Abstract

This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane.

Objectives

Upon completion of this lesson, students will:

• have been introduced to the Cartesian coordinate plane
• understand the four quadrants of the Cartesian coordinate plane
• be able to plot points on the plane
• be able to read coordinates for a point from a graph
• be able to give the ratio of rise over run for slope

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.

Represent and analyze mathematical situations and structures using algebraic symbols.

• 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

Use mathematical models to represent and understamd quantitative relationships

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

Student Prerequisites

• Arithmetic: Students must be able to:
  • perform integer and fractional arithmetic
• Algebraic: Students must be able to:
  • work with very simple linear 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:
  • Coordinates Game Suggestions
  • Maze Game Suggestions

Key Terms

• coordinates

Lesson Outline

These activities can be done individually or in teams of as many as four students. Allow for 1-2 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.

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 about graphing lines on the coordinate plane.
   • We are going to use the computers to do this 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 the number line and the coordinate plane.

4. Guided Practice
   • Practice the students' point plotting skills by having them play the Coordinates! Game The game allows users to figure out and to practice using the coordinate plane for giving the "address" or exact location of particular points.

5. Independent Practice
   • Have the students practice their graphing skills on graph paper using the tables of values they generated in the lessons on Functions and Linear Functions.
   • Have the students test their skills by playing the Maze Game.

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

• Omit one or the other of the computer activities to reduce the amount of time spent.
• Add a discussion about fractional movement on the coordinate plane.
• For students who aren't ready to handle negative numbers yet, replace the Coordinates activity with the positive numbers only alternate versions:
  • Coordinates!
    Coordinates Worksheet
  • Simple Maze Game
    Simple Maze Game Worksheet
• Motivate the next lesson by using Simpleplot to plot the tables of points that the students generated.

Suggested Follow-Up

After these discussions and activities, students will be have learned to plot points on the coordinate plane and to read the coordinates off of a graph. The next lesson Functions and Graphs will introduce students to the graphical representation of functions.