sign in sign up
<<
Home , Centimetre, Cubic metre, Litre, Millimetre

Table of Contents

Teaching and Learning The Unit 1 1 - Suggested Teaching Sequence 1 - Objectives 1 - Rules of Notation 1 - , Symbols, and Referents 2 - Metric Prefixes 2 - Linear Activities 3 - Area Measurement Activities 5 - Measurement Activities 7 - (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 Auto Mechanics 13 - Trying Out Metric Units 14 - Keep It Running 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 Auto Mechanics 20 Unit 5 21 - Objective 21 - Suggested Teaching Sequence 21 - Metric-Customary Equivalents 21 - Conversion Tables 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. 11) areas of measurement. 1. Recognize and use the (mm) square cubic centi­ (g) unit and its symbol for: (cm 3 ) tel 2. Exercises should be followed in the order 2 centimetre (em) (cm ) (kg) given to best show the relationship 2. Select, use, and read the between , area, and volume. appr<>priate measuring metre (m) square (m3) instruments for: metre 3. Assemble the metric measuring devices (m2) (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 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 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 (mm not 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 corrunas, 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 1 000 103 kilo (k~llo) k centimetre CIJ1 Width of paper clip = 2 metre m Height of door about 2 m 100 = 10 hecto (he k' to ) h

km 12- 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'tl) c

square metre m 2 Area of card table top 0.001 = 10- 3 milli ( nrli'i) m 6 ha Football field including sidelines 0.000 001 = 10- micro (ml'kro) J1 and end zones

Volume and millilitre ml Teaspoon is 5 ml Capacity litre I A little more than 1 Table 1-b cubic centimetre cm3 Volume of this container OJ cubic metre m3 A little more than a

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 ( 1 000 kilolll'ams) 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 . 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. l\1easure the size with your metre stick and write the answer in the .MEASURE.MENT colurrm.

Decide how close your estimate was to the actual measure. If 2. Hold one arm o1.1:t straight your estimate was within 25% of the actual measure you are a at shoulder height. Put "Metric l\1arvel." the metre stick along this arm until the end hits the How Close end of your fingers. Where Estimate l'vfeasurement 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 .METRE IS! 4 . Width of table. 5. Length of wall of this room. 6. Distance from you to wall. OC3'ENT£R FOR VOCAT>QNAC •DUC ATION Exercise 1 (continued on next page) 4

II. THE CENTIMETRE (em) III. THE l\11LLIMETRE (mm)

There are 100 cPntimetres in onP metre. If therP arP 4 metrP~ and There are 10 in OJW cPntimPtrP. VJhf'n a mf'asurf'ment is 3 , 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 CENTilVIETRE A. DEVELOP A FEELING FOR THE SIZE OF A l\TILLIMETRE

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. \Vhat is the distance around it? em

6. Use the tape measure to find your waist size. ____ em B. DEVELOP YOUR ABILITY TO ESTIMATE IN MILLIMETRES

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 in centimetres. For 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 of paper. postage stamp. 4. Length of a 5 . Thickness of a board pencil. or desk top. 6. Thickness of a 5. Width of a sheet of paper. button.

Exercise 1 5

AREA MEASUREMENT ACTIVITIES B. DEVELOP YOUR ABILITY TO ESTil\tlATE IN SQUARE Square Centimetre, Square Metre . CENTIMETRES You are now ready to develop your ability to estimate in square centimetres. WHEN YOU DESCRIBE THE AREA OF SOMETHING, YOU ARE SAYING HOW l'vL-\NY SQUARES OF A GIVEN SIZE IT TAKES TO Remember the size of a square centimetre. For each of the COVER THE SURF ACE. following items, follow the procedures used for estimating in metres. 2 I. THE SQUARE CENTIMETRE (cm ) How Close Estimate Measurement Were You? 2 2 A. DEVELOP A FEELING FOR A SQUARE CENTIMETRE (cm ) (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 CENTIMETRE! 4. Window pane or desk top. 3. Place your fingernail over the grid. About how many squares does it take to cover your fingernail? 2 ___cm 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 corner. 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!

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.

