Table of Contents
Teaching and Learning The Metric System Unit 1 1 - Suggested Teaching Sequence 1 - Objectives 1 - Rules of Notation 1 - Metric Units, Symbols, and Referents 2 - Metric Prefixes 2 - Linear Measurement Activities 3 - Area Measurement Activities 5 - Volume Measurement Activities 7 - Mass (Weight) Measurement Activities 9 - Temperature Measurement Activities 11 Unit 2 12 - Objectives 12 - Suggested Teaching Sequence 12 - Metrics in this Occupation 12 - Metric Units For Aviation Electronics 13 - Trying Out Metric Units 14 - Flying With Metrics 15 Unit 3 16 - Objective 16 - Suggested Teaching Sequence 16 - Metric-Metric Equivalents 16 - Changing Units at Work 18 Unit 4 19 - Objective 19 - Suggested Teaching Sequence 19 - Selecting and Using Metric Instruments, Tools and Devices 19 - Which Tools for the Job? 20 - Measuring Up In Aviation Electronics 20 Unit 5 21 - Objective 21 - Suggested Teaching Sequence 21 - Metric-Customary Equivalents 21 - Conversion Table 22 - Any Way You Want It 23 Testing Metric Abilities 24 Answers to Exercises and Test 25 Tools and Devices List References
1
UNIT OBJECTIVES The student will demonstrate these skills for the Linear, Area, Volume or Capacity, Mass, and 1 Temperature Exercises, using the metric terms and measurement devices listed here.
SUGGESTED TEACHING SEQUENCE EXERCISES
SKILLS Linear Area Volume or Capacity Mass Temperature 1. These introductory exercises may require (pp. 9. 10) two or three teaching periods for all five (pp. 3 ·4) (pp. 5. 6) (pp. 7 ·8) (p.ll) areas of measurement. 1. Recognize and use the millimetre (mm) square cubic centi· gram (g) degree Celsius 2. Exercises should be followed in the order unit and its symbol for: centimetre metre (cm3 ) (C) centimetre (em) (cm2 ) kilogram (kg) given to best show the relationship 2. Select, use, and read the cubic metre between length, area, and volume. appropriate measuring metre (m) square (m3) instruments for: metre 3. Assemble the metric measuring devices (m2) litre (I) (rules, tapes, scales, thermometers, and 3. State or show a physical reference for: millilitre (ml) measuring containers) and objects to be measured.* 4. Estimate within 25% height, width, or the area of capacity of the mass of objects the temperature of 4. Set up the equipment at work stations of the actual measure length of objects a given surface containers in grams and kilo· the air or a liquid for use by the whole class or as individu grams alized resource activities. 5. Read correctly metre stick. metric measurements a kilogram scale A Celsius thermometer tape measure, and on graduated and a gram scale 5. Have the students estimate, measure, and metric rulers volume measur· record using Exercises 1 through 5. ing devices 6. Present information on notation and make Table 1 available. 7. Follow up with group discussion of RULES OF NOTATION activities. 1. Symbols are not capitalized unless the unit is a proper name (mmnot MM). 2. Symbols are not followed by periods (m not m.). 3. Symbols are not followed by an s for plurals (25 g not 25 gs). 4. A space separates the numerals from the unit symbols ( 4 1 not 41). *Other school departments may have devices which 5. Spaces, not commas, are used to separate large numbers into groups of three can be used. Metric suppliers are listed in the reference digits ( 45 271 km not 45,271 km). section. 6. A zero precedes the decimal point if the number is less than one (0.52 g not .52 g). 7. Litre and metre can be spelled either with an -re or -er ending.
Information Sheet 1 2
METRIC UNITS, SYMBOlS, AND REFERENTS METRIC PREFIXES
Quantity Metric Unit Symbol Useful Referents Multiples and Submultiples Prefixes Symbols Length millimetre mm Thickness of dime or paper 1 000 000 = 106 mega (meg'a) M clip wire 3 kilo centimetre em Width of paper clip 1 000 = 10 (k~Uo) k metre m Height of door about 2 m 100 = 102 hecto (hek'to) h kilometre km 12-minute walking distance 10 = 101 deka (dek'a) da Area square Area of this space Base Unit 1 = 10° centimetre cm2 0.1 = 10-l deci ( deS'i) d D 2 0.01 = 10- centi (sen'ti) c 3 square metre m2 Area of card table top 0.001 = 10- milli ( nril'i) m 6 hectare ha Football field including sidelines 0.000 001 = 10- micro (nii'kro) J.1 and end zones
Volume and millilitre ml Teaspoon is 5 ml Capacity litre 1 A little more than 1 quart Table 1-b cubic centimetre cm3 Volume of this container [])
cubic metre m3 A little more than a cubic yard
Mass milligram mg Apple seed about 10 mg, grain of salt, 1 mg gram g Nickel about 5 g kilogram kg Webster's Collegiate Dictionary metric ton ( 1 ooo kilonams) t Volkswagen Beetle
Table 1-a 3 LINEAR MEASUREMENT ACTIVITIES 3. Choose a partner to stand at your side. Move apart Metre, Centimetre, Millimetre so that you can put one end of a metre stick on your partner's shoulder and the other end on I. THE :METRE (m) your shoulder. Look at the space between you. A. DEVELOP A FEELING FOR THE SIZE OF A METRE 1. Pick up one of the metre THAT IS THE WIDTH OF A METRE! sticks and stand it up on the floor. Hold it in place with one hand. Walk around the B. DEVELOP YOUR ABILITY TO ESTIMATE IN I'viETRES stick. Now stand next to the stick. With your other Now you will improve your ability to estimate in metres. hand, touch yourself where Remember where the length and height of a metre was on your the top of the metre stick body. comes on you. For each of the following items:
Estimate the size of the items and write your estimate in the THAT IS HOW HIGH A METRE IS! ESTIMATE column. Measure the size with your metre stick and write the answer in the MEASUREMENT column.
Decide how close your estimate was to the actual measure. If 2. Hold one arm out straight your estimate was within 25% of the actual measure you are a at shoulder height. Put "Metric Marvel." the metre stick along this arm until the end hits the How Close end of your fingers. Where Estimate Measurement Were You? is the other end of the (m) (m) metre stick? Touch your 1. Height of door knob self at that end. from floor. 2. Height of door. 3. Length of table. THAT IS HOW LONG A l\IETRE IS! 4. Width of table. 5. Length of wall of this room. 6. Distance from you to wall. a::3CENTER "'" VOCAT>ONAL 'OUCATION Exercise 1 (continued on next page) 4
IT. THE CENTIMETRE (em) III. THE 1\fiLLIMETRE (mm)
There are 100 cpntimetres in onP metre. If there arP 4 mPtrPs and There are 10 millimetres in one centimetrP. Wlwn a measurement is 3 centimetres, you write 403 em [ ( 4 x 100 em) + 3 em = 400 em 2 centimetres and 5 millimetres, you write 25 mm [(2 x 10 mm) + 3 em]. + 5 mm = 20 mm + 5 mm]. There are 1 000 mm in 1m.
A. DEVELOP A FEELING FOR THE SIZE OF A CENTIMETRE A. DEVELOP A FEELING FOR THE SIZE OF A l'v1ILLIMETRE
1. Hold the metric ruler against the width of your thumbnail. Using a ruler marked in millimetres, measure: How wide is it? em 1. Thickness of a paper clip wire. mm 2. :Measure your thumb from the first joint to the end. 2. Thickness of your fingernaiL mm em 3. Width of your fingernail. ____ mm 3. Use the metric ruler to find the width of your palm. em 4. Diameter (width)of a coin. ____ mm 4. :Measure your index or pointing finger. How long is it? 5. Diameter (thickness) of your pencil. ____ mm em 6. Width of a postage stamp. mm 5. Measure your wrist with a tape measure. What is the distance around it? em
6. Use the tape measure to find your waist size. ____ em B. DEVELOP YOUR ABILITY TO ESTil\1ATE IN l'viTLLIMETRES
B. DEVELOP YOUR ABILITY TO ESTIMATE IN CENTIMETRES You are now ready to estimate in millimetres. For each of the following items, follow the procedures used for estimating in You are now ready to estimate m centimetres. .r or each of the metres. following items, follow the procedures used for estimating in How Close metres. Estimate Measurement Were You? How Close (mm) (mm) Estimate Measurement Were You? 1. Thickness of a (em) (em) nickel. 1. Length of a paper 2. Diameter (thickness) clip. of a bolt. 2. Diameter (width) 3. Length of a bolt. of a coin. 4. Width of a sheet 3. Width of a postage stamp. --- of paper. 4. Length of a 5. Thickness of a board pencil. or desk top. 5. Width of a sheet 6. Thickness of a of paper. button. 5
AREA MEASUREMENT ACTIVITIES B. DEVELOP YOUR ABILITY TO ESTIMATE IN SQUARE Square Centimetre, Square Metre CENTil\1ETRES You are now ready to develop your ability to estimate in square centimetres. \VHEN YOU DESCRIBE THE AREA OF SOl\1ETHING, YOU ARE SAYING HOW MANY SQUARES OF A GIVEN SIZE ITTAKES TO Remember the size of a square centimetre. For each of the COVER THE SURFACE. following items, follow the procedures used for estimating in metres. 2 I. THE SQUARE CENTil\1ETRE ( cm ) How Close Estimate Were You? 2 A. DEVELOP A FEELING FOR A SQUARE CENTil\1ETRE (cm )
1. Take a clear plastic grid, or use the grid on page 6. 1. Index card. 2. Measure the length and width of one of these small 2. Book cover. squares with a centimetre ruler. 3. Photograph.
THAT IS ONE SQUARE CENTil\1ETRE! 4. Window pane or desk top. 3. Place your fingernail over the grid. About how many squares does it take to cover your fingernail? ___cm 2 2 II. THE SQUARE METRE (m ) 4. Place a coin over the grid. About how many squares 2 does it take to cover the coin? cm A. DEVELOP A FEELING FOR A SQUARE METRE 5. Place a postage stamp over the grid. About how many squares does it take to cover the postage stamp? 1. Tape four metre sticks together to make a square which ___cm 2 is one metre long and one metre wide. 6. Place an envelope over the grid. About how many 2. Hold the square up with one side on the floor to see how squares does it take to cover the envelope? big it is. ___cm 2 3. Place the square on the floor in a comer. Step back and 7. Measure the length and width of the envelope in centi- look. See how much floor space it covers. metres. Length em; width em. 4. Place the square over a table top or desk to see how Multiply to find the area in square centimetres. much space it covers. ____ em x em= cm2 • How close are the answers you have in 6. and in 7 .? 5. Place the square against the bottom of a door. See how much of the door it covers. How many squares would it take to cover the door? m2 THIS IS HOW BIG A SQUARE METRE IS!
~NTER FOR VOCATOONAL EDUCATOON Exercise 2 (continued on next page) 6
B. DEVELOP YOUR ABILITY TO ESTIMATE IN SQUARE CENTIMETRE GRID METRES
You are now ready to estimate in square metres. Follow the procedures used for estimating in metres.
How Close Estimate :Measurement Were You? (m2) {m2)
~ 1. Door. 2. Full sheet of newspaper. 3. Chalkboard or bulletin board. 4. Floor. 5. Wall. 6. Wall chart or poster. 7. Side of file cabinet.
Exercise 2 7 VOLUME MEASUREMENT ACTIVITIES Cubic Centimetre, Litre, Millilitre, Cubic Metre
3 I. THE CUBIC CENTIMETRE ( cm ) B. DEVELOP YOUR ABILITY TO ESTil'v1ATE IN CUBIC A. DEVELOP A FEELING FOR THE CUBIC CENTIMETRE CENTIMETRES
1. Pick up a colored plastic cube. Measure its length, You are now ready to develop your ability to estimate height, and width in centimetres. in cubic centimetres. THAT IS ONE CUBIC CENTIMETRE! Remember the size of a cubic centimetre. For each of 2. Find the volume of a plastic litre box. the following items, use the procedures for estimating in metres. a. Place a ROW of cubes against the bottom of one side How Close of the box. How many cubes fit in the row? ____ Estimate ~asurement Were You? 3 3 (cm ) (cm ) b. Place another ROW of cubes against an adjoining side of the box. How many rows fit inside the box 1. Index card file to make one layer of cubes? ____ box.
How m~ny cubes in each row? ____ 2. Freezer container. How many cubes in the layer in the bottom of the 3. Paper clip box. box? _____._ 4. Box of staples. c. Stand a ROW of cubes up against the side of the box. How many LAYERS would fit in the box? ____ II. THE LITRE (1) How many cubes in each layer? ____ A. DEVELOP A FEELING FOR A LITRE How many cubes fit in the box altogether? ____ THE VOLUME OF THE BOX IS ___CUBIC 1. Take a one litre beaker and fill it with water. CENTIMETRES. 2. Pour the water into paper cups, filling each as full as you d. Measure the length, width, and height of the box in usually do. How many cups do you fill? centimetres. Length em; width em; THAT IS HOW MUCH IS IN ONE LITRE! height em. Multiply these numbers to find the volume in cubic centimetres. 3. Fill the litre container with rice. ---em x cmx em= cm3 THAT IS HOW MUCH IT TAKES TO FILL A ONE Are the answers the same in c. and d.? --- LITRE CONTAINER!
~FOR VOCAT>ONAL EDUCAT!ON Exercise 3 (continued on next page) 8
B. DEVELOP YOUR ABILITY TO ESTL\1ATE IN LITRES B. DEVELOP YOUR ABILI'.fY TO ESTIMATE IN MILLILITRES
You are now ready to develop your ability to estimate in You are now ready to estimate in millilitres. Follow the litres. To write two and one-halflitres, you write 2.5 I, or procedures used for e::;timating metres. 2.5 litres. To write one-half litre, you write 0.5 l, or 0.5 How Close litre. To write two and three-fourths litres, you write Estimate Measurement Were You? 2.751, or 2.75 litres. .(ml) (ml)
For each of the following items, use the procedures for 1. Small juice can. estimating in metres. How Close 2. Paper cup or tea Estimate MP.asurement Were You? cup. (1) (I) 3. Soft drink can. 1. Medium-size freezer container. 4. Bottle. 2. Large freezer 3 container. IV. THE CUBIC :METRE (m ) 3. Small freezer container. A. DEVELOP A FEELING FOR A CUBIC METRE 4. Bottle or jug. 1. Place a one metre square on the floor next to the wall.
III. THE MILLILITRE (ml) 2. Measure a metre UP the wall. 3. Picture a box that would fit into that space. There are 1 000 millilitres in one litre. 1 000 ml = 1 litre. Half THAT IS THE VOLUME OF ONE CUBIC METRE! a litre is 500 millilitres, or 0.5 litre= 500 ml.
A. DEVELOP A FEELING FOR A MILLILITRE B. DEVELOP YOUR ABILITY TO ESTIMATE IN CUBIC METRES
1. Examine a centimetre cube. Anything which holds For each of the following items, follow the estimating proced 1 cm3 holds 1 mi. ures used before. How Close 2. Fill a 1 millilitre measuring spoon with rice. Empty the Estimate Measurement Were You? spoon into your hand. Carefully pour the rice into a (m3) (m3) small pile on a sheet of paper. THAT IS HOW MUCH ONE MILLILITRE IS! 1. Office desk. 3. Fill the 5 ml spoon with rice. Pour the rice into another 2. File cabinet. pile on the sheet of paper. 3. Small room. THAT IS 5 MILLILITRES, OR ONE TEASPOON!
4~ Fill the 15 ml spoon with rice. Pour the rice into a third pile on the paper. THAT IS 15 MILLILITRES, OR ONE TABLESPOON! Exercise3 ~CENTER "'"VOCATOONAO. EDUCATOQN 9 MASS (WEIGHT) MEASUREMENT ACTIVITIES Kilogram. Gram
The mass of an object is a measure of the amount of matter in the l\lass object. This amount is always the same unless you add or subtract some (kg) matter from the object. Weight is the term that most people use when. they mean ma.Ss. The weight of an object is affected by gravity; the 1. 1 kilogram box. mass of an object is not. For example, the weight of a person on earth 2. Textbook. might be 120 pounds; that same person's weight on the moon would be 20 pounds. This difference is because the pull of gravity on the moon 3. Bag of sugar. is less than the pull of gravity on earth. A person's mass on the earth 4. Package of paper. and on the moon would be the same. The metric system does not 5. Your own mass. measure weight--it measures mass. We will use the term mass here.
