NC Math 1 (North Carolina SCOS)

Number and Quantity – The Real Number System (N-RN)

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

Algebra – Seeing Structure in Expressions (A-SSE)

• 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 terms, factors, coefficients, and exponents in linear, exponential, and quadratic expressions.
• NC.M1.A-SSE.1b Interpret parts of linear, exponential, or quadratic expressions made of several parts as single entities.
• Write expressions in equivalent forms to solve problems
• NC.M1.A-SSE.3 Factor quadratic expressions to reveal solutions or zeros.

Algebra – Arithmetic with Polynomials and Rational Expressions (A-APR)

• Perform arithmetic operations on polynomials
• NC.M1.A-APR.1 Add, subtract, and multiply linear and quadratic expressions, by analogy with integers.
• Understand the relationship between zeros and factors of polynomials
• NC.M1.A-APR.3 Relate factors of a quadratic to the solutions of its equation and the zeros of its function.

Algebra – Creating Equations (A-CED)

• Create equations that describe numbers or relationships
• NC.M1.A-CED.1 Create and solve one-variable equations and inequalities for linear, exponential, and quadratic relationships.
• NC.M1.A-CED.2 Create and graph two-variable equations for linear, exponential, and quadratic relationships.
• NC.M1.A-CED.3 Create systems of linear equations and inequalities to model situations in context.
• NC.M1.A-CED.4 Solve formulas from science and mathematics for a quantity of interest.

Algebra – Reasoning with Equations and Inequalities (A-REI)

• Understand solving equations as a process of reasoning and explain the reasoning
• NC.M1.A-REI.1 Justify the chosen method and each step when solving linear and quadratic equations.
• Solve equations and inequalities in one variable
• NC.M1.A-REI.3 Solve linear equations and inequalities in one variable.
• NC.M1.A-REI.4 Find real solutions of quadratic equations by taking square roots and by factoring.
• Solve systems of equations
• NC.M1.A-REI.5 Explain why replacing one equation by its sum with a multiple of the other keeps the solutions of a system.
• NC.M1.A-REI.6 Solve systems of linear equations with tables, graphs, substitution, or elimination and interpret in context.
• Represent and solve equations and inequalities graphically
• NC.M1.A-REI.10 Understand that the graph of a two-variable equation is the set of all its solutions.
• NC.M1.A-REI.11 Explain why x-coordinates of intersection points solve f(x) = g(x) and approximate them.
• NC.M1.A-REI.12 Represent solutions of linear inequalities and systems of them as regions of the plane.

Functions – Interpreting Functions (F-IF)

• Understand the concept of a function and use function notation
• NC.M1.F-IF.1 Understand a function as assigning exactly one output to each input; its graph is y = f(x).
• NC.M1.F-IF.2 Use function notation to evaluate linear, quadratic, and exponential functions and interpret in context.
• NC.M1.F-IF.3 Recognize recursively and explicitly defined sequences as functions with integer domains.
• Interpret functions that arise in applications in terms of the context
• NC.M1.F-IF.4 Interpret key features of graphs, tables, and descriptions in context (intercepts, intervals, maximum, minimum).
• NC.M1.F-IF.5 Relate the domain and range of a function to its graph and the quantity it describes.
• NC.M1.F-IF.6 Calculate and interpret the average rate of change over an interval.
• Analyze functions using different representations
• NC.M1.F-IF.7 Show key features of linear, exponential, and quadratic functions in different representations.
• 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 its key features.
• NC.M1.F-IF.8b Interpret and explain growth and decay rates of exponential functions.
• NC.M1.F-IF.9 Compare key features of two linear, quadratic, or exponential functions given in different ways.

Functions – Building Functions (F-BF)

• 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 sequences, from graphs, descriptions, or points.
• NC.M1.F-BF.1b Combine linear, exponential, or quadratic functions by adding or subtracting, or multiply two linear functions.
• NC.M1.F-BF.2 Translate between explicit and recursive forms of arithmetic and geometric sequences.

Functions – Linear, Quadratic, and Exponential Models (F-LE)

• Construct and compare linear and exponential models and solve problems
• NC.M1.F-LE.1 Identify situations suited to linear or exponential models and justify the choice using rates of change.
• NC.M1.F-LE.3 Compare end behavior to show that exponential growth eventually exceeds linear and quadratic growth.
• Interpret expressions for functions in terms of the situation they model
• NC.M1.F-LE.5 Interpret the parameters a and b of linear and exponential models in context.

Geometry – Expressing Geometric Properties with Equations (G-GPE)

• Use coordinates to prove simple geometric theorems algebraically
• NC.M1.G-GPE.4 Use coordinates to find perimeters and areas and to classify triangles and quadrilaterals.
• NC.M1.G-GPE.5 Use coordinates to prove the slope criteria for parallel and perpendicular lines and apply them.
• NC.M1.G-GPE.6 Use coordinates to find the midpoint or an endpoint of a line segment.

Statistics – Interpreting Categorical and Quantitative Data (S-ID)

• Summarize, represent, and interpret data on a single count or measurement variable
• NC.M1.S-ID.1 Use technology to show one-variable data as histograms and box plots.
• NC.M1.S-ID.2 Compare center and spread of data sets using statistics suited to their shape.
• NC.M1.S-ID.3 Examine the effect of outliers on shape, center, and spread.
• Summarize, represent, and interpret data on two categorical and quantitative variables
• NC.M1.S-ID.6 Show two-variable data on a scatter plot and describe how the variables are related.
• NC.M1.S-ID.6a Fit a least-squares regression line with technology and use it to solve problems.
• NC.M1.S-ID.6b Judge the fit of a linear function by analyzing residuals.
• NC.M1.S-ID.6c Fit a function to exponential data with technology and use it to solve problems.
• Interpret linear models
• NC.M1.S-ID.7 Interpret slope and intercept of a linear model in context and judge predictions.
• NC.M1.S-ID.8 Use correlation, scatter plots, and residuals to describe how well a linear model fits.
• NC.M1.S-ID.9 Tell association from causation.