N: Number and Quantity

N-CN: The Complex Number System

1.1.1: Perform arithmetic operations with complex numbers.

N-CN.1: Students will: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

Points in the Complex Plane
Roots of a Quadratic

N-CN.2: Students will: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

N-CN.3: Students will: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane
Roots of a Quadratic

1.1.2: Use complex numbers in polynomial identities and equations.

N-CN.4: Students will: Solve quadratic equations with real coefficients that have complex solutions.

Points in the Complex Plane
Roots of a Quadratic

N-VM: Vector and Matrix Quantities

1.2.1: Perform operations on matrices and use matrices in applications.

N-VM.7: Students will: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

Dilations
Translations

N-VM.8: Students will: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

Dilations

N-VM.9: Students will: Add, subtract, and multiply matrices of appropriate dimensions.

Translations

N-VM.11: Students will: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

Solving Linear Systems (Matrices and Special Solutions)

A: Algebra

A-SSE: Seeing Structure in Expressions

2.1.1: Interpret the structure of expressions.

A-SSE.12: Students will: Interpret expressions that represent a quantity in terms of its context.

A-SSE.12.a: Interpret parts of an expression such as terms, factors, and coefficients.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Formulas for any Variable

A-SSE.12.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Growth and Decay
Geometric Sequences
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A-SSE.13: Students will: Use the structure of an expression to identify ways to rewrite it.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Factoring Special Products
Multiplying Exponential Expressions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

A-APR: Arithmetic with Polynomials and Rational Expressions

2.3.1: Perform arithmetic operations on polynomials.

A-APR.15: Students will: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c

2.3.2: Understand the relationship between zeros and factors of polynomials.

A-APR.16: Students will: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

Dividing Polynomials Using Synthetic Division

A-APR.17: Students will: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Graphs of Polynomial Functions
Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

2.3.3: Use polynomial identities to solve problems.

A-APR.18: Students will: Prove polynomial identities and use them to describe numerical relationships.

Factoring Special Products

2.3.4: Rewrite rational expressions.

A-APR.19: Students will: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or for the more complicated examples, a computer algebra system.

Dividing Polynomials Using Synthetic Division

A-CED: Creating Equations

2.4.1: Create equations that describe numbers or relationships.

A-CED.20: Students will: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Roots of a Quadratic
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Linear Systems (Slope-Intercept Form)
Solving Two-Step Equations
Using Algebraic Equations

A-CED.21: Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Absolute Value Equations and Inequalities
Circles
Exponential Functions
Exponential Growth and Decay
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Standard Form of a Line
Using Algebraic Equations

A-CED.22: Students will: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

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

A-CED.23: Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

A-REI: Reasoning with Equations and Inequalities

2.5.1: Understand solving equations as a process of reasoning, and explain the reasoning.

A-REI.24: Students will: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

2.5.2: Solve equations and inequalities in one variable.

A-REI.25: Students will: Recognize when the quadratic formula gives complex solutions, and write them as a ± bi for real numbers a and b.

Points in the Complex Plane
Roots of a Quadratic

2.5.3: Solve systems of equations.

A-REI.26: Students will: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Solving Linear Systems (Matrices and Special Solutions)

2.5.4: Represent and solve equations and inequalities graphically.

A-REI.27: Students will: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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)

A-CS: Conic Sections

2.6.1: Understand the graphs and equations of conic sections.

A-CS.28: Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

A-CS.28.a: Formulate equations of conic sections from their determining characteristics.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas

F: Functions

F-IF: Interpreting Functions

3.1.1: Interpret functions that arise in applications in terms of the context.

F-IF.29: Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions

3.1.2: Analyze functions using different representations.

F-IF.30: Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.30.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

F-IF.30.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

F-IF.30.c: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Exponential Functions
Exponential Growth and Decay
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

F-IF.31: Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.31.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

F-IF.31.b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Functions
Exponential Growth and Decay

F-IF.32: Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Direct and Inverse Variation
General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

F-BF: Building Functions

3.2.1: Build a function that models a relationship between two quantities.

F-BF.33: Students will: Write a function that describes a relationship between two quantities.

F-BF.33.a: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

3.2.2: Build new functions from existing functions.

F-BF.34: Students will: Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

F-BF.35: Students will: Find inverse functions.

F-BF.35.a: Solve an equation of the form f(x) = c for a simple function f that has an inverse, and write an expression for the inverse.

Logarithmic Functions
Radical Functions

F-LE: Linear, Quadratic, and Exponential Models

3.3.1: Construct and compare linear, quadratic, and exponential models and solve problems.

F-LE.36: Students will: For exponential models, express as a logarithm the solution to (ab) to the (ct) power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Logarithmic Functions

F-TF: Trigonometric Functions

3.4.1: Extend the domain of trigonometric functions using the unit circle.

F-TF.37: Students will: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Radians

F-TF.38: Students will: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function
Sine Function
Tangent Function

F-TF.39: Students will: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

3.4.3: Model periodic phenomena with trigonometric functions.

F-TF.40: Students will: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Sound Beats and Sine Waves
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

S: Statistics and Probability

S-MD: Using Probability to Make Decisions

4.1.1: Use probability to evaluate outcomes of decisions.

S-MD.41: Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

S-MD.42: Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Estimating Population Size
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

S-CP: Conditional Probability and the Rules of Probability

4.4.1: Understand independence and conditional probability and use them to interpret data.

S-CP.43: Students will: Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

Independent and Dependent Events
Permutations and Combinations

S-CP.44: Students will: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Independent and Dependent Events

S-CP.45: Students will: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

Histograms

S-CP.46: Students will: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

4.4.2: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S-CP.47: Students will: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Independent and Dependent Events

S-CP.49: Students will: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

Independent and Dependent Events

S-CP.50: Students will: Use permutations and combinations to compute probabilities of compound events and solve problems.

Binomial Probabilities
Permutations and Combinations

Correlation last revised: 3/17/2020

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