Measurement of Weight

While we are all very familiar with the idea of weight, there are some small issues to clear up in terms of the measurement of weight. One of those issues is the sometimes confusing question about whether we mean weight or mass when discussing this attribute. The distinction between mass and weight can be confusing, because under certain circumstances mass and weight are the same, and under other circumstances they are different. Technically, mass is the quantity of matter that an object contains and weight is the amount of force gravity exerts on an object. Since the weight of an object on earth is determined by how much mass the object has, the two attributes have a direct relationship. Typically, when mass changes, so does weight. However, since they are not the exact same attribute, it is possible for weight to change without a change in mass. Most of us will never experience this, but if we were to travel to outer space, we would be free of the pull of earth's gravity. We would be weightless. However, since we would still be composed of matter, our mass would not have changed. If we were to stand on the moon, our weight would be much less than it is on earth, but our mass would remain the same. Aside from these rather unusual circumstances, we can ordinarily ignore the distinction between mass and weight.

So how do we measure weight, and what do the units mean? In the metric system the basic unit of weight is directly related to units used for volume and length. The inventors of the metric system began with a liter of water (one cubic decimeter) and decreed that the weight of that amount of water would be one thousand grams, or one kilogram. Thus was invented the basic unit of weight in the metric system: the gram, which is one one-thousandth of the weight of a liter of water. Once again, the 10-to-1 relationship and the use of powers of 10 are built in to the system by design. Since liter bottles of water are common today, we have on hand a ready manipulative for internalizing the weight of a kilogram. Your bottled water, minus the insignificant weight of the bottle itself, is essentially the weight of a kilogram.

As usual, units of weight in the English Customary system have a more storied past and a more difficult working relationship with other measurement units. Obviously the pound is the basic unit of weight in the English Customary system, but what, exactly, is a pound? If you have ever done much grocery shopping you can probably remember holding a pound of meat or a pound of carrots or a pound bag of brown sugar. A typical package of butter or margarine is a pound. But aside from these everyday experiences that we have with the pound as a unit, where did this unit of weight come from? Rowlett (2001) tells us that the grain was the unit on which a pound was built. Seven thousand grains made up a pound in traditional English measurement. Evidently a grain was the weight of a single grain of wheat.

The word pound originated from the Latin, libra, which meant a weight or balance. The idea of a balance is helpful in illustrating how weight is measured. The balance scale is a tool that allows us to see directly what we are measuring when we measure weight. (On the other hand, the typical bathroom scale makes it difficult to observe how weight is actually measured.) When we work with children in our efforts to help them understand weight, a balance scale is the best tool to use. Children can even explore the principles of a balance scale by placing a pencil on their desks and placing a ruler across the pencil. The ruler becomes a platform that functions like the arm of a balance scale. If the pencil is directly under the 6-inch mark (on a 12-inch ruler), the ruler can serve as a primitive balance scale. With a small set of brass weights in increments of grams or ounces, students can weigh small objects on this simple balance scale.

Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.

Elementary Mathematics: Pedagogical Content Knowledge, by James E. Schwartz, is designed to sharpen pre-service and in-service teachers' mathematics pedagogical content knowledge. The five "powerful ideas" (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands.