YaleNew Haven Teachers Institute  Home 
by
Eric Carlson
Myriameter  —  10,000  meters 
Kilometer — 1,000 meters Hectometer — 100 meters Dekameter — 10 meters Meter — 1 meter Decimeter — 0.1 meter Centimeter — 0.01 meter
Millimeter  —  0.001  meter 
There were two important points of simplicity. Its basic units of weight and capacity were directly related to the fundamental linear unit; the liter was a cubic decimeter and the gram, the weight of a cubic centimeter of water. And, all of its secondary units were multiples or divisions by ten of the basic units. All that it is needed to know is the size of a meter, the relationship between meters and units of capacity and mass, and the meaning of the prefixes. The memorizing of the mass of arbitrary and unrelated units such as miles, feet, and acres was unnecessary. The original basis for the meter, the ten millionth of a meridian, proved to be both inaccurate and continuously changing, but that is unimportant. What is important is that most any length would do as long as it was basic to all aspects of the system and was divided and multiplied decimally.
Since the establishment of the International Conference on Weights and Measures, some changes have been made in the metric system, most of them of interest primarily to scientists and engineers. The Standard of the second has been redefined and prefixes have been added for both multiples and subdivisions to extend the scale of measurement. The prefix “tera” before meter or gram means one trillion, “giga” one billion, and “mega” one million. “Micro” means one millionth, “nano” one billionth, and “pico” one trillionth. At its 1960 meeting, the International Convention, which meets every six years, interpreted the metric system in the System International d’Unites, for which the abbreviation is S.I. in all languages. For all purposes other than scientific and advanced technical work this is merely a change in name. Actually, it is a purification and extension of the metric system to make it truly universal.
Through the years, several systems had developed which were all metric but differed in detail in various parts of the world. The S. I. also formalized the extension of the metric system to seven base units. The basic units of the complete S. I. system are:
Quantity Measured  Name of Unit  Symbol 
Length — Meter (m) Mass — Kilogram (kg) Time — Second (s) Electric Current — Ampere (A) Temperature — Kelvin (K) Luminous Intensity — Candela (cd)
Amount of Substance  —  Mole  (mol) 
Energy has many forms, but all energy is basically the product of force and distance and is convertible form one form to another. Thus, the S. I. system uses one unit for all kinds of energy; the “joule” (J) which is the amount of energy needed to push a distance of one meter against a force of one newton.
When Watt perfected the steam engine it replaced the horse so people wanted to know its capabilities in terms of the horse. So engines were rated in horsepower. When the electric motor was invented, its power was named after Watt. No matter what form power takes, it is a rate of generation or dissipation of energy, so the only unit of power in the S. I. system is called the Watt (W) which represents one joule of energy per second. One horsepower is roughly equivalent to 746 Watts.
There is no international standard liter. One liter is slightly larger than the U.S. quart. Precise measurements of volume in science are expressed in cubic centimeters (cm^{3}) or cubic millimeters (mm^{3}).
The most common unit of mass or weight is the kilogram (kg) which equals about 2.2 pounds. Grams (g) and metric tons (t) are also used.
To the general public, most of the history and all but the more basic units of the metric system are unnecessary. Some background and at least a basic awareness of all the components of the metric system are useful for those of us who will teach it.
What does all this mean to teachers of math? First of all, like it or not, this country will eventually join the rest of the world in using the metric system. Thus, we would be doing our students a disservice by not equipping them with the tools necessary to compete in the world. And even though they would learn the metric system without us, by teaching them in a manner in which they can see the usefulness of it, we can go a long way in eliminating the unfavorable way that our students compare in math with students in the rest of the world.
Besides, it’s easier. Not only does the aforementioned simplicity make it easier to teach, but also, the areas of the present curriculum which could be eliminated or at least deemphasized would also simplify our jobs. For example, the customary measures as they are now taught could be relegated to the status of simple mention as a historical footnote, or better, eliminated completely. Also, with the system of fractions and the operations using them, reduction to the introduction of the most basic such as halves, thirds, and quarters with a few simple calculations would be sufficient. Who among us hasn’t sighed at the frustration of trying to impart the concept of “inverse” when teaching the division of fractions. Time spent on these areas would be greatly reduced allowing more time for concentration on more useful areas.
