Next Generation Learning Standards

1.2.1: Perform arithmetic operations with complex numbers.

AII-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

2.1.1: Interpret the structure of expressions.

AII-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

2.1.2: Write expressions in equivalent forms to reveal their characteristics.

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

AII-A.SSE.3.a: Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.

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

Quadratics in Factored Form

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

AII-A.APR.2: 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

AII-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.

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

Polynomials and Linear Factors

2.3.1: Create equations that describe numbers or relationships.

AII-A.CED.1: Create equations and inequalities in one variable to represent a real-world context.

Arithmetic Sequences

Geometric Sequences

Solving Two-Step Equations

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

AII-A.REI.2: Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.

2.4.2: Solve equations and inequalities in one variable.

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

AII-A.REI.4.b: Solve quadratic equations by:

AII-A.REI.4.b.ii: taking square roots, Write complex solutions in a + bi form.

AII-A.REI.4.b.iii: factoring, Write complex solutions in a + bi form.

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

AII-A.REI.4.b.iv: completing the square, Write complex solutions in a + bi form.

AII-A.REI.4.b.v: the quadratic formula, and Write complex solutions in a + bi form.

AII-A.REI.4.b.vi: graphing. Write complex solutions in a + bi form.

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

2.4.4: Represent and solve equations and inequalities graphically.

AII-A.REI.11: Given the equations y = f(x) and y = g(x):

AII-A.REI.11.i: recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);

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

AII-A.REI.11.iii: find the solution of f(x) < g(x) or f(x) <= g(x) graphically; and

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

AII-A.REI.11.iv: interpret the solution in context.

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

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

AII-F.IF.4: For a function that models a relationship between two quantities:

AII-F.IF.4.i: interpret key features of graphs and tables in terms of the quantities; and

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

AII-F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Introduction to Exponential Functions

Point-Slope Form of a Line

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Slope

Standard Form of a Line

3.1.3: Analyze functions using different representations.

AII-F.IF.7: Graph functions and show key features of the graph by hand and using technology when appropriate.

AII-F.IF.7.e: Graph cube root, 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

3.1.4: Analyze functions using different representations.

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

AII-F.IF.8.b: Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.

Compound Interest

Exponential Functions

Introduction to Exponential Functions

AII-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.

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

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

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

Addition and Subtraction of Functions

AII-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.

AII-F.BF.3b: Using f(x) + k, k f(x), f(kx), and f(x + k):

AII-F.BF.3b.i: identify the effect on the graph when 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); Include recognizing even and odd functions from their graphs.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Points, Lines, and Equations

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

AII-F.BF.3b.ii: find the value of k given the graphs; Include recognizing even and odd functions from their graphs.

AII-F.BF.3b.iv: use technology to experiment with cases and explore the effects on the graph. Include recognizing even and odd functions from their graphs.

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

AII-F.BF.4a: Find the inverse of a one-to-one function both algebraically and graphically.

AII-F.BF.5a: Understand inverse relationships between exponents and logarithms algebraically and graphically.

AII-F.BF.7: Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.

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

AII-F.LE.2: Construct a linear or exponential function symbolically given:

AII-F.LE.2.i: a graph;

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Slope-Intercept Form of a Line

Standard Form of a Line

AII-F.LE.2.ii: a description of the relationship; and

Arithmetic Sequences

Linear Functions

Slope-Intercept Form of a Line

AII-F.LE.2.iii: two input-output pairs (include reading these from a table).

Arithmetic Sequences

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Slope-Intercept Form of a Line

AII-F.LE.4: Use logarithms to solve exponential equations, such as ab to the a power = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.

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

AII-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

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

AII-F.TF.2: Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.

Cosine Function

Sine Function

Tangent Function

AII-F.TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

3.4.2: Model periodic phenomena with trigonometric functions.

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

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

3.4.3: Prove and apply trigonometric identities.

AII-F.TF.8: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

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

AII-S.ID.4a: Recognize whether or not a normal curve is appropriate for a given data set.

Polling: City

Populations and Samples

Sight vs. Sound Reactions

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

AII-S.ID.6: Represent bivariate data on a scatter plot, and describe how the variables’ values are related.

AII-S.ID.6.a: Fit a function to real-world 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

4.2.1: Understand and evaluate random processes underlying statistical experiments.

AII-S.IC.2: Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.

Polling: City

Polling: Neighborhood

Populations and Samples

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

AII-S.IC.3: Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.

Polling: City

Polling: Neighborhood

AII-S.IC.4: Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/- two standard deviations) and determine if a suggested parameter is plausible.

AII-S.IC.6a: Use the tools of statistics to draw conclusions from numerical summaries.

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

AII-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

AII-S.CP.4: 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 calculate conditional probabilities.

Correlation last revised: 9/24/2019

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