you made. Jane brought me? 4. Fred, will you draw a line on the board for each book Jane brought me? 5. Walter, bring me three books. 6. Lottie, draw lines on the board to show how many books Walter brought me. 7. I will write on the board the figure that tells how many lines 8. I can show the number of books Walter brought me in two ways: 111 books, and 3 books. 9. Count the books, one, two, three. 10. Alice may hold three books in her hand. 11. Mary may take two of the books that Alice has and place them on the desk. 12. How many books have you now, Alice ? 13. Lottie, hold up one book. 14. Hold up two books. 15. Hold up three books. 16. I want some one to build a pile of three books and a pile of two books. 17. David, point to the pile of three books. 18. Emma, show me two girls. 19. George, stand three boys in line on the floor. 20. Send one of the boys to his seat. 21. How many boys are left standing ? 22. I will show on the board the number of boys we have been talking about: 23. Mary, point to something that tells three. 24. Fred, point to something else that tells three. Vary the objects counted, and continue the group pictures through twelve. The group pictures are used to represent the objects which the pupils have handled. Disks of colored paper mounted on cardboard may be used as flash cards for the recognition of these groups. The disks should represent any object whatever, and each disk represent whatever unit is selected. three may represent three boys or three apples, or it may The group The represent three ones, three nickels, or three tens. groups through twelve may be arranged thus: These groups should always represent concrete numbers, - apples, books, blocks, cents, dimes, etc. Continue oral counting until the pupils are familiar with the number scale. Never ask a pupil to “count backwards." The attention of the pupils should be called to the place that a given number occupies in the number scale by such questions as the following: In counting; what number comes just before 20? What number comes next after 17? Twenty-seven comes before what number? From the exercises in counting and in the writing of the number table, the pupils should know what number is one more than any given number, and what number is one less than any given number. Give exercises in counting by 2's to 12, using objects. Count by 2's the hands, feet, eyes, etc., of the pupils in the class. Count by 2's from 10 to 22. Count by 2's from 20 to 32, etc. Count by 5's to 15, using objects. Count by 5's, using , nickels. Count by 5's from 10 to 25, from 20 to 35, etc. Count by 5's the minutes on the clock face. Count by 10's to 110. Count by 10's from any given number, such as 1, 2, 5, 7, etc. to 110. Use the number table in connection with this work. Before taking up the study of the text, the pupils should be able to count serially in any part of the number scale below 1000. They should be able to count by 2's, beginning with even numbers, and by 5's, beginning with numbers ending in 5 and 0, up to 100. They should be able to count by 10's to 110, beginning at any place in the first hundred of the number scale. They should know the number of tens there are in 30, 40, 80, etc. From a study of the number scale, they should know what one more than any number is, and what the sum of 10 and any number less than 10 is, what the sum of 20 and any number less than 10 is, what the sum of 30 and any number less than 10 is, etc. This knowledge is essential to the work in addition. LESSON III — COMPARISON OF QUANTITIES Using the inch cubes, have the pupils build “ towers” with as many blocks as the figures on the table or the board specify, thus : 1 2 3 4 5 ILLUSTRATION. Problems: 1. Fred, tell me a story about the tower of 3 blocks and the tower of 2 blocks. Story: The tower of 3 blocks is higher than the tower of 2 blocks. 2. How many towers of 2 blocks will it take to make a tower of 4 blocks? 3. What must you put with a tower of 5 blocks to make a tower of 7 blocks? 4. How many towers of 2 blocks can you make out of a tower of 6 blocks ? 5. What must you do with a tower of 6 blocks to make a tower of 4 blocks? Of 5 blocks? Of 8 blocks ? 6. Find a tower one half as high as a tower of 8 blocks. Using blocks, build trains of as many cars as the figures on the tracks designate, thus : 1 3 2 4 1. How much longer is the train of 3 cars than the train of 2 cars ? 2. What will you have to put with the train of 4 cars to make a train of 6 cars ? 3. What will you have to do with a train of 5 cars to make it a train of 3 cars ? 4. How many trains of two cars can you make out of a train of 8 cars? 5. How many trains of 3 cars must we put together to make a train of 6 cars? Of 9 cars ? 6. Break the train of 10 cars into halves. How many cars are there in one half of it? How many are there in the other half of it? 7. Join a train of 2 cars to a train of 3 cars. It is as long as a train of 8. Join a train of 2 cars to a train of 6 cars. It is as long as a train of 4 cars and a train of cars. 9. A train of 5 cars is cars longer than a train of 3 cars. cars. a LESSON IV — GROUPS Separation into Groups. ILLUSTRATION. The teacher places 3 books on the table. Problems : 1. Harry, here are some books on the table. Take up some of them in your right hand, and the rest in your left hand. 2. How many books has Harry in his left hand? 3. How many has he in his right hand ? 4. Name the number in each hand as he holds them up. 5. Count them as he puts them together. 6. Show on the board the number of books Harry holds in his right hand. 7. Show the number he holds in his left hand. 8. Harry, place the books on the table. 9. Annie, divide them into two groups. ILLUSTRATION. Problems : 1. Fred, place 4 books on : the table. 2. Separate them into two equal piles. 3. Mary, hold up one half of the books. 4. Has she the correct number ? 5. How many books is Mary holding up ? 6. How many groups of two books are on the desk? 7. How many groups of two books is Mary holding ? 8. Mary, hold the other group of two books in your left hand. 9. . How many groups of two books is Mary holding ? 10. How many groups of two books is she holding in each hand ? 11. Mary, place the books together. How many books have you altogether? 12. Separate the groups of two books. 13. How many groups of two books are there in four books? 14. Place the books on the desk in twos. 15. Willie, hold up one half of the books. 16. How many books is Willie holding up? 17. Hold up all of the books. 18. Place two of the books on the table. Two books are one half of how books? ILLUSTRATION. Problems: 1. Place four books in a pile. 2. Remove the books, one book at a time. 3. Remove the books, one 2-book group at a time. 4. Remove many |