<c 
 
 aPER k BROTHERS. 
 
Digitized by the Internet Archive 
 
 in 2007 with funding from 
 
 IVIicrosoft Corporation 
 
 http://www.arichive.org/details/firstlessonsinnuOOfrenrich 
 
HARPER & BROTHERS. 
 

 1 1 II 
 
 
 
 
 
 
 1 1 
 
 
 ^^^ — 
 
 
 
 
 
 — ^ 
 
 OOUNTEES, AND OOOTTINQ-BOAEDS. 
 
 Every primary school-room should be supplied with a variety of 
 kinds of objects, and an abundance of each kind, to be used by the 
 pupils in learning arithmetical combinations. For this purpose, 
 Avalnuts, horse-chestnuts or buckeyes, pebbles, sea-shells, large flat 
 beans, blocks of wood, etc., may be used. 
 
 A counting-board adds very much to the convenience of both pupils 
 and teacher. This may be of any convenient length, about one foot 
 in width if placed against the wall, and from two to three feet wide if 
 standing away from it, and about two feet high. To prevent the count- 
 ers from falling off, the edge should be raised a half inch or more by 
 a thin strip of board, and the top should be divided into sections of 
 about one foot in length, and from eight to twelve inches wide, by 
 strips of lath or board. {See picture and diagrams above.) When a 
 counting-board can not be had, a table or flat desk may be used in 
 stead. 
 
FRENCH'S MATHEMATICAL SERIES. 
 
 IRST iJESSONS 
 
 \ y 
 
 IN THE NATURAL ORDER: 
 
 JIRST, VISIBLE objects; 
 
 SECOND, CONCRETE NUMBERS; 
 
 THIRD, ABSTRACT NUMBERS. 
 
 JOH 
 
 L.D. 
 
 NEW YOEK: 
 
 H A R P E R & B R O T H E R S. 
 
 1872. 
 

 4-*-> 
 
 FRENCH'S ARITHMETICS. 
 
 This Series consists of Five Books, viz.: 
 I,—FIItST Ij ESSOINS IJ^ NJJMBEItS. 
 II, — EJLJEMJENT^MT JlMITMMETI C. 
 111, — MENTAJL A.ItITM3lETIC, 
 ir.— COMMON SCSOOZ ARITHMETIC. 
 V, ^A CA D EMI C Alt I TIT ME TIC In Preparation. 
 
 Tlie Publishers present tliis Series of Text-Books to American 
 Teachers, fully believing that they contain many new and valu- 
 able features that will especially commend them to the practical 
 wants of the age. 
 
 The plan for the Series, and for each book embraced in it, was 
 fully matured before any one of the Series was completed ; and 
 as it is based upon true philosophical principles, there is a har- 
 mony, a fitness, and a real progressiveness in the books, that is 
 not found in any other Series of Arithmetics published. 
 
 Entered, according to Act of Congress, in the year 1866, by 
 
 HARPER & BROTHERS, 
 
 In the Clerk's Office of the District Court of the United States for the Southern 
 
 District of New Tork. 
 

 THIS little book is intended to give to young children clear ideas 
 of the elementary combinations of numbers, and some prac- 
 tical knowledge of their applications to the business affairs of life. 
 As its general plan is unlike other works designed for the same grade 
 of learners, it is important that teachers and parents should make 
 themselves familiar Avith its peculiar characteristics, before using it in 
 classes or families. 
 
 General Divisions. — Sections. — The book is divided into fifteen 
 sections, the first one of which is devoted to lessons in counting ; the 
 next eight to examples and combinations in Addition, Subtraction, 
 Multiplication, and Division ; the next three to the fractional parts 
 of numbers— halves, thirds, and fourths ; the thirteenth to miscel- 
 laneous problems, embracing all the classes of combinations in the 
 preceding sections ; the fourteenth section to tables of the denomina- 
 tions of money, weight and measures in common use ; and the fif- 
 teenth to combinations embracing the tables of Addition, Subtraction, 
 Multiplication, Division, Factors, and Aliquot or Fractional Parts. 
 
 Articles. — The division of the sections into articles indicates, in 
 every case, either a new class of combinations, or a review of com- 
 binations already learned. For example. Section III, as its title states, 
 teaches '' Addition and Subtraction, with the numbers 4, 5, 6, as one 
 of the parts or terms." Article A contains combinations in Addition 
 and Subtraction, with 4 as one of the parts or terms ; Article B, with 
 5 ; and Article C, with 6, as one of the parts or terms. Articles D and 
 E are reviews of all the combinations in the three preceding articles, 
 the numbers l>eing concrete, and some of them perceptive ; while the 
 questions in Article D require the briefest form of answer. 
 
 Tables of Money, Weight, and Measures.— These tables, 
 pages 97-99, contain only the tables and denominations in common 
 use. The stereotyped schoolmaster and school-book-maker arrange- 
 ment has been discarded, and the denominations are here presented as 
 they are used in business. 
 
 Tables of Combinations. — In Section XV these tables are ar- 
 ranged to be learned in the same order as they are developed in the 
 previous sections. Thus, page 101, the Addition and Subtraction tables 
 of the number 3 are so arranged that when the child has completed 
 Section II, Article C, in which he learns to add 3 to any number not 
 exceeding 10, and to subtract with 3 as one of the terms, he can turn 
 to this part of the book, and first learn the Addition, and then the 
 Subtraction table of 3 ; after which he is to recite the two tables 
 across the pi*ge, making the converse combinations upon the same 
 
6 PREFACE. 
 
 set of numbers. The same arrangement is observed in the Multipli- 
 cation and Division tables. The Factor table, if thoroughly learned, 
 can not fail to secure the promptness and accuracy so much to be 
 desired, yet so seldom acquired in Division ; and the table of Aliquot 
 or Fractional Parts will make the child familiar with the fractional 
 forms of expression so often used in Division. The two tables last 
 named are here published for the first time-; but they have been sub- 
 jected to thorough tests in the school-room, and are found to be very 
 valuable. 
 
 Converse Combinations.— Converse or opposite combinations 
 of the same numbers are embraced in the same section, throughout 
 the work, and in many cases in the same article. Thus, in Section II, 
 the child learns to add with 1, 2, or 3 as one of the parts, and to subtract 
 with the same numbers as one of the terms ; in Section VI he learns 
 to multiply with 3 or 3 as one factor, and to divide with each of the 
 same numbers as one of the terms ; in Section X he learns how to 
 find one half when the whole is given, and how to find the whole 
 when one half is given ; and so on, through the first twelve sections. 
 
 Natural Order of Mental Development. — All the combina- 
 tions embraced in the tables, pages 100, 107, have been used in the pre- 
 vious sections of the book at least three times, and are presented, suc- 
 cessively, in the natural order : first. Visible Objects ; second, Concrete 
 Numbers; third, Abstract Numbers. Every new combination is 
 introduced either in connection with the picture of an object, or with 
 the name of some object familiar to the pupil, and which the teacher, 
 in many cases, may be able to place before him. The second time the 
 combinations are used, they are associated with the names of familiar 
 objects not in sight ; and the third time they are made with abstract 
 numbers. Thus the law of the natural order of mental development, 
 viz., first, Perception (Visible Objects); second. Conception (Concrete 
 Numbers) ; third, Abstraction (Abstract Numbers), is strictly observed. 
 All the problems and examples in smaller type contain combinations 
 that have already been used once or more. 
 
 Illustrations and Examples. — The cuts are not mere counters, 
 picked up at random ; but are pictures which will cultivate the taste 
 of the child, and impart useful knowledge, besides assisting him in his 
 first steps in numbers; and the examples contain much valuable 
 information upon the various occupations, trades, and branches of 
 business, that can not fail to enlist the interest of children in the 
 study of the book. 
 
 Manual for Teachers. — ^All forms of answer and solution, re- 
 marks, notes, etc., have been omitted from the body of the work, and 
 are presented in the last thirteen pages, in the form of hints and sug- 
 gestions, as a Reference Manual for teachers. They are not intended 
 as arbitrary directions and rules ; but are to be adopted, adapted, or 
 rejected, according to circumstances. 
 
FIRST LESSONS IN NUMBERS. 
 
 SECT 10 IT I. 
 
 Exercises in Counting, 
 
 Ai. 1. If I hold up my right hand, 
 as you see in this picture, how many 
 fingers do I hold up ? 
 
 2. How many thumbs on 
 your right hand ? _^ ^ 
 
 3. How many on your left 
 hand ? How many on both 
 hands ? 
 
 4. Hold up one finger. Hold up two 
 fingers. 
 
 5. Hold up your left hand with the 
 thumb and first finger closed. How many 
 fingers are open ? 
 
 6. How many fingers on your right 
 hand? 
 
 7. Count the thumb with the fingers of 
 your right hand. How many are there 
 inaU? 
 
 8. If you count the fingers 
 and thumb of your right hand, 
 and the thumb of your left | 
 hand, how many will there be ? 
 
8 
 
 FIRST LESSONS 
 
 9. Close the thumb and fore- 
 finger of your left hand, and the 
 thumb of your right hand. How 
 many of your fingers are open ? 
 
 10. How many fingers have 
 you on both hands ? 
 
 11. Hold up all your fingers 
 and one thumb. How many 
 are there ? 
 
 12. How many fingers and 
 thumbs have you on both hands? 
 
 13. The thumb is often called a finger. Hold up three 
 fingers ; seven fingers ; five fingers ; nine fingers ; no fingers ; 
 two fingers ; six fingers ; ten fingers ; four fingers ; one finger ; 
 eight fingers. (See Manual, pages 108-110.) 
 
 Jl5. 1. How many houses do you s^e in the pic- 
 ture on the next page ? 
 
 2. How many doors do you see ? 
 
 3. Count the chimneys. How many are there ? 
 
 4. In the yard are some ladies and children. 
 Count the ladies. How many are there ? 
 
 5. How many children in the yard? 
 
 6. Count two doors. (Thus : Orw door^ two doors.) 
 
 7. Count two boys ; two girls ; two chairs. 
 
 8. Count three chimneys. (Thus : One chimney^ two cMni- 
 neys^ three chimneys.) 
 
 9. Count three books ; three slates ; three knives. 
 
 10. Count four boys ; four pencils ; four hats ; four shoes. 
 
 11. Count five girls ; five hands ; five pails ; five baskets. 
 
 12. On the limbs of a tree are some birds. Count 
 them, and tell me hov; many birds there are. 
 
IN NUMBERS. 
 
 13. How many trees 
 do you see in the picture ? 
 
 14. Count tlie cows in the road. How many are 
 there ? 
 
 15. Near the cows are some sheep. Count them, 
 and tell me how many there are. 
 
 16. How many posts of the fence can be seen ? 
 
 17. Count six birds ; six tops ; six balls ; six hoops. 
 
 18. Count seven trees ; seven marbles ; seven windows ; 
 seven desks. 
 
 2 
 
10 FIRSTLESSONS 
 
 19. Count eiglit cows; eight fingers; eight hands; eight 
 apples. 
 
 20. Count nine sheep ; nine leaves ; nine words ; nine pins. 
 
 21. Count ten posts ; ten children ; ten lines in your book ; 
 ten pictures. 
 
 22. How many horses are in tliis picture ? 
 
 23. Count the wagons. How many are there ? 
 
 24. In the picture are how many men on horse- 
 back ? 
 
 25. Count all the men in the picture. How 
 many are there, and what are they doing ? 
 
 26. Some dogs are barking at some pigs. How 
 many dogs are there ? 
 
 27. How many pigs are there ? 
 
 28. We can see some windows in the end of the 
 house, and some in the front ; count them. How 
 many windows in all ? 
 
 29. How many wheels has one wagon? How 
 many have two wagons ? 
 
 30. How many geese can you see in the picture, 
 and w^hat are they doing ? 
 
 31. In the picture are some goats. How many 
 of them are lying down ? How many are standing ? 
 How many goats in all ? 
 
 33. Count two. (Thus : One^ two.) 
 
 83. Count three, and back again. (Thus : One^ two, tTiree; 
 three, two, one.) 
 
 34. In the same manner, count four and back again. Count 
 five. Six. Seven. Eight. Nine. Ten. (Seo Manual, page no.) 
 
IN NUMBERS. 
 
 11 
 
 SSCTIOIT II. 
 
 Addition and Sahtractio7i, tvith tlie Numbers 
 1, 2, 8, as one of the parts or terms, 
 
 (See Manual, page 111.) 
 
 A.» 1. How many girls are in this picture ? 
 
 2. One girl and one girl are liow many girls ? 
 
 3. Ella had one letter block in her hand, but she 
 has just put it upon the chair. How many blocks 
 has she now in her hand ? 
 
 4. One block from one block leaves how many 
 blocks ? 
 
 5. If one of the two girls should go out of the 
 room, how many girls would remain ? 
 
 6. One girl from two girls leaves how many girls ? 
 
 7. Two kittens are playing on the floor, and one 
 Idtten is on a chair. How many kittens are in the 
 picture ? 
 
12 FIRSTLESSOJVS 
 
 8. How many more kittens are on tlie floor than 
 on the chair ? 
 
 9. In the room are three chairs, and one of them 
 is an arm-chair. How many of the chairs are with- 
 out arms ? (See Manual, page 112.) 
 
 10. Three balls are lying on the floor near the 
 table, and a kitten is playing with one baU under a 
 chair. How many balls are on the floor ? 
 
 11. On the table are four books in a pile, and one 
 book lying by itself. If I should take away one of 
 the four books, how many books would be left in 
 the pile? 
 
 12. How many books are four books and one 
 book? 
 
 13. One book from five books leaves how many 
 books? 
 
 14. Four books from five books leave how many 
 books? 
 
 15. EUa has five letter blocks on the floor, 
 and one upon the chair. How many blocks has 
 she? 
 
 16. If EUa should give one of her blocks to Clara, 
 how many would she have left ? 
 
 17. Six cherries and one cherry 
 are how many cherries ? 
 
 18. One cherry from seven 
 cherries leaves how many cher- 
 ries? 
 
 19. Six cherries from seven cherries leave how 
 many cherries ? 
 
IN NUMBERS. 
 
 13 
 
 20. How many strawberries 
 are seven strawberries and 
 one strawberry? 
 
 21. One strawberry from 
 eight strawberries leaves how 
 many strawberries ? 
 
 22. If you have eight straw- 
 berries, and eat seven of them, how many of them 
 will you have left ? 
 
 23. Eight peaches and one 
 peach are how many peaches ? 
 
 24. One peach from nine 
 peaches leaves how many 
 peaches ? 
 
 25. Eight peaches from nine peaches leave how 
 many peaches ? 
 
 26. Upon a vine 
 are nine clusters 
 of grapes, and un- 
 der it is one clus- 
 ter. How many 
 clusters of grapes 
 in all? 
 
 27. One cluster 
 from ten clusters 
 leaves how manv ^ 
 clusters? |1[J Hi T I B, <** ^ ] 
 
14 
 
 FIRST LESSONS 
 
 28. Nine clusters from ten clusters leave how 
 many clusters ? 
 
 29. Ten roses and one rose are how many roses ? 
 
 30. One rose from eleven roses leaves how many 
 roses ? 
 
 31. Ten roses from eleven roses leave how many 
 roses ? 
 
 -D. 1. In this picture we see some boys sailing 
 little boats upon the water. Two of the boys are 
 on the shore, and one boy stands in the water. 
 How many boys are two boys and one boy ? 
 
 2. Two boys from three boys leave how many 
 boys? 
 
 3. On the bridge are two boys and two girls, 
 flow many children are on the bridge ? 
 
 4. If two girls should go off the bridge, how many 
 girls would remain on the bridge ? 
 
IN NUMBERS. 
 
 15 
 
 5. On the bridge are four children, two of whom 
 are girls. How many are boys ? 
 
 6. Two boys are fishing, and three are sailing 
 boats. How many boys in all ? 
 
 7. If two of the boys should go home, how many 
 boys would remain ? 
 
 8. Four boats are sailing on the stream, and the 
 boys have two in their hands. Four boats and two 
 boats are how many boats ? 
 
 9. Two boats from six boats leave how many 
 boats ? 
 
 10. Five children and two children are how many 
 children ? 
 
 11. Seven children are how many more than two 
 children ? 
 
 12. How many trees are six trees and two trees ? 
 
 13. Eight trees are how many more than two 
 trees ? 
 
 14 Seven pinks and two pinks 
 are how many pinks ? 
 
 15. Two pinks from nine pinks 
 leave how many pinks ? 
 
 16. Seven pinks from nine 
 pinks leave how many pinks ? 
 
 17. How many acorns are eight acorns and two 
 acorns ? 
 
 18. Two acorns from ten 
 acorns leave how many acorns ? 
 
 19. Eight acorns from ten 
 acorns leave how many acorns ? 
 
16 
 
 FIRST LESSONS 
 
 eleven 
 birds? 
 
 20. How 
 many birds 
 are two 
 birds and 
 nine birds ? 
 
 21. Two birds from 
 eleven birds leave bow 
 many birds ? 
 
 22. Nine birds from 
 birds leave bow many 
 
 23. How many leaves are ten leaves and two 
 leaves ? Two leaves and ten leaves ? 
 
 24. Twelve leaves are how many more tlian two 
 leaves ? 
 
 25. Twelve leaves are how many more than ten 
 leaves ? 
 
 O. 1. How many deer 
 are three deer and three 
 deer? 
 
 2. Three deer are 
 standing, and three are 
 lying down. How many 
 more are standing than are lying down ? 
 
 3. Three deer from six deer leave how many deer? 
 
 4. Four rabbits and three 
 rabbits are how many rabbits ? 
 
 5. Three rabbits from seven 
 rabbits leave how many rab- 
 bits? 
 
IN NUMBERS. 
 
 17 
 
 6. Four rabbits from seven rabbits leave how 
 many rabbits ? 
 
 7. How many chickens are 
 five chickens and three chick- 
 ens ? 
 
 8. Three chickens from 
 eight chickens leave how 
 many chickens? 
 
 9. Five chickens from eight chickens leave how 
 many chickens ? 
 
 10. Six windows and three 
 windows are how many win- 
 dows? 
 
 11. Nine windows are how 
 many more than three win- 
 dows? 
 
 12. Nine windows are how many more than six 
 windows ? 
 
 13. Seven trees and three 
 trees are how many trees ? 
 
 14. Ten trees are how many 
 more than three trees ? 
 
 15. Ten trees are how many 
 more than seven trees ? 
 
 16. Eight swallows and 
 three swallows are how many 
 swallows ? 
 
 17. Three swallows from 
 eleven swallows leave how 
 many swallows ? 
 
18 
 
 Fi^H 
 
 ST LESSONS 
 
 18. Eight swallows from eleven swallows leave 
 how many swallows ? 
 
 19. How many ducks ^ ... _ . ^ ,, 
 are nine ducks and three 
 ducks ? 
 
 20. Three ducks from 
 twelve ducks leave how 
 many ducks ? 
 
 21. Nine ducks from 
 many ducks ? 
 
 22. Ten books and three 
 books are how many books ? 
 
 23. Three books from thir- 
 teen books leave how many 
 books ? 
 
 24. Ten books from thirteen 
 books leave how many books ? 
 
 twelve ducks leave how 
 
 jLJ. How many are 
 
 1. One pen and five pens ? 
 
 2. One top and eight tops ? 
 
 3. Two caps and six caps ? 
 
 4. Three bells and six bells ? 
 
 5. One cup and seven cups ? 
 
 6. One bird and ten birds ? 
 
 7. Three guns and nine guns ? 
 
 8. Two pins and eight pins ? 
 
 9. Three pinks and seven 
 
 pinks ? 
 10. Two boots and ten boots ? 
 
 11. One map and nine maps? 
 
 12. Three wheels and ten 
 
 wheels ? 
 
 13. Two plums and seven 
 
 plums ? 
 
 14. One book and six books ? 
 
 15. Two slates and nine slates? 
 
 16. Three plates and eight 
 
 plates ? 
 
 17. Three chairs and five 
 
 chairs ? 
 
IN NUMBERS. 
 
 19 
 
 How many will remain, if you take 
 
 18. Two hats from two liats ? 
 
 19. Two sleds from eight 
 
 sleds ? 
 
