Perimeter

Abstract

This lesson is designed to examine the mathematical concept of perimeter. These activities and discussions may be used to develop students' understanding of this mathematical concept.

Objectives

Upon completion of this lesson, students will:

  • be able to calculate the perimeter of a random shape on a grid.
  • be able to explain the affect that the shape of an object has on its perimeter.

Standards

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

Geometry

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

  • 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;

Measurements

Apply appropriate techniques tools, and formulas to determine measurements

  • select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision;

Key Terms

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

Activities

This lesson introduces students to the mathematical concept of perimeter with a fixed area through the following activity:

Student Prerequisites

  • Arithmetic: Students must be able to:
    • add, count
    • understand the concept of area
  • 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:

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:

    • Ask students to recall information about polygons.

    • You might ask students to consider how they might trace the perimeter of a polygon that is drawn on the board, or you may begin the day by running the perimeter of the school!

    • Ask students if they understand what area is. If they don't understand area give a brief explanation and include area in lesson.

  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 talking more about the perimeter of polygons. We will learn exactly what this term means, and we will learn how to calculate the perimeter of random shapes with fixed areas. We will also learn how the shape of a given area affects its perimeter.

    • We are going to use the computers to learn about perimeter, 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 the Perimeter applet first.

  3. Teacher Input

    You may choose to lead the students in a short discussion about how to find the perimeter for random shapes.

    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 in order to demonstrate this activity to the students.

    • Perimeter is the total length around the object. So imagine the grid lines are equal to one step. And imagine the outside edges of the figure are tight ropes. You want to see how many steps it will take you to get all the way around the edge. The number of steps would be the perimeter.

    • Once we have calculated the perimeter we will put our answer in the text field and click the check answer button.

    • If you choose to, you may pass out the Worksheet to Accompany The "Perimeter" Applet

  4. Guided Practice

    Try another example, letting the students direct your moves. Or, you may simply ask, "Can anyone describe the steps you will take for this assignment?"

    • If your class seems to understand the process for doing this assignment, simply ask, "Can anyone tell me what you will do now?"

    • If your class seems to be having a little trouble with this process, do another example together, but let the students direct your actions:

      • Can someone describe how I would find the perimeter of this shape?

  5. Independent Practice

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

    • Another option for independent practice is to have the students work in pairs (carefully chosen so that both students are of the same ability group). Have them race to find the correct perimeter using the Perimeter applet. Whoever wins gets a point. At the end of the allotted time for the game give the winning member of each pair a reward of some type.

  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 if there is only one available computer:

  • Don't play the game for speed. Have all students pull out a sheet of paper. Have the computer generate a set number of shapes and have them record on their paper the perimeter (you record it as well). When you are done, take up the papers and check them. The person with the most correct answers gets a reward of some type and the rest of the class gets a participation grade. That way everyone tries.

Extensions

This lesson may be followed by: