A2: N: Number and Quantity

A2: N-RN: The Real Number System

A2: N-RN.A: Extend the properties of exponents to rational exponents.

A2: N-RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Exponents and Power Rules

A2: N-CN: The Complex Number System

A2: N-CN.A: Perform arithmetic operations with complex numbers.

A2: N-CN.A.1: 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

A2: N-CN.A.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

A2: N-CN.C: Use complex numbers in polynomial identities and equations.

A2: N-CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.

Points in the Complex Plane
Roots of a Quadratic

A2: A: Algebra

A2: A-SSE: Seeing Structure in Expressions

A2: A-SSE.A: Interpret the structure of expressions.

A2: A-SSE.A.2: 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
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

A2: A-SSE.B: Write expressions in equivalent forms to solve problems.

A2: A-SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A2: A-SSE.B.3.c: Use the properties of exponents to transform expressions for exponential functions.

Dividing Exponential Expressions
Exponents and Power Rules

A2: A-APR: Arithmetic with Polynomials and Rational Expressions

A2: A-APR.B: Understand the relationship between zeros and factors of polynomials.

A2: A-APR.B.2: 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
Polynomials and Linear Factors

A2: A-APR.B.3: 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

A2: A-APR.C: Use polynomial identities to solve problems.

A2: A-APR.C.4: Use polynomial identities to describe numerical relationships.

Factoring Special Products

A2: A-CED: Creating Equations

A2: A-CED.A: Create equations that describe numbers or relationships.

A2: A-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

A2: A-REI: Reasoning with Equations and Inequalities

A2: A-REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

A2: A-REI.A.1: Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Two-Step Equations

A2: A-REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

A2: A-REI.B: Solve equations and inequalities in one variable.

A2: A-REI.B.4: Solve quadratic equations in one variable.

A2: A-REI.B.4.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

A2: A-REI.C: Solve systems of equations.

A2: A-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables. With graphic solutions, systems are limited to two variables.

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)

A2: A-REI.D: Represent and solve equations and inequalities graphically.

A2: A-REI.D.11: 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)
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

A2: F: Functions

A2: F-IF: Interpreting Functions

A2: F-IF.B: Interpret functions that arise in applications in terms of the context.

A2: F-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

A2: F-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)
Slope

A2: F-IF.C: Analyze functions using different representations.

A2: F-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

A2: F-IF.C.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions
Translating and Scaling Functions

A2: F-IF.C.7.c: 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
Roots of a Quadratic
Zap It! Game

A2: F-IF.C.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

A2: F-IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

A2: F-IF.C.8.b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Functions

A2: F-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function
Graphs of Polynomial Functions
Linear Functions
Logarithmic Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form

A2: F-BF: Building Functions

A2: F-BF.A: Build a function that models a relationship between two quantities.

A2: F-BF.A.1: Write a function that describes a relationship between two quantities.

A2: F-BF.A.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2: F-BF.A.1.b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

A2: F-BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2: F-BF.B: Build new functions from existing functions.

A2: F-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

A2: F-LE: Linear, Quadratic, and Exponential Models

A2: F-LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.

A2: F-LE.A.2: Given a graph, a description of a relationship, or two input-output pairs (include reading these from a table), construct linear and exponential functions, including arithmetic and geometric sequences, to solve multi-step problems.

Absolute Value with Linear Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
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

A2: F-LE.A.4: For exponential models, express as a logarithm the solution to a b 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.

Compound Interest
Logarithmic Functions

A2: F-LE.B: Interpret expressions for functions in terms of the situation they model.

A2: F-LE.B.5: Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.

Arithmetic Sequences
Compound Interest
Exponential Growth and Decay
Introduction to Exponential Functions

A2: F-TF: Trigonometric Functions

A2: F-TF.A: Extend the domain of trigonometric functions using the unit circle.

A2: F-TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Sine Function
Tangent Function

A2: F-TF.A.2: 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

A2: F-TF.B: Model periodic phenomena with trigonometric functions.

A2: F-TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

A2: F-TF.C: Prove and apply trigonometric identities.

A2: F-TF.C.8: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios

A2: S: Statistics and Probability

A2: S-ID: Interpreting Categorical and Quantitative Data

A2: S-ID.A: Summarize, represent, and interpret data on a single count or measurement variable.

A2: S-ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Polling: City
Populations and Samples
Real-Time Histogram

A2: S-ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

A2: S-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

A2: S-ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

A2: S-IC: Making Inferences and Justifying Conclusions

A2: S-IC.A: Understand and evaluate random processes underlying statistical experiments.

A2: S-IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Polling: City
Polling: Neighborhood
Populations and Samples

A2: S-IC.A.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Polling: City
Polling: Neighborhood
Populations and Samples

A2: S-IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

A2: S-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City
Polling: Neighborhood

A2: S-IC.B.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Polling: City
Polling: Neighborhood

A2: S-IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Polling: City
Polling: Neighborhood

A2: S-IC.B.6: Evaluate reports based on data.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram