Objective:
Students will compute the area of squares, rectangles, parallelograms, and triangles using the appropriate formula, and express the results with a decimal in nonstandard units of length. Students will draw and compute the acreage of the survey conducted at the park.

Purpose:
The purpose of this activity is for students to be able to compute area while realizing the practical applications of the formulas.

Materials:
Student workbook | Teacher Guide, pencil, calculator.

Procedure:
1. Explain the formula for computing the area of squares, rectangles, and parallelograms. Explain to the students that in Colonial Virginia, a survey was conducted to make sure the landowner would have the correct number of acres. Review the section Background Information with the students. The answers may be rounded according to your instructions.

2. Ask the students:
Why did George Washington and all the surveyors use the Gunters Chain to measure land? THE REASON IS THAT ONE SQUARE GUNTERS CHAIN EQUAL 1/10TH OF AN ACRE. The Gunters Chain was the easiest method for measuring the vast wilderness frontier and converting the survey into acres. Review the “Surveying in Colonial Virginia” section with the students. Use the “Land Measurements for Surveyors” section to make sure the students understand why a Gunters Chain was used. The students need to become familiar with the units of measure in this section to work the exercises.

Since most of the surveys were not perfect squares or rectangles, the surveyor would draw the survey and break the land survey into squares, rectangles, and parallelograms to compute the acres. Use the example in the student workbook to demonstrate the multiplication and division required for links, chains and acres.
Emphasize that the units for measuring land in colonial times were acres, chains, and links.
AREA = BASE X HEIGHT

Have the students read Math for Land Surveyors.

Math for Land Surveyors

George Washington wrote these “Geometrical Definitions” when he was your age. The exercises are included in his homework notebooks at the Library of Congress. You are studying the same math concepts as George Washington. Note the different terms such as rhomboides for a parallelogram.

Courtesy of the Library of Congress, Manuscript Division.

“Geometrical Definitions” Transcription

9th. A Segment of a Circle is a Figure contained under a right line, and a Part of the Circumference, greater or less than a Semicircle as the Figure ABC, also ADC.

10th. All three sided figures are called Triangles: as the Triangles A, B, and C

11th. Of Four sided figures a quadrant or Square is that whose Sides are equal, and its angle right as the figure A.

12th. A long Square is that which hath right Angles but unequal Sides as the Figure B.

13th. A Rhombus is a Figure Quadrangular having equal sides but not equal or right angles as the Figure C.

14th. A Rhomboides is a Figure whose opposite Sides are equal and whose opposite Angles are also equal: but it hath neither equal sides, nor right Angles as the Figure D.

15th. All Other Figures of Four Sides are called Trapezoids as L and M.

3. Students are to work Lessons One, Two, and Three in class. The answers are carried out in decimal, but can be rounded per the teacher’s instruction.

4. Explain the formula for computing area of a triangle. Point out again that in Colonial Virginia, a survey was conducted to make sure the landowner would have the correct number of acres. The surveyor could break the survey into triangles to compute the acres. Use the example in the student workbook to demonstrate the multiplication and division required.

Emphasize that the units for measuring land in colonial times were acres, chains, and links.
AREA OF A TRIANGLE = ½ BASE X HEIGHT

5. Students are to work Lesson Four in class.

6. Students will locate Washington’s Birthplace by latitude and longitude in class using a map (teacher provides). The readings will be compared with the Global Positioning System unit’s reading at the park.

7. The students visit George Washington Birthplace National Monument.

Land Measurements for Surveyors

Why did George Washington and all the surveyors use the Gunters Chain to measure land?
THE REASON IS ONE SQUARE GUNTERS CHAIN EQUAL 1/10TH OF AN ACRE. TEN SQUARE GUNTERS CHAINS EQUAL 1 ACRE—THIS IS NOT A PERFECT BLOCK OR SQUARE BUT 10 SMALLER SQUARES.

The Gunters Chain was the easiest method for measuring the vast wilderness frontier and converting the survey into acres.

LINEAR

• 1 LINK = 7.92 INCHES
• 25 LINKS = 1 POLE OR 16.5 FEET
• 100 LINKS = 1 CHAIN OR 66 FEET OR 4 POLES
• 10 CHAINS = 660 FEET OR 40 POLES
• 80 CHAINS = 1 MILE

SQUARE

• 1/10TH ACRE = 1 SQUARE GUNTERS CHAIN

• ACRE = 10 X (1 SQUARE GUNTERS CHAIN)

• ACRE = 10 X (1 GUNTERS CHAIN X 1 GUNTERS CHAIN)

• ACRE = 10 X (100 LINKS X 100 LINKS) = 100,000 SQ LINKS

• ACRE = 10 X (66 FEET X 66 FEET) = 43,560 SQ FEET

• 1 Sq Chain = 10,000 links Number of Links = Sq Chains
10,000

• 1 Acre = 100,000 links Number of Links = Acres
100,000