Math Background

Measurement: Overview

There are two basic systems of measurement. When measuring in these systems, a comparison is made to some unit recognized as a standard. The system used in the United States is called the customary system of measurement.

The units of measure in the customary system are:

Customary System
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 feet
1 yard = 36 inches
1 mile = 1,760 yards
1 mile = 5,280 feet
1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2,000 pounds
1 pint (pt) = 2 cups
1 quart (qt) = 2 pints
1 quart = 4 cups
1 gallon (gal) = 4 quarts

The other basic system of measurement is called the metric system, or SI (International System of Units). It was first adopted in France and is currently used by approximately 95% of the world's population. Liberia and Myanmar (Burma) are the only other countries besides the United States that have not officially adopted the metric system.

Within the metric system, the meter is the fundamental unit of length; the gram is the fundamental unit of mass, and the liter is the fundamental unit of capacity. The metric system is a base-ten system. Prefixes are used to designate 10 times (deka-), 100 times (hecto-), and 1,000 times (kilo-) the unit. The prefixes deci-, centi-, and milli- are used to designate one-tenth, , and of the unit, respectively.

Metric System
1 centimeter (cm) = 10 millimeters (mm)
1 decimeter (dm) = 10 centimeters
1 meter (m) = 10 decimeters
1 kilometer (km) = 1,000 meters
1 kilogram (kg) = 1,000 grams (g)
1 liter (L) = 1,000 milliliters (mL)

In this chapter, students work with the customary units of measure for length, weight and capacity and then with the metric units for the same attributes. They measure the length of various objects to the nearest inch, one-half inch, and one-fourth inch. Students review how to find the perimeter of a rectangle, recalling that perimeter is the distance around a figure and is computed by adding the lengths of the figure's sides.


Students first learned how to find perimeter in second grade. Not until fifth grade, will they be introduced to the formula perimeter = 2l + 2w.

Once they have found the perimeter of a figure, students can multiply or divide to convert feet to inches, feet to yards, yards to feet, and feet and yards to miles. In order to convert, students look up the equivalent values for the two units and then decide whether to multiply or divide. When converting from a larger unit, such as feet, to a smaller unit, such as inches, students multiply. So, to convert 8 feet to inches, students look at the table of equivalencies to find that 1 foot equals 12 inches. Then they multiply the number of feet, 8, by the number of inches in 1 foot, 12, to find that 8 feet = 96 inches.

When converting from a smaller unit, such as feet, to a larger unit, such as yards, students divide. To convert 48 feet into yards, students look at the table of equivalencies to find that 1 yard equals 3 feet. They then divide the number of feet, 48, by the number of feet in 1 yard, 3, to find that 48 feet = 16 yards. Students may have difficulty remembering when to multiply and when to divide. If so, have them think about whether there will be more or less of the unit they are converting to than of the unit they are converting from. If there will be more of the new unit, they must multiply. If there will be less, they must divide.

Students will review the customary units of capacity and weight, converting among customary units. Students should be familiar with the measures of cups, pints, quarts, and gallons, and the measures of ounces and pounds. This is the first time they will have worked with tons. As with linear measure, to convert between units of capacity or weight, students must look up the unit equivalencies and then decide whether to multiply or divide.

Students review the metric system by actually measuring objects to the nearest centimeter and millimeter. Then they progress to finding perimeter in meters and kilometers and to converting between millimeters, centimeters, decimeters, meters, and kilometers. At this point students will not work with dekameters or hectometers.

Converting units within the metric system is much simpler than within the customary system. Because the metric system is a base-ten system, students simply need to multiply or divide by powers of ten to convert. They can look up the equivalencies in the tables provided in their student book. They then multiply or divide by the appropriate power of ten, depending upon whether they are converting from larger units to smaller units or from smaller units to larger units. For example, to convert 5 meters to centimeters, students multiply the number of meters, 5, by the number of centimeters in 1 meter, 100, to find that 5 m = 500 cm. To convert 350 millimeters to centimeters, students divide the number of millimeters, 350, by the number of millimeters in 1 centimeter, 10, to find that 350 mm = 35 cm. Since the same prefixes are used to measure length, capacity, and weight, students may come to understand the relationship between the prefixes and not need to look up the equivalencies.

Students progress to converting between metric units of capacity and mass. Although the terms mass and weight are often used interchangeably, they do have different meanings. Mass is the amount of matter in an object. Weight measures the force of the Earth's gravity acting upon the mass of an object. That is why objects in space, being far from Earth and the pull of gravity, are weightless. At this point, you need not make this distinction for students unless they ask about the difference in terms.

Students will also multiply or divide by 1,000 to convert between liters and milliliters or between kilograms and grams. At this grade level, milli- and kilo- are the only prefixes that students will work with in measuring capacity and mass, since these are the most common units used in everyday life.

Finally, students will study the units of measure for temperature in both the customary and metric systems. They informally compare the two temperature scales by comparing reference points such as the temperatures at which water boils and freezes, normal body temperature, and room temperature. The Fahrenheit thermometer is part of the customary system and is named after Gabriel Daniel Fahrenheit (1686-1736), a famous physicist. This thermometer is graduated so that water freezes at 32° and boils at 212°. Normal body temperature is 98.6°. The Celsius thermometer, also known as the Centigrade scale, is named after Anders Celsius (1701-1744), a Swedish astronomer, and is one of two metric scales for temperature. The Celsius scale is graduated so that water freezes at 0° and boils at 100°. Normal body temperature is 37°.

Using a drawing of a thermometer, students can find the difference between two temperatures. This will also serve as the students' first introduction to the concept of negative numbers. Students learn that temperatures below zero on either scale are negative temperatures. In dealing with negative numbers, students can think of the thermometer as a number line and can use the drawing of a thermometer to count between temperatures to find the difference. They will not actually subtract to find differences. At this point they will not learn how to subtract integers. Once students have practiced using a thermometer to find differences between temperatures, they will use this skill to solve word problems involving temperatures.

Houghton Mifflin Math Grade 4