Content Standards

N.RN.1: Explain how the definition of rational exponents follows from extending the properties of integer exponents, allowing for a notation for radicals in terms of rational exponents.

A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

A.SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity in context.

Compound Interest

Translating and Scaling Functions

Using Algebraic Expressions

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

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

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Simplifying Trigonometric Expressions

Solving Algebraic Equations II

Using Algebraic Expressions

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

A.SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products

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

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

Quadratics in Factored Form

A.SSE.3.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.SSE.3.c: Use the properties of exponents to write equivalent expressions for exponential functions.

Dividing Exponential Expressions

Exponents and Power Rules

A.APR.1: Understand that polynomials form a system closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Addition and Subtraction of Functions

Addition of Polynomials

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

A.CED.1: Create equations and inequalities in one variable arising from situations in which linear, quadratic, and exponential functions are appropriate and use them to solve problems.

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

A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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

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

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

A.CED.4: Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Area of Triangles

Solving Formulas for any Variable

A.REI.1: Explain each step in solving an 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 Formulas for any Variable

Solving Two-Step Equations

A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

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 I

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

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

A.REI.4.a: 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.

A.REI.4.b: Derive the quadratic formula from this form completing the square.

A.REI.4.c: 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.

Factoring Special Products

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

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

Points in the Complex Plane

Roots of a Quadratic

A.REI.5: Understand the principles of the elimination method.

Solving Equations by Graphing Each Side

Solving Linear Systems (Standard Form)

A.REI.6: Solve systems of linear equations exactly and approximately by graphing, focusing on pairs of linear equations in two variables.

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)

A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Absolute Value Equations and Inequalities

Circles

Ellipses

Hyperbolas

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Standard Form of a Line

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, including but not limited to 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, quadratic and exponential.

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

A.REI.12: Graph a linear inequality (strict or inclusive) in two variables; graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Linear Inequalities in Two Variables

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

F.IF.1: Understand that a function maps each element of the domain to exactly one element of the range. 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. The graph off is the graph of the equation y = f(x).

Absolute Value with Linear Functions

Exponential Functions

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

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

F.IF.2: Use function notation, evaluate functions, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions

Translating and Scaling Functions

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

Arithmetic Sequences

Geometric Sequences

F.IF.4: For functions, including linear, quadratic, and exponential, that model 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. Key features include: intercepts; intervals where the function is increasing or decreasing, including using interval notation; maximums and minimums; symmetries.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

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

F.IF.5: Relate the domain of a function to its graph and find an appropriate domain in the context of the problem.

General Form of a Rational Function

Introduction to Functions

Logarithmic Functions

Radical Functions

Rational Functions

F.IF.7: Graph parent functions and their transformations expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.a: Graph linear, exponential, and quadratic functions and show intercepts, maxima, and minima.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Slope-Intercept Form of a Line

Standard Form of a Line

Zap It! Game

F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8.a: Use the process of graphing, factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Factoring Special Products

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

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

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

F.IF.9: Compare properties of two functions (linear, quadratic and exponential) each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

Translating and Scaling Functions

F.BF.1: Write a function (linear, quadratic, and exponential) that describes a relationship between two quantities.

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

F.BF.1.b: Determine an explicit expression from a graph.

Arithmetic Sequences

Geometric Sequences

F.BF.1.c: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula and use them to model situations.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

F.BF.3: Identify the effect on the graph of f(x) (linear, exponential, quadratic) replaced with 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 contrasting cases and illustrate an explanation of the effects on the graph using technology.

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

F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Compound Interest

Direct and Inverse Variation

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

Linear Functions

Slope-Intercept Form of a Line

F.LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Arithmetic Sequences

Compound Interest

Direct and Inverse Variation

Linear Functions

Slope-Intercept Form of a Line

F.LE.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Compound Interest

Exponential Growth and Decay

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

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

F.LE.3: Recognize, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Compound Interest

Introduction to Exponential Functions

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

S.ID.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

Reaction Time 1 (Graphs and Statistics)

S.ID.2: Use statistics appropriate to the shape and context 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

Mean, Median, and Mode

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Sight vs. Sound Reactions

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

Box-and-Whisker Plots

Describing Data Using Statistics

Least-Squares Best Fit Lines

Mean, Median, and Mode

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Real-Time Histogram

Stem-and-Leaf Plots

S.ID.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

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

S.ID.6.a: Determine the function (linear, quadratic, or exponential model) that best fits a set of data and use that function fitted to data to solve problems within context.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

Zap It! Game

S.ID.6.b: Informally and using technology assess the fit of a function by plotting and analyzing residuals.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

S.ID.6.c: Fit a linear function for a scatter plot that suggests a linear association.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

S.ID.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)

Correlation

Solving Using Trend Lines

Trends in Scatter Plots

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

S.ID.9: Distinguish between correlation and causation.

Correlation last revised: 9/15/2020

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