• Math III Topics

Unit 1:  Modeling with Statistical Studies

• Summarize, represent and interpret data on a single count or measurement variable
• Understand and evaluate random processes underlying statistical experiments
• Make inferences and justify conclusions from sample surveys, experiments, and observational studies
• Use probability to evaluate outcomes of decisions (honors only)

Unit 1 video on Sampling Methods  http://www.youtube.com/watch?v=be9e-Q-jC-0

Unit 2:  Modeling Algebraic Competency
• Use properties of rational and irrational numbers
• Interpret the structure of expressions
• Perform arithmetic operations on polynomials
• Use polynomial identities to solve problems
• Rewrite rational expressions
• Build a function that models a relationship between two quantities

Unit 3:  Modeling with Quadratic Functions & the Complex Number System

• Perform arithmetic operations with complex numbers
• Use complex numbers in polynomial identities and equations
• Write expressions in equivalent forms to solve problems
• Understand solving equations as a process of reasoning and explain the reasoning
• Solve equations and inequalities in one variable
• Represent and solve equations and inequalities graphically
• Create equations that describe numbers or relationships
• Understand the concept of a function and use function notation
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations
• Build new functions from existing functions
• Translate between the geometric description and the equation for a conic section
Imaginary numbers love story video http://www.youtube.com/watch?v=36Sd9VhAojg&feature=youtu.be

Unit 4:  Modeling with Polynomial & Rational Functions & Equations

• Understand the relationship between zeros and factors of polynomials
• Create equations that describe numbers or relationships
• Understand solving equations as a process of reasoning and explain the reasoning
• Represent and solve equations and inequalities graphically
• Understand the concept of a function and use function notation
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations

Unit 5:  Modeling with Exponential & Logarithmic Functions

• Interpret the structure of expressions
• Create equations that describe numbers or relationships
• Understand solving equations as a process of reasoning and explain the reasoning
• Represent and solve equations and inequalities graphically
• Understand the concept of a function and use function notation
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations
• Build a function that models a relationship between two quantities
• Build new functions from existing functions
• Build a function that models a relationship between two quantities
• Construct and compare linear, quadratic and exponential models and solve problems

Unit 6:  More Modeling with Functions

• Write expressions in equivalent forms to solve problems
• Create equations that describe numbers or relationships
• Understand solving equations as a process of reasoning and explain the reasoning
• Represent and solve equations and inequalities graphically
• Understand the concept of a function and use function notation
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations
• Build a function that models a relationship between two quantities
• Build new functions from existing functions
• Build a function that models a relationship between two quantities

Unit 7:  Modeling with Geometric Relationships

• Experiment with transformations in the plane
• Prove geometric theorems
• Make geometric constructions
• Understand similarity in terms of similarity transformations
• Prove theorems involving similarity

Unit 8:  Modeling with Trigonometric Functions
• Create equations that describe numbers or relationships
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations
• Extend the domain of trigonometric functions using the unit circle
• Model periodic phenomena with trigonometric functions
• Prove and apply trigonometric identities
• Experiment with transformations in the plane
• Understand and apply theorems about circles
• Find arc lengths and areas of sectors of circles
• Translate between the geometric description and the equation for a conic section
• Apply geometric concepts in modeling situations
Link to Graph to discover transformations:  http://www.desmos.com/calculator/qcgfy9mohq
Transformation Handout for use with Desmos site  function transformation handout
Trig data:  Trig Data to Model