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PART SIX.

DENOMINATE NUMBERS. PRACTICAL ESTIMATES.

No young lady could have a better safeguard against adversities of fortune, or a better resource in time of need, than a good knowledge of business affairs."

- Harriet Beecher Stowe.

PRACTICAL ARITHMETIC

IN COUNTRY SCHOOLS.

Tu *

properly done

HERE can be no work

upon

the farm with out measuring. Most of this measuring is done by what is called “rule of thumb,” or so-called practical judyment. The farmer estimates weight of cattle, hogs, or sheep by sight. He can tell how much cord wood or timber a certain area of forest will produce. In fact, measuring in everything he does is absolutely essential. There is no bet. ter way for the teacher to study the processes of measuring, or arithmetic, than to inquire into the everyday demands of farm work, and no better way to teach arithmetic than to bring the measuring necessary for farm work into the schoolroom. The elementary work, and the work that ought to be continued throughout the course, should be largely estimation with eye and hand, of length, of distance, area, volume, bulk, force, and weight; the estimates to be verified by actual measurements. That which a farmer is called upon at every turn to do, should be begun with the children. And here the parent can supplement the teacher at every step

When developing the mode of judgment, the pupil should be trained to use the chain in measuring areas, the yard-stick in measuring cord wood, forceps in lumber, dry measure for grain, scales for weights, liquid measure for milk, vinegar, or molasses.

The outcome of all raising of crops is commercial value. There should be a system of farm bookkeeping, in which writing and arithmetic play a prominent part. Children could be easily trained to keep books for their parents, and the work of the farm be made to present all the problems and conditions for a complete mastery of all essentials in arithmetic.

FRANCIS W. PARKER,
In Report of the Committee of Twelve.

DENOMINATE NUMBERS.

CALK:

Pupils necd not put much time on the mechanical perations now, if the study of fractions and decimals has been thorough. Their attention should be directed more to close, careful thought of processes.

The use of objects in illustrating points in problems zvill be very beneficial, and should be constantly used to make every step clear. After one demonstration with objects, many problems should be assigned to give the pupil a thorough test of his ability to grasp that portion of the work. He must build up his knowledge step by step, and reason out each part. The use of the reasoning power should dominate in all the work from now on.

A good plan to follow, and one which will help the pupil to reason, is this :

State a problem. Ask the pupil to tell the class to which it belongs, give the method of working it, state what is given, and what is to be found.

He will find it tedious to commit tables and definitions, but there is no use in shirking them, for they must be mastered or the work will be a failure.

The size of the units in all the denominate quantities must be known, before the pupil can reduce to a higher or a lower denomination. Hence, he must be well acquainted with the tables before he can do much with this subject. Take a little time each day for drill on tables previously used.

Do not require the pupil to learn all the tables before the addition, subtraction, multiplication and division of denominate numbers are begun.

Take the first table given in your plan of work and teach addition, subtraction, multiplication and division of the quantities

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A. H.-16

involved in that alone. Teach reduction ascending and descending with that table. Then take the second table.

Many teachers to-day begin with the liquid measure table, as it requires no work in fractions. . The order followed makes little difference and is left to the teacher.

When we speak of measures, whether they are of money, extension, time, or weight, we use terms like 5 dollars, 4 yards, 3 hours, or 10 pounds to express the quantity we are talking about. These are called simple denominate quantities.

Sometimes we use two or more terms or names to express the measure, as 3 hours, 15 minutes, 10 seconds ; 4 gallons, 3 quarts, 1 pint. These are compound denominate quantities.

Measures have different denominations to express large or small quantities. Long spaces of time are measured by days, weeks, or years, but short ones by hours, minutes, or seconds.

So it is with all denominate quantities. The different denominations of the same measure may all be reduced to any one denomination by a process called reduction.

If changed to a higher denomination, the reduction is ascending and if the change is made to a lower denomination, we call it reduction descending.

ILLUSTRATIONS.
2 hours = 120 minutes — reduction descending.
120 minutes = 2 hours reduction ascending.
24 inches = 2 feet - reduction ascending.
2 feet = 24 inches — reduction descending.

LONG OR LINEAR MEASURE. Long or linear measure is used in measuring lines and distances.

There are two systems in use in the United States, the English System and the French System.

The English System is the one commonly used, while the French System is used only in making scientific measurements. The French System has a decided advantage in being on the scale of 10— the decimal scale.

ENGLISH LINEAR TABLE.

12 inches (in.) = 1 foot (ft.)
3 feet = 1 yard (yd.)
55 yards, or 164 feet = 1 rod (rd.)

320 rods = 1 mile (mi.) The French or Metric System is fully treated in inother part of the book.

SURVEYORS' LINEAR TABLE.
7.92 inches = 1 link (1.)
25 links, or

= 1 rod (rd.)
164 feet
4 rods, or
66 feet, or 1 chain (ch.)
100 links

80 chains = 1 mile (mi.) Surveyors generally use a chain 66 feet or 100 links long, called a Gunter's chain. Civil engineers use a steel tape 100 feet long.

REDUCTION.

Reduce 10 yds. 8 ft. 10 in. to inches.
WORK :

yds. ft. in. SOLUTION :
10 8 10

10 yds. = 10 x 3 ft. = 30 ft. 3

30 ft. and 8 ft. are 38 ft. 38

38 ft. = 38 x 12 in., or 456 12

in. 456 in. + 10 in. 456

466 in, 10

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