I: Students will use the language and operations of algebra to evaluate, analyze and solve problems.

I.1: Evaluate, analyze, and solve mathematical situations using algebraic properties and symbols.

I.1.a: Solve and graph first-degree absolute value equations of a single variable.

 Absolute Value Equations and Inequalities
 Absolute Value with Linear Functions

I.1.b: Solve radical equations of a single variable, including those with extraneous roots.

 Operations with Radical Expressions
 Radical Functions

I.1.c: Solve absolute value and compound inequalities of a single variable.

 Absolute Value Equations and Inequalities
 Compound Inequalities
 Solving Linear Inequalities in One Variable

I.1.e: Simplify algebraic expressions involving negative and rational exponents.

 Dividing Exponential Expressions
 Exponents and Power Rules
 Multiplying Exponential Expressions

I.2: Solve systems of equations and inequalities.

I.2.a: Solve systems of linear, absolute value, and quadratic equations algebraically and graphically.

 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)

I.2.b: Graph the solutions of systems of linear, absolute value, and quadratic inequalities on the coordinate plane.

 Absolute Value Equations and Inequalities
 Linear Inequalities in Two Variables
 Systems of Linear Inequalities (Slope-intercept form)

I.2.c: Solve application problems involving systems of equations and inequalities.

 Linear Programming
 Systems of Linear Inequalities (Slope-intercept form)

I.3: Represent and compute fluently with complex numbers.

I.3.b: Simplify expressions involving complex numbers and express them in standard form, a + bi.

 Points in the Complex Plane

I.4: Model and solve quadratic equations and inequalities.

I.4.a: Model real-world situations using quadratic equations.

 Addition and Subtraction of Functions

I.4.c: Solve quadratic equations of a single variable over the set of complex numbers by factoring, completing the square, and using the quadratic formula.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Roots of a Quadratic

I.4.e: Write a quadratic equation when given the solutions of the equation.

 Quadratics in Polynomial Form

II: Students will understand and represent functions and analyze function behavior.

II.1: Represent mathematical situations using relations.

II.1.a: Model real-world relationships with functions.

 Determining a Spring Constant

II.1.c: Determine when a relation is a function.

 Introduction to Functions
 Linear Functions

II.1.d: Determine the domain and range of relations.

 Introduction to Functions

II.2: Evaluate and analyze functions.

II.2.b: Compose functions when possible.

 Function Machines 1 (Functions and Tables)

II.2.c: Add, subtract, multiply, and divide functions.

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

II.2.d: Determine whether or not a function has an inverse, and find the inverse when it exists.

 Function Machines 3 (Functions and Problem Solving)
 Logarithmic Functions

II.3: Define and graph exponential functions and use them to model problems in mathematical and real-world contexts.

II.3.a: Define exponential functions as functions of the form y = abx ,b > 0,b ?? 1.

 Compound Interest
 Exponential Functions
 Introduction to Exponential Functions
 Logarithmic Functions

II.3.b: Model problems of growth and decay using exponential functions.

 Compound Interest

II.3.c: Graph exponential functions.

 Compound Interest
 Exponential Functions
 Introduction to Exponential Functions
 Logarithmic Functions

II.4: Define and graph logarithmic functions and use them to solve problems in mathematics and real-world contexts.

II.4.a: Relate logarithmic and exponential functions.

 Logarithmic Functions

II.4.d: Solve exponential and logarithmic equations.

 Exponential Functions

II.4.e: Graph logarithmic functions.

 Logarithmic Functions

II.4.f: Solve problems involving growth and decay.

 Compound Interest

III: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

III.1: Examine the behavior of functions using coordinate geometry.

III.1.a: Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions.

 Radical Functions

III.1.b: Graph the absolute value, quadratic, radical, sine, and cosine functions.

 Absolute Value with Linear Functions
 Addition and Subtraction of Functions
 Cosine Function
 Exponential Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions
 Roots of a Quadratic
 Sine Function
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Zap It! Game

III.1.c: Graph functions using transformations of parent functions.

 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

III.1.d: Write an equation of a parabola in the form y = a(x − h)2 + k when given a graph or an equation..

 Parabolas

III.2: Determine radian and degree measures for angles.

III.2.a: Convert angle measurements between radians and degrees.

 Cosine Function
 Sine Function
 Tangent Function

III.2.b: Find angle measures in degrees and radians using inverse trigonometric functions, including exact values for special triangles.

 Tangent Function

III.3: Determine trigonometric measurements using appropriate techniques, tools, and formulas.

III.3.a: Define the sine, cosine, and tangent functions using the unit circle.

 Cosine Function
 Sine Function
 Tangent Function
 Translating and Scaling Sine and Cosine Functions

III.3.b: Determine the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle using reference angles.

 Cosine Function
 Sine Function
 Tangent Function

IV: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

IV.1: Apply basic concepts of probability.

IV.1.a: Distinguish between permutations and combinations and identify situations in which each is appropriate.

 Permutations and Combinations

IV.1.b: Calculate probabilities using permutations and combinations to count events.

 Binomial Probabilities
 Permutations and Combinations

IV.1.c: Compute conditional and unconditional probabilities in various ways, including by definitions, the general multiplication rule, and probability trees.

 Binomial Probabilities
 Geometric Probability
 Independent and Dependent Events
 Permutations and Combinations
 Probability Simulations
 Theoretical and Experimental Probability

IV.2: Use percentiles and measures of variability to analyze data.

IV.2.a: Compute different measures of spread, including the range, standard deviation, and interquartile range.

 Describing Data Using Statistics
 Mean, Median, and Mode
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram
 Stem-and-Leaf Plots

IV.2.b: Compare the effectiveness of different measures of spread, including the range, standard deviation, and interquartile range in specific situations.

 Box-and-Whisker Plots

Correlation last revised: 1/20/2017

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