A.SSE: Seeing Structure in Expressions

1.1: Interpret the structure of expressions.

A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

A.SSE.1.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

A.SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity in context.

Compound Interest

A.SSE.2: Recognize and 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
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

A.APR: Arithmetic with Polynomials and Rational Expressions

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

A.APR.2: Know and apply the Remainder Theorem.

Dividing Polynomials Using Synthetic Division

A.APR.3: Identify zeros of polynomials by factoring.

A.APR.3.a: When suitable factorizations are available, use the zeros to construct a rough graph of the related function.

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

A.APR.3.b: When given a graph, use the zeros to construct a possible factorization of a polynomial.

Polynomials and Linear Factors

A.CED: Creating Equations

3.1: Create equations that describe numbers or relationships.

A.CED.1: 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
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

A.CED.2: 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
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

A.CED.3: 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.4: Rewrite 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

4.1: Understand solving equations as a process of reason and explain the reasoning.

A.REI.2: Solve rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Rational functions are limited to those whose numerators are of degree at most 1 and denominators of degree at most 2. Radical functions are limited to square roots or cube roots of at most quadratic polynomials.

Radical Functions

4.2: Solve equations and inequalities in one variable.

A.REI.4: Select, justify and apply appropriate methods to solve quadratic equations in one variable. Recognize complex solutions and write them as a +/- bi for real numbers a and b.

Points in the Complex Plane
Roots of a Quadratic

4.3: Represent and solve equations and inequalities graphically.

A.REI.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, including but not limited to 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)

F.IF: Interpreting Functions

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

F.IF.4: For functions that model 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries (including even, odd, or neither); end behavior; and periodicity.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
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
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Sine and Cosine Functions

5.2: Analyze functions using different representations.

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

F.IF.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

F.IF.7.f: Graph trigonometric functions (sine and cosine), showing period, midline, and amplitude.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

F.IF.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

F.BF: Building Functions

6.1: Build new functions from existing functions.

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

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

F.BF.1.b: Determine an explicit expression from a graph.

Arithmetic Sequences
Geometric Sequences

F.BF.1.c: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

F.BF.3: Identify the effect on the graph of f(x) replaced with 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 contrasting cases and illustrate an explanation of the effects on the graph using technology.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

F.BF.4: Find inverse functions.

F.BF.4.c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

F.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

F.LE: Linear, Quadratic and Exponential Models

7.1: Construct and compare linear and exponential models and solve.

F.LE.4: For exponential models, express as a logarithm the solution to ab to the ct power = dwhere 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

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

F.TF.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions (sine and cosine) to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function
Sine Function
Tangent Function

8.2: Model periodic phenomena with trigonometric functions.

F.TF.5: Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline.

Cosine Function
Sine Function
Translating and Scaling Sine and Cosine Functions

8.3: Prove and apply trigonometric identities.

F.TF.8: Prove the Pythagorean identity sin²(A) + cos²(A) = 1 and use it to calculate trigonometric ratios.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios

N.CN: The Complex Number System

9.1: Perform arithmetic operations with complex numbers.

N.CN.1: Know there is a complex number i such that i² = -1, and every complex number has the form a + bi where a and b are real numbers.

Points in the Complex Plane
Roots of a Quadratic

9.2: Use complex numbers in polynomials identities and equations.

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

Points in the Complex Plane
Roots of a Quadratic

S.ID: Interpreting Categorical and Quantitative Data

10.1: Summarize, represent and interpret data on a single count or measurement variable.

S.ID.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

S.IC: Making Inferences and Justifying Conclusions

11.1: Understand and evaluate random processes underlying statistical experiments.

S.IC.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

S.IC.2: Determine whether a specified model is consistent with results from a given data-generating process.

Polling: City
Polling: Neighborhood
Populations and Samples

11.2: Make interferences and justify conclusions from sample surveys, experiments and observational studies.

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

Polling: City
Polling: Neighborhood

S.IC.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

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

Polling: City
Polling: Neighborhood

S.IC.6: Evaluate reports based on data.

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

Correlation last revised: 9/24/2019

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