Home » Curriculum » Quadrivium » QRV-211 Intro to Classical Arithmetic » Intro to Classical Arithmetic, Lesson 05. Dry & Liquid Measure

Intro to Classical Arithmetic, Lesson 05. Dry & Liquid Measure

To complete this lesson, complete the following tasks:

1. Study the lesson for mastery.
2. Complete your Memory Work.
3. Complete the Lesson Exercises.
4. Complete the Lesson Examination.

Lesson

We have learned that to measure any quantity, we must begin with some known quantity, which we call Unity. When we measure, we count how many times a unity or unit is contained in the quantity we wish to measure. We discussed how our everyday tasks do not usually need exact measurements–we can estimate–but in many cases exact measurements are needed. For example, an old cook might prepare a soup with “a handful of this” and “a pinch of that”, since they know exactly how much to add by their experience. On the other hand, in a science laboratory, we may need to measure liquids so exactly that one drop too much might spoil the study! For these different situations, different measuring tools are used.

We learned that men have worked together to set these units so that all men everywhere can use the same units and share measurements. In recent lessons, we’ve studied the units that men have established for measuring distance, length and weight. In this lesson, we will learn the units established for measuring dry and liquid quantities.

Units of Dry & Liquid Measure

We learned in measuring length, distance and weight that Americans use a different system of units than other countries in the world–and the same is true in measuring dry and liquid quantities. If you see the quantity of items measured in liters and milliliters, that is the Metric System. We will learn about the Metric System later in Arithmetic. Before the metric system was developed, there were two basic units used for measuring dry and liquid quantities. Of course one could have measured these quantities by weight, but there is an easier way of doing business: by Volume. Volume refers to the size of a container in which a quantity is contained. Once men knew what a certain standard container of corn or oil weighed, they could simply measure them out in containers rather than weighing them.

Dry Measure

The basic container with which dry quantities are measured is the bushel. Unfortunately, many people call any wicker basket a “bushel basket” even if it does not measure a bushel. A true bushel is known by its size: it is eighteen and one-half inches wide and eight inches deep. When filled with corn or grain, a true bushel will weigh about 60 lbs. When dry quantities are packaged for sale, they are usually measured out in “bushel bags”. If your family buys grass seed at the hardware store, for example, you will probably get it in a bushel bag quantity.

Of course, men need to measure dry quantities less than a bushel and for this we have a number of standard units. A bushel contains four pecks. One half of a peck is a gallon, which means that there are eight gallons in a bushel. If we divide a gallon into four parts, we have a quart. One half of a quart is a pint.

Around the house, we will normally use even smaller measures than these. The units of measurement used in cooking or cleaning usually begin with the cup. A cup is one half of a pint. A cup contains 16 tablespoons and in one tablespoon there are 3 teaspoons. Thus, to be a master of dry measurements, you should know how to measure any dry quantity, from as little as a teaspoon all the way up to a full bushel. We need to be careful with these measurements because if you open your silverware draw and take out a “tablespoon” or a “teaspoon” these are not measuring spoons! Just like the bushel basket, we often call these spoons by these names, but they should not be used for measuring since they are not always the same sizes. Anytime you need to measure a teaspoon or tablespoon, you will use measuring spoons.

Liquid Measure

Make sure you have it clear in your mind that the units of volume measurement we have just studied are used for dry quantities. We also measure liquid quantities by volume, however the basic container with which liquid quantities are measured is the gallon. We do not measure liquids with the peck or the bushel. The gallon is an easy unit to start with because everyone knows the size of a gallon of milk. If you measure a gallon of milk you will see that the bottom is a square with each side about six inches in length. If the container continued straight up from the bottom it would measure about six inches in height. Thus, a gallon is a container that is just about 6″ square and 6″ high. Other than the fact that liquid measures do not use the peck or bushel, the only other difference that must be known about dry and liquid measures is how they are measured.

Volume Measure Summary

This chart should be memorized:

3 teaspoons equal 1 tablespoon
16 tablespoons equal 1 cup
2 cups equal 1 pint
2 pints equal 1 quart
4 quarts equal 1 gallon
2 gallons equal 1 peck
4 pecks equal 1 bushel

Notice that it is easy to figure out how many pecks are in a bushel, but as we move to quarts and pints and on further to smaller units, it gets more difficult to continue counting how many smaller units are contained in a larger measure like a bushel. The numbers get larger and larger and therefore more difficult to keep track of. For this sort of computation, we will later learn how to multiply and divide numbers. That will make these computations very easy.

Everyday Measuring Equipment

If you look around your kitchen or garage you will find a number of different kinds of measuring cups and spoons. It is important to know the differences between these pieces of equipment and how to use them rightly. You should know the difference between measuring cups used for dry quantities and those for measuring liquid quantities. These differences are important.

