NC.M1.N: Number and Quantity

NC.M1.N-RN: The Real Number System

(Framing Text): Extend the properties of exponents to rational exponents.

NC.M1.N-RN.2: Rewrite algebraic expressions with integer exponents using the properties of exponents.

 Dividing Exponential Expressions
 Exponents and Power Rules
 Multiplying Exponential Expressions
 Simplifying Algebraic Expressions II

NC.M1.A: Algebra

NC.M1.A-SSE: Seeing Structure in Expressions

(Framing Text): Interpret the structure of expressions.

NC.M1.A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

NC.M1.A-SSE.1a: Identify and interpret parts of a linear, exponential, or quadratic expression, including terms, factors, coefficients, and exponents.

 Compound Interest

NC.M1.A-SSE.1b: Interpret a linear, exponential, or quadratic expression made of multiple parts as a combination of entities to give meaning to an expression.

 Compound Interest

(Framing Text): Write expressions in equivalent forms to solve problems.

NC.M1.A-SSE.3: Write an equivalent form of a quadratic expression-𝑎𝑥²+ 𝑏𝑥 + 𝑐, where a is an integer, by factoring to reveal the solutions of the equation or the zeros of the function the expression defines.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form

NC.M1.A-APR: Arithmetic with Polynomial Expressions

(Framing Text): Perform arithmetic operations on polynomials.

NC.M1.A-APR.1: Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions.

 Addition and Subtraction of Functions
 Addition of Polynomials

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

NC.M1.A-APR.3: Understand the relationships among the factors of a quadratic expression, the solutions of a quadratic equation, and the zeros of a quadratic function.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Roots of a Quadratic
 Zap It! Game

NC.M1.A-CED: Creating Equations

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

NC.M1.A-CED.1: Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems.

 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

NC.M1.A-CED.2: Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities.

 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Solving Equations by Graphing Each Side
 Standard Form of a Line

NC.M1.A-CED.3: Create systems of linear equations and inequalities to model situations in context.

 Cat and Mouse (Modeling with Linear Systems)
 Linear Programming
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)
 Systems of Linear Inequalities (Slope-intercept form)

NC.M1.A-CED.4: Solve for a quantity of interest in formulas used in science and mathematics using the same reasoning as in solving equations.

 Area of Triangles
 Solving Formulas for any Variable

NC.M1.A-REI: Reasoning with Equations and Inequalities

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

NC.M1.A-REI.1: Justify a chosen solution method and each step of the solving process for linear and quadratic equations using mathematical reasoning.

 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II

(Framing Text): Solve equations and inequalities in one variable.

NC.M1.A-REI.3: Solve linear equations and inequalities in one variable.

 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

NC.M1.A-REI.4: Solve for the real solutions of quadratic equations in one variable by taking square roots and factoring.

 Modeling the Factorization of x2+bx+c
 Roots of a Quadratic

(Framing Text): Solve systems of equations.

NC.M1.A-REI.5: Explain why replacing one equation in a system of linear equations by the sum of that equation and a multiple of the other produces a system with the same solutions.

 Solving Equations by Graphing Each Side
 Solving Linear Systems (Standard Form)

NC.M1.A-REI.6: Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context.

 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)

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

NC.M1.A-REI.10: Understand that the graph of a two variable equation represents the set of all solutions to the equation.

 Absolute Value Equations and Inequalities
 Circles
 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Standard Form of a Line

NC.M1.A-REI.11: Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, and/or quadratic equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥) and approximate solutions using 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

NC.M1.A-REI.12: Represent the solutions of a linear inequality or a system of linear inequalities graphically as a region of the plane.

 Linear Inequalities in Two Variables
 Linear Programming
 Systems of Linear Inequalities (Slope-intercept form)

NC.M1.F: Functions

NC.M1.F-IF: Interpreting Functions

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

NC.M1.F-IF.1: Build an understanding that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range by recognizing that: if f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

 Absolute Value with Linear Functions
 Exponential Functions
 Introduction to Exponential Functions
 Introduction to Functions
 Linear Functions
 Logarithmic Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Standard Form of a Line

NC.MI.F-IF.3: Recognize that recursively and explicitly defined sequences are functions whose domain is a subset of the integers, the terms of an arithmetic sequence are a subset of the range of a linear function, and the terms of a geometric sequence are a subset of the range of an exponential function.