The symbol for gram is g. B. DEVELOP YOUR ABILITY TO ESTIMATE IN KILOGRAMS The symbol for kilogram is kg. There are 1 000 grams in one kilogram, or 1 000 g = 1 kg. For the following items ESTIMATE the mass of the object in kilograms, then use the scale or balance to find the exact mass Half a kilogram can be written as 500 g,or 0.5 kg. of the object. Write the exact mass in the MEASUREMENT A quarter of a kilogram can be written as 250 g,or 0.25 kg. column. Determine how close your estimate is: Two and three-fourths kilograms is written as 2.75 kg. How Close Estimate Measurement Were You? (kg) (lqg) I. THE KILOGRAM (kg) 1. Bag of rice. DEVELOP A FEELING FOR THE MASS OF A KILOGRAM 2. Bag of nails. Large purse or Using a balance or scale, find the mass of the items on the table. 3. Before you find the mass, notice how heavy the object "feels" briefcase. and compare it to the reading on the scale or balance. 4. Another person. 5. A few books.
Exercise 4 (continued on next page) 10
II. THE GRAl\I (g)
A. DEVELOP A FEELING FOR A GRA.I"\1 B. DEVELOP YOUR ABILITY TO ESTI1\1ATE IN GRAMS
1. Take a colored plastic cube. Hold it in your hand. You are now ready to improve your ability to estimate in Shake the cube in your palm as if shaking dice. Feel the ;rams. Remember how heavy the 1 gram cube is, how heavy pressure on your hand when the cube is in motion, then the two gram cubes are, and how heavy the five gram cubes when it is not in motion. are. For each of the following items, follow the procedures THAT IS HOW HEAVY A GRAM IS! used for estimating in kilograms. How Close 2. Take a second cube and attach it to the first. Shake the Estimate Measurement Were You? cubes in first one hand and then the other hand; rest (g) (g) the cubes near the tips of your fingers, moving your 1. .i'wo thumbtacks. hand up and down. 2. Pencil. THAT IS THE 1\1ASS OF TWO GRAMS! 3. Two-page letter and envelope. 3. Take five cubes in one hand .and shake them around. 4. Nickel. THAT IS THE 1\1ASS OF FIVE GRAMS! 5. Apple. 6. Package of margarine.
Exercise 4 11 TEMPERATURE MEASUREMENT ACTIVITIES Degree Celsius
0 I. DEGREE CELSIUS ( C) B. DEVELOP YOUR ABILITY TO ESTil\1A TE IN DEGREES Degree Celsius tc) is the metric measure for temperature. CELSIUS
A. DEVELOP A FEELING FOR DEGREE CELSIUS For each item, ESTIMATE and write down how many degrees Celsius you think it is. Then measure and write the l\1EASURE Take a Celsius thermometer. Look at the marks on it. l\1ENT. See how close your estimates and actual measure- ments are. 1. Find 0 degrees. How Close WATER FREEZES AT ZERO DEGREES CELSIUS (0°C) Measurement Were You? (OC) WATER BOILS AT 100 DEGREES CELSIUS (100°C) 1. Mix some hot and 2. Find the temperature of the room. ___ °C. Is the cold water in a room cool, warm, or about right? container. Dip your finger into the 3. Put some hot water from the faucet into a container. water. Find the temperature. ° C. Dip your finger quickly in and out of the water. Is the water very hot, 2. Pour out some of hot, or just warm? the water. Add some hot water. Dip your 4. Put some cold water in a container with a thermometer. finger quickly into Find the temperature. ° C. Dip your finger into the water. the water. Is it cool, cold, or very cold? 3. Outdoor tempera 5. Bend your arm with the inside of your elbow around the ture. bottom of the thermometer. After about three minutes find the temperature. ° C. Your skin tempera 4. Sunny window sill. ture is not as high as your body temperature. 5. :lvlix of ice and water. NORMAL BODY TE:MPERATURE IS 37 DEGREES 6. Temperature at CELSIUS ( 37° C). floor. A FEVER IS 39°C. 7. Temperature at A VERY HIGH FEVER IS 40°C. ceiling.
Exercise 5 12
UNIT METRICS IN THIS OCCUPATION
2 Changeover to the metric system is under way. Large corporations are already using metric measurement to compete in the world market. The metric system has been used in OBJECTIVES various parts of industrial and scientific communities for years. Legislation, passed in 1975, authorizes an orderly transition to use of the metric system. As businesses and The student will recognize and use the metric industries make this metric changeover, employees will need to use metric measurement terms, units, and symbols used in this occupa in job-related tasks. tion. Table 2 lists those metric terms which are most commonly used in this occupation. • Given a metric unit, state its use in this These terms are replacing the measurement units used currently. What kinds of job occupation. related tasks use measurement? Think of the many different kinds of measurements you now make and use Table 2 to discuss the metric terms which replace them. See if you • Given a measurement task in this occupa can add to the list of uses beside each metric term . .tion, select the appropriate metric unit ·and measurement tool.
