Everest, 29,062 feet. How much greater is the distance to the bottom of the sea than to the top of Mount Everest?

WORK:

29,400 feet

- 29,062 feet

EXPLANATION:

The distance to the bottom of the

338 feet. sea is as much greater than the distance to the top of Mount Everest as the difference in the distances, which is 338 feet.

Talk on Above:

In such problems explain to the pupil that the measurement used begins at sea level.

One great trouble in the solution of problems is that pupils do not understand the conditions.

PROBLEM:

From Buffalo to Boston by rail is 499 miles. From Buffalo to Chicago by rail is 539 miles. How much farther is it from Buffalo to Chicago than from Buffalo to Boston?

WORK:

539 miles

- 499 miles

SOLUTION:

The distance from Chicago to Buffalo 40 miles. is as much farther than that from Buffalo to Boston, as the difference between 539 miles and 499 miles, which is 40 miles.

NOTE. If the pupil does not readily see what to do with such problems, illustrate the principle by the use of short distances that are familiar to him.

PROBLEM:

I had $4295 in the bank and drew out $1764. How much remained in the bank?

-1764
I had left in the bank the difference
2531 between $4295 and $1764, which is

$2531.

NOTE. Few pupils will have trouble with this problem. If there be any, use an illustration of a few cents in place of the numbers above.

PROBLEM:

In 1900 the population of Illinois was 4,821,550 and that of Texas was 3,048,710. How many more people were there in Illinois than in Texas?

WORK:

4,821,550

- 3,048,710

SOLUTION:

There were as many more people 1,772,840 in Illinois as the difference between 4,821,550 and 3,048,710, which is 1,772,840.

NOTE. If there is any trouble here, illustrate by taking the number of pupils in two rooms of your school, the number of people in two well-known families, etc.

PROBLEMS INVOLVING ADDITION AND

PROBLEM:

SUBTRACTION.

Gardner went into business with $7000. The first year he earned $925. His expenses were, $325 for rent and $732 for living. What was he worth at the end of the year?

NOTE.-Lead the pupil to see that at the end of the year, had he spent nothing, he would have $7000+$925.

Next lead him to find what the total expense was; $325+ $732 = $1057. It is an easy matter for him to see that what Gardner is now worth is the difference between $7925 and $1057, which is $6868.

PROBLEM:

A bin holds 925 bushels. On Sept. 20, I put 425 bu. of wheat into it and on Sept. 23, 325 bushels. How much more will it hold?

EXPLANATION:

1st Query. How many bu. does the bin hold!
925.

2d Query. How many bu. are in it now?

425+325750.

3d Query. How much more will it hold?

925 bu.-750 bu.= 175 bu.

NOTE. This illustrates how by a series of queries the pupil may be led to see the successive steps required in the solution of a problem.

PROBLEM:

I bought a horse for $170 and a carriage for $125. I sold both for $300. Did I gain or lose, and how much?

SOLUTION:

I paid for the horse $170
I paid for the carriage $125

I paid for both $295

I sold both for $300, so I gained $5.

PROBLEM:

I paid $2500 for a lot, built a house on it for $3750, and paid $755 for grading the lot. I sold all for $8000. Did I gain or lose, and how much?

I gained the difference between the selling price $8000 and the cost $7005= $995.

EXERCISES IN ADDITION AND SUBTRACTION.

The following tables will furnish material for much drill work in addition and subtraction. A few of the ways in which they may be used are suggested:

1. Find the areas of the different divisions.

2. Compare the different divisions.

3. Compare your state with other well-known states. Find how much larger or smaller it is than any other state you may select.

Before attempting any of this work give the child. an idea of how large a square mile is, if possible. If he lives in the city, use as many blocks in the vicinity of his home as will make a square mile, approximately. In the country some well-known farm, or farms, that approximates a square mile in area will do.