~ FQA VOCATOONAL EDUCATOON Exercise 2 7 VOLUME MEASUREMENT ACTIVITIES Cubic Centimetre, Litre, Millilitre, Cubic Metre

3 I. THE CUBIC CENTIMETRE ( cm ) B. DEVELOP YOUR ABILITY TO ESTil\1ATE 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 Measurement Were You? 3 3 (cm ) (cm ) b. Place another ROW of cubes against an adjoining side of the box. I:Iow many rows fit inside the box 1. Index card file to make one layer of cubes? ____ box. How many 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? ____ How many cubes fit in the box altogether? ____ A. DEVELOP A FEELING FOR A LITRE THE VOLUME OF THE BOX IS ___ CUBIC 1. Take a one litre beaker and fill it with . 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. 3 -----em x em x em = ---cm . THAT IS HOW MUCH IT TAKES TO FILL A ONE Are the answers the same in c. and d.? LITRE CONTAINER!

Exercise 3 (continued on next page) 8

B. DEVELOP YOUR ABILITY TO ESTI::\1ATE IN B. DEVELOP YOUR ABILITY 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-half litres, you write 2.5 l, or procedures used for estimating 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 or tea Estimate Measurement Were You? cup. (l) (l) 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 l.\1ILLILITRE 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 em 3 holds 1 ml. ures used before. How Close 2. Fill a 1 millilitre measuring spoon with rice. Empty the Measurement Were You? spoon into your hand. Carefully pour the rice into a (m3) small pile on a sheet of paper. THAT IS HOW MUCH ONE MILLILITREIS! 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 i-ice. Pour the rice into a third pile on the paper. THAT IS 15 MILLILITRES, OR ONE TABLESPOON!

~CENTER roo VOCAn<>NAC EOUCATOON Exercise3 9 MASS (WEIGHT) MEASUREMENT ACTIVITIES Kilogram, Gram

The mass of an object is a measure of the amount of matter in the Mass 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 mass. 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 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 l\1EASUREl\1ENT A 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) (kg) I. THE KILOGRAM (kg) 1. Bag of rice. DEVELOP A FEELING FOR THE MASS OF A KILOGRAM 2. Bag of nails.

Using a balance or scale, find the mass of the items on the table. 3. Large purse or 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.

a::3'£NTER '0R VOCAnoN~

II. THE GRAM (g)

A. DEVELOP A FEELING FOR A GRA.l\1 B. DEVELOP YOUR ABILITY TO ESTIMATE 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 grams. 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 used for estimating in kilograms. THAT IS HOW HEAVY A GRAM IS! How Close 2. Take a cube artd 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. Two thumbtacks. hand up and down. 2. Pencil. THAT IS THE MASS 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 MASS OF FIVE GRAMS! 5. Apple. 6. Package of margarine.

~NT

I. DEGREE CELSIUS tC) B. DEVELOP YOUR ABILITY TO ESTil\lA..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 MEASURE­ Take a Celsius thermometer. Look at the marks on it. MENT. See how close your estimates and actual measure- ments are. 1. Find 0 degrees. How Close WATER FREEZES AT ZERO DEGREES CELSIUS (0°C) Estimate l\ifeasurement Were You? tc) (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 find the temperature. ° C. Your skin tempera­ 4. Sunny window sill. ture is not as high as your body temperature. 0. 1\fix. 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."

a3CENTER ""' VOCATK>NAL '0UCATOON Information Sheet 2 13 METRIC UNITS FOR AUTO MECHANICS Quantity Unit Symbol Use

Length millimetre mm shaft size, length

centimetre em bearing sizes

Area square centimetre cm2 piston head surface

Volume/capacity cubic centimetre cm3 cylinder bore

cubic metre m3 work or storage space

millilitre ml chemicals, lubricant oils

litre l oil, fuel, storage

Temperature degree Celsius oc thermostats, engine operating temperature ranges, oil temperat ure

Mass gram g tire weights

kilogram kg batteries, engines

metric ton t vehicles, weights --

Bending moment metre N·m torque specifications (moment of force)

manifold pressure compression, Pressure/vacuum kilopascal kPa air hose pressure

Velocity per km/h speed of the vehicle

*Energy /work kilowatt-hour kW·h work efficiency of an engine

*Note: Further metric definitions for mechanics are found in Rules for SAE Use of SI (Metric) Units, Society of Automotive Engineers, Inc. Available: Society of Automotive Engineers, Inc., 400 Commonwealth Dr., Warrendale, PA 15096.