 20. Two flags from ten flags ? 
 
 21. Three keys from ten keys ? 
 
 22. One egg from nine eggs ? 
 
 23. One knife from eight 
 
 knives ? 
 
 24. One fig from eleven figs ? 
 
 25. Three trees from nine 
 
 trees ? 
 
 26. Three shoes from twelve 
 
 shoes ? 
 
 27. Two clocks from twelve 
 
 clocks ? 
 
 28. One drum from ten drums? 
 
 29. Three pears from thirteen 
 
 pears ? 
 
 30. Two balls from five balls ? 
 
 31. Three clubs from seven 
 
 clubs ? 
 
 32. Three flies from eleven 
 
 flies? 
 
 33. Two pails from nine pails 'i 
 
 34. One pan from seven pans? 
 
 35. Two forks from eleven 
 
 forks ? 
 
 36. Three spoons from eight 
 
 spoons ? 
 
 (See Manual, page 112.) 
 
 !ci. 1. In the picture on the next page are two 
 cows by the tree in front of a country tavern, and 
 one cow behind an emigrant wagon. How many 
 cows are two cows and one cow ? 
 
 2. Before the stage-coach are two two-horse 
 teams. Two horses and two horses are how many 
 horses ? 
 
 3. In the end of the tavern are three windows in 
 the upper story, and two windows in the lower 
 story. How many windows in the end of the 
 house ? 
 
 4. Three windows are how many more than two 
 windows ? 
 
 5. Two windows are how many less than five 
 \\andows ? 
 
20 
 
 FIRST LESSONS 
 
 6. Three persons are 
 
 in the coach, and three 
 
 on the outside. How 
 
 many persons are 
 
 ! aboard the coach ? 
 
 7. How many more persons are in the coach than 
 are on the outside ? 
 
 8. One of the persons on the outside is the driver. 
 How many passengers are on the outside ? ITow 
 many are aboard the coach ? 
 
 9. "We can see three doors in the lower story of 
 the house, and one door in the upper story. How 
 many doors of the house can we see ? 
 
 10. Before the stage-coach are four horses, and 
 before the emigrant wagon two horses. How many 
 horses are four horses and two horses ? Four 
 horses and one horse ? Five horses and two 
 
- I N NXJM B E R S. 21 
 
 horses? Four horses and two horses and one 
 horse ? Four horses and three horses ? 
 
 11. Two horses from six horses leave how many 
 horses ? Two horses from four horses ? Four 
 horses from six horses ? 
 
 12. How- many windows are three windows and 
 five windows ? 
 
 13. Three windows are how many less than five 
 windows ? How many less than eight windows ? 
 
 14. Eight windows are how many more than 
 five windows ? 
 
 15. One person is on horseback, and six persons 
 are aboard the coach. How many persons are 
 riding? 
 
 16. Three persons are how many less than six 
 persons ? 
 
 17. One horse from seven horses leaves how 
 many horses ? 
 
 18. Six horses from seven horses leave how 
 many horses? 
 
 19. On the piazza are two persons, and in other 
 parts of the picture nine persons. How many per- 
 sons are in the picture ? 
 
 20. Eight persons are how many less than eleven 
 persons ? 
 
 21. Two horses from seven horses leave how 
 many horses ? 
 
 22. Three horses from seven horses leave hpw 
 many horses ? 
 
 23. How many persons are six persons and two 
 persons and one person and two persons ? 
 
22 
 
 FIRST LESSONS 
 
 SBGTIOIT III. 
 
 Addition and Subtraction, with the Nunihers 
 4:, 5, 6f as one of the parts or terms. 
 
 (See Manual, page 112.) 
 
 Ai. Here is a picture of some boys playing sol- 
 dier, they are in two companies. You may count 
 the boys in each company. How many boys in the 
 smaller company ? How many in the larger ? 
 
 1. Four boys of one company are standing, and 
 three are sitting. How many boys in that com- 
 pany? 
 
 2. How many more boys are standing than are 
 sitting ? 
 
 3." How many more boys in the larger company 
 than in the smaller ? 
 
 4. Of the company of seven boys, three are sit- 
 ting. How many are standing ? 
 
 5. Eour boys of each company are standing. 
 - How many boys of both companies are standing ? 
 JHBHow many more boys of one company are 
 • "tarSiing than of the other ? 
 
INNUMBERS. 23 
 
 7. If four more boys should sit down, liow many 
 would be left standing ? 
 
 8. Five boys of one company and four of tlie other 
 have wooden guns. Five guns and four guns are 
 how many guns ? 
 
 9. Five guns are how many more than four 
 guns? 
 
 10. Four guns from nine guns leave how many 
 guns? 
 
 11. Five guns from nine guns leave how many 
 guns? 
 
 12. Six boys of one company and four of the other 
 have paper caps. Six caps and four caps are how 
 many caps ? 
 
 13. Six caps are how many more than four caps ? 
 
 14. Four caps from ten caps leave how many 
 caps? 
 
 15. Six caps from ten caps leave how m^any caps ? 
 
 16. How many boys in both companies ? 
 
 17. How many more boys in the larger company 
 than in the smaller? 
 
 18. Four boys from eleven boys leave how many 
 boys? 
 
 19. Seven boys from eleven boys leave how many 
 boys? 
 
 20. How many feet have t^\,^^^..^^^^ 
 two horses ? How many feet .'/^''^ ^^^^m 
 have two horses and a colt ? "" ' 
 
 
 21. Eight feet are how 
 many more than four feet ? 
 
 22. Four feet from twelve feet leave how many feet? 
 
24 
 
 riRST LESSONS 
 
 23. Eight feet from twelve feet leave how many 
 feet? 
 
 24. Nine barrels and four 
 barrels are how many bar- 
 rels? 
 
 25. Nine barrels are how 
 many more than four bar- 
 rels? 
 
 26. Four barrels from thir- 
 teen barrels leave Ijow many barrels ? 
 
 27. Nine barrels from thirteen barrels leave how 
 many barrels ? 
 
 28. In this picture 
 count the pupils in the 
 class. Count those at 
 their seats. How many 
 pupils in the school- 
 room? 
 
 29. How many more 
 pupils are at their seats than are in the class ? 
 
 30. Four pupils from fourteen pupils leave how 
 many pupils ? 
 
 31. Ten pupils from fourteen pupils leave how 
 many pupils ? 
 
 B. 1. Five bags and five 
 bags are how many bags? 
 
 2. Five bags are how many 
 more than five bags ? 
 
 3. Five bags from ten bags 
 leave how many bags ? 
 
IN NUMBERS. 
 
 25 
 
 4. How many doves are 
 six doves and five doves ? 
 
 5. Six doves are how 
 many more than five doves ? 
 
 6. Five doves from eleven 
 doves leave how many 
 doves ? 
 
 7. Six doves from eleven doves leave how many 
 doves ? 
 
 8. Seven sheep are 
 standing in a field, 
 and five are lying 
 down. How many 
 sheep in the field? 
 
 9. How many more sheep are standing than are 
 lying down ? 
 
 10. Five sheep from twelve sheep leave how 
 many sheep ? 
 
 11. Seven sheep from twelve sheep leave how 
 many sheep ? 
 
 12. On the land are ' -- , 
 eight saw logs, and in 
 the water are five. How 
 many logs in all ? 
 
 13. How many more 
 are on the land than in -^ 
 the water ? 
 
 14 Five logs are how many less than thirteen 
 logs? 
 
 15. Eight logs are how many less than thirteen 
 
 logs ? (See Manual, page 112.) 
 
26 
 
 FIRST LESSONS 
 
 from 
 leave 
 
 16. Nine geese and 
 five geese are how many 
 geese ? 
 
 17. Nine gees( 
 how many more 
 five geese ? 
 
 18. Five geese 
 fourteen geese 
 how many geese ? 
 
 19. Nine geese from fourteen geese leave how 
 many geese ? 
 
 20. How many are ten 
 bricks and five bricks ? 
 
 21. Ten bricks are how 
 many more than five 
 bricks ? 
 
 22. Five bricks from "~ _ _ --^ _ 
 fifteen bricks leave how many bricks ? 
 
 23. Ten bricks from fifteen bricks leave how 
 many bricks ? 
 
 O- 1. Count all the persons in the picture on 
 the next page. How many are there ? How many 
 are in the farther group ? 
 
 2. The six boys of one party and also six of the 
 other party are skating. How many boys are 
 skating ? 
 
 3. How many more boys are skating in one place 
 than in the other ? 
 
 4. Twelve boys are how many more than six boys ? 
 
IN NUMBERS.: 
 
 27 
 
 5. There are seven boys on skates in one party, and 
 six in the other. How many boys are on skates ? 
 
 6. Seven boys are how many more than six boys ? 
 
 7. Six boys from thirteen boys leave how many 
 boys? 
 
 8. Seven boys from thirteen boys leave how 
 many boys? 
 
 9. Eight children and six children are how many 
 children ? 
 
 10. Eight children are how many more than six 
 children ? 
 
 11. Six children from fourteen children leave hov>^ 
 many children ? 
 
 12. Eight children from fourteen children leave 
 how many children ? 
 
 13. There are nine persons in one group, and six 
 in the other. How many persons in both groups ? 
 
 14. How many more persons in one group than 
 in the other ? 
 
FIRST LESS OX S 
 
 15. Fifteen persons are how many more than six 
 persons ? How many more than nine persons ? 
 
 16. George bought a cent's worth of chestnuts, 
 and after giving six of them to Alice, he had ten 
 left. How many chestnuts did he buy ? 
 
 17. How many more had George than AUce ? 
 
 18. Six chestnuts from sixteen chestnuts leave 
 how many chestnuts ? 
 
 19. Ten chestnuts from sixteen chestnuts leave 
 
 how many chestnuts ? (See Manual, page 112.) 
 
 D. How 
 
 1. Four cents and seven cents? 
 
 2. Four hens and ten hens ? 
 
 3. Five axes and eight axes ? 
 
 4. Six leaves and eight leaves? 
 
 5. Five lambs and seven 
 
 lambs ? 
 
 many are 
 
 6. Six sheep and nine sheep ? 
 
 7. Four dolls and eight dolls? 
 
 8. Four muffs and nine muffs? 
 
 9. Five bags and nine bags ? 
 
 10. Five colts and six colts ? 
 
 11. Six jugs and seven jugs ? 
 
 How many wiU remain, if you take 
 
 13. Seven lamps from eleven 
 lamps ? 
 
 13. Five nails from fourteen 
 
 nails ? 
 
 14. Six skates from eleven 
 
 skates ? 
 
 15. Six hooks from twelve 
 
 hooks ? 
 
 16. Five flags from eleven 
 
 flags? 
 
 17. Ten kites from fifteen kites? 
 
 18. Six brooms from fourteen 
 
 brooms ? 
 
 19. Nine stools from fifteen 
 
 stools ? 
 
 20. Four saws from thirteen 
 
 saws? 
 
 21. Eight combs from twelve 
 
 combs ? 
 
 22. Five boxes from nine boxes? 
 
 23. Eight cakes from thirteen 
 
 cakes ? 
 
 24. Six tacks from sixteen 
 
 tacks ? 
 
 25. Ten hoops from sixteen 
 
 hoops ? 
 
 26. Six jars from thirteen jai^s ? 
 
 27. Five tubs from fifteen tubs? 
 
 28. Eight vests from fourteen 
 
 vests ? 
 
IN NUMBERS. 
 
 29 
 
 -CJ. 1. In the wagon in front of the cooper shop 
 are six barrels, and on the ground near the wagon 
 are four barrels. Six barrels and four barrels are 
 
 how many barrels ? (See Manual, page 112.) 
 
 2. By the cooper shop are six barrels in a pile. 
 Six barrels and six barrels are how many barrels ? 
 
 3. How many more barrels are on the wagon than 
 in the pile ? 
 
 4. On the ground and by the cooper shop are 
 ten barrels, and in the wagon are six barrels. How 
 many barrels in all ? 
 
 5. How many more barrels are on the ground 
 and in the pile than in the wagon ? 
 
 6. How many wheels have two wagons ? 
 
 7. Eight wheels are how many more than four 
 Tvheels ? 
 
 8. In a lumber yard five men are at work in one 
 place, and four men in another place. Five men 
 and four men are how many men ? 
 
 9. A cooper has five piles of staves in one place, 
 and five piles in another. How many piles of staves 
 has ho? 
 
30 
 
 F 1 Fk S T LESSONS 
 
 10. If he uses five piles of these staves in making 
 barrels, how many piles will he have left ? 
 
 11. Four men are how many less than nine men ? 
 
 12. In one fence near the lumber yard we can 
 see ten posts, and in another fence we can see four 
 posts. How many fence posts can we see in the 
 picture ? 
 
 13. On one side of the cooper shop are seven 
 trees, and on the other side are five trees. How 
 many trees in the picture ? 
 
 14. Ten posts are how many more than four 
 posts ? 
 
 15. Four posts from fourteen posts leave how 
 many posts ? 
 
 16. Ten posts from fourteen posts leave hov/ 
 many posts ? 
 
 17. Twelve trees are how many more than seven 
 trees ? 
 
 18. Five trees from twelve trees leave how many 
 trees ? 
 
INNUMBERS. 31 
 
 19. Charles has six marbles, and Harry has nine. 
 How many marbles have the two. boys ? 
 
 20. Flora made ten pin cushions for Christmas 
 presents, and Fanny made five. How many did 
 they both make ? 
 
 21. Ellen's father gave her fourteen cents, and 
 she paid nine cents of the money for a doll. How 
 many cents had she left? 
 
 22. In a reading class of thirteen pupils, seven 
 are boys. How many are girls ? 
 
 23. Lewis brought thirteen peaches from the 
 garden, and gave five of them to his sister. How 
 many had he left ? 
 
 24-. How many more had he than his sister ? 
 
 25. A farmer, having fifteen turkeys, sold six of 
 them. How many had he left ? 
 
 26. On one side of a street are seven houses, and 
 on the other side are five houses. How many 
 houses on both sides of the street ? 
 
 27. How many more on one side of the street 
 than on the other ? 
 
 28. In one family are six persons, and in another 
 family are ten persons. How many persons in the 
 two families ? 
 
 29. Count eleven, and back again. (Thus : One^ two^ three^ 
 four^ fite^ siXy seven^ eighty nine, ten^ eleven; eleven, teUy nine, 
 eight, seven, six. Jive, four, three, two, one.) 
 
 30. In the same manner count twelve ; thirteen ; fourteen ; 
 fifteen ; sixteen ; seventeen ; eighteen ; nineteen ; twenty. 
 
 (See Manual, pages 110, 112.) 
 
32 
 
 FIRST LESSONS 
 
 SECTION iy; 
 
 Addition and Siibtr action ^ with the Numbers 
 7 9 Sf 9, 10 f as one of the parts or terms. 
 
 -£X. 1. Seven shocks of grain are standing in one 
 harvest field, and seven shocks in another. How 
 many shocks are standing in both fields ? 
 
 2. Seven loads of wheat from fourteen loads 
 leave how many loads ? 
 
 3. In one field seven shocks of grain are stand- 
 ing, and eight shocks are down. How many shocks 
 of grain are in that field ? 
 
 4. Seven bundles of oats from fifteen bundles 
 leave how many bundles ? 
 
 "•5. Eight sheaves of rye from fifteen sheaves 
 leave how many sheaves ? 
 
 6. In the other field seven shocks are standing, 
 and nine shocks are down. How many shocks of 
 grain in that field ? 
 
IN NUMBERS. 
 
 33 
 
 7. Seven shocks of barley from sixteen shocks 
 leave how many shocks ? 
 
 8. If nine loads of straw be taken from a stack 
 containing sixteen loads, how many loads will be 
 left in the stack ? 
 
 9. "We can see seven lengths of fence between the 
 two fields, and ten lengths on the road. How many 
 lengths of the two fences are shown in the picture ? 
 
 10. Seven rails from seventeen rails leave how 
 many rails ? 
 
 11. Ten boards from seventeen boards leave how 
 
 many boards ? (See Manual, page 112.) 
 
 •D* Numbers may be expressed by words, fi 'nres, or cap- 
 ital letters. (See page 4 of cover ; also Manual, page 112.) 
 
 In the following table tlie first ten numbers are expressed 
 in all these ways : 
 
 By Wokds. 
 
 By Figures. 
 
 By Letters. 
 
 Roman 
 type. 
 
 Italic 
 type. 
 
 Script 
 type. 
 
 Roman Italic Script 
 type. type. type. 
 
 Roman 
 type. 
 
 Italic 
 type. 
 
 One. 
 
 One. 
 
 &ne. 
 
 1 1 / 
 
 I 
 
 / 
 
 Two. 
 
 Two, 
 
 <:%<AO. 
 
 % 2 S 
 
 II 
 
 II 
 
 Three. 
 
 Three, 
 
 ^/iee. 
 
 8 5 c/ 
 
 III 
 
 III 
 
 Four. 
 
 Four. 
 
 K%ai. 
 
 4 4^ 
 
 IV 
 
 ir 
 
 Five. 
 
 Five, 
 
 <S^&. 
 
 5 ^ ^ 
 
 V 
 
 V 
 
 Six. 
 
 Six. 
 
 &iv. 
 
 ^ e f 
 
 YI 
 
 YI 
 
 Seven. 
 
 Seven, 
 
 We^j^en. 
 
 7 7/ 
 
 YII 
 
 VII 
 
 Eight. 
 
 EigM. 
 
 S^a^^, 
 
 ^ 8 S" 
 
 YIII 
 
 VIII 
 
 Nine. 
 
 Nine. 
 
 *yf^ne. 
 
 9 9 p 
 
 IX 
 
 IX 
 
 Tea. 
 
 Ten. 
 
 ^en. 
 
 10 10 /{? 
 
 X 
 
 X 
 
FIRST LESSONS 
 
 O. 1. In one of these, railroad trains are 8 pas- ^ 
 senger cars, and in the cftner are 8 freight cars./' 
 How many cars in the two trains ? 
 
 2. How many more cars in the passenger train 
 than in the freight train ? 
 
 3. Sixteen cars are how many more than eight 
 cars ? 
 
 4. On one "branch are 8 cherries, and on another 
 branch are 9. How many cherries on both branches ? 
 
 5. If you take eight cherries from seventeen cher- 
 ries, how many cherries will be left ? 
 
 6. Take nine cherries from seventeen cherries, 
 How many are left ? 
 
 7. On one branch are 10 leaves, and on another 
 are 8 leaves. How many leaves are on the two 
 branches ? 
 
 8. From eighteen leaves take eight leaves. How 
 many leaves remain ? 
 
 9. Eighteen leaves are how many more than ten 
 leaves ? 
 
IN IX^UMBERS. 
 
 35 
 
 D. 1. In 
 
 this picture 
 9 diildren are 
 riding in a 
 sleigh, and 9 
 other chil- 
 dren are at play with their 
 sleds on the hill-side. How 
 many children are 9 children 
 and 9 children ? 
 2. How many more children are 
 in the sleigh than on the hill- 
 side? 
 
 3. Eighteen children are how many more than 
 nine children ? 
 
 4. In the picture 10 children have sleds. How- 
 many children are 10 children and 9 children ? 
 
 5. Ten children are how many more than nine 
 children ? 
 
 6. In this picture are nineteen children. If nine 
 of them go home, how many will remain ? 
 
 7. If ten of them go home, how many wiU re- 
 main? 
 
 8. How many persons are in the sleigh ? How 
 many persons are 10 persons and 10 persons ? 
 
 9. Ten sleds from ten sleds leave how many sleds ? 
 
 10. Twenty persons are how many more than ten 
 persons ? 
 
 11. Nine sleds and eight sleds are how many sleds ? 
 
 12. Nine muffs are how many less than sixteen 
 muffs ? 
 
36 
 
 FIRST LESSONS 
 
 13. .Three children have fur mittens, five have 
 leather mittens, and seven have yarn mittens. 
 How many children have mittens ? 
 
 E. 1. In this 
 picture of men 
 building a rail- 
 road, eight men 
 are working with 
 picks, and nine 
 men with wheelbarrows. How manj men are using 
 picks and wheelbarrows ? 
 
