Next Generation Learning Standards
1.1.1: Extend the properties of exponents to rational exponents.
AII-N.RN.1: Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
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
AII-N.CN.2: Use the relation ??² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
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
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+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 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.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
AII-A.SSE.3.c: Use the properties of exponents to rewrite exponential expressions.
Dividing Exponential Expressions
Exponents and Power Rules
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
Polynomials and Linear Factors
AII-A.APR.3: Identify zeros of polynomial functions when suitable factorizations are available.
Graphs of Polynomial Functions
Modeling the Factorization of x2+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
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.
Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
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
2.4.1: Understand solving equations as a process of reasoning and explain the reasoning.
AII-A.REI.1b: Explain each step when solving rational or radical equations 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
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:
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic
AII-A.REI.4.b.i: inspection, Write complex solutions in ?? + ???? form.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic
AII-A.REI.4.b.ii: taking square roots, Write complex solutions in a + bi form.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic
AII-A.REI.4.b.iii: factoring, Write complex solutions in a + bi form.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic
AII-A.REI.4.b.iv: completing the square, Write complex solutions in a + bi form.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic
AII-A.REI.4.b.v: the quadratic formula, and Write complex solutions in a + bi form.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Points in the Complex Plane
Roots of a Quadratic
AII-A.REI.4.b.vi: graphing. Write complex solutions in a + bi form.
Quadratics in Factored 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):
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.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.ii: find the solutions approximately using technology to graph the functions or make tables of values;
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)
3.1.1: Understand the concept of a function and use function notation.
AII-F.IF.3: Recognize that a sequence is a function 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.
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
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
AII-F.IF.4.ii: 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
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.c: 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
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
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Radical Functions
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
Exponential Growth and Decay
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.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Points, Lines, and Equations
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):
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
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
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Points, Lines, and Equations
Quadratics in Vertex Form
Radical Functions
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.
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
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
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
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
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
AII-F.LE.2.ii: a description of the relationship; and
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
AII-F.LE.2.iii: 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
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.
Compound Interest
Logarithmic Functions
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
Exponential Growth and Decay
Introduction to Exponential Functions
3.4.1: Extend the domain of trigonometric functions using the unit circle.
AII-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
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 Function
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
Zap It! Game
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
Probability Simulations
Theoretical and Experimental Probability
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: 12/9/2022