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 (metric) correct metric symbols. The more you practice, the easier it will be. 17. Milk container Estimate Actual 18. Can of oil Length 19. 1. Palm width Bucket 20. 2. Hand span Small box or package

3. Your height 21. Tool chest

4. Ceiling height of this room 22. Gasoline can

5. Width of a paper clip Mass 6. Thickness of a nickel 23. Textbook

7. Length of a valve stem 24. Nickel

8 . Width of this room 25. Yourself

9. Diameter of a piston head 26. Paper clip

Area 27. A litre of water (net) 10. Desk top 28. A quantity of oil 11. Classroom floor

12. Workbench Temperature 29. Room 13. Sheet of paper 30. Outside 14. Parking space 31. Hot tap water Volume/Capacity 32. 15. Small bottle Ice water

~

19. Distance from shop or store 1. The stroke of a piston to your home 2. Length of the fuel line 20. Length of positive battery cable 3. Length of a fanbelt

4. Diameter of a cam shaft

5. Volume of a fuel tank

6. Capacity of an acetylene cylinder

7. Amount of water in a radiator

8. Mass of battery fluid in a 12- battery 9. Tire pressure for automobile Dl I I I I 1r ..) 10. Crankshaft main journal size ,;:;: ~ 11. Bore of a cylinder UI TJJ 12. Volume of oil for crank case ~ _,) 13. Capacity of a radiator "-- - 14. Temperature of cooling system [J t--- while idling engine ...... t--- 15. Mass of small engine r----- 16. Length of exhaust pipe .C0 17. Spark plug gap

~ENT

METRIC-METRIC EQUIVALENTS UNIT3 Centimetres and Millimetres

OBJECTIVE 1 (]IIIIJillljlllljlllljlllljlllljlllljlllljlllljlllljlllljlllljlllljlll The student will recognize and use met­ ( rm m'l""'ll''l'''''''"l'''''''''l''''''ll'l''lll''lll''lll ric equivalents. 1 2 3 4 5 6 I I 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 34mm = 3cm+4mm ( 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, have the students complete Information Sheet 3 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 "Testing Metric Abilities." = em d) 680 mm = em h) 2 307 mm em

Exercise 8 a3COITER ""'VOCATOONA< '0UCATOON 17 Metres, Centimetres, and Millimetres Millilitres 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 1 00 em = 800 em, -l 000 ml is the same as -! litres, 36 m = 36 x 1 00 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. 24m = 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 = OOO litres = 28 litres. 1 (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 = = 0.5 litre (five-tenths of a litre ). So 500 ml 0.75 m = 0.75 x 1 000 mm 1 ~~~litre is the same as one-half (0.5) of a litre. 75 x 1 000 mm 100 Change 57 millilitres to litres. 1 000 75 x 100 mm 57 rn l = 1 og~ litre = 0.057 litre (fifty-seven thousandths of a 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 ern mm (ml) (I) 1 100 1 000 3 000 3 2 200 6 000 3 8 9 1-l 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 ~ENUR 'OR VOCATOONAL EOUCATOON 18 Li tres to M illili tres Kilograms to Grams What 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 mil!ilitres in one litre, or 1 litre = 1 000 ml. -l kg = -l X 1 000 g = -! 000 g, So, 23 kg = 23 X 1 000 g = 23 000 g, 0.75kg= 0.75x1 000g = 750g. 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 =1 3 x 1 000 ml =13 000 ml, Complete the following chart. 0.65 litre = 0.65 x 1 000 ml = 650 mi. kilograms grams Information Sheet 6 kg g Now you try some. Complete the following chart. 7 7 000 11 litres millilitres 25 000 I ml 0.4 0.63 8 8 000 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 There are 1 000 grams in one kilogram. This means that a ) 50 em of hose is ------m b ) 250 ml of solution is l c ) 5 em diameter hose is ______mm 2 000 grams is the same as 2 kilograms, d ) 2 500 g of grease is kg 5 000 g is the same as 5 kg, e ) 120 mm of bar steel is em 700 g is the same as 0.7 kg, and so on. f ) 0.25 litre of motor oil is ml g ) 2 000 kg of sand is t To change from grams to kilograms, you use the same procedure for h ) 0.5 litre of concentrate is ml changing from millilitres to litres. i ) 500 g of solder is kg j ) 500 ml of brake fluid is 1 Information Sheet 7 k ) 0.5 t of floor sweep is kg Try the following ones. l ) 10 m of wire is em grams kilograms m) 2.5 em diamter pipe is mm g kg n ) 2 400 mm wall panel length is em

