# Activities

• • • ##### Subject Area

• Math: Geometry: Quadrilaterals and Polygons

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 9 from the EXPLORATIONS Book:
Shaping Middle Grades Mathematics: Activities for Geoboard and the TI-73

## 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