SUGGESTED TEACHING SEQUENCE
1. Assemble metric measurement tools (rules, tapes, scales, thermometers, etc.) and objects related to this occupation.
2. Discuss with students how to read the tools.
3. Present and have students discuss Information Sheet 2 and Table 2.
4. Have students learn occupationally related metric measurements by complet ing Exercises 6 and 7.
5. Test performance by using Section A of "Testing Metric Abilities."
Information Sheet 2 Metric lJnits for Aviation Rlectronics 13
Quantity Unit Symbol Use
Length metre m wire lengths
centimetre em wire lengths, tool lengths, locating switch or box openings
millimetre mm length and diameter of fasteners, drill bit sizes, wrench sizes
Area square millimetre mm2 capacitor plate
square centimetre cm2 installing equipment, switches, control boxes
m3 Volume/Capacity cubic metre installing equipment, switches, control boxes cubic centimetre cm3
Temperature degree Celsius oc equipment specifications
Pressure kilopascal kPa equipment specifications, reading cabin pressure
Power watt w lamp sizes, energy dissipation
------··- ELECTRONIC COMPONENTS
9mm ----1 r- 8mm ___, 20mm ti_ TOP VIEW OF INTEGRATED -=====l'lm::;~ CIRCUIT 4mm MINIATURE -----r CAPACITOR I lOmm__, Q_ TRANSISTOR lliiiiilT ACTUAL SIZE OF COMPONENTS lh W RESISTOR
~R FOR VOCATIONAL EDUCATION Table 2 14 TRYING OUT METRIC UNITS
To give you practice with metric units, first estimate the measure- Estimate Actual ments of the items below. Write down your best guess next to the item. Then actually measure the item and write down your answers using the 16. Measuring cup correct metric symbols. The more you practice, the easier it will be. 17. Milk container Estimate Actual 18. Small can Length 1. Palm width 19. Bucket
2. Hand span 20. Small box
3. Your height 21. Tool tray
4. Wing span 22. Switch
5. Space between the wheels Mass 23. Textbook 6. Wheel height 24. Nickel 7. Cabin height 25. Yourself 8. Fuselage 26. Box of nylon washers 9. Propeller 27. A litre of water (net) Area 10. Wing 28. Switch
11. Parking spot Temperature 29. Inside 12. Cabin 30. Outside 13. Hangar 31. Hot tap water 14. Control box 32. Cold fountain water Volume/Capacity Small bottle 15. 33. Engine temperature
~NnR R>R VOCATK>NA\. WUCATOON Exercise 6 15 FLYING WITH METRICS It is important to know what metric measurement to use. Show 13. Diameter of the radar picture what measurement to use in the following situations. tube
1. Distance from center of cabin 14. Mass of the headset or cockpit to the fin 15. Integrated circuit width 2. Miniature capacitor length 16. Transistor diameter 3. Height of antenna mast 17. Length of 1.;2 watt resistor 4. Width of aileron 18. Power output of engine 5. Diameter of spinner
6. Height of fin
7. Width of instrument panel
8. Diameter of the panel Dl I I I I IT ammeter ~ ~ 9. Dimensions of the motor ~ ~ generator: UI lJJ a) Length ~ b) Width '- _,) c) Height 1---- r-- [l 10. Battery compartment capacity f-- 11. Dimensions of radio transmitter- l--- C) receiver: l a) Length
b) Width
c) Height
12. Area of workbench
~R FOR VOCATIONAL EDUCATOON Exercise 6 16
METRIC-METRIC EQUIVALENTS UNIT3 Centimetres and M illimetn~"'
OBJECTIVE 0 > fnllflllljlllljlllljlllljlllljlllljlllljlllljlllljlllljlllljllllj llllljlllljlllljlllljlllljlllljlllljllllj llliJlllljlllljlllljllllllll The student will recognize and use met ( ( ric equivalents. 1 2 3 4 5 6 1 2 3 4 5 6
• Given a metric unit, state an equivalent Look at the picture of the nail next to the ruler. The nail is 57 mm long. This is 5 em+ 7 mm in a larger or smaller metric unit. There are 10 mm in each em, so 1 mm = 0.1 em (one-tenth of a centimetre). This means that 7 mm = 0. 7 em, so 57 mm = 5 em + 7 mm = 5 em+ 0.7 em = 5.7 em. Therefore 57 mm is the same as 5.7 em.
SUGGESTED TEACHING SEQUENCE Now measure the paper clip. It is 34 mm This is the same as 3 em+ mm. Since each millimetre is 0.1 em (one-tenth of a centimetre), 4 mm = em. So, the paper clip is 1. :Make available the Information Sheets 34 mm = 3 em + 4 mm ( 3 - 8) and the associated Exercises 3 em+ 0.4 em (8 - 14), one at a time. 3.4 em. This means that 34 mm is the same as 3.4 em.
2. As soon as you have presented the Information Sheet 3 Information, have the students complete each Exercise.
3. Check their answers on the page titled Now you try some. ANSWERS TO EXERCISES AND TEST. a ) 26mm= em e ) 132mm = em b) 583 mm;::: em f ) 802mm = em 4. Test performance by using Section B of c ) 94mm= em g) 1400 mm em "Testing Metric Abilities." d) 680mm = em h) 2 307 mm = em
Exercise.S 17 Metres, Centimetres, and Millimetres M illili tres to Litres There are 100 centimetres in one metre. Thus, There are 1 000 millilitres in one litre. This means that
2m= 2 x 100 em= 200 em, 2 000 millilitres is the same as 2 litres, 3m = 3 x 100 em = 300 em, 3 000 ml is the same as 3 litres, 8 m = 8 x 100 em = 800 em, 4 000 ml is the same as 4 litres, 36m= 36 x 100 em= 3 600 em. 12 000 ml is the same as 12 litres. There are 1 000 millimetres in one metre, so 2 m = 2 x 1 000 mm = 2 000 mm, Since there are 1 000 millilitres in each litre, one way to change milli· 3 m = 3 x 1 000 mm = 3 000 mm, litres to litres is to divide by 1 000. For example, 6 m = 6 x 1 000 mm = 6 000 mm, 1 000 1 000 ml = 1 000 litre = 1 litre. 24 m = 24 x 1 000 mm = 24 000 mm. Or 2 000 From your work with decimals you should know that 2 000 ml = 1 000 litres = 2 litres. one-half of a metre can be written 0.5 m (five-tenths of a metre), And, as a final example, 28 000 one-fourth of a centimetre can be written 0.25 em 28 000 ml = litres = 28 litres. 1 000 (twenty-five hundredths of a centimetre). What if something holds 500 ml? How many litres is this? This is This means that if you want to change three-fourths of a metre to worked the same way, millimetres, you would multiply by 1 000. So 500 ml = litre = 0.5 litre (five-tenths of a litre ). So 500 ml 0.75 m = 0.75 x 1 000 mm 1 ~gg is the same as one-half (0.5) of a litre. 75 x 1 000 mm 100 Change 57 millilitres to litres. 1000 75 x 100 mm 57 ml = ~~ litre= 0.057 litre (fifty-seven thousandths of a 1 0 75 x 10 mm litre). 750 mm. This means that 0.75 m = 750 mm.
