Teaching Models

Customary and Metric Measurement

Measurement is the process of determining a number that represents a particular attribute of an object. This process begins by defining a “unit object” that has a measure of 1. Once a unit of measure is defined, measurement is the process of determining how many copies of this unit fit, without overlap, along a side of the given object. A number that specifies a quantity in terms of a unit of measure is called a denominate number.

Suppose a line segment S is designated as a unit segment with a measure of 1. The length of another line segment T is then determined by how many copies of S, or parts of S, fit alongside T without overlap. In the illustration below, T has a length of 2 one-half units.

Line segments

The accuracy of a measurement depends upon the size of the unit of measure being used. The smaller the unit, the more precise the measurement. For instance, a measurement rounded to the nearest sixteenth of an inch is more precise than a measurement rounded to the nearest eighth of an inch.

Abbreviations are sometimes used in denominate numbers. These abbreviations do not have periods after them, except for “in.” (A period is used in the abbreviation for inch to avoid confusion with the word in.) These abbreviations are used for both singular and plural units of measure, so “ft” is the abbreviation for foot and for feet and “m” is the abbreviation for meter and for meters. Students need to memorize the abbreviations of measure studied in this chapter.

Customary System of Measurement
In the customary system of measurement used in the United States, the common units of length include inch, foot, yard, and mile. Students should know the following equivalencies and abbreviations. Remind students that abbreviations do not take a plural s.

Length
12 inches (in.) = 1 foot (ft)
36 inches (in.) = 1 yard (yd)
1,760 yards (yd) = 1 mile (mi)

3 feet (ft) = 1 yard (yd)
5,280 feet (ft) = 1 mile (mi)

When the length and height of a rectangle are known, the perimeter of the rectangle can be found. The perimeter of, or distance around, the rectangle can be found by finding the sum of the lengths of the sides. Since perimeter is a length, the unit of measure is inches, feet, yards, or miles.

In the customary system of measurement, the common units of measure and abbreviations for weight and capacity are shown below. Students should know the following equivalencies and abbreviations.

Weight
16 ounces (oz) = 1 pound (lb)  

2,000 pounds (lb) = 1 ton (T)

Capacity
8 fluid ounces (fl oz) = 1 cup (c)
2 pints (pt) = 1 quart (qt)

2 cups (c)= 1 pint (pt)
4 quarts (qt) = 1 gallon (gal)

Metric System of Measurement
The metric system of measurement is based on 10 and powers of 10. The prefixes used for length, capacity, and mass tell what multiple of the basic unit is being considered.

kilo-
hecto-
deka-
deci-
centi-
milli-
1,000
100
10
0.1
0.01
0.001
kilo-
hecto-
deka-
deci-
centi-
milli-
k
h
da
d
c
m
as in km for kilometers
as in hm for hectometers
as in dam for dekameters
as in dm for decimeters
as in cm for centimeters
as in mm for millimeters

To change from one unit to another, multiply or divide by a power of 10.

Units of 10

To change from a larger unit to a smaller unit, multiply by the appropriate power of 10. To change from a smaller unit to a larger unit, divide by the appropriate power of 10.

Examples:
Change centi- to kilo-.
Think: small to large, so divide
Count 5 moves left, so divide
by 105, or 100,000.
Change deka- to deci-.
Think: large to small, so multiply
Count 2 moves right, so multiply
by 102, or 100.

The common units of length include millimeters, centimeters, decimeters, meters, and kilometers. Students should know the following equivalencies and abbreviations.

Length
10 millimeters (mm) = 1 centimeter (cm)
10 centimeters (cm) = 1 decimeter (dm)
10 decimeters (dm) = 1 meter (m)

1,000 millimeters (mm) = 1 meter (m)
100 centimeters (cm) = 1 meter (m)
1,000 meters (m)= 1 kilometer (km)

In the metric system of measurement, the common units of measure and abbreviations for mass* and capacity are shown below. Students should know the following equivalencies and abbreviations.

Mass
1,000 milligrams (mg) = 1 gram (g)
1,000 kilograms (kg) = 1 metric ton (t)

1,000 grams (g) = 1 kilogram (kg)

Capacity
1,000 milliliters (mL) = 1 liter (L)

10 deciliters (dL) = 1 liter (L)

* Note that the metric system commonly uses a measure of mass rather than weight. Often these terms are used interchangeably, but there is a difference. Mass measures the amount of matter in an object. Weight measures the gravitational pull on the object. In space, an astronaut who is “weightless,” still has the same mass as on Earth.


Teaching Model 12.5: Too Much or Too Little Information


Houghton Mifflin Math Grade 4