Hands-On Activities With Metrics*

Evan McFeeAssociate Professor of EducationBowling Green State UniversityBowling Green, Ohio 43403

It is estimated that over ninety percent of the world’s population is onthe metric system. After a long wait, the United States now has a legisla-tive commitment to recognize the International System of Units (SI) asthe primary measurement system. The Metric Conversion Act of 1975serves notice to educators to begin the teaching of the SI system in ourclassrooms. (1)

In order to teach the SI units in our schools, it is critical that metrics beintroduced in the early grades. (2) As a result, we first need to familiarizethe elementary educators with the use of the metric system and to assistthem in developing creative teaching methods and materials for teachingSI units. In wwking with educators \ve need to take into account thattheir attitudes and emotions play an important part in their education. Inorder to develop a positive attitude and to reduce their anxieties in theirinitial education, an easy stair-step method of instruction in SI units w^as

developed by the writer. This method has proven very successful innumerous sessions w^ith teachers in familiarizing them^vith the metricunits of length, volume, and mass. In teaching the stair-step method thefollowing instructions are given.

Conversion Within

Draw a stair-step which has seven levels as follows:km

m

[mmThe stair-step should extend from the bottom, upward to the left. On themiddle step write an //?, which would represent a meter. On the top stepput a km w^hich would represent a kilometer. On the bottom step put mmwhich would represent a millimeter. Other steps would be represented bymetric symbols which would be introduced at a later time. In initial prac-tice one might give a linear measurement in m (meters) and then convertthis to km (kilometers) by merely going three steps up to the left. For"Paper presented at the SSMA Annual Contention, Toledo, Ohio, November 12, 1976

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each step one goes up he moves the decimal one place to the left. For ex-ample, if he started with 1 meter, he would then have .001 kilometer.One would continue to practice with conversion within by then convert-ing a linear measurement in m (meters) to mm (millimeters) by goingthree steps down to the right, and for each step he goes down he wouldmove the decimal one place to the right. The student would be giventhese steps on the board or on a card for practice and for future refer-ence. He need never memorize this. After continued drill and practice us-ing the stair-step method and the three basic units, one might then intro-duce the symbols for the other steps. Too many people make the metricsystem seem difficult by introducing the full range of units in the initialstages of teaching. (3) In introducing the additional steps, one should citethat by going two steps down to the right from m, or from the middlestep, one would enter cm (centimeter). It should be pointed out that acentimeter is a commonly used unit in length. After introducing the cen-timeter, one could then go one step down from the middle step and enterdm which is the symbol for the decimeter. Going one step up from themiddle step to the left, one wxmid enter dam which w^uld represent theSI symbol for the dekameter. (4) Also, in going two steps up from themiddle to the left one would place an hm which would represent a hecto-meter. One should follow^ with continued practice and drill with conver-sion within by going up and down the stairs and emphasizing the mainunits represented by the symbols mm, cm, /??, km.By drawing another stair-step to the right and in line with the first

stair-step with the same number of steps, the same procedure for volumecan be followed by merely substituting symbols of volume for symbols oflength such as / (liter) for m (meter). The three basic units to stress involume would be the milliliter, liter, and kiloliter.By drawing a third stair-step with the same number of steps to the right

and in line with the other two, the same procedure can be followed formass by substituting symbols of mass for symbols of length such as g(gram) for / (liter). The three basic units to stress in mass would be themilligram, gram, and kilogram.The learner would then have three different stair-steps with w^hich to

practice conversion of linear, volume, and mass measurements within themetric system. These stair-steps with their symbols need not be commit-ted to memory, but should be available for the student’s use at all times.Continued drill and practice will soon familiarize the learner with thesymbols and process of conversion within the metric system. See the fol-lowing:

Hands-On Activities With Metrics 295

Intuition in Length

While teaching the stair-step method and using it for drill, simultane-ous instruction can be given in "thinking in metrics" in length, volume,and mass by providing hands-on activities with familiar everydayobjects.

In teaching length one can start by measuring a finger nail that is abouta centimeter. With this as a reference rule, they can measure the width ofa text book, the width of a paper clip, and the length of a pencil. Theycan then start estimating and measuring many other everyday objectssuch as the length of a piece of chalk, length of a spoon, and other itemsused everyday. Similar references can then be made to the meter and ac-tivities of estimating and measuring can follow.

