TITLE: Pick's Theorem
GRADE LEVELS: 6-8
SUBJECTS: Math and Science
LEARNER OUTCOMES: Students will be introduced to a quick and easy way for calculating the area of any polygon on a geoboard using what is called Pick's theorem. Pick's theorem computes the area of any polygon simply buy counting pegs on the geoboard.
DURATION: 45 minute class period
MATERIALS: Geoboards, rubber bands, overhead projector, overhead geoboard, worksheet, calculators and paper and pencil.
TECHNOLOGY TOOLS/COURSEWARE:E-Lab, Geosketchpad, Geometry Blaster, internet web site http://forum.swarthmore.edu/trscavo/geoboards/intro4.html
TEACHERS NOTES:
1. Students have just completed a lesson on finding the area of polygons by counting squares on a geoboard and using formulas to find the area of polygons.
2. The students also learned to surround their polygons by a rectangle and take half the area to find the area of the figure.
3. Students will be constantly monitored to be sure that the rubber bands will only be used to construct polygons.
PROCEDURE:
1. Students will first be introduced to Pick's Theorem. The variables will be discussed and a demonstration will be done to show how to work the formula.
2. Students will then count the boundary pegs and record them in a chart.
3. Next they will count the inside pegs.
4. The teacher will demonstrate how to put the numbers into the formula.
5. Students will make the same polygons from the overhead that they made in the previous lesson.
6. They will then apply Pick's Theorem each of the polygons.
7. Students will be given a opportunity to make a polygon on the overhead and challenge the class.
8. Students will be given a worksheet of geoboards to create a least 10 polygons and apply the theorem.
MODIFICATIONS:Lower level students may work in small groups and be able to use a calculator for all computations.
ENRICHMENT: Students will be given an extra credit project to create a polygon on Geosketchpad or in Geometry Blaster or just on graph paper and apply Pick's theorem.
EVALUATION/ASSESSMENT: Student worksheets will be graded and points for the assignment will be added to their grade.
STATE AND NATIONAL STANDARDS:
WVIGO's- Grade 6-(6.31, 6.32,
6.41, 6.19, 6.72)
Grade 7-(7.34, 7.39, 7.5, 7.15)
Grade 8-(8.35, 8.16, 8.19)
National
Standards
REFERENCES:
Cheryl Reger, Buchkhannon-Upsher
High School
Geoboards
in the Classroom
Powerpoint Presentation on Pick's Theorem
Lesson One: Identifying Polygons
Lesson Two: Geoboard Activities
Lesson Four: Applying Equations: Area Formulas
Lesson
Five: Geoplane Activity
AUTHORS:
Rita Robbins
Bridgeport Middle
School
rerobb@aol.com
Tracy Gould
Bridgeport Middle
School
tgould@access.k12.wv.us
Linda Burns
Bridgeport Middle
School
lburns@access.k12.wv.us
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