Information Sheet 4 Information Sheet 5 Fill in the following chart. Now you try some. Complete the following chart.
metre centimetre millimetre millilitres litres m em mm (ml) (I) 1 100 1000 3 000 3 2 200 6.000 3 8 9 1-t 000 5 000 23 74 300 0.3 0.8 80 700 .. 0.6 600 0.9 2.5 25 250 1-!8 0.-!7 639 275 Exercise 9 Exercise 10 ~ \Vhat do you do if you need to change litres to millilitres? Remember, To change kilograms to grams, you multiply by 1 000. there are 1 000 millilitres in one litre, or 1 litre = 1 000 ml. 4 kg = 4 X 1 000 g = 4 000 g, So, 23 kg= 23 X 1 000 g = 23 000 g, 0.75 kg= 0.75 X 1 000 g = 750 g. 2 litres = 2 x 1 000 ml = 2 000 ml, 7 litres = 7 x 1 000 ml = 7 000 ml, Information Sheet 8 13 litres =13 x 1 000 ml =13 000 ml, Complete the following chart. 0.65 litre = 0.65 x 1 000 ml = 650 ml. kilograms grams Information Sheet 6 kg g Now you try some. Complete the following chart. 7 7 000 Jitres millilitres 11 I ml 25 000 0.4 8 8 000 0.63 5 175 Exercise 13 46 32 000 Changing Units at Work 0.4 0.53 Some of the things you use in this occupation may be measured in 480 Exercise 11 different metric units. Practice changing each of the following to metric equivalents by completing these statements. Grams to Kilograms a ) 200 em of wire is ______m There are 1 000 grams in one kilogram. This means that b ) 150 ml of solution is 1 c ) 1.5 em diameter waveguide is mm 2 000 grams is the same as 2 kilograms, d ) 1 500 g of hardware is kg 5 000 g is the same as 5 kg, e ) 120 mm wide instrument panel is em f ) 0.75 litre of lubricating oil is ml 700 g is the same as 0.7 kg, and so on. g ) 1 000 kg of transmitter is t h ) 2 m board is mm To change from grams to kilograms, you use the same procedure for i ) 500 g of solder is kg . changing from millilitres to litres. j ) 500 ml of epoxy cement is l k) 10m of wire is em Information Sheet 7 Try the following ones. 1 ) 2.5 em diameter pipe is mm m) 2 400 mm wall panel length is em grams kilograms g kg 4 000 4 9 OOQ 23 000 8 300 275 Exercise 12 G:3a;o The student will recognize and use Selecting an improper tool or misreading a scale can result in an improper sales form, instruments, tools, and devices for meas damaged materials, or injury to self or fellow workers. For example, putting 207 pounds per urement tasks in aviation occupations. square inch of pressure (psi) in a tractor tire designed for 207 kilopascals (about 30 psi) could • Given metric and Customary tools, cause a fatal accident. Here are some suggestions: instruments, or devices, differentiate 1. Find out in advance whether Customary or metric units, tools, instruments, or pro" between metric and Customary. ducts are needed for a given task. • Given an aviation measurement task, select and use an appropriate tool, 2. Examine the tool or instrument before using it. instrument or device. 3. The metric system is a decimal system. Look for units marked off in whole numbers, • Given a metric measurement task, tens or tenths, hundreds or hundredths. judge the metric quantity within 25% and measure within 5% accuracy. 4. Look for metric symbols on the tools or gages such as m, mm, kg, g, kPa, etc. SUGGESTED TEACHING SEQUENCE 5. Look for decimal fractions (0.25) or decimal mixed fractions (2.50) rather than com mon fractions ( 3/8) on drill bits, feeler gages, etc. 1. Assemble metric and Customary measur ing tools and devices (rules, scales, °C 6. Some products may have a special metric symbol such as a block M to show they are thermometer, drill bits, wrenches, mi metric. crometer, vernier calipers, feeler gages) and display in separate groups at learning 7. Don't force bolts, wrenches, or other devices which are not fitting properly. stations. 8. Practice selecting and using tools, instruments, and devices. 2. Have students examine metric tools and instruments for distinguishing character istics and compare them with Customary tools and instruments. 3. Have students verbally describe charac teristics. 4. Present or make available Information Sheet 9. 5. Mix metric and Customary tools or equipment at learning station. Give students Exercises 15 and 16. 6. Test performance by using Section C of "Testing Metric Abilities." Information Sheet 9 20 WHICH TOOLS FOR THE JOB? MEASURING UP IN AVIATION ELECTRONICS Practice and prepare to demonstrate your ability to identify, For the tasks below, estimate the metric measurement to select, and use metric-scaled tools and instruments for the tasks given within 25% of actual measurement, and verify the estimation by below. You should be able to use the measurement tools to the appro- measuring to within 5% of actual measurement. priate precision of the tool, instrument, or task. Estimate Verify Select and demonstrate or describe use of tools, instruments, or devices to: 1. Select the mounting screws for a panel meter. 