Look

The Kelton was formerly engaged in carrying salt between Manistee, Michigan, and Chicago, Milwaukee, and South Chicago. up all these places on a map.

1. The Kelton left Chicago at 3:30 Monday afternoon for Manistee, 176 miles from Chicago. The boat reached Manistee at 7:30 Tuesday morning. How many hours did it take? How many miles an hour did the boat go?

2. At Manistee, the boat was loaded with 6500 bbl. of salt. The cost of loading was $1 per 100 bbl., and it took 7 hr. to load. What was the cost of loading per hour? At what hour was the loading completed, if loading began as soon as the boat reached Manistee?

3. The boat left for Milwaukee, 88 miles from Manistee, at 2:30 P. M., Tuesday, and reached Milwaukee at 12:30 A. M., Wednesday. How long did it take and how many miles an hour did the loaded boat run?

4. The unloading at Milwaukee began at 7 A. M., Wednesday, and it took 10 hours. An hour was taken for dinner. How long since the boat left Chicago?

SUMMARY FOR WORK OF PART I

I. What the pupil should know at the end of this part.

1. In Notation and Numeration:

(1) The names and meanings of the digits.
(2) The number names to 1000.

(3) How to read and write three-digit numbers.

2. In Addition and Subtraction:

(1) The meaning of the symbols +,

and

= as

short-hand for the words and, less, and is or are. (2) How to show sums and differences in symbols. (3) The meanings of add, subtract, sum, difference. (4) How to arrange work in addition and subtraction. (5) The forty-five fundamental addition facts. (6) How to add and subtract three-digit numbers.

How to add longer columns of one-digit, and shorter columns of two- and three-digit numbers. (8) How to check subtractions by addition.

(9) Correlation of addition and subtraction, as 8+5 - 13, with 13-85, and 13-5-8.

=

3. In Multiplication and Division:

(1) The meanings of X,,)___, and the words and phrases: times, multiply, divide, multiplied by, divided by, and product.

(2) How to show multiplication- and division-problems in symbols.

(3) How to arrange work for multiplication and for short division.

(4) The multiplication tables through the tens.

(5) How to multiply, and to divide two- and three-
digit numbers by one-digit numbers and by 10..
(6) How to check divisions by multiplication.
(7) Correlation of multiplication and division, as 4×8,
or 8×4=32, with of 32 =4, and of 32 -8.
(8) How to write remainders in division as fraction.

4. In Fractions:

(1) The meaning of halves, thirds, fourths, to tenths
and the forms: 1, 1, 4, 4, 4, to 1o, 1, 1o, 18.
(2) The meaning of fractional parts of a number as
division by the denominators, as of 12-12÷3.
(3) Amounts of money written decimally as dollars and
decimals of a dollar, to two places.

205

5. In Mensuration:

(1) The connection of square and linear units in measuring areas of oblongs.

(2) How to find areas of oblongs having integral dimensions.

(3) The names and ideas of the more common standards for measuring distances, areas, boxes, liquids, bulks, weights, time, and value.

6. In Form-Study:

(1) Comparative lengths of lines.

(2) Making and measuring squares and oblongs.

(3) Marking, cutting, and making boxes of simple forms.

(4) Rectangular forms used in building the tables.

(5) Meaning of terms, area, dimension, base, altitude, and perimeter.

II. Ideas and values of arithmetic work started and practiced by the pupil.

1. Forming estimates and judgments of relative magnitudes.
2. Practicing measurement as a means of checking and cor-
recting judgments of magnitudes.

3. Forming the habit of doing mentally as much of the work
as possible.

4. Forming the habit of sketching and picturing number relations to obtain clear and vivid ideas.

5. Learning in arithmetic how to study.

6. Checking calculations to cultivate independence and self-
confidence.

7. Using rectangular groups of squares in building tables,
incidentally foreshadowing and aiding in mensuration.
8. Coming first into possession of ideas with the minimum
of nomenclature.

9. Sensing addition, subtraction, multiplication, and division
as measuring processes; and their relationships.

III. Concepts and meaning of other terms learned incidentally through use.

1. Inch, foot, yard, square inch, square foot, square yard,

cubic inch, ounce, pound, gill, pint, quart, gallon, peck, bushel, hour, minute, second, and names of common coins.