NINETEENTH LESSON. 1. Look at the numbers on Chart No. I., or in the Table of Decades. How many numbers are written with one figure each? How many with two figures each? How many with three? Sometimes each of these numbers is called a period; so that some periods have three figures; some have two, and some have one figure. If we wish to read a number, having more than three figures, we begin at the right-hand and divide it into parts of three figures each, which are Thus ; called Periods. 2. How many figures in each of the first or righthand Periods? in each of the second Periods? in each of the third or left-hand Periods? The left-hand Period is the only Period which may have three figures, or two figures, or one figure. 3. The First Period is the Period of Units or Ones; the Second is the Period of Thousands; the Third is the Period of Millions. Other Periods on Chart No. I. 4. Divide into periods, and read the following numbers; 3932; 45625; 405368; 8769302; 27378028; 327025025; 368. 4568910; 27; 36890030; 72464913; 262124; 6913427; 24319416; 292827; 6839206030; 0; 999999999. Sometimes the period mark is understood; thus; TWENTIETH LESSON. 1. Read these; $333205101; £309250110416; $25; 30500210da; 607896302ft; 908025363sq.ft; 36832s. AVOIRDUPOIS WEIGHT.' Used in weighing those things which are not to be weighed by Troy or Apothecaries Weight. Its names are tons, hundred-weights, quarters, pounds, ounces, and drams. 2. Read these; 17cwt 3qr 191b.; 21T. 9cwt 1qr 201b.: 8175T. 15cwt 2qr 191b. 13oz. 14dr.; 3689oz. Used for weighing precious metals, as gold, silver, etc.; precious stones, as diamonds, etc.; also liquors and bread. Its names are pounds, ounces, pennyweights, and grains. 6 carats, or 24 grains equal 1 pennyweight - dwt or pwt. 20 pennyweights 12 ounces 3. Read these; 71b. 3oz. 18dwt 21gr.: 12dwt 13gr.; 5oz. 10pwt; 5lb. 13pwt 19gr.; 3685980pwt. For object lessons in these Tables, see Arith. No. IL ADDITION. LESSON I 1. Observe the picture at the right. How many cherries are pictured in it? What did you do to find this answer? How many stems have no cherries? How did you find this answer? How many stems in all? 2. Look at the lowest bunch of cherries. How many stems have cherries? How many have no cherries? How many stems. in all? How many cherries? How did you find the answer to these questions? We can find the answers to these questions thus; 4 stems and 1 stem equal in value 5 stems. 4 cherries and 0 cherry=4 cherries. 3. Now look at the next bunch of cherries. How many stems have cherries? How many have no cherries? How many stems in all? How many cherries? How did you find the answers to these questions? We can find them in the second or New way; thus 3 stems add 1 stem are equivalent to 4 stems. 3 cherries add 0 cherry=3 cherries. How 4. Next look at the third bunch of cherries. many stems have cherries? How many have no cherries? How many stems in all? How many cherries? How did you find the answers to these questions? 2 stems and 1 stem-3 stems. 2 cherries more by 0 cherries=2 cherries. 5. Ask the same questions about the fourth bunch. Invent the New way for finding the answers to them. 1 stem more by 1 stem=2 stems. 1 cherry plus 0 cherry=1 cherry. 6. How many stems have no cherries? How many stems in all? How many cherries? How did you find the answers to these questions? What is counting? Find the same answers by the New way. O stem and 1 stem-1 stem. O cherry and 0 cherry=0 cherry. 7. What words which are not used in counting are used in the New way of finding answers? The way of finding how many are meant by using the words, and, add, more by, plus, etc., is called Addition, which, literally, means the Science and Art of putting together. ADDITION is the name for the Science and Art of finding a number, equivalent to two, or more given numbers. 8. Instead of the words, and, add, more by, and plus, we may use a cross like this +, called the Sign of Addition. It is named, Plus, which means more; so that; The SIGN of Addition is a cross, called Plus. 9. How many are 4 boys and 1 boy? What will you call 5? Add 3 books and 1 book. Do you call 4 books a result or answer? When do you call a number, found by an operation, a result? When may you call it an answer? A result or answer in Addition, is called Sum, Sum-Total or Amount; so that;— SUM, SUM-TOTAL and AMOUNT are names of results or answers in Addition. LESSON II. 1. How many are 0 dollar + $0? How many are O dime and 0 D.? What is the amount of 0 + 0? What is the sum of 0 + 0 + 0 ? Now you may read the Table of 0, until you can recite it without the book. Recite it in turn, and remember, that the one, who is the least attentive to the reading, will be apt to make the first mistake in reciting. Begin thus, (a)' Addition Table of 0; 0 and 0 are 0; (b) 0 + 1 åre 1; (c) 0 + 2 =2, etc., to (k) 0 + 10 = 10. Then (7) may say "Open your books," at the same time opening the book, and beginning to read the next paragraph. 2. Addition Table of 0. 0+0=0 3. What is the amount of 0 yard + 0+1=1 2 yd ? of 0 yd + 8 yd ? of 0 yd +7 yd? 0 + 4? 0 + 6 + 0 + 10? 0+2=2 0+ 3 = 3 0+ 4 = 4 0+9= 9 0+10=10 4. Which is the greater number, 0 + 8, or 09? 0 + 3, or 0 + 6? 0 + 0, or 0 +10? What is the last Combination in the Table of 0? Read it from the left to the right. Read it from the right to the left. Which number did you read first when you read from the right? Why did you read the number 10, first? 5. Now read it both ways, from the left, and from the right, and tell the amount. binations above it; thus, 0 + Do the same with the com 99 or 9+ 0 = 9,0 + 8 7 or 7+0 7, etc., to (a) Letters in parenthesis indicate the different pupils. (a) first pupil,(b) second pupil, eta |