An Introduction To Quadrilaterals

Abstract

This lesson is designed to introduce students to quadrilaterals. Included in this lesson are discussions of parallelograms, rectangles, and trapezoids.

Objectives

Upon completion of this lesson, students will:

• have been introduced to quadrilaterals and their properties.
• have learned the terminology used with quadrilaterals.
• have practiced creating particular quadrilaterals based on specific characteristics of the quadrilaterals.

Standards

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

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

• precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
• understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
• create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship

Use visualization, spatial reasoning, and geometric modeling to solve problems

• draw geometric objects with specified properties, such as side lengths or angle measures

Links to other standards.

Student Prerequisites

• Geometric: Students must be able to:
  • recognize the general shape of a square and a rectangle.
  • recall information about angles (particularly right angles), parallel lines, and possibly the concept of congruency.
• 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 paper
• Copies of supplemental materials for the activities:
  • Worksheet To Accompany "An Introduction to Quadrilaterals"

Key Terms

Lesson Outline

1. Focus and Review

   Remind students of what they 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:

   • Class, you might remember that we learned about triangles before. We learned that triangles are a family of polygons and that there are different types of triangles.

   • Can anyone in here tell me what some of the types of triangles are? [i.e. right triangles, isosceles triangles, scalene triangles, etc.]

   • Just as the three-sided polygon, a triangle, has a family of shapes with names, four-sided polygons have names.

2. Objectives

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

   • Today, class, we will be talking more about the four-sided figures, called quadrilaterals.

   • We are going to use the computers to learn about quadrilaterals, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about this program first.

3. Teacher Input

   You may choose lead the students in a short discussion about quadrilaterals.

   A series of discussions will introduce students to the different types of quadrilaterals:

   • Parallelograms
   • Rectangles
   • Trapezoids

   Explain to the students how to do the assignment. You should model or demonstrate it for the students, especially if they are not familiar with how to use our computer applets.

   • Open your browser to Floor Tiles in order to demonstrate this activity to the students.

   • Explain that the quadrilateral on the screen will always remain as a quadrilateral, even though you move the sides and corners.

   • Show the students that they may access information about the sides and angles by using the Information button.

   • Pass out the Worksheet to Accompany "An Introduction To Quadrilaterals."

4. Guided Practice

   Try an example with your students, letting the students direct your moves.

   • Ask the students to help you create a trapezoid from the square on the screen. As they direct your moves, have them specify which characteristic of the trapezoid they are attempting to create.

   • When the class is satisfied with the trapezoid that has been created, show them how to gain information about the quadrilateral from the Information button.

   • Allow the students to comment on how they think the information shows that the quadrilateral is a trapezoid. Students should recognize that it is necessary to show that two of the lines in the quadrilateral are parallel. This can be done several ways:
     • Remind students to consider what they know about parallel lines. If the lines are parallel, and one of the other sides acts as a transversal, students can identify angles that should be congruent.
       

       Remind them that angles 1 and 3 are congruent (since alternate interior angles are congruent), and angles 1 and 2 are supplementary (since the two angles form a linear pair), therefore angles 2 and 3 should be supplementary, if the lines are parallel.

     • If your students are not familar with the properties of parallel lines, they may prove that the lines are parallel by calculating the slope of the lines they suspect are parallel. The Information button contains the coordinates of each vertex. Students may use these coordinates to find the slope of the appropriate lines.

5. Independent Practice
   • Allow students to work on their own and to complete the worksheet, should you choose to provide it. Monitor the room for questions and to be sure that the students are on the correct web site.

   • Another option: Let students form several groups. Each group should design a different quadrilateral and prove that its creation fits the desired characteristics of the specified quadrilateral. The groups could then show the class what they created and how they showed that the desired characteristics were present.

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. Especially emphasize the importance of knowing the characteristics of the different types of quadrilaterals.

Alternate Outlines

This lesson can be rearranged in several ways if there is only one available computer:

• Groups of students may take turns creating a quadrilateral and proving that it has the characteristics necessary to define that shape.
  • Assign each group a different quadrilateral. Let the groups take turns using the computer to create the quadrilateral and take note of the information.

  • When each group has finished, allow the groups an opportunity to teach the class what they found and how they proved that the necessary characteristics were present.

• The class may work together as a whole to create the quadrilaterals suggested on the worksheet.
  • Students may direct the instructor's movements and suggest calculations that need to be done before the class.

  • OR Students may take turns using the demonstration computer to modify the quadrilateral. The whole class can make the necessary calculations and then check them with a partner.

Suggested Follow-up

• Length, Perimeter, and Area: Introduces students to finding the length, perimeter, and area or two dimensional figures.

• Surface Area and Volume: A lesson that introduces students to determining the surface area and volume of three dimensional figures.