College and Career-Ready Frameworks

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.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.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.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.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.

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.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)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

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.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.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.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.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.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.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.

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.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.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.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.

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.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

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

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

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.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 *x*^{2}+*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.

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

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

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

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.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.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.

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

Points in the Complex Plane

Roots of a Quadratic

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.

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.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 *x*^{2}+*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.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.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.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.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: 1/22/2020

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