Creating Measurement Units
Suppose you are self-employed and you are looking for a way to measure your performance. You can't simply look at the "bottom line" to see how much money you made, because that doesn't tell you how hard you worked to achieve that bottom line. What other factors should be taken into consideration? How can you develop a measurement unit that takes all of these variables into consideration?
Other factors that should be taken into account for measuring your own performance might be the number of hours worked, the number of times you had to redo a job to get it right, the cost of materials, and/or the cost of wasted materials used on "mistakes". If you wanted to combine these factors into a measurement unit you would have to decide how much weight to give each of them. You might concoct a hyphenated measurement unit to represent all the important factors.
With the rapidly rising cost of gasoline, you are exploring whether it would be worthwhile to trade in your gasoline-powered car for a hybrid car. Develop a measurement unit that takes into account the number of miles you drive, the cost of a gallon of gasoline, the cost of driving the new hybrid car, and the cost of driving your current gasoline-powered car. The purpose of this measurement unit is to help you know whether or not you'll save money by switching to a hybrid car.
A measurement unit for comparing costs of cars might be a dollars-per-mile unit or, if you could specify a certain number of miles you would drive each week for each month, you might be able to express it as a dollars-per-week or dollars-per-month unit.
Imagine all the water that is used on your school's campus in a single day. How could you measure this usage? How could you estimate how much water is used on an annual basis?
Measurement of the water usage of a school campus would be very complicated. If each building had a water meter, someone could be dispatched to read the meters on each building in the morning on two consecutive days. Then the readings from the first day could be subtracted from the readings for the second day. Then all these individual meter results could be added together. If you don't have individual meters on the buildings, you could find out if there is a master meter for the entire campus. Without such a device, you would have to estimate the amount of usage, perhaps from each of the different types of fixtures, and multiply by the number of those fixtures. It would be a very complex problem, and the best you could hope for would be an estimate.
You have been given your best friend's mother's pie crust recipe. It calls for "a little salt" and "a teeny bit of baking powder." This recipe makes the best pie crust, by far, that you have ever tasted, and you want to share it with your friends. How do you translate those amounts into quantities that your friends can measure with everyday measurement tools so that they can enjoy the same quality pie crust that you enjoy? Keep in mind that baking powder is an active ingredient and too much or too little will change the chemistry of the recipe.
If you have successfully made the recipe several times, and you know how much "a little salt" is and "a teeny bit of baking powder" is, you could put those amounts into measuring spoons and then translate those amounts into standard measuring spoon units like 1⁄8 teaspoon or some such thing.
Self-Check
How can a nonstandard unit, such as a piece of notebook paper, be used as a tool for measuring distances?
A piece of notebook paper can be used as a measuring device, even though it is a nonstandard length, as long as you maintain its size and use it as a unit. If you use it to measure a distance such as the length of a whiteboard, you will know the number of notebook-paper-units that whiteboard is.
What might be some benefits and drawbacks of using nonstandard units for measuring?
A benefit of a nonstandard unit is that is available. Often when you need to measure something you don't have a ruler. With an understanding of nonstandard units you might be able to accomplish your measurement goals using whatever you have available as your measurement unit. A drawback is that you cannot carry on any communication with someone who doesn't know the size of your unit. It is a purely personal and isolated measurement device if it uses nonstandard units.
What is the difference between linear measurement and area measurement?
Linear measurement is simply a distance between two points. It is one dimensional. Area measurement has both length and width; it is two dimensional. Area units are squares, whereas linear units are distances.
What is a significant issue that learners face when they are learning to measure volume?
A significant issue in the measurement of volume is that the units are three-dimensional cubes, but the space we are interested in measuring is rarely cube shaped. These cube-shaped units are abstract.
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What is a significant issue that learners face when they are learning to measure weight?
A significant issue in the measurement of weight is that there is, in rare cases, a difference between mass and weight. We should know what both terms mean and be able to explain when they are different and when they are not.
What is a significant issue that learners face when they are learning to measure time?
A significant issue in the measurement of time is that the units of minutes and hours use two different grouping systems. With minutes, the grouping value is 60; with hours the grouping value is 12. Also, each time occurs twice each day. This can be confusing to children.
How is the metric system superior to the "traditional" system of measurement?
The metric system is an easier system to use (if you learn it from the beginning) because all conversions from unit to unit are on the basis of powers of ten.
Explain what we mean when we say that measurement is always an estimate.
Measurement is always an estimate because no matter what tool we use to measure with, there are always unit marking and unit-partition markings. Reading a measuring tool always involves a decision as to which marking is the closest to the thing we are measuring.
Explain the role composing has in the topic of measurement.
In measurement, composing is involved in deciding which measurement unit is most appropriate.
Explain the role decomposing has in the topic of measurement.
In measurement, decomposing is involved in the dividing up of the measurement unit we are using to measure. Decomposing determines how much precision we are measuring with. More precision comes from finer-grained partitions.
How does representation play a role in measurement?
When we measure something and then use the measurement to describe that thing, we are representing that object in a certain way.
Further enhance your math curriculum with more Professional Development Resources for Teaching Measurement, Grades K-5.
