1: Polynomial, Rational, and Radical Relationships

1.3: Perform arithmetic operations with complex numbers.

1.N.CN.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

1.4: Use complex numbers in polynomial identities and equations.

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

Points in the Complex Plane
Roots of a Quadratic

1.5: Interpret the structure of expressions.

1.A.SSE.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
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Expressions

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

1.A.APR.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

1.A.APR.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

1.8: Use polynomial identities to solve problems.

1.A.APR.4: Prove polynomial identities and use them to describe numerical relationships.

Factoring Special Products

1.A.APR.5: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

Binomial Probabilities

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

1.A.REI.1: Explain each step in solving a simple 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 Two-Step Equations

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

Radical Functions

1.11: Solve equations and inequalities in one variable.

1.A.REI.4: Solve quadratic equations in one variable.

1.A.REI.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 reveals that the quadratic equation has “no real solutions”.

Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic

1.12: Solve systems of equations.

1.A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

1.13: Represent and solve equations and inequalities graphically.

1.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, 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

1.15: Translate between the geometric description and the equation for a conic section.

1.G.GPE.2: Derive the equation of a parabola given a focus and directrix.

Parabolas

2: Trigonometric Functions

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

2.F.TF.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

2.2: Model periodic phenomena with trigonometric functions.

2.F.TF.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

2.3: Prove and apply trigonometric identities.

2.F.TF.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 of the angle.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios

2.4: Summarize, represent, and interpret data on two categorical and quantitative variables.

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

2.S.ID.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

3: Modeling with Functions

3.2: Create equations that describe numbers or relationships.

3.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

3.3: Understand the concept of a function and use function notation.

3.F.IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences
Geometric Sequences

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

3.F.IF.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
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

3.F.IF.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

3.5: Analyze functions using different representations.

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

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

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

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

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

Compound Interest
Exponential Functions

3.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

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

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

3.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

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

Addition and Subtraction of Functions

3.F.BF.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

3.7: Build new functions from existing functions.

3.F.BF.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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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

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

3.F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Absolute Value with Linear Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions
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

3.F.LE.4: 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

3.9: Interpret expressions for functions in terms of the situation they model.

3.F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

Arithmetic Sequences
Compound Interest
Introduction to Exponential Functions

4: Inferences and Conclusions from Data

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

4.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

4.2: Understand and evaluate random processes underlying statistical experiments.

4.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

4.S.IC.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

4.3: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

4.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

4.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

4.S.IC.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

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

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

4.4: Use probability to evaluate outcomes of decisions.

4.S.MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Probability Simulations
Theoretical and Experimental Probability

4.S.MD.7: 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
Probability Simulations
Theoretical and Experimental Probability

5: Applications of Probability

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

5.S.CP.1: 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

5.S.CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Independent and Dependent Events

5.S.CP.3: 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

5.S.CP.4: 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

5.S.CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

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

5.S.CP.6: 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

5.S.CP.8: 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

5.S.CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

Binomial Probabilities
Permutations and Combinations

5.3: Use probability to evaluate outcomes of decisions.

5.S.MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Probability Simulations
Theoretical and Experimental Probability

5.S.MD.7: 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
Probability Simulations
Theoretical and Experimental Probability

Correlation last revised: 7/15/2019

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