College and Career-Ready Frameworks

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

Points in the Complex Plane

Roots of a Quadratic

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.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 *x*^{2}+*bx*+*c*

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

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

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.

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.

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 *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

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.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)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

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

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

Arithmetic Sequences

Geometric Sequences

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.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.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.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.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.

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.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.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.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.

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.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.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.

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.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.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: 1/22/2020

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