NC Math 3 (North Carolina SCOS)

Number and Quantity – The Complex Number System (N-CN)

• Use complex numbers in polynomial identities and equations
• NC.M3.N-CN.9 Use the Fundamental Theorem of Algebra to find the number and type of solutions of a polynomial equation.

Algebra – Seeing Structure in Expressions (A-SSE)

• 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 piecewise, absolute value, polynomial, exponential, and rational expressions.
• NC.M3.A-SSE.1b Interpret parts of expressions made of several parts as single entities in context.
• NC.M3.A-SSE.2 Use the structure of an expression to find ways to rewrite it.
• Write expressions in equivalent forms to solve problems
• NC.M3.A-SSE.3 Rewrite exponential expressions using properties of exponents to reveal rates over different intervals.

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

• Understand the relationship between zeros and factors of polynomials
• NC.M3.A-APR.2 Understand and apply the Remainder Theorem.
• NC.M3.A-APR.3 Relate factors of polynomials, solutions of equations, and zeros of functions.
• Rewrite rational expressions
• NC.M3.A-APR.6 Rewrite simple rational expressions as a quotient plus a remainder over the divisor.
• NC.M3.A-APR.7 Understand the similarity between arithmetic with rational expressions and with rational numbers.
• NC.M3.A-APR.7a Add and subtract rational expressions with linear denominators.
• NC.M3.A-APR.7b Multiply and divide rational expressions.

Algebra – Creating Equations (A-CED)

• Create equations that describe numbers or relationships
• NC.M3.A-CED.1 Create and solve one-variable equations and inequalities for absolute value, polynomial, exponential, and rational relationships.
• NC.M3.A-CED.2 Create and graph two-variable equations for absolute value, polynomial, exponential, and rational relationships.
• NC.M3.A-CED.3 Create systems of equations and/or inequalities to model situations.

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

• Understand solving equations as a process of reasoning and explain the reasoning
• NC.M3.A-REI.1 Justify the method and each step when solving equations.
• NC.M3.A-REI.2 Solve and interpret rational equations from contexts, explaining extraneous solutions.
• Represent and solve equations and inequalities graphically
• NC.M3.A-REI.11 Explain why intersection x-coordinates solve f(x) = g(x) and approximate solutions.

Functions – Interpreting Functions (F-IF)

• Understand the concept of a function and use function notation
• NC.M3.F-IF.1 Recognize trigonometric ratios as functions of angle measure.
• NC.M3.F-IF.2 Use function notation to evaluate piecewise functions and interpret statements in context.
• Interpret functions that arise in applications in terms of the context
• NC.M3.F-IF.4 Interpret key features in context, including periodicity and discontinuities.
• Analyze functions using different representations
• NC.M3.F-IF.7 Analyze key features of a range of function types in different representations, by hand or with technology.
• NC.M3.F-IF.9 Compare key features of two functions given in different representations.

Functions – Building Functions (F-BF)

• 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 from graphs, descriptions, or ordered pairs.
• NC.M3.F-BF.1b Combine standard function types with arithmetic operations to build functions from contexts.
• Build new functions from existing functions
• NC.M3.F-BF.3 Understand how k·f(x), f(x) + k, f(x + k), and f(kx) change graphs and tables.
• NC.M3.F-BF.4 Find an inverse function.
• NC.M3.F-BF.4a Understand inverse relationships between exponential and logarithmic, quadratic and square root, and linear functions.
• NC.M3.F-BF.4b Decide whether an inverse function exists using tables, graphs, and equations.
• NC.M3.F-BF.4c Represent an inverse with a table, graph, or equation and use it in context.

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

• Construct and compare linear, quadratic, and exponential models and solve problems
• NC.M3.F-LE.3 Compare end behavior using rates of change over equal intervals: exponentials eventually exceed polynomials.
• NC.M3.F-LE.4 Use logarithms to solve exponential equations of the form a·b^(ct) = d and evaluate them with technology.

Functions – Trigonometric Functions (F-TF)

• Extend the domain of trigonometric functions using the unit circle
• NC.M3.F-TF.1 Understand radian measure as arc length divided by radius.
• NC.M3.F-TF.2 Use tables, graphs, and technology to represent sine and cosine functions.
• NC.M3.F-TF.2a Interpret sine as the y-coordinate of the point where a terminal ray meets the unit circle.
• NC.M3.F-TF.2b Interpret cosine as the x-coordinate of the point where a terminal ray meets the unit circle.
• Model periodic phenomena with trigonometric functions
• NC.M3.F-TF.5 Use technology to explore the parameters of sine functions to model periodic phenomena.

Geometry – Congruence (G-CO)

• Prove geometric theorems
• NC.M3.G-CO.10 Verify experimentally properties of triangle centers: centroid, incenter, and circumcenter.
• NC.M3.G-CO.11 Prove theorems about parallelograms, including sides, angles, diagonals, and rectangles.
• NC.M3.G-CO.14 Apply properties and theorems of two-dimensional figures to prove theorems and solve problems.

Geometry – Circles (G-C)

• Understand and apply theorems about circles
• NC.M3.G-C.2 Apply theorems about angles, lines, and segments related to circles.
• NC.M3.G-C.5 Show arc length is proportional to radius, define the radian, and find arc lengths and sector areas.

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

• Translate between the geometric description and the equation for a conic section
• NC.M3.G-GPE.1 Derive the equation of a circle and complete the square to find its center and radius.

Geometry – Geometric Measurement and Dimension (G-GMD)

• Explain volume formulas and use them to solve problems
• NC.M3.G-GMD.3 Use volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
• Visualize relationships between two-dimensional and three-dimensional objects
• NC.M3.G-GMD.4 Identify cross-sections of solids and solids generated by rotating flat shapes.

Geometry – Modeling with Geometry (G-MG)

• Apply geometric concepts in modeling situations
• NC.M3.G-MG.1 Use geometric and algebraic ideas to model real objects, density, design, and optimisation problems.

Statistics – Making Inferences and Justifying Conclusions (S-IC)

• Understand and evaluate random processes underlying statistical experiments
• NC.M3.S-IC.1 Understand how inferences about a population are made from a random sample.
• Make inferences and justify conclusions from sample surveys, experiments, and observational studies
• NC.M3.S-IC.3 Recognize the purposes of and differences between surveys, experiments, and observational studies, including randomisation.
• NC.M3.S-IC.4 Use simulation to estimate a population mean or proportion and a margin of error.
• NC.M3.S-IC.5 Use simulation to decide whether differences between samples show the populations differ.
• NC.M3.S-IC.6 Evaluate reports and websites by source, study design, and data displays.