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 ax2+bx+c
Modeling the Factorization of x2+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 ax2+bx+c
Modeling the Factorization of x2+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 x2+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 ax2+bx+c
Modeling the Factorization of x2+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 ax2+bx+c
Modeling the Factorization of x2+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