Intuition of Volume

In teaching volume, familiar reference points for the milliliter and litercan be found, and activities of estimating and measuring should follow.Such reference points could include a bottle cap which would be about 5ml or a mayonnaise jar filled to the brim, which would be a liter. Addi-tional handy familiar objects might include a spoon, a tableglass, a babyjar, and a paper cup. Simultaneous instruction should include practiceusing the stair-step method to convert units from larger to smaller andvice versa within the metric system.

Intuition of Mass

In teaching mass, one should treat mass as weight for the beginnerwith only a brief statement of the difference. One good familiar startingpoint could be the weight of an M&M candy piece which weighs about agram. Many similar objects could be used such as a bean or a raisin.Candy suckers or other objects weighing about 5 grams could then be in-troduced providing a 5 gram reference point. Gradually, heavier objects

296 School Science and Mathematics

such as a spoon, knife, or fork which are used daily could be estimatedand weighed. Finally heavier objects that are familiar such as an apple,orange, or a can of beans (which weighs about a kilogram) could be in-troduced to make the activities meaningful and realistic. (5)By using these above methods and providing hands-on activities with

inexpensive materials, teachers can soon get an intuitive feeling forlength, mass, and volume. They can soon "think in metrics" and canalso easily convert from units within the system to larger or smaller units.With pleasurable success and familiar objects used in their initial instruc-tions, teachers are more apt to have a positive attitude and a willingnessto want to teach the metric system in a meaningful manner.

REFERENCES

1. New from the Metric Association, "Editorial Comment" Metric News, Vol. 3, No. 1(Jan.-Feb.) p. 24.

2. CHIPLEV, DONALD R. and TRUEBLOOD, CECIL R., "Monitoring the Move to Metrica-tion: A Research Strategy and Survey Summary/’ School Science and Mathematics,LXXV1, No. 8 December 1976, 704.

3. DUBINSCH, Rov. "Some comments on teaching the metric system," The ArithmeticTeacher, Vol. 23, No. 2 (February 1976) 106.

4. U.S. Department of Commerce/National Bureau of Standards, The Internationaf Sys-tem of Units (SI). NBS Special Publication 330, 1974 Edition, U.S. Government Prim-ing Office, Washington D.C.. 1974. p. 49.

5. CHAIUPSKV, At.BERT B.. and CR-\WIORD, JACK J., "Preparing the Educator To GoMetric," Phi Delta Kappan. Vol. 57. No. 4 (December 1975) p. 264.

NEW TELESCOPE

Early in 1978, probably in April, the Multiple Mirror Telescope will receive"first light," and scientists will then start judging how successful this astronomi-cal experiment will be. The Multiple Mirror Telescope, or MMT, is being builton Mt. Hopkins about 40 miles southeast of Tucson. It’s a joint project of theUniversity of Arizona and Smithsonian Astrophysical Observatory.The MMT is really an S8 million experiment testing a new idea in ground-

based astronomy. It will combine the light gathered by six identical 72-inchmirrors to provide the light-gathering capacity of a single 175-inch mirror.There are only two others in the world bigger. They are the 200-inch on Mt.

Palomar in California that was placed in operation in 1948 and a 236-inchtelescope built by the Russians in the 1970s.Many astronomers believe that 200 inches is about the maximum size for a

single-mirror reflecting telescope. So far there has not been much news about\\o\\ the Russian telescope is working.

Reflecting telescopes gather the light of a star or planet or other body andmagnify it with a parabolic mirror. There are some refracting telescopes, thosethat magnify the light through a lens. The largest is 40 inches, built in the 1890s.Larger refracting telescopes are not practical because the lenses absorb too muchlight.

If the MMT is successful, others could be built to exceed the 200-inch or 236-inch telescopes. The cost of the MMT is about half of what it would cost to builda 176-inch single mirror telescope.What will the world’s third largest telescope be used for? It will be used by

both astronomers who study the stars and interstellar space, and planetaryscientists who study the planets and their satellites in our solar system.