 2. Seven men are drilling rock for blasting, and 
 breaking it in pieces. How many men are at work 
 with picks and at the rock ? 
 
 3. How many men are at work with wheelbarrows 
 and at the rock ? 
 
 4. How many more men are using picks and 
 wheelbarrows than are working at the rock ? 
 
IN NUMBERS. 
 
 37 
 
 5. How many more men are working at the rock 
 and with picks than are using wheelbarrows ? 
 
 6. How many more men are working at the rock 
 and with wheelbarrows than with picks ? 
 
 Jj . How many are 
 
 1. 7 shovels and 7 shovels ? 
 
 2. 8 loads and 8 loads ? 
 
 3. 10 crow-bars and 10 crow- 
 
 bars ? 
 
 4. 10 pipes and 10 pipes ? 
 
 5. 8 saddles and 10 saddles ? 
 
 6. 7 bridles and 10 bridles ? 
 
 7. 9 halters and 9 halters ? 
 
 How many will remaiQ, if you take 
 
 8. Seven picks from sixteen 
 
 picks ? 
 
 9. Eight spades from seven- 
 
 teen spades ? 
 
 10. Seven rails from fourteen 
 
 rails ? 
 
 11. Nine stumps from nine- 
 
 teen stumps ? 
 
 12. Seven spikes from fifteen 
 
 spikes ? 
 
 13. Nine rocks from sixteen 
 
 rocks ? 
 
 14. Ten kegs from seventeen 
 
 kegs? 
 
 15. Eight cars from eighteen 
 
 cars ? 
 
 16. Eight boats from fifteen 
 
 boats ? 
 
 17. Nine whips from seventeen 
 
 whips ? 
 
 18. Ten hubs from nineteen 
 
 hubs? 
 
 19. Ten seats from eighteen 
 
 seats ? 
 
 20. Ten stages from twenty 
 
 stages ? 
 
 21. Nine travelers from eight- 
 
 een travelers ? 
 
 22. Write in figures the numbers expressed by these letters : 
 
 y, VIII, II, IV. 
 
 23. Express by letters the numbers 1, 6, 10, 3, 7, 9. 
 
 24. Write the first ten numbers in words, figures, and letters. 
 
 (See Manual, page 112.) 
 
38 F I R S T L E S S O N S 
 
 SECTIOH Y. 
 
 Miscellaneous Eocercises in Addition and 
 
 Subtraction, (See Manual, page 112.) 
 
 XX. 1. Maria has 7 peaches, and Mary has 6. 
 How many peaches have the two girls ? 
 
 2. How many are 7 and 6 ? 
 
 3. Edward, having thirteen cherries, gave five of 
 them to Emma. How many had he then ? 
 
 4. Five from thirteen leave how many ? 
 
 5. Henry paid 10 cents for a speller, and 8 cents 
 for a slate ? How many cents did he pay for both ? 
 
 6. How many are 10 and 8 ? 8 and 10 ? 
 
 7. Sarah gave her teacher 8 roses, and Ida gave 
 her 7. How many roses did they both give her ? 
 
 8. How many are 8 and 7 ? 7 and 8 ? 
 
 9. Thirteen boys were at play in the yard, but 
 nine of them have gone into the school-house. 
 How many of them remain in the yard ? 
 
 10. I^ake nine from tliirteen, and how many will be left ? 
 
 11. Eichard had eleven rabbits, but he gave six 
 of them to his cousin Bobert. How many rabbits 
 did he keep ? 
 
 12. Take six from eleven, and how many will be left ? 
 
 13. In going through the woods, "William saw 9 
 red squirrels and 4 gray ones. How many squirrels 
 did he see ? 
 
 14. How many are 9 and 4 ? 4 and 9 ? 
 
 15. Otis had 8 marbles, and he bought 6 more. 
 How many had he then ? 
 
INNUMI3ERS. 39 
 
 16. Eufus brought 10 eggs from the barn one^ 
 day, and 9 eggs the next day. How many eggs 
 did he bring from the barn in both days ? 
 
 17. How many are 10 and 9 ? 
 
 18. Martha has 6 birds in one cage, and 4 in 
 another. How many birds has she ? 
 
 19. 4 and 6 are how many ? 6 and 8 are how many ? 
 
 20. George's father gave him eighteen cents, and 
 he paid ten cents of the money for a rubber ball. 
 How many cents had he left ? 
 
 21. Ten from eighteen leave how many ? 
 
 22. In one room are 8 chairs, and in another 
 room are 5. How many chairs in both rooms ? 
 
 23. How many are 5 and 8 ? 8 and 5 ? 
 
 24. A cooper made fifteen cider barrels, and sold 
 eight of them. How many had he left ? 
 
 25. Eight from fifteen leave how many ? 
 
 26. A merchant has 9 kegs of nails under one 
 counter, and 6 kegs under another. How many 
 kegs of nails has he ? 
 
 27 How many are 6 and 9 ? 9 and 6 ? 
 
 28. Nine cows are in one field, and seven are in 
 another. How many cows are in the two fields ? 
 
 29. How many are 7 and 9 ? 9 and 7 ? 
 
 30. In the stable were eleven horses, but seven 
 of them have been taken out. How many horses 
 are left in the stable ? 
 
 31. Seven from eleven leave how many ? Four from eleven ? 
 
 32. In a garden are 9 cherry-trees and 9 plum- 
 trees. How many fruit-trees in the garden ? 
 
 33. 9 and 9 are how many ? 
 
4:0 FIRST LESSONS 
 
 34. Lyman caught fifteen trout, and sold nine of 
 them. How many did he keep ? 
 
 35. Nine from fifteen leave how many ? 
 
 36. A fruit peddler bought seventeen oranges, 
 and sold nine of them. How many had he left ? 
 
 37. Nine from seventeen leave how many ? 
 
 38. Olive had thirteen letter blocks, but she has 
 lost six of them. How many has she now ? 
 
 39. Seven from thirteen leave how many ? 
 
 40. Eliza had sixteen cents, but she spent ten of 
 them for a primer. How many cents had she then ? 
 
 41. Ten from sixteen leave how many ? 
 
 42. Jacob found fourteen apples under a tree, 
 and picked up nine of them. How many did he 
 leave on the ground ? 
 
 43. Nine from fourteen leave how many ? 
 
 44. From a bush containing fourteen roses, 
 Emily picked eight. How many roses remained on 
 the bush ? 
 
 45. Eight from fourteen leave how many ? 
 
 46. A man paid 10 dollars for a stove, and 4 dol- 
 lars for a load of wood. How many doUars did the 
 stove and wood cost him ? 
 
 47. Ten boys were playing ball, and six boys 
 were flying kites. How many boys were at play ? 
 
 48. How many are 10 and 4 ? 6 and 10 ? 
 
 49. A grocer having nineteen chests of tea, sold 
 nine of them. How many chests had he left ? 
 
 50. Nine from nineteen leave how many ? (Manual, page lis.) 
 
 JD. We have already learned how to express the first ten 
 numbers by figures. The remainder of the first fifty numbers 
 are expressed in words and figures, as shown on the next page : 
 
IN NUMBERS. 
 
 41 
 
 By "Words. By Figures. 
 
 Eleven 
 
 Twelve 
 
 Thirteen 
 
 Fourteen 
 
 Fifteen 
 
 Sixteen 
 
 Seventeen 
 
 Eighteen 
 
 Nineteen 
 
 Twenty 
 
 Twenty-one 
 
 Twenty-two 
 
 11 // 
 
 12 /S 
 13 /J' 
 14 /^ 
 15/^ 
 
 16 /^ 
 
 17 // 
 
 18 /cf 
 
 19 /p 
 
 20 SO 
 
 21 S/ 
 
 22 2S 
 
 Twenty-three 23 2S 
 
 By Words. By Figures. 
 
 Twenty-four 24 U 
 
 Twenty-five 25 2S 
 
 Twenty-six 26 Sd' 
 Twenty-seven 27 i'/ 
 
 Twenty-eight 28 SS" 
 
 Twenty-nine 29 Sp 
 
 Thirty 30 SO 
 
 Thirty-one 31 S/ 
 
 Thirty-two 32 S2 
 
 Thirty three 33 SS 
 
 Thirty-four 34 S^ 
 
 Thirty-five 35 SJ 
 
 Thirty-six 36 S6 
 
 Thirty-seven 37 S^ 
 
 By Words. By Figures. 
 
 Thirty-eight 38 SS" 
 Thirty-nine Z^ SP 
 Forty 40 -^0 
 
 Forty-one 41 ^/ 
 Forty-two 42 ^S 
 Forty-three 43 -// 
 Forty-four 44 -^'^ 
 Forty-five 45 -^^ 
 Forty-six 46 '^6 
 Forty-seven 47 -^Z 
 Forty-eight 48 -/cf 
 Forty-nine 49 -/>' 
 Fifty 60 SO 
 
 (See Manual, page 118.) 
 
 c. 
 
 1. Count twenty-one and back again. In the same 
 manner count twenty-two ; twenty-three ; twenty-four ; twenty- 
 five; twenty-six; twenty-seven; twenty-eight; twenty-nine; 
 
 thirty. (See Manual, pages 111, 113,) 
 
 2. Count 31 and back again. In the same manner, count 
 32; 33; 34; 35; 36; 37; 38; 39; 40. 
 
 3. Count 41 and back again. In the same manner, count 
 42; 43; 44; 45; 46; 47; 48; 49; 50. 
 
 Read the numbers in the twelve columns below . 
 
 (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 
 21 8 47 36 25 12 1 40 29 5 4 44 
 33 22 48 37 26 13 18 41 30 6 19 
 45 34 23 10 49 38 27 14 20 42 31 16 
 
 Write the following numbers in figures : 
 
 (lb) (17) (18) (19) 
 
 Seventeen, thirty-four, thirty-nine, four, 
 forty-six, eleven, twenty-eight, forty-three, 
 
 thirty-five, fifty, fifteen, thirty-two. 
 
 4 
 
42 FIRSTLESSONS 
 
 SBCTIOIT YI- 
 
 Multiplication and Division, with 2 or S as one 
 
 factor or tertn, (See Manual, page 113.) 
 
 .ix. 1. On tlie opposite page is a picture of a 
 menagerie going from one town to another. Do 
 you see two camels one behind the other? One 
 camel and one camel are how many camels ? Then 
 
 2 times 1 camel are how many camels ? 
 
 2. One of the wagons containing wild beasts is 
 drawn by elephants. Two elephants are harnessed 
 together in one pair, and two in another pair. How 
 many elephants are 2 elephants and 2 elephants ? 
 How many elephants are 2 times 2 elephants ? 
 
 3. On the top of this wagon are two seats, and 
 on each seat are three men. How many men are 
 
 3 men and 3 men ? How many men are 2 times 3 
 men? 
 
 4. Four men are riding on the elephants, and 
 four men on horseback. How many are 4 men and 
 
 4 men ? How many are 2 times 4 men ? 
 
 5. The band wagon has a long seat on each side, 
 and on each seat are five men. How many men 
 are 5 men and 5 men ? How many men are 2 times 
 
 5 men ? 
 
 6. The small carriage is drawn by three pairs of 
 ponies. How many ponies are 2 ponies and 2 
 ponies and 2 ponies? How many ponies are 3 
 times 2 ponies ? 
 
IN NUMBERS. 
 
 
 7. The band 
 wagon is 
 drawn by 
 four pairs of 
 horses. How 
 many horses 
 are 2 horses 
 and 2 horses 
 and 2 horses and 2 horses ? 
 How many horses are 4 
 times 2 horses ? 
 
 8. Each of the five other 
 wagons which contain wild 
 beasts is drawn by two 
 horses. How many horses 
 are 2 horses and 2 horses 
 and 2 horses and 2 horses and 2 horses? 
 many horses are 5 times 2 horses ? 
 
 How 
 
44 
 
 FIRST LESSONi 
 
 and 6 pupils? 
 pupils ? 
 
 9. In a school- 
 room are 2 seats 
 for classes, and on 
 each seat are 6 
 pupils. How many 
 pupils are on the 
 2 seats? How many 
 pupils are 6 pupils 
 How many pupils are 2 times 6 
 
 10. These pupils sit at 6 desks, 2 pupils at each 
 desk. How many pupils are 2 pupils and 2 
 pupils and 2 pupils and 2 pupils and 2 pupils 
 and 2 pupils? How many pupils are 6 times 2 
 pupils ? 
 
 11. Here are 
 some young per- 
 sons taking a 
 sleigh-ride. How 
 many ladies are there? 
 How many gentlemen ? 
 How many persons are 
 7 persons and 7 persons ? 
 How many persons are 2 times 
 7 persons ? 
 
 12. How many persons in . ,^^ ^ 
 one sleigh? How many per- 
 sons in 2 sleighs ? In 3 sleighs ? In 4 sleighs ? 
 In 5 sleighs ? In 6 sleighs ? In 7 sleighs ? 
 How many persons are 7 times 2 persons ? 
 
B E R S. 
 
 45 
 
 13. These men 
 are taking their 
 horses to the city 
 to sell them. The 
 horses are hitched 
 by pairs to a long 
 rope, as you see 
 in the picture. 
 How many horses on each side 
 of the rope ? How many horses 
 on both sides ? How many horses 
 are 8 horses and 8 horses ? How many horses are 
 2 times 8 horses ? 
 
 14. How many pairs of horses are there ? How 
 many horses in 1 pair ? In 2 pairs ? In 3 pairs ? 
 In 4 pairs ? In 5 pairs ? In 6 pairs ? In 7 pairs ? 
 In 8 pairs? How many horses are 8 times 2 
 horses ? 
 
 15. If you have 9 chestnuts in each hand, how 
 many will you have in both hands? How many 
 chestnuts are 2 times 9 chestnuts ? (See Manual, page 113.) 
 
 16. If each of 9 boys has 2 apples, how many 
 apples have 2 of the boys? How many apples 
 have 3 boys ? 5 boys ? 9 boys ? 9 times 2 apples 
 are how many apples ? 
 
 17. One boy has 10 fingers. How many fingers 
 have 2 boys ? How many fingers are 2 times 10 
 fingers ? 
 
 18. One girl has 2 hands. How many hands 
 have 10 girls ? How many hands are 10 times 2 
 hands ? 
 
46 
 
 FIRST LESSONS 
 
 Jd. 1. Two oxen make one 
 one pair or yoke. How many 
 yoke of oxen are 4 oxen ? 
 
 2. 4 oxen are how many times 2 
 oxen ? 4 oxen are 2 times how many 
 oxen ? 
 
 f:l«^-^," 
 
 3. If 6 persons ride in 
 a carriage, and sit 2 on 
 a seat, how many seats 
 will they occupy ? 
 
 4. How many seats 
 will they occupy if 3 sit 
 on a seat ? 
 
 5. 6 persons are how many times 2 persons ? 
 6 persons are how many times 3 persons ? 
 6 persons are 3 times how many persons ? 
 6 persons are 2 times how many persons ? 
 
 6. Eight marbles are how 
 many times two marbles ? 
 How many times four marbles ? 
 
 7. Eight marbles are four 
 times how many marbles? 
 Two times how many marbles ? 
 
 8. If you pay 2 cents apiece for peaches, how 
 many can you buy for 10 cents ? 
 
 9. At 5 cents apiece, how many oranges can be 
 bought for 10 cents ? 
 
 10. 10 cents are 
 
 How many times 5 cents ? I 2 times how many cents ? 
 How many times 2 cents ? | 5 times how many cents ? 
 
 (See Manual, page 113.) 
 
XN NUMBERS. 
 
 47 
 
 11. How many days will 
 12 eggs last a cook, if she 
 uses 2^ eggs each day ? 
 
 12. How many days will 
 they last her, if she uses 6 
 eggs a day ? 
 
 13. 12 eggs are 
 
 How many times 6 eggs ? I 2 times how many eggs ? 
 How many times 2 eggs ? | 6 times how many eggs ? 
 
 14. If a tailor earns 2 dollars in one day, how 
 many days will it take him to earn 14 dollars ? 
 
 15. If a laborer earns 7 doUars in one week, how 
 many weeks must he work to earn 14 dollars ? 
 
 16. 14 dollars are 
 
 How many times 7 dollars ? I 2 times how many dollars ? 
 How many times 2 dollars ? | 7 times how many dollars ? 
 
 17. If you eat 2 apples every day, how many days 
 wiU 16 apples last you ? 
 
 18. How many days will 16 figs last you, if you 
 eat 8 figs in a day ? 
 
 19. 16 pears are 
 
 How many times 8 pears ? I 2 times how many pears ? 
 How many times 2 pears ? | 8 times how many pears ? 
 
 20. How many days will it take a boy to learn 
 18 letters, if he learns 2 letters each day ? 
 
 21. How many times will 18 melons fill a basket 
 which holds only 9 melons ? ^^^.^^^:,:^;.^^'ii^iis£ 
 
 22. 18 pins are 
 
 How many times 9 pins ? I 2 times how many pins ? 
 How many times 2 pins ? | 9 times how many pins ? 
 
48 
 
 FIRST LESSONS 
 
 23. A man 
 who is mak- 
 ing maple 
 sugar has a 
 tub tliat will 
 hold twenty 
 bucketfuls. If 
 he carries two 
 buckets at a 
 time, how many times will he have to bring them 
 full of sap to fill the tub ? 
 
 24. If he puts 20 bucketfuls into barrels which 
 hold 10 bucketfuls each, how many barrels will he 
 fiU? 
 
 25. 20 pailfuls of water are 
 
 How many times 10 pailfuls ? I 2 times how many pailfuls ? 
 How many times 2 pailfuls ? | 10 times how many pailfuls ? 
 
 (See Manual, page 118.) 
 
 0« 1. A ship has 3 masts. 
 How many masts have 2 
 ships? How many masts 
 have 3 ships? How many 
 masts are 3 masts and 3 
 masts and 3 masts? How 
 many masts are 3 times 3 
 masts ? 
 
 2. How many feet have 3 
 dogs? How many feet are 4 
 feet and 4 feet and 4 feet ? 
 How many feet are 3 times 4 
 feet? 
 
XN NUMBERS. 
 
 49 
 
 windows and 5 windows are how 
 How many windows are 3 times 
 
 3. How many dogs are 3 dogs and 3 dogs and 3 
 dogs and 3 dogs ? 4 times 3 dogs are how many dogs ? 
 
 4 We see 5 
 windows in each 
 of these houses. 
 How many win- 
 dows can we see 
 in the 3 houses? 
 5 windows and 5 
 many windows? 
 5 windows ? 
 
 5. How many doors are 3 doors and 3 doors and 
 3 doors and 3 doors and 3 doors ? 5 times 3 doors 
 are how many doors ? 
 
 6. How many are 
 3 times 6 soldiers ? 
 
 (See Manual, page 114 ) 
 
 7. How many 
 gtms are 6 times 3 
 guns? 
 
 8. How many sol- 
 diers in 3 squads of 7 soldiers each ? 
 
 9. How many are 
 3 times 7 flags ? 
 7 times 3 tents ? 
 
 10. One pas- 
 senger car has 
 8 wheels. How 
 many wheels 
 have 3 passen- 
 ger cars ? 
 
 "^^ 
 
 -'"-I 
 
 hBB|lll«limiKISBMIimEI 
 
50 
 
 FIRST LESSONS 
 
 11. At tliis railroad station are persons in 3 groups, 
 and 9 persons in eacli group. How many persons 
 are at the station ? 
 
 12. How many ladies are in 3 ears, if there are 
 10 ladies in each ear ? 
 
 13. 
 
 How many are 
 
 3 times 8 wheels ? 
 3 times 9 persons ? 
 3 times 10 ladies ? 
 
 8 times 3 cars ? 
 
 9 times 3 trunks ? 
 10 times 3 seats ? 
 
 D. 1. A father di- 
 vides 9 apples among 
 his children, giving 3 
 apples to each child. 
 How many children 
 has he ? 
 
 2. 9 apples are how many- 
 times 3 apples ? 9 apples 
 are 3 times how many apples. 
 
 3. How many 
 boats will be re- 
 quired that 12 
 boys may take 
 a ride on the 
 river, if 3 boys 
 ride in each boat ? 
 
