them, and they must reason out the conclusions for themselves. No pains have been spared to make a book that can be used with the minimum amount of labor on the part of the teacher, and which will at the same time give the best possible results. It is hoped that teachers may find it in line with educational progress and worthy of use. TARRYTOWN, N. Y., GEORGE E. ATWOOD. CONTENTS. Addition, numbers expressed in words. Addition, numbers expressed in figures. Addition of denominate numbers. Addition of United States money. Subtraction, numbers expressed in figures. Subtraction of denominate numbers. Subtraction of United States money. Multiplication, numbers expressed in figures. Multiplication of denominate numbers. Multiplication involving United States money. Division, numbers expressed in figures. Division of denominate numbers. Division involving United States money. Concrete problems involving division. Expression of numbers in words. Use of parenthesis and vinculum. ALL WORK OF FIRST TERM CONTINUED. Fractional parts of numbers, simple and denominate. Area of rectangular surfaces, when the dimensions are expressed in FOURTH GRADE-THIRD TERM. ALL WORK OF FIRST AND SECOND TERMS CONTINUED. Volume of rectangular solids, when the dimensions are expressed FIFTH GRADE-FIRST TERM. MOST OF THE WORK OF THE FOURTH GRADE CONTINUED. Sum of two numbers and one of them given, to find the other. Difference between two numbers and one of them given, to find the The product and one or more factors given, to find the other. The divisor and quotient given, to find the dividend. Concrete problems involving two or more of the fundamental rules. MOST OF THE PREVIOUS WORK CONTINUED. Reduction of fractions to higher terms. Reduction of fractions to lower terms. Reduction of improper fractions to whole or mixed numbers. Reduction of fractions to a common denominator. MOST OF THE PREVIOUS WORK CONTINUED. COURSE OF STUDY. FIRST GRADE. TEACH numbers to ten. Teach one number at a time. Teach each number as a whole first, and then lead the pupils to discover by the use of objects all combinations of two numbers by addition and multiplication that make the number, and all separations by subtraction and division. Lead them to discover also the equal parts of numbers, as halves of 2, 4, 6, 8, and 10; thirds of 3, 6, and 9; and fourths of 4 and 8. Show that one-half of a thing is one of its two equal parts; one-third, one of its three equal parts; two-thirds, two of its three equal parts, etc. After each number is known and the combinations and separations have been discovered from the use of objects, teach the figures and signs necessary to express all the facts learned. After they have learned the facts in each number, omit the use of objects, and use the language of arithmetic. Guard against teaching only the language of arithmetic. Be sure that when pupils see a figure or hear the numbers used, they can show that number of things; and that when they see indicated combinations and separations, they can show their meaning by the use of objects. Write such expressions as 4 + 3 = 7, 523, 42's 8, 4 × 2 8, and 8 ÷ 2 = 4 on the board, and have pupils show what they mean. Also make such combina = = tions and separations of objects before the class and have pupils represent them, using figures and signs. Keep up a constant drill, both in oral and written work, to fix thoroughly in mind all combinations and separations learned. Throughout the year make practical application of the facts learned in a variety of concrete problems. For pupils' work, write on the board such expressions as 4 + 2, 63, 3 × 2, 82, and of 6, and have pupils make problems, using these numbers and their indicated relations. Frequently require pupils to illustrate with objects the solution of problems. SECOND GRADE 1. Teach numbers to 16, including fractional parts to fifths. Notice carefully the suggestions for first grade. Teach the inch, foot, and yard, and lead pupils to discover the number of inches in a foot, feet in a yard, gills in a pint, pints in a quart, quarts in a gallon, quarts in a peck, and pecks in a bushel. Have pupils make problems and illustrate the solution of problems as in first grade. Constant application throughout the year of all knowledge of numbers to the solution of concrete problems. Write numbers to 50. 2. Teach numbers to 20, including fractional parts to sixths. Teach the number of units in a dozen and halfdozen, the number of ounces in a pound, and the number of feet in a rod. Let the concrete problems given this term frequently involve two or more of the fundamental rules. Have pupils give oral and written problems from indicated work on the board. Constant drill, oral and written, with abstract numbers to fix thoroughly in mind all combinations and separations in numbers to 20. Teach Roman notation to 20. Write numbers to 500. |