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	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

Activity Downloads:

(file types)

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

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