Certainly, there would also be drawbacks. The major one, of course, is monetary. The expense of converting all packaging, signs, much machinery, etc. would be astronomical. Along with the cost would be the inconvenience. Most of the population has not grown up learning metrics and therefore might find conversion annoying at best. An argument could certainly be made for just allowing the “creeping conversion” now going on to simply continue. At some future time conversion would be complete with far less disruption and cost.
I am of the opinion that compromise is probably the best route to go. Immediate, legislated conversion would not be practical. Yet, by concentrated education of our youth in the metric system, the next generation would hasten and complete the conversion as they assumed roles of responsibility. That brings us back to our unit.
ThirdGrade Competencies (age 9)
By the end of the third grade, students should be able to . . .
1. Identify the centimeter and the meter as units of linear measure; identify the kilogram as a unit of weight (mass) measure; and identify the liter as a unit of volume (liquid) measure.
 2. Distinguish between models of the meter and the centimeter.
 3. Use a centimeter ruler (without millimeter markings) to measure line segments and linear objects to the nearest centimeter, and to draw a line segment having a given measure in centimeters to the nearest centimeter.
 4. Identify the unit name associated with each of the symbols cm, m, kg, 1, (but not necessarily reverse the process).
 5. Find the weight (mass) of an object to the nearest kilogram.
 6. Distinguish a liter model from another capacity model at least 50 percent larger or smaller; and use a liter container to measure the volume of a liquid or granular substance.
 7. Read a temperature (positive, zero, and negative) from a Celsius scale thermometer to the nearest degree; and identify a zero Celsius temperature as “freezing” and a negative Celsius temperature as “below freezing”.
SixthGrade Competencies (age 12)
At the end of the sixth grade, students should be able to . . .
1.  Select a unit model for each of the units meter, decimeter, centimeter, liter, and kilogram; and measure lengths to the nearest of millimeters. 
________10 cm = 1 cm, 100 cm = 1 m, 10 dm = 1 m, and 1000 m = 1 km.
2. Use a meterstick (or other rule) with millimeter markings to measure line segments and linear objects to the nearest tenth of a centimeter, tenth of a decimeter, and tenth of a meter; use the kilometer to describe experiencerelated travel distances; and apply the following equivalences:
3. Make a direct reading of the weight (mass) measure of an object to the nearest tenth of a kilogram from a scale; read the measure of a liquid or granular substance in a graduated container to the nearest ten milliliters. 4. State application for each metric unit which they have basic familiarity, from areas such as commerce, industry, science, and the arts. 5. Identify the unit name associated with each of the symbols mm, cm, dm, m, km, g, kg, ml, 1, and degrees Celsius, and, in most cases, reverse the process. 6. State that the linear dimensions of the standard model of a square centimeter and a cubic centimeter are 1 cm by 1 cm and 1 cm by 1 cm by 1 cm, respectively; make a similar statement for the dimensions of the standard models of a square and cubic meter. 7. Recognize and apply the following relationships: 1 meter is a little more than a yard, 1 kilometer is a little more than 1/2 mile, 1 kilogram is a little more than 2 pounds, 2.5 cm is about 1 inch, and 1 liter is a little more than 1 quart. This is the extent of conversions between the two systems recommended for the interim changeover period. 8. Relate zero degree Celsius and 100 degrees Celsius to the freezing and boiling temperatures of water; identify 27 degrees Celcius as “normal” body temperature; and identify temperatures in the human “comfort zone” (about 22 to 25 degrees Celcius). 9. Estimate distances up to 5 meters in whole meters and lengths up to 10 centimeters in whole centimeters. 10. Estimate volumes up to 5 liters in whole liters and estimate 250 millimeters (approximately 1 cup). 11. Compute sums and differences of measures expressed in decimal form such as:
1.36 m  4.200 1 
+ 2.49 m Đ1.600 1 3.85 m 2.600 1
NinthGrade Competencies (age 15)
By the end of the ninth grade, students should be able to . . .
1. Arrange in a greaterto less sequence the prefixes kilo, hecto, deca, (unit), deci, centi and milli and relate them to the multiplication constants 1000, 100, 10 (1), 0.1, 0.01, 0.001; and read lengths directly from a meterstick or metric tape as decimal measures, for example, 37.5 for 375 mm length, or 2.55 m for 255 cm length.