 4. If 4 boys should ride in each boat, how many 
 boats would be required ? 
 
 5. 12 children are 
 
 How many times 3 children ? I How many times 4 children ? 
 4 times how many children ? j 3 times how many childien ? 
 
IN NUMBERS. 
 
 51 
 
 6. A carman can 
 draw 3 hogslieads of 
 sugar at one load. How 
 many loads will 15 
 togslieads make ? 
 
 7. If 15 hogsheads of 
 sugar be placed in rows 
 of 5 hogsheads each, 
 how many rows will there be ? 
 
 8. 15 hogsheads of molasses are 
 
 How many times 3 hogsheads ? I 5 times how many hogsheads ? 
 How many times 5 hogsheads ? | 3 times how many hogsheads ? 
 
 9. A cutler used 18 blades in making pocket- 
 knives, using 3 blades for each knife. How many 
 knives did he make ? 
 
 10. If he uses 18 blades, putting 6 blades in each 
 knife, how many knives wiU he make ? 
 
 11. 18 pocket-knives are 
 
 How many times 3 knives ? I 6 times how many knives ? 
 How many times 6 knives ? | 3 times how many knives ? 
 
 12. One day James picked 21 ripe melons from 
 the vines in his garden, gathering 3 melons from a 
 hill. How many hills of vines had he in his garden ? 
 
 13. He raised 21 hiUs of beans, in rows of 7 hiUs 
 each. How many rows were there ? 
 
 14. 21 melons are 
 
 How many times 3 melons ? I 7 times how many melons ? 
 How many times 7 melons ? | 3 times how many melons ? 
 
 15. Irene gathered 24 flowers, which she ar- 
 ranged in bouquets, putting 8 flowers in each. 
 How many bouquets did she make ? 
 
 16. 24 roses are 
 
 How many times 3 roses ? I 8 times how many roses ? 
 ' How many times 8 roses ? I 3 times how many roses ? 
 
52 
 
 FIRST LESSONS 
 
 17. A man 
 
 put 27 baskets 
 of apples into 
 barrels, put- 
 ting 3 basket- 
 fuls into each 
 barrel. How 
 many barrels 
 didhefiU? 
 
 18. He gathered 9 basketfuls from each tree. 
 From how many trees did he gather the apples ? 
 
 19. 27 baskets are 
 
 How many times 3 baskets ? I 9 times how many baskets ? 
 How many times 9 baskets ? | 3 times how many baskets ? 
 
 20. If 3 loads of hay will keep one cow through 
 the winter, how many cows will 30 loads keep ? 
 
 21. On Christmas morning, Albert found some 
 stems of raisins in his stocking. There were 10 
 raisins on each stem, and 30 raisins in all. How 
 many stems were there ? 
 
 22. 30 pictures are 
 
 How many times 3 pictures ? I 10 times how many pictures ? 
 How many times 10 pictures ? | 3 times how many pictures ? 
 
 (See Manual, pag3 114.) 
 
 E. 1. Julia has 3 cages, with 2 canary-birds in 
 each cage. How many birds has she ? 
 
 2. Two boys have five rabbits each. How many 
 rabbits have both boys ? 
 
 3. John found 3 nests, with 4 eggs in each. How 
 many eggs did he find ? 
 
 4. At 2 cents apiece, how many peaches can you 
 buy for 4 cents ? 
 
INNUMBERS. 53 
 
 5. If a man can earn 2 dollars in one day, how 
 many days will it take him to earn 12 dollars ? 
 
 6. If you can buy 2 slate-pencils for one cent, 
 how many cents must you pay for 10 pencils ? 
 
 7. If 7 yards of merino will make a dress, how 
 many yards will be required for 2 dresses ? 
 
 8. A hardware merchant sold 3 plows, at 7 dol- 
 lars apiece. How much did he receive for them ? 
 
 9. There are 6 chairs in a set. How many chairs 
 in 2 sets ? How many chairs in 3 sets ? 
 
 10. Frank paid 24 cents for lemons, at 3 cents 
 apiece. How many lemons did he buy ? 
 
 11. If school is in session 3 hours each half-day, 
 how many hours of school in 10 haK-days ? 
 
 12. Eugene bought 3 penholders, paying 8 cents, 
 for each. How many cents did they cost ? 
 
 13. Each one of a class of 9 pupils answered 3 
 questions. How many questions did they all answer ? 
 
 14. How many boots are there in 10 pairs ? 
 
 15. Sixteen shoes are how many pairs of shoes ? 
 
 16. A father gave 30 cents to his children, giving 
 10 cents to each child. How many children had he ? 
 
 17. Harriet arranged 27 books in her book-case, 
 putting 9 books on each shelf. How many shelves 
 in her book-case ? 
 
 18. How many leaves are on 8 stems of clover, 
 there being 3 leaves on each stem ? 
 
 19. Anna has 2 books, each of which contains 9 
 pictures. How many pictures in both books ? 
 
 20. To how many persons can I give 21 oranges, 
 if I give 3 oranges to each person ? 
 
54 JbMRSTLESSONS 
 
 21. A man gave 14 apples to some boys, giving 
 
 2 apples to each boy. How many boys were there ? 
 
 22. 18 gloves are how many pairs of gloves ? 
 
 23. Twenty skates are how many pairs of skates ? 
 
 24. In 9 pairs of mittens, how many mittens ? 
 
 25. Ira found 27 chestnuts in burs, each bur con- 
 taining 3 chestnuts. How many burs were there ? 
 
 26. If Oscar can write a line in his writing-book 
 in 3 minutes, how many lines can he write in 30 
 minutes ? 
 
 27. A man paid 15 dollars for picture-frames, at 
 
 3 dollars apiece. How many frames did he buy ? 
 
 28. How much will 2 sheets of drawing paper 
 cost, at 4 cents a sheet ? 
 
 29. How many times can you fill a tub which 
 holds 5 pailfuls, from a barrel containing 15 pail- 
 fuls? 
 
 30. Jay makes 2 pictures in his drawing book each 
 day. How many pictures does he draw in 8 days ? 
 
 31. At 6 cents a quart, how many quarts of milk 
 can be bought for 12 cents ? 
 
 32. How much will 3 boxes of strawberries cost, 
 at 10 cents a box ? . 
 
 33. If one barrel of flour can be made from 4 
 bushels of wheat, how many barrels can be made 
 from 8 bushels ? 
 
 34. If a man walks 3 miles in one hour, how 
 many miles can he walk in 6 hours ? 
 
 35. How many sets of spoons are 18 spoons ? 
 
 36. A man paid 18 cents for a fresh fish, at 9 
 cents a pound. How much did the fish weigh ? 
 
IN NUMBERS. 
 
 55 
 
 SSCTIOIT YII, 
 
 Muvtiplication and Division^ with 4 or 5 as one 
 
 factor or term, (See Manual, page 114.) 
 
 A.. 1. How many horseshoes will it take to 
 shoe 4 horses, if 4 shoes are put upon each horse ? 
 
 2. 4 times 4 horses are how many horses ? 
 
 3. How many teeth in a harrow which has 4 rows 
 of teeth, with 5 teeth in each row ? 
 
 4. How many horseshoes will be required to shoe 
 5 horses all round ? 
 
 5. 4 times 5 hammers are how many hammers ? 
 5 times 4 wedges are how many wedges ? 
 
 6. On the wall of the shop are 4 rows of horse- 
 shoes, and 6 shoes in each row. How many horse- 
 shoes are on the wall ? 
 
56 FIRSTLESSONS 
 
 7. How many wagon tires in 6 sets, there being 
 4 tires in one set ? 
 
 8. 4 times 6 bolts are how many bolts ? 
 
 6 times 4 linchpins are how many linchpins ? 
 
 9. A blacksmith shod 7 horses each day for 4 
 days. How many horses did he shoe ? 
 
 10. How many horseshoes did he use in one 
 day? 
 
 11. 4 times 7 nail rods are how many nail rods ? 
 
 7 times 4 plow points are how many plow points ? 
 
 12. If a blacksmith uses 8 nails in setting one 
 shoe, how many nails will he use in setting 4 
 shoes? 
 
 13. If he can make 4 iron rings in one hour, how 
 many rings can he make in 8 hours ? 
 
 14. 4 times 8 files are how many files ? 
 
 8 times 4 rivets are how many rivets ? 
 
 15. A blacksmith has 4 pieces of chain, and in 
 each piece are 9 links. How many links in the 4 
 pieces ? 
 
 16. How many tines have 9 pitchforks, each fork 
 having 4 tines ? 
 
 17. 4 times 9 shovels are how many shovels ? 
 How many are 9 times 4 iron bands ? 
 
 18. A blacksmith made 4 iron hoops for a cask, 
 and used 10 feet of iron for each hoop. How many 
 feet of hoop iron did he use ? 
 
 19. How many wagon tires will be required for 
 all the wheels of 10 wagons ? 
 
 30. How many are 4 times 10 hooks ? 
 How many are 10 times 4 staples ? 
 
IN MUMBERS. 
 
 57 
 
 B. 1. A 
 
 drover wish- 
 es to have 16 
 cattle taken 
 across a riv- 
 er, but only 
 4 cattle can 
 be taken on the 
 ferry-boat at one 
 trip. How many 
 loads will the 16 cattle make ? 
 ?. 16 cattle are 
 
 How many times 4 cattle ? | 4 times how many cattle ? 
 
 3. How many boat loads would 20 cattle make ? 
 
 4. K 5 horses can be ferried across the river at 
 one load, how many loads will 20 horses make ? 
 
 5. 20 oxen are 
 
 How many times 4 oxen ? I 4 times how many oxen ? 
 How many times 5 oxen ? | 5 times how many oxen ? 
 
 6. A lady put 24 quarts of berries into cans which 
 held 4 quarts each. How many cans did she fill ? 
 
 7. Some children who had gathered 24 quarts of 
 beiries, found on dividing them that each child 
 would have 6 quarts. How many children were there ? 
 
 8. How many 4-quart pans will 24 quarts of milk 
 fill ? How many 6-quart pans ? 
 
 9. If a basket maker can make 7 market baskets 
 in one day, how many days will it take him to make 
 28 market baskets ? 
 
 10. How many days will it take him to make 28 
 corn baskets, if he makes 4 in one day ? 
 
 11. 28 baskets are 
 
 How many times 4 baskets ? | 7 times how many baskets ? 
 
58 FIRSTLESSONS 
 
 12. Isaac planted 32 beans in hills, putting 4 
 beans in each hill. How many hills did he plant ? 
 
 13. He planted 32 hills of com in rows of 8 hills 
 each. How many rows were there ? 
 
 14. 33 ears of com are 
 
 How many times 4 ears ? | 4 times how many ears ? 
 
 15. 32 quarts of beans are 
 
 How many times 8 quarts ? | 8 times how many quarts ? 
 
 16. A tin peddler gave 36 cents for paper rags, at 
 4 cents a pound. How many pounds did he buy ? 
 
 17. He paid for them in tin basins, at 9 cents 
 apiece. How many basins did it take ? 
 
 18. 36 dippers are 
 
 Uow many times 4 dippers ? I 4 times how many dippers ? 
 How many times 9 dippers ? j 9 times how many dippers ? 
 
 19. A farmer sold 40 bushels of apples to custom- 
 ers, selling 4 bushels to each. To how many cus- 
 tomers did he sell the apples ? 
 
 20. He sold 40 bushels of potatoes in lots of 10 
 bushels each. To how many persons did he sell 
 the potatoes ? 
 
 31. 40 bushels of oats are 
 
 How many times 4 bushels ? | 4 times how many bushels ? 
 22. 40 bushels of wheat are 
 
 How many times 10 bushels ? | 10 times how many bushels ? 
 
 O- 1. A cabinet maker made 5 bureaus, with 5 
 drawers in each. How many bureau drawers did 
 he use ? 
 
 2. He made 5 dining tables, each table having 
 6 legs. How many table legs did he use ? 
 
INNUMBERS. 59 
 
 3. He sold a set of mahogany chairs at 5 dollars 
 apiece. How much did he receive for them ? 
 
 4. 5 times 5 wasli-stands are how many wash-stands ? 
 
 5. 5 times 6 footstools are how many footstools ? 
 
 6. 6 times 5 picture-frames are how many picture-frames ? 
 
 7. A furniture dealer sold in one day 5 lounges, 
 at 7 dollars apiece. How much did he receive for 
 them ? 
 
 8. The same day he sold 7 bedsteads, at 5 dol- 
 lars apiece. How much did they come to ? 
 
 9. 5 times 7 what-nots are how many what-nots ? 
 
 10. 7 times 5 desks are how many desks ? 
 
 11. If a pile of wood that contains one cord is 
 8 feet long, how many feet long is a pile that con- 
 tains 5 cords ? 
 
 12. How much will 8 cords of wood cost, at 5 
 dollars a cord? 
 
 13. 8 times 5 pairs of tongs are how many pairs of tongs ? 
 
 14. 5 times 8 fire shovels are how many fire shovels ? 
 
 15. If a steamboat bums 9 tons of coal in making 
 one trip, how many tons will she burn in making 5 
 trips ? 
 
 16. A coal train left 9 cars at a station, and each 
 ear contained 5 tons of coal. How many tons of 
 coal were left ? 
 
 17. How many are 5 times 9 axes ? 9 times 5 saws ? 
 
 18. How much will 10 tons of coal cost, at 5 
 dollars a ton ? 
 
 19. How much will 5 bushels of charcoal cost, at 
 10 cents a bushel? 
 
 20. How many are 5 times 10 coal scuttles ? 
 
 21. How many are 10 times 5 pokers ? 
 
60 
 
 FIRST LESSONS 
 
 U* 1. How many lengths of fence, 5 rails high, 
 can be built with 25 rails ? 
 
 2. How many lengths can be built with 30 rails ? 
 
 3. How many lengths can be built with 35 rails ? 
 
 4. How many lengths of fence, 6 rails high, can 
 be built with 30 rails? 
 
 5. If a man builds 7 rods of stone wall in a day, 
 how many days will it take him to build 35 rods ? 
 
 6. 25 fence stakes are how many times 5 stakes ? 
 
 7. 30 pickets are 
 
 How many times 5 pickets ? I 5 times liow many pickets ? 
 How many times 6 pickets ? I 6 times how many pickets ? 
 
 8. 35 fence posts are 
 
 How many times 5 posts ? I 7 times how many posts ? 
 5 times how many jDosts ? | How many times 7 posts ? 
 
 9. In one month a Hvery-man fed his horses 40 
 bushels of oats, giving each horse 8 bushels. How 
 many horses had he ? 
 
 10. He paid 40 dollars for straw, at 5 dollars a 
 load. How many loads did he buy ? 
 
 11. 40 whips are 
 How many times 5 whips ? 
 How many times 8 whips ? 
 
 12. 40 halters are 
 
 5 times how many haltei-s ? 
 
 8 times how many halters ? 
 
i N N U M B E R S. 61 
 
 13. In one term Clara attended school 45 days, 
 How many weeks did slie attend, there being 5 
 school-days in a week ? 
 
 14. How many rows of 9 desks each in a school- 
 room containing 45 desks ? 
 
 15. 45 slates are 
 
 How many times 5 slates ? 
 5 times how many slates ? 
 
 16. 45 maps are 
 How many times 9 maps '^ 
 9 times how many maps ? 
 
 17. A farmer took 50 bushels of wheat to mill, 
 and for every 5 bushels, he received one barrel of 
 flour. How many barrels of flour did he receive ? 
 
 18. A miller sent 50 barrels of flour to market, in 
 wagon loads of 10 barrels each. How many loads 
 were there ? 
 
 19. 50 sacks of buckwheat flour are 
 
 How many times 5 sacks ? I 5 times how many sacks ? 
 
 How many times 10 sacks ? | 10 times how many sacks ? 
 
 (See Manual, page 114.) 
 
 Jii. 1. How much will 4 lead-pencils cost, at 5 
 cents apiece ? 
 
 2. If you can buy 4 plums for one cent, how many 
 can you buy for 6 cents ? 
 
 3. A hatter sold 5 silk hats, at 5 dollars each. 
 How much did he receive for them ? 
 
 4. At 5 cents apiece, how much will 6 pears cost? 
 
 5. At 4 cents a cake, how many cakes of maple 
 sugar can I buy for 16 cents ? 
 
 6. Eunice paid 25 cents for thread, at 5 cents a 
 spool. How many spools did she buy ? 
 
 7. A farmer received 20 dollars for fat sheep, at 
 5 dollars a head. How many sheep did he sell ? 
 
62 FIRSTLESSONS 
 
 8. A woman paid 36 cents for iron spoons, at 6 
 cents apiece. How many spoons did slie buy ? 
 
 9. How many days are there in 4 weeks ? 
 
 10. If a seamstress uses 4 skeins of tkread in 
 making one linen coat, how many skeins will she 
 use in making 8 coats ? 
 
 11. How many dimes, or ten-cent pieces, will pay 
 for a pocket-knife that costs 50 cents ? 
 
 12. A printer worked 10 hours a day for 5 days. 
 How many hours did he work ? 
 
 13. If 5 yards of muslin will make the curtains 
 for one window, how many yards will be required 
 for 7 windows ? 
 
 14. A builder paid 28 doUars for window-bHnds, 
 at 4 doUars a pair. How many pairs did he buy ? 
 
 15. Twenty-four tea-spoons are how many sets ? 
 
 16. If 8 candles weigh one pound, how many 
 pounds will 32 candles weigh ? 
 
 17. In making flour barrels, a cooper puts 10 
 hoops upon every barrel. How many hoops does 
 
 he put upon 4 barrels ? (See Manual, page 114.) 
 
 18. A tin peddler bought 5 pounds of old brass, 
 at 9 cents a pound. How much did it come to ? 
 
 19. If I pay 45 cents for beef, at 9 cents a poimd, 
 how many pounds do I buy ? 
 
 20. If one sheet of paper makes 4 leaves of a 
 writing-book, how many leaves wiU 9 sheets make ? 
 
 21. If a packet-boat on a canal runs 5 miles an 
 hour, how many hours will it be in running 35 miles? 
 
 22. A grocer paid 36 dollars for vinegar, at 4 
 dollars a barrel How many barrels did he buy ? 
 
IN NUMBXiKS. 
 
 63 
 
 SECTIOIT YIII* 
 
 Multiplication and Division, with 6 or 7 as one 
 
 factor or term, (See Manual, page 114.) 
 
 xL* 1. In the main part of 
 this Gothic window are 6 sash 
 or sections, and in each section 
 are 6 panes of glass. How 
 many panes of glass in the 6 
 sections ? 
 
 2. There are 6 panes also in 
 each of the 3 circular sections. 
 In 7 sections of the window, how 
 many panes of glass ? 
 
 3. How many panes of glass 
 in 8 sections ? 
 
 4 How many panes of glass 
 in the whole window ? 
 
 5. 6 times 6 boxes of glass are how many boxes ? 
 
 6. How many pounds of putty are 7 times 6 pounds ? 
 
 7. 8 times 6 sash weights are how many sash weights ? 
 
 8. 9 times 6 sashes are how many sashes ? 
 
 9. Six tea knives are called a set. 
 Imives in 10 sets? 
 
 10. How many silver forks are 6 times 10 forks ? 
 
 11. A farmer carried 6 bushels of clover seed to 
 a seed store, and sold it at 7 dollars a bushel. 
 How much did he receive for it ? 
 
 12. 6 times 7 bushels of grass seed are how many bushels ? 
 
 How many 
 
64 FIRSTLESSONS 
 
 13. A stove dealer sold 6 parlor stoves at 8 dol- 
 lars apiece. How mucli did lie receive for them ? 
 
 14. How many stove legs are 6 times 8 stove legs ? 
 
 15. How many dollars will a joiner earn in 6 
 weeks, if lie earns 9 dollars in one week ? 
 
 16. 6 times 9 planes are how many planes ? 
 
 17. How much, must I pay a glazier for setting 6 
 panes of glass, at 10 cents a pane ? 
 
 18. 6 times 10 paint brushes are how many paint brushes ? 
 
 19. How much will 7 cocoa-nuts cost, at 7 cents 
 apiece ? 
 
 20. How many pine-apples are 7 times 7 pine-apples ? 
 
 21. If a sheet-iron worker can make 7 lengths of 
 stove pipe in an hour, how many lengths can he 
 make in 8 hours ? 
 
 22. In a tin-ware factory are 7 workmen, and 
 each of them can make 8 milk pails in a day. 
 How many can all of them make ? 
 
 23. 7 times 8 baking tins are how many baking tins ? 
 
 24. 8 times 7 toasting-forks are how many toasting-forks ? 
 
 25. A boy 9 years old asked his grandfather his 
 age, who replied, " I am 7 times as old as you." 
 How old was the grandfather ? 
 
 26. How many days in 9 weeks ? 
 
 27. How many months are 7 times 9 months ? 
 
 28. How many hours are 9 times 7 hours ? 
 
 29. In 7 dimes, how many cents ? 
 
 30. How much wiU 10 bunches of grapes cost, at 
 7 cents a bunch ? 
 
 31. 7 times 10 tomatoes are how many tomatoes ? 
 
 32. 10 times 7 cucumbers are how many cucumbers 2 
 
INCUMBERS. 65 
 
 H. 1. A crockery dealer sold 36 coffee cups, in 
 sets of 6 cups each. How many sets did lie sell ? 
 
 2. Forty-two tea plates are how many sets ? 
 
 3. A woman paid 42 cents for sauce plates, at 7 
 cents apiece. How many did she buy ? 
 
 4. 36 pint bowls are 
 
 How many times 6 bowls ? | 6 times how many bowls ? 
 
 5. 42 goblets are 
 
 How many times 6 goblets ? I 6 times how many goblets ? 
 How many times 7 goblets ? | 7 times how many goblets ? 
 
 6. At 6 cents apiece, how many salt-cellars can 
 you buy for 48 cents ? 
 
 7. A lady paid 48 cents for tumblers, at 8 cents 
 apiece. How many did she buy ? 
 
 8. 48 wine-glasses are 
 
 How many times 6 glasses ? I How many times 8 glasses ? 
 6 times how many glasses ? I 8 times how many glasses ? 
 
 9. How many egg-cups can be bought for 54 
 cents, at 6 cents apiece ? 
 
 10. How many match safes, at 9 cents each, can 
 be bought for 54 cents ? 
 
 11. 54 pitchers are 
 
 How many times 6 pitchers ? i 6 times how many pitchers ? 
 How many times 9 pitchers ? | 9 times how many pitchers ? 
 
 12. At 6 cents a dozen, how many dozen clothes- 
 pins can be bought for 60 cents ? 
 
 13. If a turner can turn 10 roUing-pins in an 
 hour, how many hours must he work to turn 60 
 rolling-pins ? 
 
 14. 60 wooden bowls are 
 
 6 times how many bowls ? I How many times 6 bowls ? 
 10 times how many bowls ? | How many times 10 bowls ? 
 
QQ FIRSTLBSSONS 
 
 15. A willow-ware dealer paid 49 dollars for wil- 
 low wagons, at 7 dollars apiece. How many wagons 
 did he buy ? 
 
 16. 49 peck measures are 
 
 How many times 7 measures ? | 7 times how many measures ? 
 
 17. If a man can paint 7 wash-tubs in an hour, 
 how many hours will it take him to paint 56 wash- 
 tubs? 
 
 18. A blacksmith paid 56 cents for hammer 
 handles, at 8 cents apiece. How many did he buy ? 
 
 19. 56 wash-boards are 7 times how many wash-boards? 
 8 times how many washboards ? 
 
 How many times 7 washboards ? 
 How many times 8 washboards ? 
 
 20. How many yards of broadcloth will be re- 
 quired for 63 cloth caps, if 7 caps can be made 
 from one yard ? 
 
 21. A hatter paid 63 dollars for muffs, at 9 dol- 
 lars apiece. How many muffs did he buy ? 
 
 23. 63 straw hats are 
 
 9 times how many hats ? I How many times 7 hats ? 
 7 times how many hats ? | How many times 9 hats ? 
 
 23. If 7 wool hats can be made from one pound 
 of wool, how many pounds will be required for 70 
 hats? 
 
 24. A livery-man paid 70 doUars for buffalo 
 robes, at 10 dollars apiece. How many robes did 
 he buy ? 
 
 25. 70 hat-boxes are 
 
 How many times 7 boxes ? I 7 times how many boxes ? 
 How many times 10 boxes ? | 10 times how many boxes ? 
 
INNUMBBRS. 67 
 
 C. 1. A family bouglit 6 loaves of bread of a 
 baker, at 6 cents a loaf. How much did it cost them ? 
 
 2. They also bought 7 pounds of crackers, at 9 
 cents a pound. How much did the crackers cost ? 
 
 3. A woman paid 60 cents for a pair of flat-irons, 
 at 6 cents a pound. How much did they weigh ? 
 
 How much must be paid 
 
 4. For 8 pocket combs, at 6 cents apiece ? 
 
 5. For 10 reams of printing paper, at 7 dollars a 
 ream? 
 
 6. For 8 pounds of potash, at 7 cents a pound ? 
 
 7. For 10 fat sheep, at 6 dollars apiece ? 
 
 8. If one pair of sheets can be made from 9 
 yards of Merrimac sheeting, how many pairs can be 
 made from 63 yards ? 
 
 9. If a woman packs 8 pounds of butter in one 
 week, how many weeks wiU it take her to fill a tub 
 which holds 48 pounds ? ^- " 
 
 10. How many yards in a carpet which contains 
 6 breadths, each 7 yards long ? 
 
 11. A church is lighted by 6 chandeliers, of 9 
 burners each. How i^^ burners in all ? 
 
 12. 56 yards of cloi^Bp||©w many times 8 yards ? 
 
 13. How many we^f^m 49 days ? 
 
 14. At 6 cents a cake, how many cakes of toilet 
 soap can be bought for 42 cents ? 
 
 15. How many paper window-curtains, at 10 cents 
 apiece, can be bought for 70 cents ? 
 
 16. A farmer sowed 54 pounds of grass seed upon 
 his meadojAusing 9 pounds to the acre. How 
 many acr^J^Bthe meadow ? 
 
 doj^usii 
 
 w 
 
68 
 
 FIRST LESSONS 
 
 SKCTIOK IX. 
 
 MtUtiplication and Division^ with 8, 9^ or 10 , as 
 
 one factor or term. (See Manual, page 114.) 
 
 dCX. 1. If 8 pieces are 
 used in making one farm 
 gate, how many boards 
 must be used for 8 farm 
 gates ? 
 
 2. How many pieces will be required for 9 farm 
 gates ? 
 
 3. How many pieces for 10 gates ? 
 
 4. A carpenter uses 9 pick- 
 ets in making one small 
 gate. How many pickets 
 will lie use in making 
 gates ? 
 
 5. How many pickets will 
 lie use in makiag 9 gates ? 
 
 6. How many pickets in making 10 gates ? 
 
 7. How many 
 fence posts can 
 a man set in 8 
 days, if lie sets y 
 10 posts each 
 day? 
 
 8. How many posts can lie set in 9 days ? 
 
 9. How many posts in 10 days ? 
 
^ INNUMBERS. 69 
 
 10. How many dolls are 8 times 8 dolls ? 
 
 11. How many kites are 9 times 10 kites ? 
 
 12. 9 times 8 balls are how many balls ? 
 
 13. 8 times 10 tops are how many tops ? 
 
 14. 9 times 9 hoops are how many hoops ? 
 
 15. How many picture books are 10 times 8 picture books ? 
 
 16. How many skipping-ropes are 10 times 9 skipping- 
 ropes ? 
 
 17. 8 times 9 tin trumpets are how many tin trumpets ? 
 
 18. 10 times 10 marbles are how many marbles 
 
 15. 1. If 8 candles will last a family one week, 
 how many weeks will 64 candles last them ? 
 
 2. How many pounds of tallow must a woman 
 use to make 72 candles, if she makes 8 candles from 
 one pound ? 
 
 3. At 9 cents apiece, how many tin candlesticks 
 can be bought for 72 cents ? 
 
 4. 64 lamp wicks are 
 
 How many times 8 wicks ? ] 8 times how many wicks ? 
 
 5. 72 lamps are 
 
 How many times 8 lamps ? I 8 times how many lamps ? 
 How many times 9 lamps ? | 9 times how many lamps ? 
 
 6. How many balls of candle wicking can be 
 bought for 80 cents, at 8 cents a ball ? 
 
 7. How many quarts of kerosene will a shop- 
 keeper burn in 80 days, if one quart lasts him 10 
 days ? 
 
 8. 80 lanterns are 
 
 How many times 8 lanterns ? I 10 times how many lanterns % 
 8 times how many lanterns ? | How many times 10 lanterns \ 
 
70 FIRSTLESSONS 
 
 9. A grocer paid 81 dollars for kerosene, at 9 dol- 
 lars a barrel. How many barrels did he buy ? 
 
 10. 81 street lamps are 
 
 9 times how many street lamps? i How many times 9 street lamps? 
 
 11. Imogene used 90 skeins of worsted in making 
 lamp mats, using 9 skeins for each mat. How 
 many lamp mats did she make ? 
 
 12. A merchant received 90 cents for lamp shades, 
 at 10 cents apiece. How many shades did he sell ? 
 
 13. 90 gas-lights are 
 
 How many times 10 lights ? I 9 times how many lights ? 
 10 times how many lights ? | How many times 9 lights ? 
 
 14. At 10 cents each, how many lamp chimneys 
 can I buy for one dollar, or 100 cents ? 
 
 15. 100 oil cans are 
 
 10 times how many oil cans ? | How many times 10 oil cans ? 
 
 (See Manual, page 114.) 
 
 O. 1. A trunk maker sold 8 trunks, at 8 dollars 
 apiece. How much did he receive for them ? 
 
 2. A publisher paid 72 dollars for book paper, at 
 8 dollars a ream. How many reams did he buy ? 
 
 3. How many sheets of paper will be required to 
 make a book of 80 leaves, if one sheet is folded into 
 8 leaves ? 
 
 4. How much will 8 baking plates cost, at 10 
 cents each ? 
 
 5. How many plow-points, each weighing 8 
 pounds, can be made from 64 pounds of iron ? 
 
 6. How much will a turner receive for turning 8 
 bed posts, at 9 cents each ? 
 
INNUMBERS. 71 
 
 7. How much will 10 pounds of fresh fish cost, at 
 8 cents a pound ? 
 
 8. A man bought a turkey at 10 cents a pound, 
 and paid 80 cents for it. How many pounds did it 
 weigh ? 
 
 9. If a family use 9 pounds of lard in a month, 
 how many months will 72 pounds last them ? 
 
 10. How many pork barrels will a cooper make 
 in 9 days, if he makes 8 barrels each day ? 
 
 11. A pail maker uses 10 staves in making one 
 wooden pail. How many staves will he use in 
 making 9 pails ? 
 
 12. How many pieces of lightning-rod, each 9 
 feet long, will be required to reach from the top of 
 a church steeple, 81 feet high, to the ground ? 
 
 13. In building a chimney, a mason laid 9 courses 
 of bricks in an hour. HoW many hours did it take 
 him to lay 90 courses ? 
 
 14. A teamster drew 9 loads of stone each day 
 for 9 days. How many loads did he draw ? 
 
 15. How many hours will it take a steamboat, 
 running at the rate of 10 miles an hour, to make a 
 trip of 90 miles ? 
 
 16. A barber's price for shaviQg one man, is 10 
 cents. How much will he receive for shaving 10 
 men? 
 
 17. How much will a music teacher receive from 
 10 scholars, in one quarter, if each one pays her 9 
 dollars? 
 
 18. How many dimes in one dollar, or 100 cents? 
 
72 PIKST LESSONS 
 
 SSGTIOIT X* 
 
 Fractional parts of Numbers, — Halves. 
 
 JlX. WTien any number of things is divided into two equal 
 partSy each part is one half of the number of things. 
 
 If I divide 2 pine-apples equally between two per- 
 sons, each person will receive one half of tlie two pine- 
 apples, which is one pine-apple. If I divide 4 pine- 
 apples equally between two persons, each person will 
 receive one half of 4 pine-apples, which is 2 pine-apples. 
 One half of 6 pine-apples is 3 pine-apples, and one half 
 
 of 8 pine-apples is 4 pine-apples. (See Manual, page 115.) 
 
 1. Thomas bought 2 oranges, and gave one half 
 of them to his sister. How many ^d he give her? 
 
 2. Mr. Abbott divided 4 peaches equally between 
 his 2 children. What part of the 4 peaches did 
 he give to each child ? Hoio many peaches did he 
 give to each child ? 
 
 3. Jane brought 6 plums from the garden, and 
 divided them equally between her sister and herself. 
 What part of the 6 plums had each of the girls ? 
 How many plums had each ? 
 
^ INCUMBERS. 73 
 
 4. On a pear-tree were 8 pears, bnt one haM of 
 them dropped off. How many dropped off? How 
 many remained on the tree ? 
 
 5. Joseph had 10 apples, and Edgar had one half 
 as many. How many apples had Edgar ? 
 
 6. One half of 2 doves is how many doves ? 
 
 7. How many ducks are one half of 4 ducks ? 
 
 8. How many robins are one half of 6 robins ? 
 
 9. How many pigeons are one half of 8 pigeons ? 
 
 10. How many canary-birds are one half of 10 canary-birds ? 
 
 Eemark. — One half is expressed by figures thus, ^. 
 
 11. A farmer having 12 cows, sold J of them. 
 How many cows did he sell ? 
 
 12. A butcher bought 14 calves, and killed | of 
 them. How many calves did he kill ? 
 
 13. A drover sold 16 horses one day, and J as 
 many the next day. How many horses did he sell 
 the second day? 
 
 14. A farmer's wife raised 18 turkeys, and at 
 Thanksgiving sold J of them. How many turkeys 
 did she sell ? 
 
 15. One afternoon 2 men sheared 20 sheep, each 
 man shearing | of the number. How many sheep 
 did one man shear ? 
 
 16. How many hoes are ^ of 12 hoes ? 
 
 17. How many spades are | of 14 spades ? 
 
 18. Hew many rakes are ^ of 16 rakes ? 
 
 19. How many shovels are ^ of 18 shovels ? 
 
 20. How many pitchforks are | of 20 pitchforks ? 
 (See Manual, page 115.) 
 
74 
 
 FIRST LESSONS 
 
 Jli. WJien any thing is divided into 2 equal pa/rts^ each of the 
 fo/rts is \ of the thing. 
 
 Two halves of any thing make the whole of the thing. 
 
 If I cut an apple into two 
 equal parts, each part will be ^ 
 of the apple. 
 
 1. A father divided a large 
 pear equally between his two 
 children. What part of the 
 pear did he give to each child? 
 
 2. A mother divided a yard of silk into 2 equal 
 parts, for aprons for her two girls. How much silk 
 did she use for each apron ? 
 
 3. Byron worked one day in hoeing the potatoes 
 in his garden, and J as long in hoeing his corn. 
 What part of a day did it take him to hoe his com? 
 
 If I wish to divide 3 
 apples equally between 2 
 children, I can first divide 
 2 of the apples, by giving 
 each child 1 apple ; and I 
 can then divide the other 
 apple, by giving each child 
 ^ of it ; and then each child will have one apple and h 
 of an apple, which are one and one haK apples. 
 
 Eemark. — One and one half is expressed by figures 
 thus, 1^. 
 
 If I divide 5 apples 
 equally between 2 chil- 
 dren, each child will re- 
 ceive 2^ apples. 
 
 (See Manual, page 115.) 
 
 4. If I divide 3 pears equally between 2 children, 
 how many pears will each child receive ? 
 
INNUMBERS. 75 
 
 5. One moming a hotel keeper bought 5 melons, 
 and l of them were eaten at dinner. How many- 
 melons were eaten ? How many were left ? 
 
 6. How many lemons are ^ of 3 lemons ? J of 5 
 lemons ? 
 
 7. How many sheets of paper are | of 3 sheets? 
 J of 5 sheets ? 
 
 8. If a barrel of flour costs 7 dollars, how many 
 dollars will J of a barrel cost ? 
 
 9. If 2 barrels of sweet potatoes cost 7 dollars, 
 how many dollars will one barrel cost ? 
 
 10. If a man can cradle 9 acres of wheat in 2 
 days, how many acres can he cradle in one day ? 
 
 11. If 11 acres of grass can be cut by a mowing- 
 machine in one day, how many acres can be cut in 
 iday? 
 
 12. Two boys gathered 13 quarts of chestnuts, 
 which they shared equally. How many quarts of 
 chestnuts in each boy's share ? 
 
 13. If Andrew can husk 15 bushels of com in one 
 day, how many bushels can he husk in J day ? 
 
 14. If 17 roUs of wall paper are used in papering 
 2 rooms of equal size, how many roUs are used for 
 one room ? 
 
 15. If a train of cars runs 19 miles in one hour, 
 how many miles will it run in J hour ? 
 
 How much is ^ 
 
 16. Of 3 pounds of cheese ? 
 
 17. Of 9 ounces of mdigo ? 
 
 18. Of 7 pounds of soap ? 
 
 19. Of 13 gallons of vinegar ? 
 
 20. Of 5 bushels of beans ? 
 
 21. Of 17 pounds of codfish ? 
 
 22. Of 15 ounces of cloves j 
 
 23. Of 11 barrels of sugar? 
 
 24. Of 19 pounds of rice? 
 
76 FIRSTLESSONS 
 
 V^* Any nurnber of things is ^ of two times tJiat nuniber of 
 
 things, (See Manual, page 115.) 
 
 1. Esther gave to a blind man 1 cent, whicli was 
 I of all her money. How many cents did she have ? 
 
 2. If Harry should pay 2 cents for a top, it would 
 take ^ of his money. How many cents has he ? 
 
 3. Keuben's boots cost J as much as his coat, and 
 his boots cost 3 dollars. How much did his coat 
 cost? 
 
 4. On Saturday a laborer expended 4 dollars, 
 which was \ of his week's wages. How many dol- 
 lars did he earn that week ? 
 
 5. A grocer sold 5 barrels of salt, which was \ of 
 as many barrels as he had left. How many barrels 
 had he left ? 
 
 6. One inkstand is \ of how many inkstands ? 
 
 7. Two paperrfolders are \ of how many paper-folders ? 
 
 8. Three pen-knives are ^ of how many pen-knives ? 
 
 9. Four slates are \ of how many slates ? 
 
 10. Five photographs are \ of how many photographs ? 
 
 11. How many hours will it take a man to hoe 
 one acre of corn, if he hoes J acre in 6 hours ? 
 
 12. If a reaping machine will cut 7 acres of wheat 
 in \ day, how many acres will it cut in one day ? 
 
 13. If \ bushel of charcoal costs 8 cents, how 
 many cents wiU one bushel cost ? 
 
 14. Last year a farmer sold 9 tons of hay, which 
 was I of his hay crop. How many tons of hay did 
 he raise ? 
 
INNUMBERS. 77 
 
 15. In a haK-ream of paper are 10 quires. How 
 many quires in a ream ? 
 
 16. Six bonnets are one-half of how many bonnets ? 
 
 17. Seven vails are one-half of how many vails ? 
 
 18. Eight collars are one-half of how many collars ? 
 
 19. Nine shawls are one-half of how many shawls ? 
 
 30. Ten scarfs are one-half of how many scarfs ? ^ ^ / 
 
 (See Manual, page 115.) 
 
 D. 1. One and 1-half peaches are | of how many- 
 peaches ? (See Manual, page 115.) 
 
 2. One and 1-half barrels of beef are J of how 
 many barrels of beef? 
 
 3. Susan put 2 J pailfuls of water into a tub, and 
 the tub was then half fiUed. How many pailfuls 
 would the tub hold ? 
 
 4. If it takes 3 J yards of broadcloth for one over- 
 coat, how many yards will it take for 2 overcoats ? 
 
 5. A certain blackboard is J as wide as it is long, 
 and it is 4^ feet wide. How many feet long is it ? 
 
 6. In one rod there are 5J yards. How many 
 yards in 2 rods? 
 
 7. If 6^ pounds of sugar can be bought for a 
 half-dollar, how many pounds can be bought for a 
 doUar? 
 
 8. A miller exchanged 2 barrels of flour, worth 
 7J dollars a barrel, for a barrel of mackerel. How 
 much was the mackerel worth ? 
 
 9. In a week a farmer's wife sold 8^ pounds of 
 butter, which was J of all she made. How many 
 pounds did she make ? 
 
78 FIRST LESSONS 
 
 10. How many dollars will 2 rocking-chairs cost, 
 at 9| dollars apiece ? 
 
 11. 1| pounds of butter are ^ of how many pounds ? 
 ' 12. 3| yards of calico are ^ of how many yards ? 
 
 13. 7| pounds of starch are ^ of how many pounds? 
 
 14. 4 1 ounces of nutmegs are | of how many ounces ? 
 
 15. 2| tons of plaster are ^ of how many tons ? 
 16 8| gallons of oil are | of how many gallons ? 
 
 17. 5 J bushels of charcoal are | of how many bushels ? 
 
 18. 9| barrels of pork are i of how many barrels ? 
 
 19. 6 1 bushels of turnips are | of how many bushels ? 
 
 Jui. J/i any one thing there are 2 hahea ; and in any number 
 of things there are two times as many hahes as whole ones. 
 
 1. If I divide 2 water-melons into halves, how 
 many halves will there be ? (See Manual, page iie.) 
 
 2. Alice gave an orange to her sisters, giving J an 
 orange to each. How many sisters had she ? 
 
 3. Among how many scholars will I divide 3 pen- 
 cils, if I give \ pencil to each scholar ? 
 
 4. If I use \ sheet of paper to cover one book, 
 how many books can I cover with 4 sheets of paper? 
 
 5. How many half-days of school are there in 5 
 school-days ? 
 
 6. How many halves in 1 peach ? 
 
 7. How many halves in 2 turnips ? 
 
 8. How many halves in 3 heads of 'cabbage ? 
 
 9. How many halves in 4 pumpkins ? 
 
 10. How many halves in 5 loaves of bread ? 
 
 11. A cap maker received 6 dollars for making 
 caps, at J dollar apiece. How many caps did she 
 make ? 
 
IN NUMBERS. f ff r>t ^IQ 
 
 12. How many times cau a haK-BljAel measure 
 be filled from 7 bushels of potatoes ? 
 
 13. How many bushels of apples can I buy for 8 
 dollars, at | dollar a bushel ? 
 
 14. How many days will it take you to write 9 
 pages, if you write J page each day ? 
 
 15. If a shoemaker can make a pair of shoes in ^ 
 day, how many pairs can he make in 10 days ? 
 
 16. How many half-hours are there in 6 hours ? 
 
 17. In 7 pailfuls of water, how many half-pailfuls ? 
 
 18. If you cut 8 pies into halves, how many halves will 
 there be ? 
 
 19. How many half-dollars are 9 dollars ? 
 
 20. In 10 bushels of apples, how many half-bushels ? 
 
 Jb . 1. Two halves of an apple are equal to how 
 
 many apples. (See Mauual, page 116.) 
 
 2. Four half-apples are equal to how many apples ? 
 
 3. How many whole loaves of cake are 6 half- 
 loaves equal to ? 
 
 4. How many pints of ink can be put into 8 half- 
 pint bottles ? 
 
 5. A grocer sold 10 haH-pound packages of tea. 
 How many pounds did he sell ? 
 
 6. How many acres of land in 12 half-acre lots ? 
 
 7. If you* are absent from" sdhool ^ day each 
 week, how many days of schooUng do you lose in a 
 term of 14 weeks ? 
 
 8. How many feet long is a board which can be 
 cut into 18 pieces, each ^ foot in length ? 
 
 9. If a sewing girl earns ^ dollar a day, how 
 many doUars can she earn in 20 days ? 
 
80 
 
 FIRST LESSONS 
 
 10. A mercliant tailor made 16 cravats, using | 
 yard of silk for each cravat. How many yards of 
 silk did he use for all? 
 
 11. How many hours in 2 half-hours ? 
 
 12. How many minutes in 6 half-minutes ? 
 
 13. How many dollars in 10 half-dollars ? 
 
 14. How many miles in 8 half-miles ? 
 
 15. How many inches in 4 half-inches ? 
 
 16. In 12 half-tons of coal, how many tons ? 
 
 17. In 18 half-cords of wood, how many cords ? 
 
 18. In 14 half-gallons of syrup, how many gallons ? 
 
 19. In 20 half-barrels of fish, how many barrels ? 
 
 20. In 16 half-pecks of tomatoes, how many pecks ? 
 
 G. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 13. 
 14. 
 15. 
 16. 
 17. 
 18. 
 19. 
 20. 
 
 1. I of 2 is 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 How many 
 
 how many ? 
 
 21. 
 
 are i of 5 ? 
 
 22. 
 
 are iof4? 
 
 23. 
 
 are ^ of 7 ? 
 
 24. 
 
 are j of 9 ? 
 
 25. 
 
 are | of 6 ? 
 
 26. 
 
 are J of 8 ? 
 
 27. 
 
 are | of 13 ? 
 
 28. 
 
 are ^ of 19 ? 
 
 29. 
 
 are | of 12 ? 
 
 30. 
 
 are | of 1 ? 
 
 31. 
 
 are | of 10 ? 
 
 32. 
 
 are | of 3 ? 
 
 33. 
 
 are | of 15 ? 
 
 34. 
 
 are S of 18 ? 
 
 35. 
 
 are | of 11 ? 
 
 36. 
 
 are | of 14 ? 
 
 37. 
 
 are | of 20 ? 
 
 38. 
 
 are | of 17 ? 
 
 39. 
 
 are | of 16 ? 
 
 40 
 
 , 1 is ^ of how many ? 
 , 2 are ^ of how many ? 
 , 5 are I of how many ? 
 
 4 are \ of how many ? 
 
 1^ are | of how many ? 
 
 2| are ^ of how many ? 
 
 6 are i of how many ? 
 , 3^ are | of how many ? 
 , 9 are ^ of how many ? 
 , 4| are ^ of how many ? 
 , 3 are I of how many ? 
 , 5^ are i of how many ? 
 , 7 are J of how many ? 
 , 81 are I of how many ? 
 . 10 are I of how many ? 
 ! ^ of how many ? 
 
IN NUMBJERS. 
 
 8J 
 
 SECTION XI. 
 
 Fractional parts of Numbers, — Thirds. 
 
 Jl^* When any number of tMngs is divided into three equal 
 parts J each part is one thikd of the number of things ; and two 
 rf the parts are two thirds of the number of things. 
 
 1. In tins picture we see 3 boys at play, and one 
 third of their number is in the street. How many 
 boys are in the street ? 
 
 2. In the picture are also 6 girls at play, and one 
 third of their number is in the street. How many 
 girls are in the street ? (See Manual, page iie.) 
 
 3. One third of the 9 children are playing ball. 
 How many children are playing ball ? 
 
 4. Two thirds of the 3 children rolling hoop are 
 girls. How many girls are roUing hoop ? 
 
 5. Two thirds of the 6 children in the yard are 
 girls. How many girls are in the yard ? 
 
 7 
 
82 FIRSTLESSONS 
 
 6. Two thirds of the 9 children at play are girls. 
 How many girls are at play ? 
 
 Remark. — One third is expressed by figures thus, | ; 
 and two thirds is expressed thus, |. 
 
 7. How many hoops are J of 3 hoops ? 
 
 8. How many hoops are f of 3 hoops ? 
 
 9. How many trees are g^ of 6 trees ? 
 
 10. How many trees are f of 6 trees ? 
 
 11. How many posts are j of 9 posts ? 
 
 12. How many posts are f of 9 posts ? 
 
 13. Some children presented to their teacher 12 
 flowers, ^ of which were dahlias, and | roses. How 
 many of the flowers were dahlias ? How many of 
 them were roses ? 
 
 14. How many chickens are J of 15 chickens ? 
 
 15. How many rabbits are | of 15 rabbits ? 
 
 16. One third of twenty-one pictures are how 
 many pictures ? 
 
 17. Two thirds of 21 leaves are how many leaves ? 
 
 18. A dress-maker earned 18 dollars in 3 weeks. 
 What part of 18 dollars did she earn in one week ? 
 
 How many dollars did she earn in one week ? 
 
 19. What part of the 18 dollars did she earn in 
 two weeks ? How many dollars did she earn in two 
 weeks ? 
 
 20. Jay has 27 marbles, and Hiram has | as 
 many. How many marbles has Hiram ? 
 
 21. Charles has f as many marbles as Jay. How 
 many marbles has Charles ? 
 
 22. How many beans are J of 24 beans ? 
 
 23. How many beans are f of 24 beans ? 
 
INNUMBERS. 83 
 
 24. One third of 30 kernels of com are how many 
 kernels ? 
 
 25. Two thirds of 30 kernels of corn are hoY/ 
 many kernels ? 
 
 J3. Any number of things is ^ of ^ times that number of 
 things. 
 
 1. Homer bought some sea-shells, and gave his 
 sister 1 of them, which was J of all he bought. 
 How many did he buy ? 
 
 2. Arthur picked 2 melons, which were \ of all 
 that grew on the vine. How many grew on the vine? 
 
 3. One fish hook is ^ of how many fish-hooks ? 
 
 4. Two nets are 1 third of how many nets ? 
 
 5. Three fish lines are \ of how many fish lines ? 
 
 6. Four oars are 2 thirds of how many oars ? 
 
 7. Five vials are J of how many vials ? 
 
 8. If J of a barrel of pork costs 6 dollars, how 
 
 much does a barrel cost ? (See Manual, page 116.) 
 
 9. Nine bushels of wheat grew on | of an acre of 
 land. How many bushels would 1 acre produce, at 
 the same rate ? 
 
 10. Seven days are \ of how many days ? 
 
 11. The water in a certain well is 10 feet deep, 
 and the depth of the water is ^ of the depth of the 
 well. How deep is the well ? 
 
 12. If a family use 8 pounds of sugar in J of 
 a month, how many pounds will they use in a 
 month ? 
 
84 FIRSTLESSONS 
 
 0» When any thing is divided into three equal parts ^ one of 
 the parts is \ of the thing ; and two of the parts are § of the thing. 
 
 In any thing there are 3 thirds ; and in any number of things 
 there are 3 times as many thirds as whole (mes. 
 
 If I cut an apple into 3 
 equal parts, each part will be 
 \ of the apple, and 2 of the 
 parts will be | of the apple. 
 I of an apple make the whole 
 apple. 
 
 1. Among how many girls can I divide an apple, 
 if I give each of them \ of the apple ? 
 
 2. Into how many thirds can 2 pies be cut ? 
 
 (See Manual, page 117.) 
 
 3. How many pounds of coffee can I buy for 3 
 dollars, at J of a dollar a pound ? 
 
 4. If a horse eats J of a bushel of oats in one day, 
 how many days will 5 bushels last him ? 
 
 5. A milliner cut 4 yards of bonnet wire into 
 pieces, and each piece was J of a yard long. How 
 many pieces did the 4 yards make ? 
 
 6. How many thirds in 6 pine-apples ? 
 
 7. How many thirds of an hour in 8 hours ? 
 
 8. A paper-hanger cut 7 rolls of wall paper into 
 strips, each containing J of a roU. How many strips 
 were there ? 
 
 9. A lady used 9 pounds of sugar in canning 
 strawberries, using ^ of a pound for each can. How 
 many cans did she put up ? 
 
 10. In 10 barrels of water lime, how many thirds 
 of a barrel ? 
 
IN NUMBERS. 
 
 85 
 
 1-). 1. How many cords of wood in 3 tliirds of a 
 cord? 
 
 2. If 1 pair of shoes can be made from J of a 
 calf-skin, how many calf-skins will be used for 6 
 pairs of shoes ? 
 
 3. A milliner had 9 remnants of ribbon, each piece J 
 of a yard long. How many yards in all the remnants ? 
 
 4. A brick is ^ of a foot wide. How many feet 
 in width is a walk that consists of 12 rows of bricks? 
 
 5. A dog crosses a road at 18 leaps, of J of a rod 
 each. How many rods wide is the road ? 
 
 6. A silversmith made 30 spoons, using I of an 
 ounce of silver for each. How many ounces of 
 silver did he use ? 
 
 7. If an engine bums J of a ton of coal in one 
 day, how many tons will it bum in 24 days ? 
 
 8. If J of a barrel of flour will last a family a 
 month, how many barrels will last them 15 months ? 
 
 9. One foot is equal to ^ of a yard. 27 feet are 
 equal to how many yards ? 
 
 10. How much must a laboring man pay for pas- 
 turing his cow 27 weeks, at ^ of a dollar a week ? 
 
 E 
 
 1. I of 3 is how many ? 
 
 2. How many are i of 6 ? 
 
 3. How many are i of 15 ? 
 
 4. How many are i of 24 ? 
 
 5. How many are ^ of 9 ? 
 
 6. How many are |^ of 21 ? 
 
 7. How many are ^ of 18 ? 
 
 8. How many are ^ of 30 ? 
 
 9. How many are ^ of 27 ? 
 10. How many are J of 12 ? 
 
 11. 1 is 1 of how many ? 
 
 12. 2 are J of how many ? 
 
 13. 5 are ^ of how many ? 
 
 14. 4 are ^ of how many ? 
 
 15. 6 are ^ of how many ? 
 
 16. 3 are ^ of how many ? 
 
 17. 10 are J of how many ? 
 
 18. 8 are i of how many ? 
 
 19. 7 are ^ of how many ? 
 
 20. 9 are ^ of how many ? 
 
86 
 
 FIRST LESSONS 
 
 SECTIOIT XII. 
 
 Fractional Parts of lumbers. — Fourths. 
 
 J\^* When any 
 number of things is 
 divided into 4 equal 
 parts^ one of the 
 parts is o^^ foukth, 
 two of the parts are 
 TWO FOURTHS, and 
 three of the parts^ 
 
 THREE FOURTHS of 
 
 the number of things. 
 
 Remark. — One fourth is expressed by figures thus, \ ; 
 two fourths are expressed thus, f ; and three fourthi» 
 thus, |. 
 
 1. How many marks are | of 4 marks ? 
 
 2. How many marks are J of 8 marks ? 
 
 3. How many marks are \ of 12 marks ? 
 
 4. How many marks are \ of 16 marks ? 
 
 5. How many marks are f of 12 marks ? 
 
 6. How many marks are | of 4 marks ? 
 
 7. How many marks are f of 16 marks ? 
 
 8. How many marks are | of 8 marks ? 
 
 9. How many marks are | of 8 marks ? 
 
 10. How many marks are | of 4 marks ? 
 
 11. How many marks are f of 12 marks ? 
 
 12. How many marks are | of 16 marks ? 
 
 13. In one peck of wahiuts there are 8 quarts. 
 How many quarts in J of a peck ? (See Manual, page 117.) 
 
INNUMBERS. 8? 
 
 14. In I of a peck of cherries, how many quarts ? 
 
 15. How many quarts in | of a peck of grass seed? 
 
 16. In one foot there are 12 inches. How many 
 inches in | of a foot ? 
 
 17. How many inches in | of a foot ? 
 
 18. How many inches in | of a foot ? 
 
 19. In one pound there are 16 ounces. How 
 many ounces in | of a pound ? 
 
 20. How many ounces in | of a pound ? 
 
 21. How many ounces in | of a pound ? 
 
 22. If 4 loaves of bread cost 20 cents, what part 
 of 20 cents will 1 loaf cost ? How many cents will 
 1 loaf cost ? 
 
 23. What part of 20 cents wiU 2 loaves cost? 
 How many cents wiU 2 loaves cost ? 
 
 24. How many cents will 3 loaves cost ? 
 
 25. There are 24 hours in one day. How many 
 hours in I of a day ? 
 
 26. How many hours in | of a day ? 
 
 27. In I of a day, how many hours ? 
 
 28. There are 36 inches in one yard. How many 
 inches in ^ of a yard ? 
 
 29. How many inches in | of a yard of ribbon ? 
 
 30. A teamster feeds to his horses one ton of hay 
 in 28 days. How many days will J of a ton last 
 them? 
 
 31. How many days will | of a ton last them ? 
 
 32. A man set out 40 fruit-trees, but J of them 
 died. How many of the trees died ? 
 
88 JFIRSTLESSONS 
 
 33. Of the trees set out, | were apple-trees, and 
 the others were cherry-trees. How many fourths 
 were cherry-trees ? How many trees were cherry- 
 trees ? How many were apple-trees ? 
 
 34. Since | of the trees died, how many fourths 
 of them hved ? How many trees lived ? 
 
 Xj. 1. If I of a yard of silk velvet costs 1 doUar, 
 How much wiU 1 yard cost ? 
 
 2. One dollar is I of how many dollars ? 
 
 3. How much will 1 pound of putty cost, if | of a 
 
 pound costs 2 cents ? (See Manual, page 117.) 
 
 4. Two cents are I of how many cents ? 
 
 5. Three eggs are J of a dozen. How many eggs 
 make a dozen ? 
 
 6. How many ounces in 1 pound of tea, there 
 being 4 ounces in | of a pound ? 
 
 7. In J of a ton of hay there are 5 hundred 
 pounds. How many hundred pounds in a ton of 
 hay? 
 
 8. There are 6 sheets of paper in J of a quire. 
 How many sheets of paper in a quire ? 
 
 9. If a man can do | of a certain job of work in 7 
 days, in how many days can he do all of it ? 
 
 10. If a boy can earn 8 cents in | of a day, how 
 many cents can he earn in a day ? 
 
 11. If a printer can print 9 business cards in J of 
 a minute, how many cards can he print in one 
 minute ? 
 
 12. How much wiU 1 pound of cinnamon cost, at 
 the rate of 10 cents for ^ of a pound ? 
 
INNUMBERS. 89 
 
 vy« When any tiling is dimded 
 into four equal pa/rts^ one of the 
 parts is J, two of the pa/rts a/re f , 
 and three of the pa/rts are ^ of the 
 
 In any thing there a/re four fourths; 
 and in any number of things there a/re four times as many fourths 
 OjS whole ones. 
 
 1. Among how many children can I divide 1 
 apple, if I give them \ of an apple apiece ? 
 
 2. Into how many village lots can 2 acres of land 
 be divided, and each lot contain \ acre ? 
 
 3. If one glass of lemonade can be made from \ 
 of a lemon, how many glasses can be made from 3 
 
 lemons ? (See Manual, page 117.) 
 
 4 In a tinsmith's shop is a pile of boxes of sheet 
 tin. Each box is J of a foot thick, and the pile is 
 4 feet high. How many boxes are there ? 
 
 5. How many boxes of strawberries can be bought 
 for 5 doUars, at J of a dollar a box ? 
 
 6. If 1 sack of flour is equal to J of a barrel, how 
 many sacks are equal to 6 barrels ? 
 
 7. How many fourths of a day in 7 days ? 
 
 8. How many quarter-barrel kegs can be fiUed 
 from 8 barrels of white-fish ? 
 
 9. In 9 cords of wood, how many fourths of a 
 cord? 
 
 10. A grocer bought 10 pounds of ground pepper 
 in quarter-pound boxes. How many boxes did he 
 buy? 
 
90 
 
 FIRST LESSONS 
 
 JD, 1. A bookseller sold 4 books, at J of a dollar 
 each. How many dollars did he receive for them? 
 
 2. How many dollars are 8 fourths of a doUar ? 
 
 3. How many bushels in 36 fourths of a bushel ? 
 
 4. A millmer made 16 head-dresses, using | of a 
 yard of lace for each. How many yards of lace did 
 
 she use for all ? (See Manual, page 117.) 
 
 5. How many hours will it take Andrew to hoe 
 20 rows of corn,.if he hoes one row in ^ of an hour? 
 
 6. A boy sold 24 old newspapers, at |^ of a cent 
 apiece. How much did he get for them ? 
 
 7. In one day a carman drew 28 loads of freight, 
 at 1 quarter of a dollar a load. How many dollars 
 did he receive for his day's work ? 
 
 8. If one quart of mUk wiU make | of a pound of 
 cheese, how many pounds of cheese can be made 
 from 32 quarts of mUk ? 
 
 9. My writing-book contains 12 leaves, and each 
 leaf is I of a sheet of foolscap paper. How many 
 sheets of foolscap in the book ? 
 
 10. How many doUars will 40 pounds of raisiQS 
 cost, at ^ of a dollar a pound ? 
 
 E. 
 
 1. J of 4 is how many ? 
 
 2. How many are J of 8 ? 
 
 3. How many are J of 32 ? 
 
 4. How many are i of 20 ? 
 
 5. How many are J of 36 ? 
 
 6. How many are J of 12 ? 
 
 7. How many are ^ of 28 ? 
 
 8. How many are | of 40 ? 
 
 9. How many are J of 16 ? 
 10. How many are i of 24 ? 
 
 11. 1 is ^ of how many ? 
 
 12. 5 are i of how many ? 
 
 13. 9 are i of how many ? 
 
 14. 2 are | of how many ? 
 
 15. 7 are i of how many ? 
 
 16. 10 are I of how many ? 
 
 17. 4 are J of how many ? 
 
 18. 6 are i of how many ? 
 
 19. 3 are | of how many ? 
 
 20. 8 are } of how many ? 
 
I N N U M B E R S. 91 
 
 SBGTIOIT Xin, 
 
 3Iiscellaneous Problems : 
 
 EMBKACma ALL THE CLASSES OF COMBINATIONS IN THE 
 PRECEDING SECTIONS. — {See Manual, Page 118.) 
 
 1. A lady paid 9 dollars for a breastpin, and 4 dollars for a 
 ring. How many dollars did slie pay out ? 
 
 2. Louise, having 13 cents, paid 5 cents for a spool of thread. 
 How many cents had she left ? 
 
 3. How many bottles of ink, at 6 cents a bottle, can be 
 bought for 42 cents ? 
 
 4. If your father gives you 5 cents each day, how many cents 
 will he give you in 7 days ? 
 
 5. How many cords of wood in a x^ile 56 feet long, -if 8 feet 
 in length make one cord ? 
 
 6. If a cow gives 7 quarts of milk in the morning, and 8 
 quarts at night, how many quarts does she give in a day ? 
 
 7. A boy worked 8 months, at 6 dollars a month. How 
 many dollars did he earn ? 
 
 8. How many days in 9 school weeks, of 5 days each ? 
 
 9. If 3 pounds of starch cost 30 cents, how much will 1 
 pound cost ? 
 
 10. How much will J of a barrel of mackerel cost, at 16 
 dollars a barrel ? 
 
 11. If a mason can earn 19 dollars in 2 weeks, how much 
 can he earn in 1 week ? 
 
 12. How much will \ dozen eggs cost, at 18 cents a dozen ? 
 
 13. When vinegar is 20 cents a gallon, how much must I 
 pay for \ gallon ? 
 
 14. I paid 12 cents for 4 oranges. How much did they cost 
 me apiece ? 
 
 15. A man paid 6 dollars for J of a chest of tea. What was 
 the price of the whole chest ? 
 
 16. If \ ton of hay costs 6 dollars, how much will 1 ton 
 cost ? 
 
92 FIRSTLESSONS 
 
 17. If a boy earns 21 dollars in 3 months, how much does he 
 earn in a month ? 
 
 18. A newsboy has 16 papers, 9 of which are dailies, and 
 the others are illustrated weeklies. How many are weeklies ? 
 
 19. A grocer having 15 gallons of molasses in a barrel, drew 
 out 7 gallons. How many gallons remained in the barrel ? 
 
 20. A man set out 11 peach-trees in his garden, but 6 of 
 them died. How many lived ? 
 
 21. At 10 cents a pound, how many pounds of grapes can I 
 buy for 80 cents ? 
 
 22. A servant girl deposited 9 dollars in a savings-bank at 
 one time, 5 dollars at another, and 7 dollars at another. How 
 much money did she deposit ? 
 
 23. Oliver, having 19 cents, paid 10 cents for a ball, and 4 
 cents for an orange. How many cents had he left ? 
 
 24. A nursery -man sold to a customer 9 young apple-trees, 
 6 pear-trees, and 4 cherry-trees. How many trees did the 
 customer buy ? 
 
 25. A lady bought of a market gardener 8 cucumbers, at 3 
 cents apiece, and a quart of string beans for 6 cents. How 
 much did she pay the gardener ? 
 
 26. A printer worked 6 weeks for 9 dollars a week, and 
 1 week for 10 dollars. How much did he earn in the seven 
 weeks ? 
 
 27. A milkman brought to market 5 gallons of milk in one 
 can, and 8 gallons in another. After selling 10 gallons, how 
 many gallons had he left ? 
 
 28. How many 10-dollar bills will be required to pay for 5 
 yards of broadcloth, at 4 dollars a yard ? 
 
 29. If grandmother can knit 3 pairs of stockings in a week, 
 how many pairs can she knit in 6 weeks ? 
 
 30. How much will J bushel of lime cost, at 16 cents a 
 bushel ? 
 
 31. How much will | of a yard of canvas cost, at 40 cents a 
 yard ? 
 
 32. I bought I yard of cambric, at 14 cents a yard. How 
 much did it cost me ? 
 
 83. At 8 cents a dozen, how much will ^ dozen cucumbers 
 cost ? 
 
INNUMBEKS. 93 
 
 34. If you pay 9 cents for 3 yards of tape, what is tlie price 
 of 1 yard ? 
 
 35. How much will | dozen tea knives cost, at 7 dollars a 
 dozen ? 
 
 36. When clover seed is 8 dollars a bushel, how much must 
 a farmer pay for 1 peck, or I bushel ? 
 
 37. My parlor is 7 yards long, and 6 yards wide. How many 
 breadths of carpeting, 1 yard wide, will it take to cover the 
 floor ? How many yards must I buy for a carpet ? 
 
 38. One day a livery horse was driven at the rate of 6 miles 
 an hour, for 9 hours. How many miles did he travel ? 
 
 39. A farmer paid out 36 dollars for sheep, at 4 dollars a 
 head. How many sheep did he buy ? 
 
 40. At 9 dollars a ton, how many tons of coal can be bought 
 for 54 dollars ? 
 
 41. A boy worked 8 weeks, for 3 dollars a week, and spent 10 
 dollars of his wages for a coat. How much money had he left ? 
 
 42. A charcoal man sold 7 bashels of coal to one , -rson, 3 
 bushels to another, and 5 to another. How many bushels did 
 he sell to the three persons ? 
 
 43. A boy, having 18 cents, paid 5 cents for a ball, and 6 
 cents for a club. How many cents had he left ? 
 
 44. How many pairs of boots, at 3 dollars a pair, will pay 
 for 3 tons of coal, at 8 dollars a ton ? 
 
 45. At 7 cents a pound, how much must a woman pay for 3 
 flat-irons which weigh 5 pouniis each ? 
 
 46. If a bricklayer works 4 days in a week, at 2 dollars a 
 day, how much will he earn in 9 weeks ? 
 
 47. How much will I ton of old iron come to, at 9 dollars a 
 ton? 
 
 48. A shoemaker hired a shop for 36 dollars a year, agreeing 
 to pay the rent at the end of every quarter, that is, at the end 
 of every I of the year. How much was the rent for 1 quarter ? 
 How much for 3 quarters ? 
 
 49. The railroad fare from Boston to Bufiklo is 11 dollars, 
 and children between 5 and 12 years old are carried for half- 
 fare. How much will 1 half-fare ticket cost ? 
 
 50. A tailor received 15 dollars for making 2 fine coats. 
 How much did he receive for making each ? / 
 
94 FIRSTLESSONS 
 
 51. If four pounds of cotton bats cost 32 cents, how much 
 will 1 pound cost ? How much will 7 pounds cost ? 
 
 52. A woman sold 3 quarts of berries for 27 cents. How 
 much was that for 1 quart ? 
 
 53. If a surveyor can earn 15 dollars in 3 days, how much 
 can he earn in 1 day ? 
 
 54. A map agent sold 9 maps of the United States, at 8 dol- 
 lars apiece. How many dollars did he receive for them ? 
 
 55. A grocer bought 6 dozen eggs of one man, aiid 8 dozen 
 of another. How many dozen eggs did he buy ? 
 
 56. After selling 10 dozen of the eggs, how many dozen 
 would he have left ? 
 
 57. Samuel set out 63 cabbage plants, putting 9 plants in a 
 row. How many rows were there ? 
 
 58. A man bought 5 cords of hard wood, at 5 dollars a cord, 
 and 1 cord of soft wood for 4 dollars. How much did all the 
 wood cost him ? - 
 
 59. If a farmer can dig 5 bushels of potatoes in an hour, and 
 his boy 4 bushels, how many bushels can they both dig in 6 
 hours ? 
 
 60. Frances bought 7 yards of calico, at 10 cents a yard, and 
 a spool of thread for 5 cents. How much did her purchases 
 amount to ? 
 
 61. A father earns 8 dollars a week, and his son earns 2 
 dollars. How much do both of them earn in 9 weeks ? 
 
 62. How many 6-acre lots of land are equal to 3 10-acre lots ? 
 
 63. If a barber can earn 5 dollars in one day, how much can 
 he earn in \ day ? 
 
 64. Two farmers paid 17 dollars for a horse-rake, each pay- 
 ing i of the price. How many dollars did each man pay ? 
 
 65. A farmer pays a hired man 18 dollars a month, and a 
 boy ^ as much. How much a month does he pay the boy ? 
 
 66. How much will | of a pound of cloves cost, at 28 cents 
 a pound ? 
 
 67. How many melons, at 6 cents apiece, must be given for 
 9 oranges, at 4 cents apiece ? 
 
 68. If 5 oranges cost 15 cents, how much will 9 oranges cost ? 
 
 69. If 4 slates cost 32 cents, how much will 10 slates cost ? 
 
INNUMBJERS. 95 
 
 70. A shoemaker made 8 pairs of boots, and sold them at 5 
 dollars a pair, and the stock which he used in them cost him 
 9 dollars. How much did he receive for his labor ? 
 
 71. A stage-coach started with 9 passengers, and on the trij) 
 6 more passengers got aboard the stage, and 8 left it. How 
 many passengers were aboard, at the end of the trip ? 
 
 72. If a man can build 24 rods of stone-wall in 6 days, how 
 many rods can he build in 9 days ? 
 
 73. If # panes of window-glass cost 30 cents, how much will 
 8 panes cost ? 
 
 74. How much must be paid for 6 quarts of milk, if 5 quarts 
 cost 25 cents ? 
 
 75. A boy paid 18 cents for 2 fish-lines. How much would 
 5 fish-lines cost, at the same rate ? 
 
 76. If 9 lead pencils cost 27 cents, how much will 10 lead 
 pencils cost ? 
 
 77. How much, must I pay for 4 weeks' board, if I jDay at 
 the rate of 21 dollars for 7 weeks ? 
 
 78. K 5 pounds of iron castings cost 20 cents, how much 
 will 7 poimds cost ? 
 
 79. David and Levi paid 8 cents for 16 apples. Levi paid 3 
 cents of the money. How many of the apples ought he to have ? 
 
 80. Horace paid 15 cents for a spelling-book, and | as much 
 for a writing-book. How much did his writing-book cost him ? 
 
 81. Lemuel bought | of a dozen buttons for his coat, at 24 
 cents a dozen. How much did they cost him ? How many 
 buttons did he buy ? 
 
 82. Eight men gave five dollars apiece to buy a cow for a 
 soldier's widow. After paying for the cow, the widow had 
 four dollars of the money left. How much did the cow cost ? 
 
 83. If one tinsmith can make 4 milk-pans in an hour, and 
 another can make 3, how many milk-pans can they both make 
 in 10 hours ? 
 
 84. A carpenter earned 10 dollars one week, and 9 dollars 
 the next, and, after paying his expenses for the two weeks, he 
 had 5 dollars left. How much were his expenses ? 
 
 85. A farmer raised 30 bushels of beans, and sold | of them. 
 How many bushels did he sell ? 
 
96 PIRSTLESSONS 
 
 86. A. blacksmitli pays 6 dollars a month for the rent of his 
 house, and 3 dollars a month for the rent of his shop. How 
 much rent does he pay in 6 months ? 
 
 87. A shoemaker bought 36 pounds of leather, and | of it 
 was sole-leather; How much sole-leather did he buy ? 
 
 88. How much will J of a bushel of turnips cost, at 20 
 cents a bushel ? 
 
 89. A busliiel of oats weighs 32 pounds. How much does 
 I of a bushel weigh ? 
 
 90. K 4 pounds of maple sugar can be made from 8 gallons 
 of sap, how many gallons of sap will be required for I pound 
 of sugar ? 
 
 91. If 24 hogs can be fattened on the com that grows on 6 
 acres of land, how many hogs can be fattened on the com that 
 grows on \ acre ? 
 
 92. If a farmer's boy can harrow 18 acres of land in 2 days, 
 how many acres can he harrow in J of a day ? 
 
 93. It takes a stage-coach | of an hour to run the distance 
 between two villages, running at the rate of 54 miles in 9 
 hours. How many miles apart are the two villages ? 
 
 94. If it takes 40 bushels of potatoes to plant 5 acres of 
 land, how many bushels will it take to jolant J of an acre ? 
 
 95. How many bushels mil it take to plant I of an acre ? 
 
 96. If a blacksmith, by working 10 hours a day, can make 
 60 horseshoes, how many shoes can he make in 1 J hours ? 
 
 97. 4 times 2 are ^ of what number ? 
 
 98. 3 times 3 are | of what number ? 
 
 99. 4 times 5 are | of what number ? 
 100. 
 101. 
 
 102. 9 is 1 of how many ? 104. 
 
 103. 10 is I of how many? 105. 30 is | of what number? 
 
 106. I of 30 are how many times 5 ? 
 
 107. I of 36 are how many times 3 ? 
 
 108. f of 40 are how many times 10 ? 
 
 109. I of 30 are how many times 4 ? 
 
 110. I of 32 are how many times 6 ? 
 
 111. 7 is ^ of how many times 2 ? 
 
IN NUMBERS. 
 
 SBGTION XIY. 
 
 Tables of the Denominations of Money, Weighty 
 and Measures, in Common Use, 
 
 (See Manual, page 118 > 
 
 A. UNITED STATES MOKEY* 
 
 10 mills are 1 cent, I 1 dollar is 100 cents, 
 
 100 cents are 1 dollar. | 1 cent is 10 mills. 
 
 A Coin is a piece of metal, stamped by authority 
 of government, to give it a fixed value. 
 
 The American Coins are of Copper, Nickel, Silver, 
 and Gold. 
 
 Copper and NicJcel Coins. — Cent, 2-cent piece, 
 3-cent piece. 
 
 Silver Coins. — 3-cent piece, 5-cent piece or half- 
 dime, 10-cent piece or dime, 25-cent piece or quar- 
 ter-dollar, 50-cent piece or half-dollar. 
 
 Gold Coins. — DoUar, 2|^-dollar piece or quarter- 
 eagle, 3-dollar piece, 5-dollar piece or half-eagle, 
 lO-doUar piece or eagle, 20-doUar piece or double- 
 eagle, 50-doUar piece. 
 
 Eemakk. — ^United States Money is also called Federal 
 Money. 
 
 B. WEIGHT* 
 
 16 ounces are 1 pound, 
 100 pounds are 1 hundred- 
 weight, 
 20 hundred-weight are 1 ton. 
 
 1 ton is 20 hundred-weight, 
 1 hundred-weight is 100 
 
 pounds, 
 1 pound is 16 ounces. 
 
 Remark. — This weight is called Avoirdupois Weight. 
 
98 
 
 12 inches 
 3 feet 
 5^ yards, or \ 
 16| feet ' 
 
 320 rods 
 
 Kemakk. — This measure is also called Linear Measure, 
 and Long Measure. 
 
 FIRST LESSONS 
 
 
 IxINE MEASURE* 
 
 
 are 1 foot, 
 
 1 mile is 320 
 
 rods, 
 
 are 1 yard, 
 are 1 rod, 
 are 1 mile. 
 
 1 rod is} ig 
 
 1 yard is 3 
 1 foot is 1*2 
 
 feet, or 
 yards, 
 feet, 
 inches. 
 
 D. 
 
 LIQUID MEASURE. 
 
 4 gills are 1 pint, 
 2 pints are 1 quart, 
 4 quarts are 1 gallon. 
 
 1 gallon is 4 quarts. 
 1 quart is 2 pints, 
 1 pint is 4 gills. 
 
 E. 
 
 DRY MEASURE* 
 
 2 pints are 1 quart, 
 8 quarts are 1 peck, 
 4 pecks are 1 bushel. 
 
 1 bushel is 4 pecks, 
 1 peck is 8 quarts, 
 1 quart is 2 pints. 
 
 F. 
 
 PAPER* 
 
 24 sheets are 1 quire, 
 20 quires are 1 ream. 
 
 1 ream is 20 quires, 
 1 quire is 24 sheets. 
 
 G. 
 
 COUNTING* 
 
 12 things are 1 dozen, 
 12 dozen are 1 gross. 
 
 20 things are 1 score, 
 5 score are 1 hundred. 
 
 1 gross is 12 dozen, 
 1 dozen is 12 things. 
 
 1 himdred is 5 score, 
 1 score is 20 things. 
 
IN NUMBERS, 
 
 99 
 
 H. 
 
 TIME. 
 
 60 seconds are 1 minute, 
 60 minutes are 1 hour, 
 24 hours are 1 day, 
 7 days are 1 week, 
 52 weeks 1 day, ) are 1 com- 
 
 or 365 days ) mon year, 
 52 weeks 2 days, ) are 1 leap- 
 
 or 366 days ) year, 
 100 years are 1 century. 
 
 1 century is 
 
 1 leap-year is ] 
 
 1 common 
 
 year is 
 1 week 
 1 day 
 1 hour 
 1 minute 
 
 100 years, 
 366 days, or 
 52 weeks 2 days 
 365 days, or 
 52 weeks 1 day^ 
 7 days, 
 24 hours, 
 60 minutes, 
 60 seconds. 
 
 Second Day, , 
 Third Day,. . 
 Fourth Day, . 
 
 DAYS OF THE WEEK. 
 
 First Day, Sunday ; 
 
 . Monday ; 
 . Tuesday ; 
 . Wednesday; 
 
 Fifth Day, Thursday , 
 
 Sixth Day, Friday ; 
 
 Seventh Day, . . . Saturday. 
 
 MONTHS OF THE YEAR. 
 
 First Month, January, . . 
 
 Second Mctoth, . . . „ . February, . 
 
 Third Month, March, . . . 
 
 Fourth Month, April, . . . 
 
 Fifth Month, May, . . . . 
 
 Sixth Month, June, . . . . 
 
 Seventh Month, July, . . . . 
 
 Eighth Month, August, . . 
 
 Ninth Month, September, . 
 
 Tenth Month, October, . . 
 
 Eleventh Month, .... November, . 
 Twelfth Month, December, 
 
 days, 
 days, 
 days. 
 February has 28 days in a common year, and 29 in a leap yeaio 
 
 31 
 28 
 31 
 30 
 31 
 30 
 31 
 31 
 30 
 31 
 30 
 31 
 
 days. 
 
 days, 
 days. 
 
 days, 
 days, 
 days. 
 
 THE SEASONS. 
 SUMMER. FALL, Or AUTUMN. WINTER. 
 
 Mareh, 
 
 April, 
 
 May. 
 
 June, 
 July, 
 August. 
 
 September, 
 
 October, 
 
 November. 
 
 December, 
 
 January, 
 
 February. 
 
100 
 
 JblRST LESSONS 
 
 SECTIOIT XY. 
 
 Tables of Combinations in Addition and Subtract 
 tioUf Multiplication and Division. 
 
 (For methods of teaching these Tables, see Manual, pages 118.) 
 
 A. 
 
 ADDITION AND SUBTRACTION. 
 
