Measurement

Presented by C.E. Tanner and M.A.H. Smith
Virginia Air and Space Center
January 23, 1993


Goal:

To provide a positive science experience and introduce students to fundamental concept of measurement.

Objectives:

Understand fundamental concepts of measurement through activities (give in parentheses).

  1. Absolute vs. relative measurement (balance, hygrometer, compare lengths of string)
  2. Accuracy and precision (balance, linear measures)
  3. Standards (body parts as units; metric overview)
  4. Estimating large quantities/distances ("count" rice; Da Vinci odometer)

Take-home project: balance

Materials:

Balance:
plastic ruler with holes (x20)
ten to twenty paper clips (x20)
two 3-5 oz. plastic or paper cups (x20)
10-20 pennies (x20)
5-10 nickels (x20)
masking tape
scissors and/or 1-hole punch
Objects to be weighed (eraser, 1 ft.length of nylon cord, large nail, piece of sponge, seashell, piece of black chalk)
Weight data sheet
"standard" scientific balance
2-5 lab stands with clamps to support balances

Body:
Tape measures (various lengths, metal and cloth)
Yardsticks and other measuring sticks
machinist's rule
calipers
nylon cord (fathom, yard)
handouts about units of measure (4 sheets)
poster board or blackboard to record results
marker(s)

Rice:
10-lb. bag of rice
two large plastic buckets
1/8 cup and 4 cup measures

Misc:
pencils
scissors


MEASUREMENTS LESSON PLAN

(Times were estimated before class was taught.)


  1. Introduction - talk about measurements in students' daily lives and in NASA work (15 min.).

  2. Body parts as units of measurement (20 min.)

  3. Tour of Da Vinci's models (30 min.)

  4. Standards (10 min.)

  5. Measuring weight (30-45 min.)

  6. Estimate large quantities (choose one activity or both if time permits) - problem solving (15 min. max)


STUDENTS BALANCE

Image of Student's balance MATERIALS:

Stand of some kind (for hanging balance)
Ruler with holes
Paper clips to attach pieces
Paper cups
Hole puncher (for cups)
Masking tape (to ad to rulers in order to evenly balance the empty cups)

ACTIVITIES

  1. Students make balance, using masking tape to ensure the empty cups actually balance and to hold the paper clips in place if the rule has slots or large holes.

  2. Students order test objects according to weight, determining only the relative weight.

  3. Students select a "standard" (such as a penny, a nickle, a B-B, or a paper clip) and "weigh" the test objects, recording the weights in their given units (3 pennies +/- a half penny). Precision will vary based on standard.

  4. Students compare their weights with the true standard, using a precision scientific scale.


Image of egyptian measurements

The Egyptians and other ancient peoples
used parts of their bodies
as measurement units.


NAME ______________________________________

BODY PARTS AS UNITS OF MEASUREMENT

INCH Originally was the length of three barley grains placed end to end. Distance from tip of thumb to first knuckle, or from first to second knuckle on index finger.

My INCH = ____________________ INCHES

FOOT Length of foot from longest toe to heel

My FOOT = _____________________ INCHES

YARD Distance from tip of nose to end of thumb with arm outstretched (cloth merchants, King Henry I)

My YARD = _______________________ INCHES

HAND Width of one hand, including the thumb (height of horses)

My HAND = ________________________ INCHES

CUBIT Length from point of bent elbow to middle fingertip (Egyptian pyramids, Noah's ark)

My CUBIT = _______________________ INCHES

BRACCIO Italian for "an arm's length" (Da Vinci's parachute)

My BRACCIO = _______________________INCHES

FATHOM From the Anglo-Saxon word for "embrace," it was the length of rope held between two hands with the arms outstretched. (sailors)

My FATHOM = ________________________ INCHES

PACE Length of a single step. In Roman times one pace was a double step, and our MILE came from the Latin mille passuum, meaning 1000 paces.

