AI.DS: Data Analysis and Statistics

AI.DS.1: Understand statistics as a process for making inferences about a population based on a random sample from that population. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Estimating Population Size
Polling: City
Polling: Neighborhood
Populations and Samples
Sight vs. Sound Reactions
Time Estimation

AI.DS.3: Use technology to find a linear function that models a relationship between two quantitative variables to make predictions, and interpret the slope and y-intercept. Using technology, compute and interpret the correlation coefficient.

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

AI.DS.4: Describe the differences between correlation and causation.

Correlation

AI.NE: Number Systems and Expressions

AI.NE.1: Explain the hierarchy and relationships of numbers and sets of numbers within the complex number system. Know that there is an imaginary number, i, such that the square root of -i = i. Understand that the imaginary numbers along with the real numbers form the complex number system.

Points in the Complex Plane

AI.NE.2: Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.

Dividing Exponential Expressions

AI.NE.3: Simplify square roots of monomial algebraic expressions, including non-perfect squares.

Simplifying Radical Expressions

AI.NE.4: Factor quadratic expressions (including the difference of two squares, perfect square trinomials and other quadratic expressions).

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

AI.NE.5: Add, subtract, and multiply polynomials. Divide polynomials by monomials.

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

AI.F: Functions

AI.F.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. Understand that 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. Understand the graph of f is the graph of the equation y = f(x) with points of the form (x, f(x)).

Introduction to Functions
Linear Functions
Points, Lines, and Equations

AI.F.2: Evaluate functions for given elements of its domain, and interpret statements in function notation in terms of a context.

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

AI.F.3: Identify the domain and range of relations represented in tables, graphs, verbal descriptions, and equations.

Introduction to Functions
Radical Functions

AI.F.4: Describe, qualitatively, the functional relationship between two quantities by analyzing key features of a graph. Sketch a graph that exhibits given key features of a function that has been verbally described, including intercepts, where the function is increasing or decreasing, where the function is positive or negative, and any relative maximum or minimum values, Identify the independent and dependent variables.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions

AI.L: Linear Equations, Inequalities, and Functions

AI.L.1: Represent real-world problems using linear equations and inequalities in one variable, including those with rational number coefficients and variables on both sides of the equal sign. Solve them fluently, explaining the process used and justifying the choice of a solution method.

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

AI.L.2: Solve compound linear inequalities in one variable, and represent and interpret the solution on a number line. Write a compound linear inequality given its number line representation.

Compound Inequalities

AI.L.3: Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line). Find the equation of a line, passing through a given point, that is parallel or perpendicular to a given line.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

AI.L.4: Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

AI.L.5: Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

AI.L.6: Represent real-world problems using linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable. Graph the solutions to a linear inequality in two variables as a half-plane.

Linear Inequalities in Two Variables

AI.L.7: Solve linear and quadratic equations and formulas for a specified variable to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

AI.SEI: Systems of Linear Equations and Inequalities

AI.SEI.1: Understand the relationship between a solution of a system of two linear equations in two variables and the graphs of the corresponding lines. Solve pairs of linear equations in two variables by graphing; approximate solutions when the coordinates of the solution are non-integer numbers.

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)

AI.SEI.2: Verify 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, including cases with no solution and infinitely many solutions. Solve systems of two linear equations algebraically using elimination and substitution methods.

Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

AI.SEI.3: Write a system of two linear equations in two variables that represents a real-world problem and solve the problem with and without technology. Interpret the solution and determine whether the solution is reasonable.

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)

AI.SEI.4: Represent real-world problems using a system of two linear inequalities in two variables. Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes with and without technology. Interpret the solution set and determine whether it is reasonable.

Systems of Linear Inequalities (Slope-intercept form)

AI.QE: Quadratic and Exponential Equations and Functions

AI.QE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. Understand that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Compare linear functions and exponential functions that model real-world situations using tables, graphs, and equations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

AI.QE.2: Represent real-world and other mathematical problems that can be modeled with simple exponential functions using tables, graphs, and equations of the form y = ab^x (for integer values of x > 1, rational values of b > 0 and b not equal to 1) with and without technology; interpret the values of a and b.

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

AI.QE.3: Use area models to develop the concept of completing the square to solve quadratic equations. Explore the relationship between completing the square and the quadratic formula.

Quadratics in Vertex Form
Roots of a Quadratic

AI.QE.4: Solve quadratic equations in one variable by inspection (e.g., for x² = 49), finding square roots, using the quadratic formula, and factoring, as appropriate to the initial form of the equation.

Quadratics in Factored Form
Roots of a Quadratic

AI.QE.5: Represent real-world problems using quadratic equations in one or two variables and solve such problems with technology. Interpret the solution(s) and determine whether they are reasonable.

Quadratics in Polynomial Form

AI.QE.6: Graph exponential and quadratic functions with and without technology. Identify and describe key features, such as zeros, lines of symmetry, and extreme values in real-world and other mathematical problems involving quadratic functions with and without technology; interpret the results in the real-world contexts.

Exponential Functions
Introduction to Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

AI.QE.7: Describe the relationships among a solution of a quadratic equation, a zero of the function, an x-intercept of the graph, and the factors of the expression. Explain that every quadratic has two complex solutions, which may or may not be real solutions.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic