcenter).

Concurrent Lines, Medians, and Altitudes

NC.M3.G-CO.11: Prove theorems about parallelograms. Opposite sides of a parallelogram are congruent. Opposite angles of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Parallelogram Conditions

Special Parallelograms

(Framing Text): Understand and apply theorems about circles.

NC.M3.G-C.2: Understand and apply theorems about circles. Understand and apply theorems about relationships with angles and circles, including central, inscribed and circumscribed angles. Understand and apply theorems about relationships with line segments and circles including, radii, diameter, secants, tangents and chords.

Chords and Arcs

Inscribed Angles

NC.M3.G-C.5: Using similarity, demonstrate that the length of an arc, s, for a given central angle is proportional to the radius, r, of the circle. Define radian measure of the central angle as the ratio of the length of the arc to the radius of the circle, s/r. Find arc lengths and areas of sectors of circles.

(Framing Text): Translate between the geometric description and the equation for a conic section.

NC.M3.G-GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

(Framing Text): Explain volume formulas and use them to solve problems.

NC.M3.G-GMD.3: Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.

Prisms and Cylinders

Pyramids and Cones

(Framing Text): Apply geometric concepts in modeling situations.

NC.M3.G-MG.1: Apply geometric concepts in modeling situations: Use geometric and algebraic concepts to solve problems in modeling situations. Use geometric shapes, their measures, and their properties, to model real-life objects. Use geometric formulas and algebraic functions to model relationships. Apply concepts of density based on area and volume. Apply geometric concepts to solve design and optimization problems.

(Framing Text): Understand and evaluate random processes underlying statistical experiments.

NC.M3.S-IC.1: Understand the process of making inferences about a population based on a random sample from that population.

Polling: City

Polling: Neighborhood

Populations and Samples

(Framing Text): Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

NC.M3.S-IC.3: Recognize the purposes of and differences between sample surveys, experiments, and observational studies and understand how randomization should be used in each.

Polling: City

Polling: Neighborhood

NC.M3.S-IC.4: Use simulation to understand how samples can be used to estimate a population mean or proportion and how to determine a margin of error for the estimate.

Polling: City

Polling: Neighborhood

Populations and Samples

NC.M3.S-IC.5: Use simulation to determine whether observed differences between samples from two distinct populations indicate that the two populations are actually different in terms of a parameter of interest.

Polling: City

Polling: Neighborhood

Populations and Samples

NC.M3.S-IC.6: Evaluate articles and websites that report data by identifying the source of the data, the design of the study, and the way the data are graphically displayed.

Describing Data Using Statistics

Polling: City

Polling: Neighborhood

Populations and Samples

Real-Time Histogram

Correlation last revised: 9/16/2020

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