1. Mount an antenna mast. 2. Find the size of the motor 2. Install the radio transmitter. generator brushes. 3. Install external microphone jack on airplane. 3. The diameter of the motor generator armature bearing. 4. Replace panel ammeter with suitable replacement. 4. Replace a rotary switch in 5. Install a motor generator. the instrument panel. 6. Cut off enough wire for the antenna transmission line. 5. Install the proper mike jack to match the mike plug. 7. Replace the receiver on-off volume control. 6. Replace the transmitter unit 8. Cut hole in the instrument panel to mount a VU meter. with another one. 9. Replace the bearing in the motor generator. 7. Prepare an order for the fasteners needed to install a 10. Replace the brushes in the motor generator. receiver in an airplane. 11. Replace a microphone cord. 8. Write a work order for the repair of a motor generator 12. Install a chassis mounted connector. with worn bearings. 13. Replace a set of instrument knobs. 9. Write a purchase order for the drill bits needed to install 14. Rewire interior cabin lights. a long wire antenna. 10. The shaft length and diameter of a radio control. Exercise 15 Exercise 16 o:::3C Below is a table of metric-Customary equivalents which tells you what the metric replace ments for Customary units are.* This table can be used with Exercise 17, Part 1 and Part 3. The SUGGESTED TEACHING SEQUENCE symbol :::::: means "nearly equal to." 1. Assemble packages and containers of materials. 1 em ~ 0.39 inch 1 inch:::::: 2.54 em 1 ml:::::: 0.2 tsp 1 tsp ~ 5 ml 2. Present or make available Information 1 m ~ 3.28 feet 1 foot:::::: 0.305 m 1 ml :::::: 0.07 tbsp 1 tbsp ~ 15 ml Sheet 10 and Table 3. 1m:::::: 1.09 yards 1 yard :::::: 0.91 m 1 1 :::::: 33.8 fl oz 1 fl oz ~ 29.6 ml 1 km:::::: 0.62 mile 1 mile :::::: 1.61 km 11:::::: 4.2 cups 1 cup~ 237 ml 2 2 3. Have students find approximate metric 1 cm :::::: 0.16 sq in 1 sq in :::::: 6.5 cm 11:::::: 2.1 pts 1 pt ~ 0.47 l 2 2 Customary equivalents by using 1 m ~ 10.8 sq ft 1 sq ft:::::: 0.09 m 11:::::: 1.06 qt 1 qt ~ 0.95 l 2 2 Exercise 17. 1 m :::::: 1.2 sq yd 1 sq yd:::::: 0.8 m 11:::::: 0.26 gal 1 gal~ 3.79 l 1 hectare :::::: 2. 5 acres 1 acre :::::: 0.4 hectare 1 gram :::::: 0.035 oz 1 oz ~ 28.3 g 3 3 4. Test performance by using Section D of 1 cm :::::: 0.06 cu in 1 cu in :::::: 16.4 cm 1 kg~ 2.2 lb 1lb ~ 0.45 kg 3 3 "Testing Metric Abilities." 1 m :::::: 35.3 cu ft 1 cu ft:::::: 0.03 m 1 metric ton:::::: 2205lb 1 ton~ 907.2 kg 1m3 ~ 1.3 cu yd 1 cu yd :::::: 0.8 m 3 1 kPa :::::: 0.145 psi 1 psi ~ 6.895 kPa *Adapted from Let's Measure Metric. A Teacher's Introduction to Metric Measurement. Division of Educational Redesign and Renewal, Ohio Department of Education, 65 S. Front Street, Columbus, OH 43215, 1975. ~·NT·R 100 3.93 10 0.39 1 0.04 0.1 0.004 200 7.87 20 0.79 2 0.08 0.2 0.008 300 11.81 30 1.18 3 0.12 0.3 0.012 400 15.74 40 1.57 4 0.16 0.4 0.016 500 19.68 50 1.97 5 0.20 0.5 0.020 600 23.62 60 2.36 6 0.24 0.6 0.024 700 27.56 70 2.76 7 0.28 0.7 0.028 800 31.50 80 3.15 8 0.31 0.8 0.031 900 35.43 90 3.54 9 0.35 0.9 0.035 1 000 nun or 1 metre = 39.37 inches INCHES TO MILLIMETRES Inches mm Inches nun Inches nun Inches nun 1 25.4 0.1 2.54 .01 0.25 .001 0.03 2 50.8 0.2 5.08 .02 0.51 .002 0.05 3 76.2 0.3 7.62 .03 0.76 .003 0.08 4 101.6 0.4 10.16 .04 1.02 .004 0.10 5 127.0 0.5 12.70 .05 1.27 .005 0.13 6 152.4 0.6 15.24 .06 1.52 .006 0.15 7 177.8 0.7 17.78 .07 1.78 .007 0.18 8 203.2 0.8 20.32 .08 2.03 .008 0.20 9 228.6 0.9 22.86 .09 2.29 .009 0.23 10 inches = 254 mm 12 inches or 1 feet = 304.8 nun or 30.48 em Table 3 23 ANY WAY YOU WANT IT 1. You are working in an aviation electronics service shop. With c ) 610 mm, ______inches the change to metric measurement some of the things you order, sell or use are marked only in metric units. You will d) 1 inch mm need to be familiar with appropriate Customary equivalents e ) 2.006 inch mm in order to communicate with customers and suppliers who f ) 0.75 inch mm use Customary units. To develop your skill use the Table on Information Sheet 10 and give the approximate metric 3. Complete the Requisition Form using the items listed. Convert quantity (both number and unit) for each of the following the customary quantities to metric before filling out the form. Customary quantities. Complete all the information (Date, For, Job No. etc.). Requisition one of each of the following: