Math 1 State Standards
Solving Equations
NC.M1.A-SSE.1a Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its context. a. Identify and interpret parts of a linear, exponential, or quadratic expression, focusing on terms, factors, coefficients, and exponents.
NC.M1.A-REI.1 Understand solving equations as a process of reasoning and explain the reasoning. Justify a chosen solution method and each step of the solving process for linear and quadratic equations using mathematical reasoning.
Linear relationships
NC.M1.F-LE.5: Interpret expressions for functions in terms of the situation they model. 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
NC.M1.A-CED.1: Create equations that describe numbers or relationships. Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems
NC.M1.A-CED.2: Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities.
NC.M1.A-CED.3: Create systems of linear equations and inequalities to model situations in context.
NC.M1.G-GPE.5 Use coordinates to prove simple geometric theorems algebraically. 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
Functions
NC.M1.F-IF.1 Understand the concept of a function and use function notation. 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 𝑓𝑓 is the graph of the equation 𝑦 = 𝑓(𝑥)
NC.M1.F-IF.3 Understand the concept of a function and use function notation. 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.
NC.M1.F-IF.4 Interpret functions that arise in applications in terms of the context. 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.
NC.M1.F-IF.5 Interpret functions that arise in applications in terms of the context. Interpret a function in terms of the context by relating its domain and range to its graph and, where applicable, to the quantitative relationship it describes
NC.M1.F-IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically
NC.M1.F-IF.9 Analyze functions using different representations. Compare key features of two functions (linear, quadratic, or exponential) each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions).
STATS
NC.M1.S-ID.6a Summarize, represent, and interpret data on two categorical and quantitative variables. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a least squares regression line to linear data using technology. Use the fitted function to solve problems
NC.M1.S-ID.7: Interpret linear models. 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.
NC.M1.S-ID.9 Interpret linear models. Distinguish between association and causation.
NC.M1.S-ID.2 Summarize, represent, and interpret data on a single count or measurement variable. 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.
Solve Systems of Linear Equations
NC.M1.A-REI.5 Solve systems of equations. 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
NC.M1.A-REI.6 Solve systems of equations. 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
NC.M1.A-REI.10 Represent and solve equations and inequalities graphically Understand that the graph of a two-variable equation represents the set of all solutions to the equation.
NC.M1.A-REI.11 Represent and solve equations and inequalities graphically Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, 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 a graphing technology or successive approximations with a table of values.
Exponents and Scientific Notation
NC.M1.N-RN.2 Extend the properties of exponents. Rewrite algebraic expressions with integer exponents using the properties of exponents