College- and Career-Readiness Standards

1.1.1: Extend the properties of exponents to rational exponents

N-RN.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.

1.3.1: 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 with a and b real.

Points in the Complex Plane

Roots of a Quadratic

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

1.3.2: Use complex numbers in polynomial 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

2.1.1: Interpret the structure of expressions

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

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Simplifying Trigonometric Expressions

Solving Algebraic Equations II

Using Algebraic Expressions

2.1.2: Write expressions in equivalent forms to solve problems

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

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

Dividing Exponential Expressions

Exponents and Power Rules

2.2.1: Understand the relationship between zeros and factors of polynomials

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

Polynomials and Linear Factors

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 (limit to 1st- and 2nd-degree polynomials).

Graphs of Polynomial Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

2.2.2: Use polynomial identities to solve problems

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

2.3.1: 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

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

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

Compound Interest

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

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 non-viable options in a modeling context.

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

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

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 Formulas for any Variable

Solving Two-Step Equations

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

2.4.2: Solve equations and inequalities in one variable

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

A-REI.4b: 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.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

2.4.3: Solve systems of equations

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

2.4.4: 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, 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

3.1.1: Understand the concept of a function and use function notation

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

Arithmetic Sequences

Geometric Sequences

3.1.2: Interpret functions that arise in applications in terms of the context

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

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

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

3.1.3: Analyze functions using different representations

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.

F-IF.7c: 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

F-IF.7e: 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

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

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

Compound Interest

Exponential 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

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

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

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

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

Addition and Subtraction of Functions

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

3.2.2: Build new functions from existing functions

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.

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

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

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

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

F-LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Compound Interest

Introduction to Exponential Functions

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.

Compound Interest

Logarithmic Functions

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

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

Arithmetic Sequences

Compound Interest

Exponential Growth and Decay

Introduction to Exponential Functions

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

F-TF.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

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

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

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

5.1.1: 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

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

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

S-ID.6a: 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

5.2.1: 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: 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

5.2.2: Make inferences 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

Polling: Neighborhood

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

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

Describing Data Using Statistics

Polling: City

Polling: Neighborhood

Real-Time Histogram

5.3.1: Understand independence and conditional probability and use them to interpret data

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

Probability Simulations

Theoretical and Experimental Probability

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

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

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.

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

Independent and Dependent Events

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

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

Correlation last revised: 9/15/2020

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