Customary Quantity Metric Quantity a ) 100 ft. roll of hook-up wire b ) 1 lb. spool of solder a ) 1 pt. of solvent c ) 1 pint of control cleaner d ) 1 roll of 3/4 inch insulating tape b) lib. of grease e ) 1 box of 1 inch 4 amp fuses c ) 35 ft. of cable REQUISITION d) 14 in. of hook-up wire Date e ) 2 ft. of wire lead For f ) 4 fl. oz. of epoxy glue g ) 6 in. circuit board Job No. Date Wanted h) 1 in. screw Deliver to 1 lb. of hand cleaner 4 fl. oz. of silicone spray QTY UNIT ITEM k) two-mile range I ) 4 in. spacing m) 2 in. clearance n ) 8 in. mounting bracket 2. Use the conversion tables from Table 3 to convert the following: Requested by a ) 6 mm inches Approved by b ) 50 mm inches G::3CENTER..,.. VOCAnoNAL EDUCATOON Exercise 17 24 SECI'ION A 6. The correct way to write twelve 11. Estimate the length of the line Use this conversion table to thousand millimetres is: segment below: answer questions 15 and 16. lL One kilogram is about the mass of a: [A] 12,000 mm. (A] 23 grams [A) nickel (B] 12.000mm mm in. mm in. [ B ] 6 centimetres [ B I apple seed [C) 12 OOOmm [C] 40 millimetres 10 0.39 1 0.04 [C I basketball (D] 12 000 mm 2 0.08 (D] 14 pascals 20 0.79 [D] Volkswagen "Beetle" 30 1.18 3 0.12 SECTION B 40 1.57 4 0.16 2. A square metre is about the 7. A board 20 centimetres wide 50 1.97 5 0.20 12. Estimate the length of the line 0.24 area of: is the same as: 60 2.36 6 segment below: 70 2.76 7 0.28 [A ] this sheet of paper [A] 0.2 millimetre f--l 80 3.15 8 0.31 90 3.54 9 0.35 [B] a card table top [B) 200 millimetres (A] 10 millimetres 100 3.94 [ C ] a bedspread [ C] 2 millimetres (B] 4 centimetres [D] a postage stamp (D] 2 000 millimetres [ C ] 4 pascals [D] 23 milligrams 3. The length of bolts and screws 8. A 250 millilitre bottle of control is measured in: cleaner is the same as: 15. The equivalent of 75 mm is: SECTIOND [A] metres [A] 2.5 litres [A] 29.6 in. 13. The metric unit which replaces [ B] millilitres [B] 0.025 litre the fluid ounce is: [B) 2.96 in. [ C] millimetre& [C) 0.25litre (A] gram [C) .75in. [D) grams [D] 25 litres [B] hectare [D) 7.5 in. 4. Cabin pressure is measured in: [C] millilitre SECTION C 16. The equivalent of 25 mm is: [A] kilograms [D) litre [A] .99 in. 9. For measuring in metres you [B] grams would use a: 14. The metric unit which replaces [B] 2.5 in. [ C] millilitres [A] pressure gage pounds is: [C] 4 in. [D] kilopascals [B] container [A] litres (D] .25 in. 5. The correct way to write twenty [ C] thermometer [B ] kilograms grams is: [D) tape [C) grams [A] 20 gms [D] metres 10. For measuring in millimetres [B] 20 Gm. you would use a: [C] 20 g. [A] pressure gage [D I 20 g [B) rule [C] scale [D] container o::3'"'"'" ""'VOCATION~ •oucAnON TESTING METRIC ABILITIES ANSWERS TO EXERCISES AND TEST 25 EXERCISES 1 THR U 6 Exercise 10 Exercise 13 Part 2. The answers depend on the items used for the activities. kilograms grams a ) 0.24 in. millilitres litres b) 1.97 in. ml I kg g EXERCISE 7 e ) 24.01 in. Currently accepted metric units of 3 000 3 7 7 000 d) 25.4 mm measurement for each question are 6 000 (6) 11 (11 000) e) 50.95 mm shown in Table 2. Standards in each (8 000) 8 (25) 25 000 f ) 19.05 mm occupation are being established 0.4 (400) now, so answers may vary. (14 000) (14) (23 000) 23 0.63 (630) EXERCISE 8 300 0.3 (0.175) 175 Part 3. a) 2.6 em e) 13.2 em 700 (0.7) a) 30.5 m b) 58.3 em f) 80.2 em (900) 0.9 Exercise 14 b) 0.45 kg c) 9.4 em g) 140.0 em 250 (0.25) a) 2m h) 2 000 mm e ) 0.4 7 litre d) 68.0 em h) 230.7 em (470) 0.47 b) 0.15 litre i ) 0.5 kg d) 1.905 em 275 (0.275) EXERCISES 9 THRU 13 c ) 15mm j ) 0.5 litre e) 2.54 em d) 1.5 kg k) 1 000 em Tables are reproduced in total. An Exercise 11 swers are in parentheses. e ) 12 em I ) 25mm litres millilitres f ) 750 ml m) 240em Exercise 9 g ) 1t I ml TESTING METRIC ABILITIES metre centimetre millimetre 8 8 000 m em mm 5 (5 000) EXERCISES 15 AND 16 1. c 9. D 2. B 10. B 1 100 1 000 46 (46 000) The answers depend on the 3. c 11. B 2 200 (2 000) (32) 32 000 items used for the activities. 4. D 12. A 3 ( 3J:J_O) (3 000) 0.4 (400) 5. D 13. c 9 (900) {9 0001 0.53 (530) 6. D 14. B (5) (500) 5 000 (0.48) 480 EXERCISE 17 7. B 15. B 7-! (7 400) (7 4 000) Partl. Exer-cise 12 8. c 16. A 0.8 80 (800~ a ) 0.47 litre h) 2.54 em 0.6 (60) 600 grams kilograms b) 0.45 kg i ) 0.45 kg (0.025) 2.5 25 g kg c ) 10.675 m j ) 118.4 ml (0.1-!8) (14.8j 148 d) 35.56 em k) 3.22 km -! 000 4 (6.39) 639 (6 390) e ) 0.61 m I ) 10.16 em 9 000 (9) f ) 118.4 ml m) 5.08 em 23 000 (23) g) 15.24 em n) 20.32 em (8 000) 8 300 (0.3) 275 _[0.275) ~C u U.S. GOVERNMENT PRINTING OFFICE: 1976-757-069/6209 Region No. 5-11