144 square inches (sq. in.) = 1 square foot (sq. ft.)

9 square feet

30 square yards, or

272 square feet

160 square rods

SUMMARY FOR WORK OF PART II

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:

=

as

(1) The meaning of the symbols +, and
-
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.
(7) 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 1 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: 1⁄2, 1, 7, 1, 4, to 1o, 1%, 10, 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.

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.

SUMMARY FOR WORK OF PART III

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

1. In Notation and Numeration:

(1) The meaning of first-place, second-place, etc.
(2) The meaning of place-value.

(3) How to read and to write four- five-, and six-digit

numbers.

(4) How to read, write, and use the Roman numerals of the clock-face.

(5) Decimal point as used in writing amounts of money.

2. In Addition and Subtraction:

(1) When to add and to subtract in problems not too difficult.

(2) How to add and to subtract all sorts of whole numbers, and simple common fractions, and mixed numbers. (3) Enough to solve addition and subtraction problems under reasonable time limitations.

(4) The reason that addition checks subtraction.

(5) The meaning of the terms sum, difference, minuend, and subtrahend.

(6) How to find totals and to check footings with tables of data.

3. In Multiplication and Division:

(1) The meanings of times, multiplicand, multiplier, product, dividend, divisor, quotient, and remainders in both subtraction and division.

(2) How to multiply and to divide quickly by multiples of 10, 100, 1000.

(3) How to find the products and the quotients of easy fractions by one- and two-digit numbers, and to show the results diagrammatically.

(4) The multiplication table through the twelves automatically.

(5) The division facts that are the correlates of the products of the multiplication table