(5) Enough land measure to enable pupils to read intelligently the descriptions of land in deeds, to locate the land and to calculate the areas, when tract is regular, from the description.

11. In Percentage:

(1) The necessary language of percentage.

(2) The connections of percentage with whole numbers, and with common and decimal fractions.

(3) The necessary laws of the subject.

(4) The equation-method of solving percentage problems. (5) How to find the percentage, the percent, the base, or the amount, and how to show these ways in an equation with either numbers or letters.

(6) Applications to gain or loss, to other school subjects, to commission, to trade discount, and to marking goods.

12. In Interest:

(1) The necessary language of the subject.

(2) The connection of percentage with "interest for one year."

(3) How to find the interest; the principal; the rate; the time, by the common method.

(4) The six-percent method.

(5) How to compute an interest table.

(6) How to show the laws for calculating any element of the interest-problem both with arithmetical and with general numbers.

(7) Applications to promissory notes and to discounting

notes.

(8) Bank discount.

13. In General Number:

(1) How to express sums, differences, products, quotients, and powers of general number.

(2) How to express common fractions in general number. (3) How to express perimeters, and areas of squares,

rectangles, parallelograms, and triangles in general
number.

(4) How to indicate the unknown number of an arith-
metical problem by a letter, to formulate a simple
equation, using it, and to solve this equation.
(5) How to solve simple formal equations of the type
6x+8=20, and 5y-7-13.

14. In Form-Study and the Rudiments of Geometry:
(1) Such geometrical relations as are involved in the
rational study and use of the square, the rectangle,

the parallelogram, the triangle, the circle, the cube,
and the square box.

II. The pupil should have considerable skill in the following:

(1) In adding long columns, vertically, and checking results. (2) In adding lines, horizontally, and checking.

(3) In adding, subtracting, multiplying and dividing whole numbers and fractions, and checking.

(4) In the mechanics of long division.

(5) In finding perimeters and areas of the forms studied.

(6) In analyzing a problem involving 3, or 4, simple steps.
(7) In telling how a problem should be solved before actually
solving it.

(8) In estimating approximate results.

(9) In mental addition, subtraction, multiplication, and division. (10) In making problems from given conditions.

(11) In judging what is the best way to proceed with a problem. (12) In the use of cancellation to shorten work.

(13) In expressing the solution of the problem in convenient form for the use of cancellation.

(14) In discerning factors of numbers.

(15) In exhibiting the meaning of operations with fractions, by means of divided rectangles.

(16) In solving easy percentage and interest problems.

(17) In finding circumferences and areas of circles from given dimensions, or for dimensions obtained by measurement.

III. Ideas and values in arithmetical study, advanced or begun in Part I.

(1) Arousing an intelligent interest in growth and extent of the
nation, and in business arithmetic.

(2) Feeling of value of arithmetical study in affairs of life.
(3) Heightening the feeling of ability to do with some skill,
things worth doing.

(4) Joy in consciousness of power over some real difficulties.
(5) Consciousness of ability to see into, and through some

things.

(6) Growth in feeling of independence, developed through checking.

(7) Pleasure in the kind of definite thinking called for in arith. metic.

(8) Increased insight through doing habitually all one can with his head, adding to the stock of "spot cash" knowledge. (9) Augmented ability to know (1) what to do, (2) when to do it, and (3) how to do it, without hints, or suggestions, of any sort.

(10) Feeling that a knowledge of arithmetic makes many difficulties much easier.

(11) Engendering taste for continued mathematical study and school work in general.

SUMMARY OF WORK OF PART II

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

1. In Notation and Numeration, and Fundamental Operations:

(1) How to read and to write with ease, and to add, sub-
tract, multiply, and divide with ease, certainty, and
steadiness, whole numbers and any sort of fractions,
in any sort of reasonable combinations.

(2) How to apply the foregoing severally and in combi-
nation, to a wide range of problems of daily life.
(3) Through reviews, a deeper and firmer hold on pre-
vious knowledge of these topics.

(4) Meaning and use of easy literal notation and of
operations applied to literal numbers.

(5) Addition and division of lines and angles.

(6) How to get differences of angles, of longitudes, and of times.

(7) Most convenient practical ways of pointing quotients of decimals.

(8) Products of sums and differences of lines and of numbers.

(9) Greatest common divisor and least common multiple and how to find them by the factoring process.

2. In Form-Study, Mensuration, and the Rudiments of Geometry:

(1) Areas and perimeters of common forms.

(2) Construction of developments and models of solids, and nature of surfaces of solids.

(3) Mensuration of the trapezoid.

(4) Mensuration of cube, right and oblique prism, the
pyramids, the cylinder, the cone, and the sphere.
(5) Fundamental concepts of perpendicularity, parallel-
ism, bisection of angles, learned through paper-
folding.

(6) Classifications of quadrilaterals.

(7) Angles learned through the turning of clock-hands.

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(8) Measurement of angles with the protractor.
(9) Angle-sums of triangles, parallelograms, etc.
(10) Land measure, townships, sections, fractions of sec-
tions, lots, meridians, base lines, ranges, and how to
interpret legal descriptions of locations of farms.
(11) That the square on the hypothenuse of a right tri-
angle equals the sum of the squares on the other
two sides.

(12) Practical uses of similar triangles.

3. In Longitude and Time:

(1) Use of longitude and latitude to locate places on the earth.

(2) Dependence of measurement of time on the rotation of the earth.

(3) Connection of longitude and time.

(4) The terminology and the table of converting time and longitude.

(5) Meaning and use of standard time, time belts, and the date line.

4. In Percentage and Interest:

(1) Applications to insurance, taxes, trade discount, stocks and bonds, compound interest, savings deposits, and partial payments.

(2) The essential terminology of all the foregoing topics. NOTE.-These applications furnish a review, just before leaving the elementary school, of percentage and interest.

5. In Uses of Arithmetic in Other School Subjects and in Common Affairs:

(1) In elementary science, air pressure, longitude and time, standard time, laws of conversion of thermometer readings.

(2) In transportation problems, movements of trains, and pulling force of engines.

(3) In industrial studies, the ordinary commercial topics, insurance, taxes, commercial discounts, etc.

(4) In constructive art of the builder, exercises in modeling, making, and calculating properties of the standard geometrical forms.

(5) Many practical questions and problems, distributed in their appropriate places.