Education Technology

Pick and Choose! Using Pick's Theorem!

Activity Overview

In this activity, students use Pick's Theorem to find the area of a variety of geoboard shapes.

Before the Activity

  • Start the Geoboard App and format it
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 95 - 107 from the attached PDF file for your class
  • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Draw a polygon on the Geoboard
  • Determine the number of boundary points and the number of interior points and calculate its area
  • Repeat with different polygons
  • Draw polygons without any interior points and find the area
  • Draw polygons with one interior point and find the area
  • Draw polygons with two interior points and find the area
  • Prepare a table with number of boundary points, number of interior points, and area
  • Discover that the relationship between b the number of boundary points, i the number of internal points, and the area of the geoboard polygon is given by Pick's formula A = (b - 2) / 2 + i
  • Use Pick's theorem to calculate areas of other polygons
  • Find areas of lakes and land regions by using a scaled map on grid paper and Pick's formula
  • 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