# 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)
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.)
• Discussion of historial origin of common length measurements.
• Activity for students to measure their own inch, foot, yard, etc., and compare results.

3. Tour of Da Vinci's models (30 min.)
• Parachute - relate to "braccio" unit of length
• Odometer - relate to estimation
• Milling machine - relate to concept of precision
• Hygrometer - discuss absolute vs. relative measurements
• Tensile strength tester - using weight measurement to estimate wire strength, relate to NASA structural load tests.

4. Standards (10 min.)
• Review differences in body part measurements
• Discuss need for standards
• Overview of metric system
• Discuss appropriate standards - demonstrate rulers and tape measures that don't agree, show metal machinist's rule and prevision calipers; talk about standard meters kept in Paris and at National Institute of Standards and Technology in the U.S.

5. Measuring weight (30-45 min.)
• Build a simple balance from ruler, paper clips, and paper cups.
• Use balance to compare weights; discuss relative and absolute measurements.
• Students choose a standard unit (penny, nickel, or paper clip), and use their balance to weigh 6 common small objects (eraser, length of cord, nail, sponge, seashell, piece of chalk), and record results on a worksheet.
• Convert weight measurements to grams using weight of their "standard" on a scientific balance; compare weights of same objects and disucss accuracy and precision.

6. Estimate large quantities (choose one activity or both if time permits) - problem solving (15 min. max)
• Length of room (relate to Da Vinci odometer)
• Number of rice grains in a large container (use balances)

## STUDENTS 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 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. Students order test objects according to weight, determining only the relative weight. 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. Students compare their weights with the true standard, using a precision scientific scale.

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

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
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 UNITS WEIGHT IN GRAMS Eraser ______________________________ ______________________________ 1 ft. nylon cord ______________________________ ______________________________ Nail ______________________________ ______________________________ Sponge ______________________________ ______________________________ Seashell ______________________________ ______________________________ Black chalk piece ______________________________ ______________________________

 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 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 teaspoon 1.25 milliliters 1/2 teaspoon 2.5 milliliters 1 teaspoon 5 milliliters 1 tablespoon 15 milliiters 1 fluid ounce 30 milliliters 1/4 cup 60 milliliters 1/3 cup 80 milliliters 1/2 cup 120 milliliters 1 cup 240 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 pounds 1 kilogram (1000 grams)
*approximately
Oven Temperature Equivalencies