HSN.RN: The Real Number System

HSN.RN.1: Extend the properties of exponents to rational exponents

HSN.RN.A.1: Explain how extending the properties of integer exponents to rational exponents provides an alternative notation for radicals.

Exponents and Power Rules

HSN.RN.2: Use properties of rational and irrational numbers

HSN.RN.B.4: Simplify radical expressions. Perform operations (add, subtract, multiply, and divide) with radical expressions. Rationalize denominators and/or numerators.

Operations with Radical Expressions
Simplifying Radical Expressions

HSN.CN: The Complex Number System

HSN.CN.4: Perform arithmetic operations with complex numbers

HSN.CN.A.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

HSN.CN.A.2: Use the relation 𝑖² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Points in the Complex Plane

HSN.CN.A.3: Find the conjugate of a complex number. Use conjugates to find quotients of complex numbers.

Points in the Complex Plane
Roots of a Quadratic

HSN.CN.5: Use complex numbers in polynomial identities and equations

HSN.CN.C.7: Solve quadratic equations with real coefficients that have real or complex solutions.

Points in the Complex Plane
Roots of a Quadratic

HSN.VM: Vector and Matrix Quantities

HSN.VM.6: Perform operations on matrices and use matrices in applications

HSN.VM.C.7: Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).

Dilations

HSA.SSE: Seeing Structure in Expressions

HSA.SSE.7: Interpret the structure of expressions

HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions

HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

HSA.SSE.8: Write expressions in equivalent forms to solve problems

HSA.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Use the properties of exponents to transform expressions for exponential functions.

Dividing Exponential Expressions
Exponents and Power Rules
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Simplifying Algebraic Expressions II

HSA.APR: Arithmetic with Polynomials and Rational Expressions

HSA.APR.9: Perform arithmetic operations on polynomials

HSA.APR.A.1: Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

HSA.APR.10: Understand the relationship between zeros and factors of polynomials.

HSA.APR.B.2: Know and apply the Factor and Remainder Theorems: 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

HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available. 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

HSA.CED: Creating Equations

HSA.CED.13: Create equations that describe numbers or relationships

HSA.CED.A.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
Exponential Growth and Decay
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.

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

HSA.CED.A.3: Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.

Linear Inequalities in Two Variables
Linear Programming
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

HSA.CED.A.4: Rearrange literal equations using the properties of equality.

Area of Triangles
Solving Formulas for any Variable

HSA.REI: Reasoning with Equations and Inequalities

HSA.REI.14: Understand solving equations as a process of reasoning and explain the reasoning

HSA.REI.A.1: Assuming that equations have a solution, construct a solution and justify the reasoning used.

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

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

Radical Functions

HSA.REI.15: Solve equations and inequalities in one variable

HSA.REI.B.4: Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring. Recognize complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.

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

HSA.REI.16: Solve systems of equations and inequalities graphically.

HSA.REI.C.5: Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

HSA.REI.C.6: Solve systems of equations algebraically and graphically.

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)

HSA.REI.C.7: Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically.

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)

HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

HSA.REI.17: Solve systems of equations

HSA.REI.D.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 by using technology to graph the functions, making tables of values, finding successive approximations. Include cases (but not limited to) where f(x) and/or g(x) are linear, polynomial, rational, exponential (Introduction in Algebra 1, Mastery in Algebra 2), 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

HSA.REI.D.12: Solve linear inequalities and systems of linear inequalities in two variables by graphing.

Linear Inequalities in Two Variables
Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

HSF.IF: Interpreting Functions

HSF.IF.19: Interpret functions that arise in applications in terms of the context

HSF.IF.B.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

HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)
Slope

HSF.IF.20: Analyze functions using different representations

HSF.IF.C.7: Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior. Graph trigonometric functions, showing period, midline, and amplitude.

Absolute Value with Linear Functions
Cosine Function
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions
Zap It! Game

HSF.IF.C.8: Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Functions
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

HSF.BF: Building Functions

HSF.BF.21: Build a function that models a relationship between two quantities

HSF.BF.A.1: Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation. Combine standard function types using arithmetic operations. (e.g., given that f(x) and g(x) are functions developed from a context, find (f + g)(x), (f – g)(x), (fg)(x), (f/g)(x), and any combination thereof, given 𝑔(𝑥) ≠ 0.) Compose functions.

Addition and Subtraction of Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Geometric Sequences

HSF.BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, and translate between the two forms. Use arithmetic and geometric sequences to model situations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

HSF.BF.22: Build new functions from existing functions

HSF.BF.B.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 of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without 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
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

HSF.IF.B.5: Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Logarithmic Functions
Radical Functions
Rational Functions

HSF.LE: Linear, Quadratic, and Exponential Models

HSF.LE.23: Construct and compare linear, quadratic, and exponential models and solve problems

HSF.LE.A.2: Construct linear and exponential equations, 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

HSF.LE.A.4: Express exponential models as logarithms. Express logarithmic models as exponentials. Use properties of logarithms to simplify and evaluate logarithmic expressions (expanding and/or condensing logarithms as appropriate). Evaluate logarithms with or without technology.

Compound Interest
Logarithmic Functions

HSS.ID: Interpreting Categorical and Quantitative Data

HSS.ID.24: Summarize, represent, and interpret data on a single count or measurement variable

HSS.ID.A.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 and/or spreadsheets to estimate areas under the normal curve.

Polling: City
Populations and Samples
Real-Time Histogram

HSS.ID.25: Make inferences and justify conclusions from sample surveys, experiments and observational studies

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

HSS.IC: Making Inferences and Justifying Conclusions

HSS.IC.26: Understand and evaluate random processes underlying statistical experiments

HSS.IC.A.1: Recognize 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

HSS.IC.A.2: Compare theoretical and empirical probabilities using simulations (e.g. such as flipping a coin, rolling a number cube, spinning a spinner, and technology).

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

HSS.IC.27: Make inferences and justify conclusions from sample surveys, experiments and observational studies

HSS.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies. Explain how randomization relates to sample surveys, experiments, and observational studies.

Polling: City
Polling: Neighborhood

HSS.IC.B.6: Read and explain, in context, the validity of data from outside reports by identifying the variables as quantitative or categorical, describing how the data was collected, indicating any potential biases or flaws, identifying inferences the author of the report made from sample data.

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