Lines, Rays, Line Segments, and Planes

Abstract

This lesson is designed to introduce students to lines, rays, line segments and planes.

Objectives

Upon completion of this lesson, students will:

• have been introduced to lines, rays, line segments and planes
• have learned the differences between lines, rays, line segments and planes
• have practiced graphing lines, rays, line segments and planes

Standards

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

Geometry

specify locations and describe spatial relationships using coordinate geometry and other representational systems

• use coordinate geometry to represent and examine the properties of geometric shapes;

Student Prerequisites

• Arithmetic: Students must be able to:
  • draw and understand the coordinate plane
  • graph a line
• 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 (optional for this lesson)
• Pencil and paper
• Ruler
• Copies of supplemental materials for the activities:
  • Graph paper

Key Terms

• coordinate plane
• line
• ray
• line segment
• infinity

Lesson Outline

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:

   • Begin drawing a number line on the board, and ask the students if they know what you are making.

   • Draw a vertical line through the zero point of your number line, as if you were going to turn it into a coordinate plane.

2. Objectives

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

   • Today, class, we will be learning about lines, rays and the coordinate plane.

3. Teacher Input

   The discussion presents an outline to use for explaining to students the key words of the lesson.

   • Draw several lines, rays, line segments and planes that have characteristics in common. Write a function on the board, and show students how to graph it. Then make a ray and line segment that correspond to the given line.

   • Proceed by graphing a second line on the same sheet of graph paper. Again, draw a corresponding ray and line segment. Now that you have two lines on the page you can construct the corresponding plane.

   • After modeling how to draw similar lines, rays, line segments and planes, discuss with students how the figures are similar to each other.

   • Next, repeat the exercise, this time drawing non-corresponding lines, rays, line segments and planes.

   • After modeling how to draw non-similar lines, rays, line segments and planes, discuss how the figures are different from each other.

4. Guided Practice

   Pass out 4 sheets of graph paper to each student (or use 2 double-sided sheets).

   Try another function, this time letting the students direct your moves as you graph it and draw some similar, and then non-similar, lines. Ask the students to follow you by doing the exercise with you on their graph paper.

   • After students graph the function you give them, instruct them to make a ray and line segment that correspond to the given line.

   • Proceed by giving them a second line to graph on the same sheet of graph paper. Then have them construct the corresponding ray and line segment. Now that you have two lines on the page you can construct the corresponding plane.

   • After they practice drawing similar lines, rays, line segments and planes, have them discuss how the figures they drew on their papers are similar to each other.

   • Next, have them repeat the exercise, this time drawing non-corresponding lines, rays, line segments and planes.

   • After they practice drawing non-similar lines, rays, line segments and planes, have them discuss how the figures they drew on their papers are different from each other.

5. Independent Practice
   • Allow the students to work on their own or in groups of 2 - 4. Give them several other functions to work with to complete the exercise above, this time working independently or in groups. Monitor the room for questions and to be sure that the students are focused on the assignment.

6. Closure

   You may wish to bring the class back together and have each group show their results. 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 if there is only one available computer:

• As this is an introductory lesson, students do not need to use computers. However, if there is time, groups of students could read the discussion before beginning the line drawing activity. This would give more time during one class period for students to complete the hands-on part of the lesson.

Extensions