HSN.RN: The Real Number System

HSN.RN.1: 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

HSA.SSE: Seeing Structure in Expressions

HSA.SSE.3: 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

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.4: 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.

 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.5: 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.6: Understand the relationship between zeros and factors of polynomials.

HSA.APR.B.3: Identify zeros of polynomials (linear, quadratic only) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Quadratics in Vertex Form

HSA.CED: Creating Equations

HSA.CED.9: 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
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 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.

 Solving Formulas for any Variable

HSA.REI: Reasoning with Equations and Inequalities

HSA.REI.10: 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 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.11: Solve equations and inequalities in one variable

HSA.REI.B.3: Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.

 Absolute Value Equations and Inequalities
 Area of Triangles
 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 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 Linear Inequalities in One Variable
 Solving Two-Step Equations

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. (Algebra 2 only)

 Modeling the Factorization of x2+bx+c
 Roots of a Quadratic

HSA.REI.12: 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.13: Solve systems of equations

HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

 Absolute Value Equations and Inequalities
 Circles
 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Standard Form of a Line

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, absolute value, exponential. (Introduction in Algebra 1, Mastery in Algebra 2)

 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.14: Understand the concept of a function and use function notation

HSF.IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. Understand that if f is a function and 𝑥 is an element of its domain, then f(𝑥) denotes the output of f corresponding to the input 𝑥. Understand that the graph of 𝑓 is the graph of the equation 𝑦 = 𝑓(𝑥).

 Absolute Value with Linear Functions
 Exponential Functions
 Introduction to Exponential Functions
 Introduction to Functions
 Linear Functions
 Logarithmic Functions
 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Standard Form of a Line

HSF.IF.15: 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
 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

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.

 Introduction to Functions
 Logarithmic Functions
 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.16: 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 linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Standard Form of a Line
 Translating and Scaling 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 process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context.

 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.17: 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.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences
 Points, Lines, and Equations

HSF.BF.18: 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 (𝑘, a constant 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
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Translations
 Zap It! Game

HSF.LE: Linear, Quadratic, and Exponential Models

HSF.LE.19: Construct and compare linear, quadratic, and exponential models and solve problems

HSF.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. Show that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

 Arithmetic Sequences
 Compound Interest
 Direct and Inverse Variation
 Exponential Functions
 Introduction to Exponential Functions
 Linear Functions
 Slope-Intercept Form of a Line

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
 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.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.

 Compound Interest
 Introduction to Exponential Functions

HSF.LE.20: Interpret expressions for functions in terms of the situation they model

HSF.LE.B.5: In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.

 Arithmetic Sequences
 Cat and Mouse (Modeling with Linear Systems)
 Compound Interest
 Introduction to Exponential Functions

HSS.ID: Interpreting Categorical and Quantitative Data

HSS.ID.21: Summarize, represent, and interpret data on a single count or measurement variable

HSS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).

 Box-and-Whisker Plots
 Histograms
 Mean, Median, and Mode

HSS.ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Real-Time Histogram
 Sight vs. Sound Reactions

HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

 Mean, Median, and Mode
 Reaction Time 2 (Graphs and Statistics)

HSS.ID.22: Summarize, represent, and interpret data on two categorical and quantitative variables

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.ID.23: Interpret linear models

HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

 Cat and Mouse (Modeling with Linear Systems)

HSS.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.

 Correlation

Correlation last revised: 4/4/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.