 2. Select the appropriate type of unit for a given measurement situation, such as linear unit for length, volume unit for volume, weight (mass) unit for weight (mass), and select a convenient size unit for similar situations.
 3. Convert from one unit to a larger (or smaller) unit of the same type. For example, 136 cm = 1.36 and 25 m = 0.25 km.
 4. Relate square centimeter, cubic centimeter, square meter, cubic meter, square millimeter, and cubic millimeter to their respective symbols (cm 2, cm, c, m , mm, and mm ).
 5. Identify the liter as a special name for 1 cubic decimeter (and also for 1000 cubic centimeters); identify 1 cubic centimeter and 1 milliliter as equivalent; and rename 1000 kilograms as 1 ton (lt) and vice versa.
 6. Estimate distances up to 100 meters in multiples of 10 meters; and estimate distances up to 100 centimeters in multiples of 10 centimeters.
 7. Use referents for varying amounts of weight (mass), such as paper clip (about 1 g) a liter of milk (about 1 kg), or personal weight (mass) (perhaps) 50 kg); and give a meaningful referent for 1 kilometer.
 8. Convert a combination measurement expression to a decimal multiple of one of the two units used such as: 1 m 34 cm = 1.3m ( or 134 cm) and 1 liter 300 ml = 1.3000 liter (or 1300 ml).
 9. Convert from smaller to larger (or larger to smaller) square and cubic units, such as: 3000 cm = 0.3 m^{2} or 7500 mm = 7.5 cm^{3}.
One thing that should probably be avoided is teaching conversion from one system to another. This would encourage thinking in both systems. Conversion tables and some simple ability in the process will probably be necessary but beyond that it would only serve to confuse and complicate instruction in the metric system.
Lastly, evaluation should be an important part of the curriculum. Continuous change and improvement will be necessary to provide a better working system. As we learn what works and what doesn’t we can accommodate this into our curriculum. It would also be useful to have students evaluate the curriculum so that we may see, from their perspective, what they feel is effective and what isn’t.
In English, the idea of prefixes and base words could become a unit. One could assign interviews or letters to persons in science, business, or government relating to the metric system.
In Industrial Arts, comparisons of the advantages and disadvantages of the American system to the metric system, or how elements of the metric system are already in place are possible topics. There could be an investigation into the decision by General Motors to go metric and its ramifications.
The area of homemaking will be greatly affected by the change to the metric system. Many possibilities exist here. Will all measuring utensils and recipes change? Will sizes of clothes necessitate changes of machines and measuring?
Even in the area of physical education, the fact that the rest of the world competes on fields and in events which are measured in metric means that many traditional concepts will have to change. Will Jose Conseco’s towering home run be only 120 meters instead of 400 feet. Will Kareem Jabar be a whopping 220 centimeters instead of a mere 7 feet 2 inches?
Objective
To introduce the metric system
To show conversion of units by powers of ten
Procedure
 1. Briefly explain what the metric system is and how it came about.
 2. Show how meters, centimeters, and millimeters can be converted using powers of 10. Use a metric ruler and a meter stick for illustration.
 3. Have students measure various items such as pencils, books, desks, and other students and decide which unit is most appropriate.
 4. Homework might be to find and measure at least two items appropriate to each unit of measure; meters, centimeters, and millimeters.
Objective
To think in metrics
To measure in metrics
To convert from one unit of measure to another
Plan
Make a metric scale drawing
Procedure
3. The following class assignment would be to make a scale drawing to some appropriate scale such as 1 m to 1 cm or 1 m to 5 cm. Additional assignments might include other scale drawings or maps using estimated metric distances.
 1. Make a meter stick. This could be done in class with various materials. It could also be an assignment for an industrial arts class.
 2. Students would be instructed to measure their house or some area of it. (They might practice by measuring the classroom or hallway.)
Another assignment might be the construction of a measuring wheel. The dimensions might be calculated in class while the actual construction could take place at home or in industrial arts.
Objective
To understand the size of an atom
To multiply and divide by powers of ten To practice estimation
Materials needed
Film “Powers of Ten” (available from the central A.V. office)
Procedure
 1. Review the fact that the metric base unit of length is the meter and show the meter stick so there a concrete display of size.