My PACE = ___________________________ INCHES


STANDARD INTERNATIONAL (SI or metric) UNITS

METER Defined by the french Republic in 1793 to be 1 ten-millionth of the distance from the Equator to the North Pole, as measured through Paris.
CENTIMETER 1/100 of a meter
MILLIMETER 1/10 of a centimeter
KILOMETER 1000 meters
GRAM Weight of pure water in a cube-shaped container having each side 1 centimeter long.
KILOGRAM 1000 grams (also called KILO)
MILLILITER Volume of pure water in a cube-shaped container having each side 1 centimeter long (also called CUBIC CENTIMETER or CC)
LITER 1000 milliliters

    ENGLISH UNITS       and   METRIC EQUIVALENTS
1 INCH         = about 2-1/2 CENTIMETERS
1 FOOT = 12 INCHES = about 30 CENTIMETERS
1 YARD = 3 FEET = 36 INCHES = about 1 METER
1 HAND = about 4 INCHES = about 10 CENTIMETERS
1 CUBIT = about 1/2 YARD = about 46 CENTIMETERS
1 BRACCIO = 15 to 39 INCHES = about 1/2 to 1 METER
1 FATHOM = 6 FEET = about 2 METERS
1 MILE = 5,280 FEET = about 1-1/2 KILOMETERS
1 OUNCE          = about 28 GRAMS
1 POUND = 16 OUNCES = about 1/2 KILOGRAM
1 TEASPOON          = about 5 MILLILITERS
1 TABLESPOON = 3 TEASPOONS = about 15 MILLILITERS
1 CUP = 16 TABLESPOONS = about 250 MILLILITERS
1 QUART = 4 CUPS = about 1 LITER
1 GALLON = 4 QUARTS = about 4 LITERS


TO LEARN MORE. . .

GOVERNMENT PUBLICATIONS ABOUT MEASUREMENTS

SN003-003-03096-1 (SP 304) large poster
"Modernized Metric System" . . . . . . . . . . . . . . . . . . . . . . . . . $2.50 each

SN003-003-03097-0 (SP 304A) small 2-page color chart
"A Brief History of Measurement". . . . . . . . . . . . . . . . . . . . . . $1.25 each

SN003-003-03090-2 (SP 365) wallet-size plastic ard
"Metric Conversion Chart". . . . . . . . . . . . . . . . . . . . . . . . . .$8.13 per 100

SN003-003-03089-9 (SP 376) small (17 cm) plastic ruler
"Metric Measures Up". . . . . . . . . . . . . . . . . . . . . . . . . . . . $28.00 per 100

ORDER FROM:
Superintendent of Documents
U.S. Government Printing Office (GPO)
Washington, DC 20402

Phone: (202) 783-3238
Fax:     (202) 512-2250

OTHER INFORMATION IS AVAILABLE FROM:

U.S. Department of Commerce
National Institute of Standards and Technology
Publications and Program Inquiries
Room A047, Administration Building
Gaithersburg, MD 20899

Phone: (301) 975-3058
Fax:     (301) 975-2128

Call (301) 957-3585 to make reservations for tours of the NIST facilities in Gaithersburg, conducted on Thursday mornings.


NAME _________________________________

WEIGHT DATA SHEET

My unit of weight is ____________________.

One __________________ weighs _____________ GRAMS.

     OBJECT     WIEGHT IN MY UNITSWEIGHT IN GRAMS
Eraser ______________________________ ______________________________
1 ft. nylon cord ______________________________ ______________________________
Nail ______________________________ ______________________________
Sponge ______________________________ ______________________________
Seashell ______________________________ ______________________________
Black chalk piece ______________________________ ______________________________




Metric Chocolate Chip Cookies 550  mL unsifted flour
5 mL baking soda
5 mL salt
250 mL butter or margarine, softened
175 mL granulated sugar
175 mL firmly packed brown sugar
5 mL vanilla extract
2 eggs
2 168 gram packages semisweet chocolate chips
250 mL chopped nuts
Image of chocolate chip cookies Preheat the oven to 190oC. In small bowl, combine flour, baking soda, and salt; set aside. In large bowl, combine butter, sugar, brown sugar, and vanilla; beat until creamy. Beat in eggs. Gradually add flour mixture; mix well. Stir in chocolate chips and nuts. Using 5 mL measure, drop by rounded measures onto ungreased cookie sheet. Bake 8 to 10 minutes. Makes 100 5 cm cookies.


Liquid and Dry Measure Equivalencies*
Customary Metric

1/4 teaspoon1.25 milliliters
1/2 teaspoon2.5 milliliters
1 teaspoon5 milliliters
1 tablespoon15 milliiters
1 fluid ounce30 milliliters
1/4 cup60 milliliters
1/3 cup80 milliliters
1/2 cup120 milliliters
1 cup240 milliliters
1 pint (2 cups)480 milliliters
1 quart (4 cups, 32 ounces)960 milliliters (0.96 liters)
1 gallon (4 quarts)3.84 liters
1 ounce (by weight)28 grams
1/4 pound (4 ounces)114 grams
1 pount (16 ounces)454 grams
2.2 pounds1 kilogram (1000 grams)
*approximately
Oven Temperature Equivalencies