birds flew away. 6. Edna may bring three more birds to the fence. 7. Walter may tell the story. Story: There were two birds on a fence. Three more birds flew to the fence. There are five birds on the fence. 8. We can tell this story on the 2 birds There are two birds left on the fence. board in this way: + 3 birds. The mark + means more. 5 birds 9. It means that three more birds came to the fence. Looking at the board, Fred may tell us the story again. 10. Now there are five birds on the fence. Willie may help two of the birds to fly away. 11. Grace may tell the story about the birds. 12. We can tell this story on the 5 birds board in this way: 2 birds. 13. Looking at the board, 3 birds means Mary may tell the story again. 14. The mark less. It means that there were two less birds on the fence after the two birds flew away. 15. I am going to write a different story on the board, and I want to see who can 2 birds tell it. +4 birds. Story: There were two birds on a 6 birds fence. Four more birds came to the fence. There were then six birds on the fence. 16. Who can give the story that this tells? on a fence. 4 birds 3 birds. Story: There were four birds. 1 bird Three of the birds flew away. There was one bird left on the fence. 17. Who can give the story that this tells? 2 boys +2 boys. This lesson, like all other 4 boys lessons in this chapter, should be expanded by the teacher. Objects should be used to illustrate all of the problems given under this lesson, and the groups should not exceed six objects. The operation involved in each problem is thus made evident to the pupils. They should be made familiar with the language forms associated with these operations. They should also learn to express the operations in such written forms as are given in Problems 8 and 12. Given the written forms, they should be able to make number stories (problems) from them. They should be able to illustrate these by means of objects. No attempt should be made to have the pupils memorize the results in any of the problems. Teach the names of the days of the week. Use these names in written work. Teach the names of the months, their abbreviations, and the number of days in each. The number of days in each month should be taught without the use of rhyme. The pupils should be able to tell which is the sixth month, the third month, what month July is, October is, etc., without naming the months from the beginning of the year. Pupils should be able to tell the time of day, and to estimate without the use of a timepiece the length of seconds and minutes. SUMMARY OF CHAPTER I The work outlined in Chapter I should be completed before the book is placed in the hands of the pupils. Upon the completion of this work the pupils should be able: 1. To count serially in any part of the number scale below 1,000; to tell from the study of the number scale what one more than any number is, and what one less than any number is; to tell the number of tens there are in 20, 30, etc.; to tell what the sum is when any number less than ten is added to 10, 20, etc.; to count by tens to 110, beginning with any of the first ten numbers in the scale; to count by fives to 110, beginning with 5, and by twos to 50, beginning with 2. 2. To read and write numbers of two periods readily; to tell the place value of figures in numbers less than 1,000. 3. To measure short distances in inches, feet, and yards; to draw lines to represent these units of measure with a fair degree of accuracy; to estimate lengths of less than two feet in inches, of less than ten feet in feet, and of less than five yards in yards; to compare the length of the inch, foot, and yard; to use the pint, the quart, and the gallon measures in measuring liquids; to give the number of pints there are in a quart, and the number of quarts there are in a gallon. 4. To recognize the circle, the square, and the oblong. 5. To show what is meant by one half, one third, and one fourth; to find these fractional parts of small groups of objects. 6. To measure groups of objects using given units of measure. 7. To solve simple problems objectively, and to express the solution correctly in both the oral and the written form. 1ST BK ARITII-3 CHAPTER II GENERAL INTRODUCTION ADDITION Step A. Five addition combinations are made to constitute a lesson in addition. These should be perfectly memorized. Sufficient drill should be given to make them perfect reflexes. Following each new set of combinations, on the same page are a number of oral problems, in solving which the pupils may refer, if necessary, to the combinations at the top of the page. Many similar problems, involving the same combinations, should be given by the teacher, and the pupils should be encouraged to make simple problems involving the combinations of each lesThese should deal with things within the experience of the pupils. son. After the pupils have memorized the combinations of a lesson, as given with answers in the text, they should take up the study of the lesson as arranged without answers on the succeeding page. This study should be pursued as indicated on pp. 48, 49. The combinations should be written on the board, and the pupils should be given a rapid and thorough drill upon them. The order in which they are arranged on the board should vary, and the pupils should not depend for their knowledge of the combinations upon any sequence in the drill exercises. The pointer should always rest upon the upper number of the combination, as the pupils will commence at the foot of the columns to add. The pupils should give the sums without naming the numbers in the combinations. In speaking of a combination, the lower number should be named first. The combinations of Lesson A are 2 and 3, 5 and 4, etc. The lesson should be thoroughly mastered through Step A before the pupils undertake to study it as directed in Step B. Step B. After the combinations of a lesson have been memorized and have been used in simple problems, a study exercise is provided. The teacher should see that these exercises are diligently and correctly studied as explained on pp. 48, 49. The teacher should study the lessons with the pupils until they are able to continue without assistance. The purpose of this study exercise is to prepare the pupils for column addition. Nowhere in column addition, except in the first combination added, will the combinations occur as they were memorized in Step A. In the addition of the column, the combination is no longer 2 and 3, but is, instead, 12 and 3, 22 and 3, etc. At each step in the addition of a column, after the first sum has been obtained, the lower number is retained mentally. For this reason, in studying the lessons through Step B, the pupil is required to retain mentally the tens of the lower number in each combination. Oral and written exercises in which the lower number is increased by 10, 20, 30, etc., to 100, may supplement this study, but should not supplant it. It should be noted that the combinations as they occur in column addition are in the form 24 and 5, and not 5 and 24. For this reason the former should be the form used by the teacher in both oral and written combinations. After studying a lesson through Step B, the pupils should |