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