4 000 4 9000 23 000 8 300 275 Exercise 12

Exercise 14 19 UNIT SELECTING AND USING METRIC INSTRUMENTS , TOOLS AND DEVICE-S OBJECTIVE Selecting an improper tool or misreading a scale can result in an improper sales form, damaged materials, or injury to self or fellow workers. For example, putting 207 pounds per The student will recgonize and use square of pressure (psi} in a tractor tire designed for 207 kilopascals (about 30 psi) coulrl instruments, tools, and devices for mea­ cause a fatal accident. Here are some suggestions: surement tasks in this occupation. • Given metric and Customary tools, 1. Find out in advance whether Customary or metric units, tools, instruments, or pro­ instruments, or devices, differentiate ducts are needed for a given task. between metric and Customary. 2. Examine the tool or instrument before using it. • Given a measurement task, select and use an appropriate tool, in­ 3. The metric system is a decimal system. Look for units marked off in whole numbers, strument or device. tens or tenths, hundreds or hundredths. • Given a metric measurement task, 4. Look for metric symbols on the tools or gages such as m, mm, kg, g, kPa, etc. judge the metric quantity within 20% and measure within 2% accuracy. 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. SUGGESTED TEACHING SEQUENCE 6. Some products may have a special metric symbol such as a block M to show they are 1. Assemble metric and Customary measur­ metric. ing tools and devices (rules, scales, °C thermometer, drill bits, wrenches, mi­ 7. Don't force bolts, wrenches, or other devices which are not fitting properly. crometer, vernier , feeler gages) and display in separate groups at learning 8. Practice selecting and using tools, instruments, and devices. stations. 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."

OO·NT·R •OR VOCATOON=

6. Pull the head of an engine, replace head gasket, and 5. Volume of an engine cylinder. replace head. 6. A fuel line requires 600 mm of 7. Adjust valve settings. tubing. From several cut pieces, select the piece for the job with - 8. Describe the difference between a Customary and the least waste. a metric crescent wrench. 7. Select new bearing to fit a 9. Replace brake lines. crankshaft.

10. Renew an exhaust system. 8. Select the amount of fluid for brake master cylinder.

9. Change the spark plugs.

10. Select the amount of oil for a complete oil change.

Exercise 15 Exercise 16 a:3'ENTER H>R VOCATOONAL ";.>CATOON 21 UNIT ~------5 METRIC-CUSTOMARY EQUIVALENTS During the transition period there will be a need for finding equivalents between systems. OBJECTIVE Conversion tables list calculated equivalents between the two systems. When a close equivalent is needed, a conversion table can be used to find it. Follow these steps: The student will recognize and use metric and Customary units interchangeably in order­ 1. Determine which conversion table is needed. ing, selling, and using products and supplies in this occupation. 2. Look up the known number in the appropriate column; if not listed, find numbers you can add together to make the total of the known number. • Given a Customary (or metric) measure­ ment, find the metric (or Customary) 3. Read the equivalent(s) from the next column. equivalent on a conversion table. Table 3 on the next page gives an example of a metric-Customary conversion table which • Given a Customary unit, state the re­ you can use for practice in finding approximate equivalents. Table 3 can be used with Exercise placement unit. 17, Part 2 and Part 3.

