Abstract

This lesson is designed to introduce students to graphing functions and to reading simple functions from graphs. Many of the examples are motivated by a situation described by the graph.

Objectives

Upon completion of this lesson, students will:

• have practiced plotting functions on the Cartesian coordinate plane
• seen several categories of functions, including lines and parabolas
• be able to read a graph, answering questions about the situation described by the graph

Standards

The activities and discussions in this lesson address the following NCTM standards:

Algebra

Understand patterns, relationships and functions

• represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
• relate and compare different forms of representation for a relationship;
• identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.

• develop an initial conceptual understanding of different uses of variables;
• explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
• use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;
• recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

• model and solve contextualized problems using various representations, such as graphs, tables, and equations

• use graphs to analyze the nature of changes in quantities in linear relationships.

Measurements

Apply appropriate techniques, tools and formulas to determine measurements

• solve simple problems involving rates and derived measurements for such attributes as velocity and density.

Student Prerequisites

• Arithmetic: Students must be able to:
  • perform integer and fractional arithmetic
  • plot points on the Cartesian coordinate system
  • read the coordinates of a point from a graph
• Algebraic: Students must be able to:
  • work with very simple algebraic expressions
• Technological Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• Access to a browser
• pencil and graph paper
• Copies of supplemental materials for the activities:
  • Information into Graphs Problems
  • Information into Formulas and Graphs Problems

Key Terms

constant function constants concave up coordinate coordinate plane

function graph origin velocity

Lesson Outline

This lesson assumes that the students are familiar with information from the Graphs and Functions lesson.

These activities can be done individually or in teams of as many as four students. Teams work best for the story-telling activities. Allow for 2-3 hours of class time for the entire lesson if all portions are done in class.

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   Can anyone give me an example of a function? Can anyone give me an example of an everyday situation that a function can be applied to?

2. Objectives

   Let the students know what it is they will be doing and learning today. Say something like this:

   • Today, class, we are going to learn more about functions.
   • We are going to use the computers to learn more about functions, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

3. Teacher Input

   • Lead a discussion on gathering information from graphs.
   • Lead a discussion on making new graphs from old ones: graphs involving distance, velocity, and acceleration.

4. Guided Practice

   • Have the students try to build graphs from several situationsusing graph paper.

5. Independent Practice
   • Have the students try to build formulas from several situations, and then graph them using Graph Sketcher.
6. Closure

   • You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outlines

This lesson can be rearranged in several ways.

• Omit the discussion on distance, velocity and acceleration.

Suggested Follow-Up

After these discussions and activities, students will have more experience with functions and relationship between the English description, graphical and algebraic representations. The next lesson, Impossible Graphs, shows the students that not all graphs make sense in certain situations.