Reading Graphs

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

Activities

This lesson introduces students to graphing functions through the following activity:

• Graph Sketcher

Standards

The activities and discussions in this lesson address the following Standards:

• Number sense, number operations and number relationships
• Patterns, relationships and functions
• Algebra

Key Terms

This lesson introduces students to the following terms through the included discussions:

• constants
• constant functions
• origin
• velocity
• concave up

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

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. Lead a discussion on gathering information from graphs.

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

3. Have the students try to build graphs from several situations using graph paper.

4. Have the students try to build formulas from several situations, and then graph them using Graph Sketcher.

Alternate Outlines

This lesson can be rearranged in several ways.

• Omit the discussion on distance, velocity and acceleration.

Extensions

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.