A1.A: Algebra

A1.A.SSE: Seeing Structure in Expressions

A1.A.SSE.A: Interpret the structure of expressions.

A1.A.SSE.A.1: Interpret expressions that represent a quantity in terms of its context.

A1.A.SSE.A.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest

A1.A.SSE.A.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Compound Interest

A1.A.SSE.A.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
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

A1.A.SSE.B: Write expressions in equivalent forms to solve problems.

A1.A.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A1.A.SSE.B.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Quadratics in Factored Form

A1.A.SSE.B.3.b: Complete the square in a quadratic expression in the form Ax² + Bx + C to reveal the maximum or minimum value of the function it defines.

Quadratics in Vertex Form

A1.A.APR: Arithmetic with Polynomials and Rational Expressions

A1.A.APR.A: Perform arithmetic operations on polynomials.

A1.A.APR.A.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
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A1.A.APR.B: Understand the relationship between zeros and factors of polynomials.

A1.A.APR.B.2: 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
Polynomials and Linear Factors
Quadratics in Factored Form

A1.A.CED: Creating Equations

A1.A.CED.A: Create equations that describe numbers or relationships.

A1.A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems.

Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Roots of a Quadratic
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

A1.A.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.

Absolute Value Equations and Inequalities
Exponential Functions
Introduction to Exponential Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line

A1.A.CED.A.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 Programming

A1.A.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Roots of a Quadratic
Solving Formulas for any Variable

A1.A.REI: Reasoning with Equations and Inequalities

A1.A.REI.A: Understand solving equations as a process of reasoning and explain the reasoning.

A1.A.REI.A.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
Quadratics in Factored Form
Solving Algebraic Equations II
Solving Two-Step Equations

A1.A.REI.B: Solve equations and inequalities in one variable.

A1.A.REI.B.2: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

A1.A.REI.B.3: Solve quadratic equations and inequalities in one variable.

A1.A.REI.B.3.a: Use the method of completing the square to rewrite 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

A1.A.REI.B.3.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions.

Quadratics in Factored Form
Roots of a Quadratic

A1.A.REI.C: Solve systems of equations.

A1.A.REI.C.4: Write and solve a system of linear equations in context.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

A1.A.REI.D: Represent and solve equations and inequalities graphically.

A1.A.REI.D.5: 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
Exponential Functions
Introduction to Exponential Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Standard Form of a Line

A1.A.REI.D.6: 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 approximate solutions using technology.

Absolute Value Equations and Inequalities
Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)

A1.A.REI.D.7: 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
Systems of Linear Inequalities (Slope-intercept form)

A1.F: Functions

A1.F.IF: Interpreting Functions

A1.F.IF.A: Understand the concept of function and use function notation.

A1.F.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. 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).

Introduction to Functions
Linear Functions
Points, Lines, and Equations

A1.F.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions
Exponential Functions
Points, Lines, and Equations
Quadratics in Polynomial Form

A1.F.IF.B: Interpret functions that arise in applications in terms of the context.

A1.F.IF.B.3: 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
Slope-Intercept Form of a Line
Standard Form of a Line

A1.F.IF.B.4: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Absolute Value with Linear Functions
Exponential Growth and Decay
Points, Lines, and Equations

A1.F.IF.B.5: 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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope

A1.F.IF.C: Analyze functions using different representations.

A1.F.IF.C.6: Graph functions expressed symbolically and show key features of the graph, by hand and using technology.

A1.F.IF.C.6.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Point-Slope Form of a Line
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
Translating and Scaling Functions

A1.F.IF.C.6.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

A1.F.IF.C.7: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

A1.F.IF.C.7.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.

Quadratics in Factored Form
Quadratics in Vertex Form

A1.F.BF: Building Functions

A1.F.BF.A: Build a function that models a relationship between two quantities.

A1.F.BF.A.1: Write a function that describes a relationship between two quantities.

A1.F.BF.A.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A1.F.BF.B: Build new functions from existing functions.

A1.F.BF.B.2: Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

A1.F.LE: Linear, Quadratic, and Exponential Models

A1.F.LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.

A1.F.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

A1.F.LE.A.1.a: Recognize that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

Arithmetic and Geometric Sequences

A1.F.LE.A.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Arithmetic Sequences
Arithmetic and Geometric Sequences

A1.F.LE.A.1.c: Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another.

Arithmetic and Geometric Sequences
Compound Interest
Exponential Growth and Decay
Geometric Sequences

A1.F.LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions
Exponential Growth and Decay
Geometric Sequences
Introduction to Exponential Functions
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

A1.F.LE.A.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.

Arithmetic and Geometric Sequences

A1.F.LE.B: Interpret expressions for functions in terms of the situation they model.

A1.F.LE.B.4: Interpret the parameters in a linear or exponential function in terms of a context.

Compound Interest
Exponential Growth and Decay
Slope-Intercept Form of a Line
Standard Form of a Line

A1.S: Statistics and Probability

A1.S.ID: Interpreting Categorical and Quantitative Data

A1.S.ID.A: Summarize, represent, and interpret data on a single count or measurement variable.

A1.S.ID.A.1: Represent single or multiple data sets with dot plots, histograms, stem plots (stem and leaf), and box plots.

Box-and-Whisker Plots
Histograms
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

A1.S.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
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

A1.S.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).

Populations and Samples
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

A1.S.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

A1.S.ID.B.4: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

A1.S.ID.B.4.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

A1.S.ID.B.4.b: 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

A1.S.ID.C: Interpret linear models.

A1.S.ID.C.5: 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

A1.S.ID.C.6: Use technology to compute and interpret the correlation coefficient of a linear fit.

Correlation

A1.S.ID.C.7: Distinguish between correlation and causation.

Correlation