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 ~ 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 11 ~ 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 I 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 I 2 2 Exercise 17. 1 m ~ 1.2 sq yd 1 sq yd ~ 0.8 m 11 ~ 0.26 1gal~3.79l 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 1 lb ~ 0.45 kg 3 3 "Testing Metric Abilities." 1 m ~ 35.3 cu ft 1 cu ft ~ 0.03 m 1 metric ton ~ 2205 lb 1 ton ~ 907.2 kg 3 3 1m ~ 1.3 cu yd 1 cu yd ~ 0.8 m 1 kPa ~ 0.145 psi 1 psi ~ 6.895 kPa

*Adapted from Let's Measure Metric. A Teacher 's Introduction to Metric Afeasurement. Division of Educational Redesign and Renewal, Ohio Department of Education, 65 S. Front Street, Columbus, OH 43215. 197 5. o:::7·~

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 mm or 1 metre = 39.37 inches INCHES TO MILLIMETRES

Inches mm Inches mm Inches mm Inches mm

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 mm or 30.48 em

a:3'BmR O'OR VOCAnONAC 'DUCATOON Table 3 23 ANY WAY YOU WANT IT

1. You are working in a repair shop or auto parts house. With the change to metric measurement some of the things you order, sell g ) o . om~ in. = mm i ) 250mm = in. or use are marked only in metric units. You will need to be h) 152mm = in. j. ) 1 000 rom= in. familiar with appropriate Customary equivalents in order to communicate with customers and suppliers who use Customary units. To develop your skill use the Table on Information Sheet 10 and give the approximate metric quantity (both number and 3. Complete the Requisition Form using the items listed. Convert unit) for each of the following Customary quantities. the Customary quantities to metric before filling out the form. Complete all the information (Date, For, Job No., etc.). Customary Quantity Metric Quantity Requisition one of each of the following: a ) 2 lbs. of heavy lube a ) 25ft. of 5/16 in. fluid hose b ) 4 qts. of brake fluid b) 12 fl. oz. spray can of paint c ) 3/4 in. pipe c ) 5 lb. spool of 50/50 solder d) 1 ft. by 2 ft. piece of gasket material d ) 10 lbs. of sawdust ~ ) 1 gal. of parts cleaning solvent e ) 18 in. bar steel f ) two- can REQUISITION g ) 30 ft. of air hose Date h ) 4 fl. oz. of additive For i ) two-mile distance j ) 2 in. bolt Job No. Date Wanted k ) 2 fl. oz. of silicone spray Deliver to l ) llb. of hand cleaner m) 1 gal. of solvent QTY UNIT ITEM n ) 1ft. length of hose o ) 1/4 in. drill bit

2. Use the conversion tables from Table 3 to convert the following:

a ) 254mm = in. d ) 2.25 in. = rom Requested by b) 0.025 in. = rom e ) 0.25 in. = rom Approved by c ) 7.1 rom = in. f ) 10 in. = rom

Exercise 17 a:3CENTER FCR VOCATK>NAL EDUCATION 24 SECfiON 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. 1. One kilogram is about the mass of a: [A] 12.000 mm. [A] 23 grams (A] nickel [BI 12.000 mm mm in. mm in. I [BI 6 centimetres [ B I apple seed [C] 12 OOOmm [C] 40 millimetres 100 3.94 10 0.39 [ C] basketball [D] 12 000 mm 200 7.87 20 [D] 14 pascals 0.79 [D] Volkswagen "Beetle" 300 11.81 30 1.18 SECTION B 400 15.74 40 1.57 2. A square metre is about the 7. A part 20 centimetres long also 500 19.68 50 1.97 area of: has a length of: 12. Estimate the length of the line 600 23.62 60 2.36 segment below: 700 27.56 70 2.76 [A] this sheet of paper [A] 2 000 millimetres f------1 800 31.50 80 3.15 900 35.43 ( B I a card table top [B] 200 millimetres [A] 10 millimetres 90 3.54 [ C] a bedspread [C] 2 millimetres [B] 4 centimetres [D] a postage stamp [D] 0.2 millimetre [C] 4 pascals [D] 23 milligrams 15. The equivalent of 610 mm is: [A] 61 in. 3. Fuel pump pressures of automobile 8. Seven hundred fifty grams of SECTION D [B] 24.01 in. engines are normally given in: heavy gear lube is the same as: 13. The metric unit for liquid measure [C] 6 .10 in. [A ] kilometres [A] 0 .75 kilogram which replaces the is: [D] 30in. (B] grams per cubic centimetre [B] 7 50 000 kilograms [A] hectare ( C ] kilopascals [C] 7 500 kilograms [B] millilitre [D] kilolitres [ D ] 7. 5 kilograms [C] litre 16. The equivalent of 460 mm is: [D] gram SECTION C [A] 12.34 in. 4. Torque pressure is measured in: 9 . For measuring in millimetres you [B] 24.00 in. would use a: [C] 11.41 in. [A] newton metres 14. The metric unit for liquid measure [A] container [B] kilopascals which replaces the gallon is: [D] 18.10 in. [B] pressure gage [ C I grams per metre [A] gram [C] rule [D] centimetres [ B ] kilogram [D] scale [ C ] kilolitre [D] litre 5. The correct way to write twenty 10. For measuring kilopascals you grams is: would use a: [A] 20 gms [A ] pressure gage [B] 20Gm. [B] rule [CI 20 g. [C] scale [D] 20 g [D] container

