• 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
       Why imaginary numbers    http://www.youtube.com/watch?v=SocNkRRVSsM
       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

    rational functions and asymptotes:    http://www.khanacademy.org/math/algebra2/polynomial_and_rational/asymptotes-graphing-rational/v/asymptotes-of-rational-functions 

     

    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