1: Relationships between Quantities and Reasoning with Equations

1.2: Interpret the structure of expressions.

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

1.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

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

 Compound Interest
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

1.3: Create equations that describe numbers or relationships.

1.A.CED.1: Create equations and inequalities in one variable and use them to solve problems.

 Absolute Value Equations and Inequalities
 Arithmetic Sequences
 Exploring Linear Inequalities in One Variable
 Geometric Sequences
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Equations on the Number Line
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations
 Using Algebraic Equations

1.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
 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

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

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

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

 Area of Triangles
 Solving Formulas for any Variable

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

1.A.REI.1: Explain each step in solving a simple 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 Two-Step Equations

1.5: Solve equations and inequalities in one variable.

1.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 II
 Solving Equations on the Number Line
 Solving Formulas for any Variable
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

2: Linear and Exponential Relationships

2.1: Solve systems of equations.

2.A.REI.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

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

2.A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), 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)

2.2: Represent and solve equations and inequalities graphically.

2.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
 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Standard Form of a Line

2.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, e.g., 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, polynomial, rational, absolute value, exponential, and 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

2.A.REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and 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)

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

2.F.IF.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. 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 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

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

 Arithmetic Sequences
 Geometric Sequences

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

2.F.IF.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

2.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

 Introduction to Functions
 Logarithmic Functions
 Radical Functions

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

 Cat and Mouse (Modeling with Linear Systems)
 Slope

2.5: Analyze functions using different representations.

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

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

 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
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Standard Form of a Line
 Zap It! Game

2.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

2.6: Build a function that models a relationship between two quantities.

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

2.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

2.7: Build new functions from existing functions.

2.F.BF.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. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

 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

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

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

2.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
 Introduction to Exponential Functions
 Slope-Intercept Form of a Line

2.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

2.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

2.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
 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

2.F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

 Compound Interest
 Introduction to Exponential Functions

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

2.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: Descriptive Statistics

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

3.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

3.S.ID.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
 Mean, Median, and Mode
 Polling: City
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram

3.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)
 Real-Time Histogram
 Stem-and-Leaf Plots

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

3.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.

 Histograms

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

3.S.ID.6.a: 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

3.S.ID.6.b: Informally 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

3.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

3.3: Interpret linear models.

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

 Correlation
 Solving Using Trend Lines
 Trends in Scatter Plots

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

 Correlation

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

 Correlation

4: Expressions and Equations

4.3: Interpret the structure of expressions.

4.A.SSE.2: 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

4.4: Write expressions in equivalent forms to solve problems.

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

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

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

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

 Quadratics in Vertex Form

4.5: Perform arithmetic operations on polynomials.

4.A.APR.1: Understand that polynomials form a system analogous to the integers, namely, they are 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 x2+bx+c

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

4.A.APR.3: Identify zeros of polynomials when suitable factorizations are available, and 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

4.7: Create equations that describe numbers or relationships.

4.A.CED.1: Create equations and inequalities in one variable and use them to solve problems.

 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

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

 Addition and Subtraction of Functions
 Exponential Functions
 Linear Functions
 Modeling and Solving Two-Step Equations
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Solving Equations by Graphing Each Side
 Standard Form of a Line
 Translating and Scaling Functions

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

 Area of Triangles
 Solving Formulas for any Variable

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

4.A.REI.1: Explain each step in solving a simple 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 Two-Step Equations

4.9: Solve equations and inequalities in one variable.

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

4.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. Derive the quadratic formula from this form.

 Roots of a Quadratic

4.A.REI.4.b: 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. Recognize when the quadratic formula reveals that the quadratic equation has “no real solutions”.

 Modeling the Factorization of x2+bx+c
 Points in the Complex Plane
 Roots of a Quadratic

5: Quadratic Functions and Modeling

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

5.F.IF.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
 Graphs of Polynomial Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions

5.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

 Radical Functions

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

 Translating and Scaling Functions

5.2: Analyze functions using different representations.

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

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

 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
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Standard Form of a Line
 Zap It! Game

5.F.IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

 Absolute Value with Linear Functions
 Radical Functions
 Translating and Scaling Functions

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

5.F.IF.8.a: Use the process of 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.

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

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

 Graphs of Polynomial Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Translating and Scaling Functions

5.3: Build a function that models a relationship between two quantities.

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

5.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
 Introduction to Exponential Functions

5.4: Build new functions from existing functions.

5.F.BF.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. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

 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

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

5.F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

 Compound Interest
 Introduction to Exponential Functions

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

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

5.S.ID.6.a: 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
 Zap It! Game

Correlation last revised: 4/4/2018

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