00 ~'"'"'" ' vocATOONAHD<>CATOON TESTING METRIC ABILITIES ANSWERS TO EXERCISES AND TEST 25

EXERCISES 1 THRU 6 Exercise 10 Exercise 13 Part 2. The answers depend on the items a ) 10.00 in. f ) 254mm used for the activities. millilitres litres kilograms grams ml l kg I g b ) 0.64 mm g ) 0.20mm EXERCISE 7 e ) 0.284 in. h) 5.98 in. 7 7 000 Currently accepted metric units of 3 000 3 d) 57.15 mm ) 9.84 in. 11 (11 000) measurement for each question are 6 000 (6) e ) 6.35 mm j ) 39.37 in. shown in Table 2. Standards in each (8 000) 8 (25) 25 000 occupation are being established (14) 0.4 (400) now. so answers may vary. (14 000) (23 000) 23 0.63 (630) (0.175) 175 EXERCISE 8 300 0.3 Part 3. a) 2.6 em e) 13.2 em 700 (0.7) b) 58.3 em f) 80.2 em (900) 0.9 Exercise 14 a ) 7.625 m of .794 em c) 9.4 em g) 140.0 em 250 (0.25T a ) 0.5 m h) 500 ml b) 355.2 ml d) 68.0 em h) 230.7cm (470) 0.47 b) 0.25 litre i ) 0.5 kg e ) 2.25 kg 275 (0.275) d ) 0.305 m by 0.61 m EXERCISES 9 THRU 13 e ) 50mm j ) 0.5 litre d) 2.5 kg k) 500 kg e ) 3.79 litres Tables are reproduced in total. An­ Exercise 11 swers are in parentheses. e ) 12 em l ) 1 000 em litres millilitres f ) 250 ml m) 25mm Exercise 9 l ml g } 2t n) 240 em TESTING METRIC ABILITIES metre centimetre millimetre 8 8 000 m em mm 5 (5 000) EXERCISES 15 AND 16 1. c 9. c 1 100 1 000 46 (46 000) The answers depend on the 2. B 10. A 2 200 (2 000) (32) 32 000 items used for the activities. 3. c 11. B 3 (300) (3 000) 0.4 (400) 4. A 12. A 9 (900) (9 000) 0.53 (530) 5. D 13. B D 14. (5) (500) 5 000 (0.48) 480 6. D 7-! (7 400) (74000) 7. B 15. B Exerdse 12 EXERCISE 17 8. A 16. D 0.8 80 (800)_ Part 1. 0.6 ( 60) 600 grams kilograms 0.9 kg i ) 3.22 km (0.025) 2.5 25 g kg a ) b) j ) 5.08 em (0.1-!8) (14.8) 148 3.8 litres -! 000 4 k) 59.2 ml (6.39) 639 (6 390) e ) 1.905 em 9 000 (9) d) 4.5 kg l ) 0.45 kg 23 000 (23) e ) 45.72 em m) 3.79 litres (8 000) 8 f ) 7.58 litres n) 0.305 m 300 (0.3 ) g ) 9.15m 0) 0.635 em 275 (0.27 5) h) 118.4 ml o:3'"mR 'OR VOCATOONAC ON

U. S. GOVERNMENT PRINTING OFFICE: 1976- 757-069/6207 Region No. 5- 11