 2. Discuss the concept of atoms so that students are aware that everything is made up of atoms. This might lead to discussions of the states of matter or similar things.
 3. Show the film “Powers of Ten” and discuss.
 4. Discuss the fact that, in metrics, different units result from multiplying or dividing by powers of ten. Thus a meter divided by ten equals a decimeter which divided by ten equals a centimeter and so on. So, if a meter divided into a thousand parts equals a millimeter, then a millimeter divided into 10 million parts is roughly the size of an atom; or mathematically an atom equals
_____1m____  or  ___1mm__  10,000,000,000  10,000,000 
 ____If the concept of negative powers of ten has been introduced, then it can be shown as 10 m or 10 mm. Remind students that when numbers are expressed as powers of ten and multiplied or divided, the exponents are simply added or subtracted.
 5. Moving on to a concrete representation of the relative sizes, suppose that a grain of sand is i mm long. Then in the length of 1 grain of sand there would be 10,000,000 atoms or 10^{7}. But, because the grain of sand also has width and height, it would be 10^{7} wide and 10^{7} high. Knowing that volume equals length times width times height (v=lwh) then 10^{7} 10^{7} 10^{7} =10^{21} or 1,000,000,000,000,000,000,000 atoms in a grain of sand. This should give students the idea of just how miniscule an atom is. Another way to say it would be to figure a trip to the sun. If the sun is roughly 100,000,000 km away, how far would a journey equal to the length of 1 atom be? (100,000,000 km = 10^{8} km = 10^{11}m divided by 10^{10} which is the number of atoms in a meter gives us 10^{1} or 10 meters in our journey to the sun.)
 ________A possible assignment might be to have students think of other situations which might lend themselves to estimation, powers of ten and the atom.
Kemp, Albert F. and Richards, Thomas J. The Metric System Made Simple Laidlaw Brothers, 1973
Consumers Association of Canada, “Metrics and Measurements” and “S.I. is Simple” from Canadian Consumer Jan. and Nov. 1972
The World Book Encyclopedia, “Metrics” 1977
The Mafex Teacher’s Press “The Painless Metric System” from Metric Idea Exchange, Area Cooperative Educational Services, Nov. 1978
National Bureau of Standards Technical News Bulletin, “The Metric Changeover” Vol. 57, No. 5
For Reading
Donovan, Frank Prepare Now For A Metric Future, Web and Talley, N.Y. 1970 (good for history, advantages, and disadvantages of metrics)
Kemp, Albert F. and Richards, Thomas J. The Metric System Made Simple Laidlaw Brothers, 1973 (good for brief explanations and examples)
Consumer’s Association of Canada, “Metrics and Measurements” and “S. I. Is Simple” from Canadian Consumer, Jan. and Nov. 1972 (shows how Canada handled conversion)
Holden, Alan The Nature of Solids Columbia University Press, 1972 (deep, but shows scientific application)
National Bureau of Standards Technical News Bulletin, “The Metric Changeover” Vol. 57 No. 5 Pgs. 103106 (discusses America’s progress toward change)
Szabo, Dr. Michael and Trueblood, Dr. Cecil R. A K12 Curriculum Activities Handbook for Teachers The Norhteastern Metric Educational Consortium, 1977 (sample activities for all grade levels in all disciplines)
Evans, Richard, Wixon, Edwin, and Hanson,Susan Make Your Own Metric Measuring Aids Area Cooperative Educational Services (ACES) (excellent for all levels)
These last two plus a number of “Metric Idea Exchange” pamphlets which contain topical articles on the metric system are available from the ACES office at 800 Dixwell Ave. in New Haven. There are also numerous publishers and supply catalogs offering metric materials such as Education Supplements, 163 Westport Ave., Norwalk, Conn. 06851, and Enrich, 760 Kifer Rd., Sunnyvale, CA. 94086. I haven’t reviewed these materials.
Also, SNET Co. published a nice little metric conversion booklet but I’m not sure it’s still available.
Available from Cooper Group
P.O. Box 728
Apex, N.C. 27502
Metric Packet
National Bureau of Standards Metric Information Office
Washington, D.C. 20234
The United States Metric System
Federal Reserve Bank of Minneapolis
Minneapolis, Mn. 55480
Contents of 1989 Volume VI  Directory of Volumes  Index  YaleNew Haven Teachers Institute
