In order to consider a concentrated effort to teach the metric system, we should know what students should be learning and when various experiences should take place. The National Council of Teachers of Mathematics recommends an activity approach to the learning of measurement and the use of estimation as a means of learning to think metric. A report, approved and released by the NCTM Board of Directors acting on the recommendation of Instructional Affairs Committee listed the following competencies as suggestions for a basic guide for planning instructional programs.:
3.1 Grade three
Third-Grade 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”.
3.2 Sixth grade
Sixth-Grade 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.
|
-
|
|
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 experience-related travel distances; and apply the following equivalences:
|
____
____
10 cm = 1 cm, 100 cm = 1 m, 10 dm = 1 m, and 1000 m = 1 km.
-
|
|
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:
|
|
|
|
+ 2.49 m
|
Ð1.600 1
|
|
|
|
3.85 m
|
|
2.600 1
|
3.3 Ninth grade
Ninth-Grade Competencies (age 15)
By the end of the ninth grade, students should be able to . . .
1. Arrange in a greater-to 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 re-name 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
.
