Advanced Functions and Modeling
Lesson Resources by Topic

Advanced Functions and Modeling provides students an in-depth study of modeling and applying functions. Home, work, recreation, consumer issues, public policy, and scientific investigations are just a few of the areas from which applications should originate. Appropriate technology, from manipulatives to calculators and application software, should be used regularly for instruction and assessment.

These AFM lessons originate from a variety of sources. If the lesson was created by NCSSM faculty, “NCSSM” will appear in the link. The lessons developed by NCSSM faculty members include a student handout and teacher notes, complete with solutions. Other lessons were created by NCSSM faculty for the Algebra 2 website and others are lessons from external sources such as the Shodor Foundation website or Hands On Activities from Georgetown University. Materials from websites other than NCSSM will not necessarily have the same format but may be very useful in teaching the AFM course.

 1.  Technology Resources  6.  Exponential Functions 11.  Other Functions
 2.  Modeling Activities  7.  Piecewise Functions 12.  Parametric Equations
 3.  Linear Functions  8.  Power Functions 13.  Univariate Data
 4.  Quadratic Functions  9.  Trigonometric Functions 14.  Probability
 5.  Polynomial Functions 10.  Logarithmic Functions 15.  Recursion

  1. Technology Resources
    1. Data Flyer
    2. Function Flyer
    3. Function Transfromations Student Handout (NCSSM)

  2. Modeling Activities
    1. Each year there is a mathematical modeling competition held for high school students. Information about the contest and problems done in the past years are available at The Mathematical Contest in Modeling.
    2. The Hands On Math project presents a number of applications of high school mathematics to real world settings. Each problem has both a student handout and teacher notes. Information and problems are available at Download Modules.
    3. Reading Graphs
    4. The Midge Problem (NCSSM)

  3. Linear Functions (includes data analysis)
    1. Linear Inequalities with a Parallelogram (NCSSM)
    2. Linear Programming (NCSSM)
    3. Guess the Age (NCSSM)
    4. Introduction to Linear Data Analysis (NCSSM)
    5. Price of Apples (NCSSM)
    6. Hurricane Fran (NCSSM)
    7. Modeling Orbital Debris
    8. Understanding the Least Squares Regression Line with a Visual Model

  4. Quadratic Functions (includes data analysis)
    1. Pig Problem: Writing and Solving Quadratic Equations
    2. Football and Braking Distance: Model Data with Quadratic Functions (NCSSM)
    3. Collecting and Fitting Quadratic Data with the CBL (NCSSM)
    4. Modeling Orbital Debris

  5. Polynomial Functions
    1. Polynomials as Models (NCSSM)
    2. The Box Problem (NCSSM)

  6. Exponential Functions
    1. Caffeine in Your Body
    2. Half-life and Doubling Time (NCSSM)
    3. Purchasing a New Car (NCSSM)
    4. Calculate When the Oil Industry Will Dry Up
    5. Hurricane Fran (NCSSM)
    6. Graphing Exponential Functions and e (NCSSM)
    7. Voltage Problem (NCSSM)
    8. Modeling Orbital Debris
    9. Modeling the Price of a Subway Token in New York City (NCSSM)

  7. Piecewise Functions
    1. Piecewise Defined Functions as Models (NCSSM)
    2. New Jersey Turnpike (NCSSM)

  8. Power Functions
    1. Equations with Radical Expressions (NCSSM)
    2. Data Gathering (NCSSM)

  9. Trigonometric Functions
    1. Modeling the Motion of a Swing (NCSSM)
    2. Modeling with the Sine Function
    3. Trigonometry Drills
    4. Ferris Wheel Applet
    5. Modeling the Behavior of an Oscillating Spring (NCSSM)

  10. Logarithmic Functions
    1. Radio Dial (NCSSM)

  11. Other Functions
    1. Applications of Rational Functions (NCSSM)

  12. Parametric Equations
    1. Ring Toss (NCSSM)
    2. Parametric Equations (NCSSM)
    3. Modeling the Motion of a Swing (NCSSM)

  13. Univariate Data
    1. Determine the Best of Three Baseball Players (NCSSM)
    2. Comparing Temperature Data at Raleigh Durham Airport (NCSSM)
    3. How Typical or Atypical is Your Community
    4. Stadium Consultants
    5. Technology for Graphs of Univariate Data
      1. Bar Graph
      2. Stem and Leaf Plotter
      3. Histogram
      4. Pie Chart
      5. The Normal Distribution
      6. Plot It!

  14. Probability
    1. Probability and Sports
    2. Ideas that Lead to Probability
    3. Introduction to the Concept of Probability
    4. Probability and Geometry
    5. Conditional Probability and Probability of Simultaneous Events
    6. Expected Value
    7. Study of Malaria and Sickle Cell Anemia

  15. Recursion
    1. An Introduction to Arithmetic and Geometric Sequences
    2. Pass The Candy Activity (NCSSM)
    3. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
    4. Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body
    5. Lesson 1: Introduction to Recursion (NCSSM)
    6. Lesson 2: Applications of Recursion (NCSSM)

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