Education Technology

Walking the Fence Line

Published on 06/09/2008

Activity Overview

In this activity, students use the Geoboard to determine the perimeter of polygons. They learn to picture square roots visually as the side length of a square.

Before the Activity

  • Start the Geoboard App and format it
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 65 - 72 from the attached PDF file for your class
  • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Construct a decagon whose sides are vertical or horizontal and find its perimeter by counting the number of unit line segments
  • Use the calculator to find the perimeter of the decagon and check the answer
  • Note it is easy to count units when the sides are vertical and horizontal lines, however diagonal lines, are not easy to measure as they are sometimes irrational numbers and must be estimated


  • Construct a diagonal segment
  • Build a square with the diagonal as a side and find its area by counting squares and half-squares, by using a surrounding rectangle, or dissection methods
  • Note that the exact length of the side of the square is the square root of the area of the square
  • Use the calculator to measure the length of the diagonal
  • Observe that this is an approximation as the length of this side squared does not give the exact area


  • For each given line segment, find the exact length by building squares and the approximate length by using the Geoboard application


  • Find different ways in which a rectangle can be divided to form three shapes that are equal in area
  • After the Activity

    Students complete the Activity sheet and answer questions.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary