IA.AAPR: Arithmetic with Polynomials and Rational Expressions

IA.AAPR.1: Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations.

 Addition and Subtraction of Functions
 Addition of Polynomials
 Modeling the Factorization of x2+bx+c

IA.ACE: Creating Equations

IA.ACE.1: Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable.

 Compound Inequalities
 Linear Inequalities in Two Variables
 Solving Equations on the Number Line
 Solving Two-Step Equations

IA.ACE.2: Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales.

 Absolute Value Equations and Inequalities
 Circles
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Solving Equations on the Number Line
 Standard Form of a Line
 Using Algebraic Equations

IA.ACE.4: Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

 Area of Triangles
 Solving Formulas for any Variable

IA.REI: Reasoning with Equations and Inequalities

IA.AREI.2: Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise.

 Radical Functions

IA.AREI.4: Solve mathematical and real-world problems involving quadratic equations in one variable.

IA.AREI.4.a: Use the method of completing the square to transform any quadratic equation in 𝑥 into an equation of the form (x − h)² = k that has the same solutions. Derive the quadratic formula from this form.

 Roots of a Quadratic

IA.AREI.4.b: Solve quadratic equations by inspection, 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 gives complex solutions and write them as a + bi for real numbers a and b.

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

IA.AREI.11: Solve an equation of the form f(x) = g(x) graphically by identifying the x- coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and y = g(x).

 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

IA.ASE: Structure and Expressions

IA.ASE.1: Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions.

 Compound Interest
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

IA.ASE.2: Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

IA.ASE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

IA.ASE.3.a: Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Roots of a Quadratic
 Zap It! Game

IA.FBF: Building Functions

IA.FBF.1: Write a function that describes a relationship between two quantities.

IA.FBF.1.a: Write a function that models a relationship between two quantities using both explicit expressions and a recursive process and by combining standard forms using addition, subtraction, multiplication and division to build new functions.

 Addition and Subtraction of Functions
 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

IA.FBF.1.b: Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations.

 Addition and Subtraction of Functions
 Function Machines 1 (Functions and Tables)
 Function Machines 3 (Functions and Problem Solving)

IA.FBF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

IA.FBF.3: Describe the effect of the transformations kf (x), f(x) + k, f(x +k), and combinations of such transformations on the graph of y = f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph.

 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

IA.FIF: Interpreting Functions

IA.FIF.3: Define functions recursively and recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

 Arithmetic Sequences
 Geometric Sequences

IA.FIF.4: Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.

 Absolute Value with Linear Functions
 Compound Interest
 Exponential Functions
 Function Machines 1 (Functions and Tables)
 Function Machines 3 (Functions and Problem Solving)
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Introduction to Functions
 Logarithmic Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions

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

 Introduction to Functions
 Logarithmic Functions
 Radical Functions

IA.FIF.6: Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context.

 Cat and Mouse (Modeling with Linear Systems)
 Slope

IA.FIF.7: Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases.

 Exponential Functions
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Introduction to Exponential Functions
 Introduction to Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions

IA.FIF.8: Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function.

IA.FIF.8.b: Interpret expressions for exponential functions by using the properties of exponents.

 Compound Interest
 Exponential Functions

IA.FIF.9: Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal.

 General Form of a Rational Function
 Graphs of Polynomial Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Polynomial Form

IA.FLQE: Linear, Quadratic, and Exponential

IA.FLQE.2: Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables.

 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

IA.FLQE.5: Interpret the parameters in a linear or exponential function in terms of the context.

 Arithmetic Sequences
 Compound Interest
 Introduction to Exponential Functions

IA.NCNS: Complex Number System

IA.NCNS.1: Know there is a complex number 𝑖 such that i² =−1, and every complex number has the form a + bi with a and b real.

 Points in the Complex Plane
 Roots of a Quadratic

Correlation last revised: 1/19/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.