The easiest mark by which you may identify a liquid measuring cup (see right) is the pouring spout at the top that allows the liquids to be easily poured after measuring. You can see on the cup the markings for cups and ounces. By setting the cup on a flat surface, simply add or pour off the liquid until the surface of the liquid lines up with the desired measurement. Liquid measuring cups are normally made of glass that allows the liquids to be heated without melting the cup.

Dry measuring cups (see left) are made and used differently. Since they will be filled with a dry material like sugar, flour or soap powder, they are made to be filled to the top with no pouring spout. Each cup measures a different unit (cup, half cup, etc..) and they are filled and then leveled off by scraping a straight-edged utensil across the top.

It is important to use dry measuring cups correctly because if you simply scoop the dry substance out of a container it will pack down inside the measuring cup and you will actually be using much more than you should. Dry substances are to be taken from their container with a spoon and added to the measuring cup so that they stay loose–not packed down tightly in the cup–unless the instructions say to do otherwise.

For tablespoons and teaspoons, we use measuring spoons (see right). These are the same for both liquid and dry measures. Since they contain small quantities, we need not be afraid of spills and they are easily dumped into a bowl or pot for mixing. Each spoon measures a different quantity and we simply fill them up, level them off and dump them out.

Scientific Measuring Equipment

In science laboratories, where very exact measurements are needed, different equipment is used that that in the home. All measurements in laboratories, however, are made with metric units, which we will learn about later. Nevertheless, it is still worthwhile to learn the different pieces of measuring equipment used in the laboratory. Dry quantities are normally measured by weight, not volume, so we will ignore them here.

First, the beaker is used for most larger liquid quantities, and come in many different sizes. Second, more exact quantities are normally measured with the taller and more accurate graduated cylinder. To measure very small quantities of liquids, scientists use burettes, which allow drops of a liquid to be added to a mixture. In the past, this was controlled by a valve that one simply opened and shut by hand, but today electronic burettes are available to make measurements even more accurate.

Summary

As we have learned, we cannot measure any quantity unless we find some known quantity to measure it with. The “known quantity” we use is called unity or a unit, and we may use any quantity we wish as unity. However, so that men can measure more exactly and share their measurements with others, units of measurement have been established for all. For measuring length using the American system, these units include the inch, the foot, the yard and the mile. For measuring weight using the Avoirdupois system, these units include the ounce, the pound and the ton. For measuring quantities by volume, these units range from the bushel down to the peck, gallon, quart, pint, cup, tablespoon and teaspoon.

Remember that in addition to these systems of units is the modern Metric System, which we will see is much easier to use. We will learn about the Metric System later in Arithmetic.

Memory Work

Directions: The following questions help you to memorize the most important points of this lesson. Commit them perfectly to memory and have a parent or praeceptor quiz you to test your mastery before taking your lesson exam.

15. (Review) What is Unity, or a Unit?
Unity, or a Unit, is a known quantity we refer to as One.

37. What is a Volume Measure?
A Volume Measure is a measure used to measure a quantity by the size of its container.

38. What are the two systems of volume measurement?
The two systems used are the American system and the Metric system.

39. What are the eight basic units of volume measure in the American system?
In the American system, the eight basic units of volume measure are the bushel, the peck, the gallon, the quart, the pint, the cup, the tablespoon and the teaspoon.

40. What differences exist between the volume measurement of Dry and Liquid quantities?
The differences between the volume measurement of Dry and Liquid quantities is that dry measure is based on the bushel and liquid measure on the gallon and the two are measured with different equipment.

41. How great is the bushel and how is it written?
The bushel contains 4 pecks or 8 gallons and is written “bu.”.

42. How great is the peck and how is it written?
The peck is one fourth of a bushel and contains 2 gallons. It is written “pk.”.

43. How great is the gallon and how is it written?
The gallon is one eighth of a bushel and one half of a peck and contains 4 quarts. It is written “gal.”.

44. How great is the quart and how is it written?
The quart is one fourth of a gallon and contains 2 pints. It is written “qt.”.

45. How great is the pint and how is it written?
The pint is one half of a quart and contains 2 cups. It is written “pt.”.

46. How great is the cup and how is it written?
The cup is one half of a pint and contains 16 tablespoons. It is written “c.”.

47. How great is the tablespoon and how is it written?
The tablespoon is one-sixteenth of a cup and contains 3 teaspoons. It is written “Tbsp.”.

48. How great is the teaspoon and how is it written?
The teaspoon is one-third of a tablespoon and contains 76 drops. It is written “tsp.”.

49. What equipment is used to measure volume?
Measuring cups are used for larger quantities and measuring spoons for lesser. In laboratories, beakers, graduated cylinders and burettes are used for great accuracy.