Functions

This module builds an intuitive understanding of functions. Students develop mathematical models for real-world situations using functions. The activities require students to collect data, make predictions, analyze data, discuss findings, and write explanations. A primary goal of the module is to engage all students in learning the material through viewing, reading, thinking, discussing, computing, interpreting, writing, and reflecting. This enables students to construct their own knowledge of functions as they work through the activities. Lesson 1 What is a Function? Students develop an intuitive understanding of function using mapping and are introduced to the vocabulary used with functions. Lesson 2 Four Representations of a Function Students use the rule of four to describe functions and to determine whether the relationship given is a function. Lesson 3 Function Notation This lesson introduces students to function notation and provides many different situations in which to use and understand the notation. Lesson 4 Families of Functions Students develop of library of functions that will be used to model situations throughout the rest of the module. Lesson 5 Modeling Data with Functions In this lesson, students will graph a set of data and determine if there is a function that models the data. This function will be used to predict future behavior. Lesson 6 Stopping Distance Students explore the stopping distance of an automobile, analyze the data using successive differences, and make a prediction based on the data. This lesson sets up the context for Lesson 10 and inverse functions. Lesson 7 The Allegory of the Cave Students set up an experiment and collect data and model the data using functions. The model is used to make predictions and to strengthen students understanding of function notation. Lesson 8 Transformations of Functions. In this lesson, students will analyze weather data and learn how to represent the transformation of this data either vertically or horizontally using function notation. Lesson 9 More Transformations of Functions This lesson continues the study of transformations of functions using weather data to aid in making the connection to the function notation for transformations of functions. Lesson 10 Functions at the Scene of an Accident The concept of inverse functions is motivated by extending Lesson 6: Stopping Distance. Lesson 11 Inverse Functions This lesson presents inverse functions in a more formal sense than Lesson 10. Students are given a function and asked to determine its inverse. Compare this module to traditional course topics in the Matrix of Course Competencies. If one of the lessons has a link, you can preview that lesson. Other modules: Beat Ratios Functions Exp. Growth Data & Graphs Representing Data Finance Geometry Sampling Non-linear Behavior Linear Behavior Sets and Logic Patterns Probability Systems Right Tri. Trig.