 Arithmetic Sequences
 Geometric Sequences

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

NC.M1.F-IF.4: Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; and maximums and minimums.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Slope-Intercept Form of a Line

NC.M1.F-IF.6: Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically.

 Cat and Mouse (Modeling with Linear Systems)
 Slope

(Framing Text): Analyze functions using different representations.

NC.M1.F-IF.7: Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior.

 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Slope-Intercept Form of a Line
 Translating and Scaling Functions

NC.M1.F-IF.8: Use equivalent expressions to reveal and explain different properties of a function.

NC.M1.F-IF.8a: Rewrite a quadratic function to reveal and explain different key features of the function.

 Quadratics in Vertex Form

NC.M1.F-IF.8b: Interpret and explain growth and decay rates for an exponential function.

 Compound Interest
 Introduction to Exponential Functions

NC.M1.F-IF.9: Compare key features of two functions (linear, quadratic, or exponential) each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions).

 Exponential Functions
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Slope-Intercept Form of a Line
 Translating and Scaling Functions

NC.M1.F-BF: Building Functions

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

NC.M1.F-BF.1: Write a function that describes a relationship between two quantities.

NC.M1.F-BF.1a: Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (include reading these from a table).

 Absolute Value with Linear Functions
 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Compound Interest
 Exponential Functions
 Geometric Sequences
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

NC.M1.F-BF.1b: Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic functions with addition and subtraction or two linear functions with multiplication.

 Addition and Subtraction of Functions

NC.M1.F-BF.2: Translate between explicit and recursive forms of arithmetic and geometric sequences and use both to model situations.

 Arithmetic Sequences
 Geometric Sequences

NC.M1.F-LE: Linear, Quadratic, and Exponential Models

(Framing Text): Interpret expressions for functions in terms of the situation they model.

NC.M1.F-LE.5: Interpret the parameters 𝑎 and 𝑏 in a linear function 𝑓(𝑥) = 𝑎𝑥 + 𝑏 or an exponential function 𝑔(𝑥) = 𝑎𝑏ˣ in terms of a context.

 Arithmetic Sequences
 Compound Interest
 Introduction to Exponential Functions

NC.M1.G: Geometry

NC.M1.G-GPE: Expressing Geometric Properties with Equations

(Framing Text): Use coordinates to prove simple geometric theorems algebraically.

NC.M1.G-GPE.5: Use coordinates to prove the slope criteria for parallel and perpendicular lines and use them to solve problems. Determine if two lines are parallel, perpendicular, or neither. Find the equation of a line parallel or perpendicular to a given line that passes through a given point.

 Cat and Mouse (Modeling with Linear Systems)

NC.M1.S: Statistics and Probability

NC.M1.S-ID: Interpreting Categorical and Quantitative Data

(Framing Text): Summarize, represent, and interpret data on a single count or measurement variable.

NC.M1.S-ID.1: Use technology to represent data with plots on the real number line (histograms, and box plots).

 Histograms
 Real-Time Histogram
 Stem-and-Leaf Plots

NC.M1.S-ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Polling: City
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram

NC.M1.S-ID.3: Examine the effects of extreme data points (outliers) on shape, center, and/or spread.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Least-Squares Best Fit Lines
 Mean, Median, and Mode
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram
 Stem-and-Leaf Plots

(Framing Text): Summarize, represent, and interpret data on two categorical and quantitative variables.

NC.M1.S-ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

NC.M1.S-ID.6a: Fit a least squares regression line to linear data using technology. Use the fitted function to solve problems.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

NC.M1.S-ID.6b: Assess the fit of a linear function by analyzing residuals.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

(Framing Text): Interpret linear models.

NC.M1.S-ID.7: Interpret in context the rate of change and the intercept of a linear model. Use the linear model to interpolate and extrapolate predicted values. Assess the validity of a predicted value.

 Correlation
 Solving Using Trend Lines
 Trends in Scatter Plots

NC.M1.S-ID.8: Analyze patterns and describe relationships between two variables in context. Using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship. Use a scatter plot, correlation coefficient, and a residual plot to determine the appropriateness of using a linear function to model a relationship between two variables.

 Correlation
 Least-Squares Best Fit Lines
 Polling: City
 Solving Using Trend Lines

NC.M1.S-ID.9: Distinguish between association and causation.

 Correlation

Correlation last revised: 4/4/2018

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