Measuring with Metric Units &
Scaling a Model
Adopted from WonderScience, a publication supporting National Science Education Standards
SOL 5.1 and 6.1
Materials:
Meter stick
String
Data table on the board
Chalk
Paper
The first length units were created in antiquity and were based on the human body. These include the cubit—the distance from the elbow to the fingertip—and the foot. Because it was inconvenient to use one particular forearm or foot for all measurements, these distances were transferred to standards made of some sturdy material. Then someone, such as a merchant, who made frequent measurement could make a copy of the standard. This process is called calibration. The meter, a more modern unit, was devised in France at the end of the seventeenth century. A meter is a certain fraction of the circumference of the Earth.
The most important metric units of length are the millimeter, the centimeter, the meter and the kilometer. These units are related to each other by powers of 10. For instance, 1 centimeter is 10 millimeters, 1 meter is 100 centimeters, and 1 kilometer is 1,000 meters. These ratios make it easy to convert from one unit to another. To find the number of centimeters in a kilometer, for instance, you only need to multiply 1,000 by 100. It’s easy!
Scientists all over the world use the metric system, and that promotes effective communication among scientists. When a scientist publishes results, other scientists use these results to design new experiments and to create new theories. That’s how science moves ahead. Having one standard measurement system promotes the good communication that helps scientists everywhere build on each other’s work.
Measuring in metric units…
Students measure their height in centimeters using a string. To make things easier and more accurate, you can place a mark on the string so the mark is just under the edge of the student’s shoe. Students should realize that they will need to control the tightness of the string to get an accurate measurement. For heights greater than 1 meter, the height can be written as 1 meter plus the remaining number of centimeters. This conversion from centimeters to meters plus centimeters brings out the basic process of measuring length: counting how many times the distance unit goes into the length, and then adding the remainder. It’s division!
As the children measure their heights, have them record their results in a data table on the board. You can extend this lesson by guiding children to create graphs or find averages using the class’s results.
How the metric system is superior…
There is a powerful advantage of the metric length units. The centimeter is subdivided into only one unit, the millimeter. Ten millimeters make one centimeter. Now compare that simplicity with the division of the inch. There’s half an inch, one quarter of an inch, an eighth of an inch, and a sixteenth of an inch. Adding fractions of an inch requires converting to a common denominator, such as eighths of sixteenths. It’s a lot of work. Students will need to work with both systems, but working in metric does have its advantages. You could create other math problems involving the metric system in calculating cost to give students extra problem-solving practice.
Metric Map Maneuvers
It’s easy to get mixed up in converting miles to kilometers or vice versa. Here’s how to do it. To convert 8 kilometers to miles, for example, you need to know how many miles in 1 kilometer, and then you’ll multiply that number by 8. One kilometer is about six-tenths (.6) of a mile. Now let’s figure out:
1 km = 0.6 mi
8 km = 8 x 0.6 mi = 4.8 mi
So we get the relationship 8 km = 4.8 mi. For a given distance, which is greater, the number of miles or the number of kilometers? The number of kilometers is always greater, because the kilometer is the smaller unit. So that’s an easy way to check your conversion.
Let’s go the other way and convert 5 miles to kilometers. One mile is about 1.6 kilometers. Now, to convert 5 miles to kilometers:
1 mi = 1.6 km
5 mi = 5 x 1.6 km = 8 km
Again, let’s check: the number of kilometers (8) is greater than the number of miles (5), just as we expect.
Extension: Scaling. Extend this exercise by having children make scale models of themselves. If a child is one meter tall, his or her model might be 1 centimeter tall. The child’s arms and legs should be to scale, as well. For even further extension, ask the child to calculate the scalar model’s height in inches.