 Oandl is 1, 
 
 1 and is 
 
 1 
 
 ; Ofrom 1 
 
 © 1, 
 
 1 from 1 
 
 |0 
 
 1 and 1 are 2 ; 
 
 
 1 from 
 
 1 
 
 2 leaves 1 
 
 1 
 
 2 and 1 are 3, 
 
 1 and 2 are 
 
 3 
 
 ; 2 from 3 
 
 
 Ifrom 3 
 
 -2 
 
 3 and 1 are 4, 
 
 1 and 3 are 
 
 4 
 
 ; 3 from 4 
 
 " 1, 
 
 1 from 4 
 
 " 3 
 
 4 and 1 are 5, 
 
 1 and 4 are 
 
 5 
 
 ; 4 from 5 
 
 ii 1 
 
 1 from 5 
 
 " 4 
 
 5 and 1 are 6, 
 
 1 and 5 are 
 
 6 
 
 ; 5 from 6 
 
 H i 
 
 1 from 6 
 
 " 5 
 
 6 and 1 are 7, 
 
 . 1 and 6 are 
 
 7 
 
 ; 6 from 7 
 
 " 1, 
 
 1 from 7 
 
 " 6 
 
 7 and 1 are 8, 
 
 1 and 7 are 
 
 8 
 
 ; 7 from 8 
 
 " 1, 
 
 1 from 8 
 
 " 7 
 
 8 and 1 are 9, 
 
 1 and 8 are 
 
 9 
 
 ; 8 from 9 
 
 a i 
 
 Ifrom 9 
 
 " 8 
 
 9 and 1 are 10, 
 
 1 and 9 are 
 
 10 
 
 9 from 10 
 
 " 1, 
 
 1 from 10 
 
 " 9 
 
 10 and 1 are 11, 
 
 1 and 10 are 
 
 11 
 
 2 
 
 10 from 11 
 
 4% 
 
 
 1 from 11 
 
 "10 
 
 and 2 are 2, 
 
 2 and are 
 
 2 
 
 Ofrom 2 
 
 S2, 
 
 2 from 2 
 
 |0 
 
 — 1 and 2 are 3, 
 
 2 and 1 are 
 
 3 
 
 1 from 3 
 
 |2, 
 
 2 from 3 
 
 |l 
 
 2 and 2 are 4 ; 
 
 
 2 from 
 
 
 4 leaves 2 
 
 .2 
 
 3 and 2 are 5, 
 
 2 and 3 are 
 
 5 
 
 3 from 5 
 
 '' 2, 
 
 2 from 5 
 
 " 3 
 
 4 and 2 are 6, 
 
 2 and 4 are 
 
 6 
 
 4 from 6 
 
 " 2, 
 
 2 from 6 
 
 " 4 
 
 5 and 2 are 7, 
 
 2 and 5 are 
 
 7 
 
 5 from 7 
 
 " 3, 
 
 2 from 7 
 
 " 5 
 
 6 and 2 are 8, 
 
 2 and 6 are 
 
 8 
 
 6 from 8 
 
 ^^2, 
 
 2 from 8 
 
 " 6 
 
 7 and 2 are 9, 
 
 2 and 7 are 
 
 9 
 
 7 from 9 
 
 " 2, 
 
 2 from 9 
 
 " 7 
 
 8 and 2 are 10, 
 
 2 and 8 are 
 
 10 
 
 8 from 10 
 
 " 2, 
 
 2 from-lO 
 
 " 8 
 
 9 and 2 are 11, 
 
 2 and 9 are 
 
 11 
 
 9 from 11 
 
 " 2, 
 
 2 from 11 
 
 " 9 
 
 xO and 2 are 12, 
 
 2 and 10 aro 
 
 12, 
 
 10 from 12 
 
 " 2, 
 
 2 from 12 
 
 "10 
 
IN NUMBERS. 
 
 101 
 
 and 3 are 3, 
 
 3 and are 3 
 
 ; from 3 2 3, 
 
 8 from 3 
 
 2 
 
 1 and 3 are 4, 
 
 3 and 1 are 4 
 
 ; 1 from 4^3, 
 
 3 from 4 
 
 |l 
 
 2 and 3 are 5, 
 
 3 and 2 are 5 
 
 ; 2 from 5 "" 3, 
 
 3 from 5 
 
 ^ 2 
 
 3 and 3 are 6 ; 
 
 3 from 6 leaves 3, 
 
 
 4 and 3 are 7, 
 
 3 and 4 are 7 
 
 ; 4 from 7 " 3, 
 
 3 from 7 
 
 " 4 
 
 5 and 3 are 8, 
 
 3 and 5 are 8 
 
 ; 5 from 8 " 3, 
 
 3 from 8 
 
 " 5 
 
 6 and 3 are 9, 
 
 3 and 6 are 9 
 
 ; 6 from 9 " 3, 
 
 3 from 9 
 
 " 6 
 
 7 and 3 are 10, 
 
 3 and 7 are 10 
 
 7 from 10 " 3, 
 
 3 from 10 
 
 " 7 
 
 8 and 3 are 11, 
 
 3 and 8 are 11 
 
 ; 8 from 11 " 3, 
 
 3 from 11 
 
 " 8 
 
 9 and 3 are 12, 
 
 3 and 9 are 12 
 
 ; 9 from 12 " 3, 
 
 3 from 12 
 
 " 9 
 
 10 and 3 are 13, 
 
 3 and 10 are 13 
 
 ; 10 from 13 " 3, 
 
 L 
 
 3 from 13 
 
 "10 
 
 and 4 are 4, 
 
 4 and are 4 
 
 ; from 4 2 4, 
 
 4 from 4 
 
 SO 
 
 1 and 4 are 5, 
 
 4 and 1 are 5 
 
 1 from 5 1 4, 
 
 4 from 5 
 
 ^1 
 
 
 
 2 and 4 are 6, 
 
 4 and 2 are 6 
 
 2 from 6^4, 
 
 4 from 6 
 
 ^2 
 
 3 and 4 are 7, 
 
 4 and 3 are 7 
 
 3 from 7 " 4, 
 
 4 from 7 
 
 " 3 
 
 4 and 4 are 8 ; 
 
 4 from 8 leaves 4, 
 
 
 5 and 4 are 9, 
 
 4 and 5 are 9 
 
 5 from 9 " 4, 
 
 4 from 9 
 
 " 5 
 
 6 and 4 are 10, 
 
 4 and 6 are 10 
 
 6 from 10 " 4, 
 
 4 from 10 
 
 " 6 
 
 7 and 4 are 11, 
 
 4 and 7 are 11 
 
 7 from 11 " 4, 
 
 4 from 11 
 
 " 7 
 
 8 and 4 are 12, 
 
 4 and 8 are 12 
 
 8 from 12 " 4, 
 
 4 from 12 
 
 " 8 
 
 9 and 4 are 13, 
 
 4 and 9 are 13 
 
 9 from 13 " 4, 
 
 4 from 13 
 
 " 9 
 
 10 and 4 are 14, 
 
 4 and 10 are 14 
 
 10 from 14 " 4, 
 
 4 from 14 
 
 "10 
 
 and 5 are 5, 
 
 5 and are 5 
 
 from 5 % 5, 
 
 5 from 5 
 
 |0 
 
 1 and 5 are 6, 
 
 5 and 1 are 6 , 
 
 1 from 6 1 5, 
 
 5 from 6 
 
 Si 
 
 (0 
 
 2 and 5 are 7, 
 
 5 and 2 are 7 
 
 2 from 7 '" 5, 
 
 5 from 7 
 
 ^2 
 
 3 and 5 are 8, 
 
 5 and 3 are 8 , 
 
 3 from 8 " 5, 
 
 5 from 8 
 
 " 3 
 
 4 and 5 are 9, 
 
 5 and 4 are 9 , 
 
 4 from 9 " 5, 
 
 5 from 9 
 
 " 4 
 
 5 and 5 are 10 ; 
 
 5 from 10 leaves 5, 
 
 
 6 and 5 are 11, 
 
 5 and 6 are 11 , 
 
 6 from 11 " 5, 
 
 5 from 11 
 
 " 6 
 
 7 and 5 are 12, 
 
 5 and 7 are 12 , 
 
 7 from 12 " 5, 
 
 5 from 12 
 
 " 7 
 
 8 and 5 are 13, 
 
 5 and 8 are 13 , 
 
 8 from 13 " 5, 
 
 5 from 13 
 
 " 8 
 
 9 and 5 are 14, 
 
 5 and 9 are 14 , 
 
 9 from 14 " 5, 
 
 5 from 14 
 
 " 9 
 
 iO and 5 are. 15, 
 
 5 and 10 are 15 ; 
 
 10 from 15 " 5, 
 
 5 from 15 
 
 "10 
 
102 
 
 FIRST LESSONS 
 
 6. 
 
 Oand 
 
 1 and 
 
 2 and 
 
 3 and 
 
 4 and 
 
 5 and 
 
 7 and 
 
 Sand 
 
 9 and 
 
 10 and 
 
 6 are 6, 
 6 are 7, 
 6 are 8, 
 6 are 9, 
 6 are 10, 
 6 are 11, 
 6 and 6 
 6 are 13, 
 6 are 14, 
 6 are 15, 
 6 are 16, 
 
 6 and 
 6 and 
 6 and 
 6 and 
 6 and 
 6 and 
 are 12 
 6 and 
 6 and 
 6 and 
 
 Oare 6 
 
 1 are 7 
 
 2 are 8 
 
 3 are 9 
 
 4 are 10 
 
 5 are 11 
 
 7 are 13 
 
 8 are 14 
 
 9 are 15 
 
 6 and 10 are 16 
 
 from 
 
 1 from 
 
 6 g 
 
 8^6, 
 
 2 from 
 
 3 from 9 " 6, 
 
 4 from 10 " 6, 
 
 5 from 11 " 6, 
 
 6 from 12 
 
 7 from 13 " 6, 
 
 8 from 14 " 6, 
 
 9 from 15 " 6, 
 10 from 16 " 6, 
 
 6 from 6 
 6 from 7 
 6 from 8 ' 
 6 from 9 
 6 from 10 
 6 from 11 
 leaves 6, 
 6 from 13 
 6 from 14 
 6 from 15 
 6 from 16 
 
 ' 9 
 10 
 
 and 
 
 1 and 
 
 2 and 
 
 3 and 
 
 4 and 
 
 5 and 
 
 6 and 
 
 8 and 
 
 9 and 
 10 and 
 
 and 
 
 1 and 
 
 2 and 
 
 3 and 
 
 4 and 
 
 5 and 
 
 6 and 
 
 7 and 
 
 Q and 
 10 and 
 
 7 are 7, 
 7 are 8, 
 7 are 9, 
 7 are 10, 
 7 are 11, 
 7 are 12, 
 7 are 13, 
 
 7 and 7 
 7 are 15, 
 7 are 16, 
 7 are 17, 
 
 7 and 
 7 and 
 7 and 
 7 and 
 7 and 
 7 and 
 7 and 
 are 14 ; 
 7 and 8 
 7 and 9 
 7 and 10 
 
 are 7 
 are 8 
 are 9 
 are 10 
 are 11 
 are 12 
 are 13 
 
 are 15 
 are 16 
 are 17 
 
 from 7 g 
 
 1 from 8 g 
 
 2 from 9 '^ 
 
 3 from 10 " 
 
 4 from 11 " 
 
 5 from 12 " 
 
 6 from 13 " 
 
 7 from 
 
 8 from 15 " 
 
 9 from 16 " 
 10 from 17 " 
 
 8 are 8, 
 8 are 9, 
 8 are 10, 
 8 are 11, 
 8 are 12, 
 8 are 13, 
 8 are 14, 
 8 are 15, 
 8and^ 
 8 are 17, 
 8 are 18, 
 
 8 and 
 8 and 
 8 and 
 8 and 
 8 and 
 8 and 
 8 and 
 8 and 
 are 16 
 8 and 
 8 and 
 
 are 
 
 1 are 
 
 2 are 
 
 3 are 
 
 4 are 
 
 5 are 
 
 6 are 
 
 7 are 
 
 9 are 
 10 are 
 
 8 § 
 
 8. 
 
 from 
 
 1 from 
 
 2 from 
 
 3 from 
 
 4 from 
 
 5 from 
 
 6 from 
 
 7 from 
 
 8 
 
 9 from 
 
 10 from 
 
 9 1 
 
 (D 
 
 10" 
 
 11 " 
 
 12 " 
 
 13 " 
 
 14 " 
 
 15 " 
 from 
 
 17 " 
 
 18 " 
 
 7 from 
 7 from 
 7 from 9 
 7 from 10 
 7 from 11 
 7 from 12 
 7 from 13 
 14 leaves 7, 
 7, 7 from 15 
 7, 7 from 16 
 7, 7 from 17 
 
 8 from 8 
 8 from 9 
 8 from 10 ' 
 8 from 11 
 8 from 12 
 8, 8 from 13 
 8, 8 from 14 
 8, 8 from 15 
 16 leaves 8, 
 8, 8 from 17 
 8, 8 from 18 
 
 8, 
 
 
 
 1 
 "2 
 " 3 
 u 4 
 
 " 5 
 '* 6 
 
 " 8 
 " 9 
 
 no 
 
 go 
 
 '2 
 ' 3 
 ' 4 
 
 ' 5 
 ' 6 
 
 ' 7 
 
 ' 9 
 10 
 
IN NUMBERS. 
 
 103 
 
 and 
 
 1 and 
 
 2 and 
 
 3 and 
 
 4 and 
 
 5 and 
 
 6 and 
 
 7 and 
 
 8 and 
 
 10 and 
 
 9 are 9, 
 9 are 10, 
 9 are 11, 
 9 are 12, 
 9 are 13, 
 9 are 14, 
 9 are 15, 
 9 are 16, 
 9 are 17, 
 9andS 
 9 are 19, 
 
 9 and 
 9 and 
 9 and 
 9 and 
 9 and 
 9 and 
 9 and 
 9 and 
 9 and 
 are 18 ; 
 9 and 10 
 
 9. 
 
 are 9 
 are 10 
 are 11 
 are 12 
 are 13 
 are 14 
 are 15 
 are 16 
 are 17 
 
 are 19 ; 
 
 from 
 
 1 from 
 
 2 from 
 
 3 from 
 
 4 from 
 
 5 from 
 
 6 from 
 
 7 from 
 
 8 from 
 
 9 
 10 from 
 
 9 S 
 
 11^ 
 
 12 " 
 
 13 " 
 
 14 " 
 
 15 " 
 
 16 " 
 
 17 " 
 from 
 19 " 
 
 9 from 
 
 9 from ; 
 
 9 from: 
 
 9 from: 
 
 9 from : 
 
 9 from : 
 
 9 from : 
 
 9 from : 
 9, 9 from : 
 18 leaves 9, 
 9, 9 from 19 "10 
 
 9 , 
 lIO 
 ill ' 
 l12 
 l13 
 l14 
 .15 
 .16 
 .17 
 
 and 
 
 1 and 
 
 2 and 
 
 3 and 
 
 4 and 
 
 5 and 
 
 6 and 
 
 7 and 
 
 8 and 
 
 9 and 
 
 10 are 10, 10 and 
 10 are 11, 10 and 
 10 are 12, 10 and 
 10 are 13, 10 and 
 10 are 14, 10 and 
 10 are 15, 
 10 are 16, 
 10 are 17, 
 10 are 18, 
 10 are 19, 
 
 10. 
 
 10 and 
 10 and 
 10 and 
 10 and 
 10 and 
 
 are 10 
 
 1 are 11 
 
 2 are 12 
 
 3 are 13 
 
 4 are 14 
 
 5 are 15 
 
 6 are 16 
 
 7 are 17 
 
 8 are 18 
 
 9 are 19 
 
 10 and 10 are 20 ; 
 
 from 10 g 
 
 1 from 11 08 
 
 2 from 12 '^ 
 
 3 from 13 " 
 
 4 from 14 " 
 
 5 from 15 " 
 
 6 from 16 " 
 
 7 from 17 " 
 
 8 from 18 " 
 
 9 from 19 " 
 
 10 from 
 
 10, 10 from 10 \ 
 10, 10 from 11 I 
 10, 10 from 12" 
 10, 10 from 13 ' 
 10, 10 from 14 ' 
 10, 10 from 15 ' 
 10, 10 from 16 ' 
 10, 10 from 17 ' 
 10, 10 from 18* 
 10, 10 from 19 ' 
 20 leavas 10. 
 
 B. 
 
 MULTIPLICATION AND DIVISION* 
 
 Once 1 is 1 ; 
 
 2 timejs 1 are 2, Once 
 
 3 times 1 are 
 
 4 times 1 are 
 
 5 times 1 are 
 
 6 times 1 are 
 
 7 times 1 are 
 
 8 times 1 are 
 
 9 times 1 are 
 
 3, 
 4, 
 5, 
 6, 
 
 7, 
 
 9, 
 
 Once 
 Once 
 Once 
 Once 
 Once 
 Once 
 Once 
 
 2 is 
 
 3 is 
 
 4 is 
 
 5 is 
 
 6 is 
 
 7 is 
 
 8 is 
 
 9 is 
 
 10 times 1 are 10, Once 10 is 10 ; 1 in 10 
 
 lin 
 lin 
 lin 
 lin 
 lin 
 lin 
 lin 
 lin 
 
 1 in 1 1 time, 
 
 2 times, 2 in 
 
 3 times, 
 
 4 times, 
 
 5 times, 
 
 6 times, 
 
 7 times, 
 
 8 times, 
 
 9 times, 
 10 times. 
 
 3 in 
 
 4 in 
 
 5 in 
 
 6 in 
 
 7 in 
 
 8 in 
 
 9 in 
 
 10 in 10 
 
104 
 
 FIRST LESSONS 
 
 2. 
 
 Itime 2 is 2, 
 
 2 times 1 are 2 
 
 ; 2 in 2 
 
 1 s, 
 
 lin 2 
 
 2 
 
 2 times 2 are 4 ; 
 
 2 in 4 
 
 2 times, 
 
 
 3 times 2 are 6, 
 
 2 times 3 are 6 
 
 ; 2 in 6 
 
 3% 
 
 3 in 6 
 
 2 
 
 4 times 2 are 8, 
 
 2 times 4 are 8 
 
 ; 2 in 8 
 
 4", 
 
 4in 8 
 
 2 
 
 5 times 2 are 10, 
 
 2 times 5 are 10 
 
 2 in 10 
 
 5", 
 
 5 in 10 
 
 2 
 
 6 times 2 are 12, 
 
 2 times 6 are 12 
 
 ; 2 in 12 
 
 6", 
 
 6 in 12 
 
 2 
 
 7 times 2 are 14, 
 
 2 times 7 are 14 
 
 ; 2 in 14 
 
 7", 
 
 7 in 14 
 
 2 
 
 8 times 2 are 16, 
 
 2 times 8 are 16 
 
 2 in 16 
 
 8", 
 
 8 in 16 
 
 2 
 
 9 times 2 are 18, 
 
 2 times 9 are 18 
 
 2 in 18 
 
 9", 
 
 9 in 18 
 
 2 
 
 times 2 are 20, 
 
 2 times 10 are 20 
 
 2 in 20 10 " , 
 
 10 in 20 
 
 2 
 
 3. 
 
 Itime 3 is 3, 
 
 3 times 1 are 3 ; 
 
 3 in 3 1 S, 
 
 lin 3 
 
 3 
 
 2 times 3 are 6, 
 
 3 times 2 are 6 ; 
 
 3 in 6 2|, 
 
 2 in "6 
 
 3 
 
 3 times 3 are 9 ; 
 
 3 in 9 
 
 3 times. 
 
 
 4 times 3 are 12, 
 
 3 times 4 are 12 ; 
 
 3 in 12 4", 
 
 4 in 12 
 
 3 
 
 5 times 3 are 15, 
 
 3 times 5 are 15 ; 
 
 3 in 15 5", 
 
 5 in 15 
 
 3 
 
 6 times 3 are 18, 
 
 3 times 6 are 18 ; 
 
 3 in 18 6", 
 
 6 in 18 
 
 3 
 
 7 times 3 are 21, 
 
 3 times 7 are 21 ; 
 
 3 in 21 7", 
 
 7 in 21 
 
 3 
 
 8 times 3 are 24, 
 
 8 times 8 are 24 ; 
 
 3 in 24 8", 
 
 8 in 24 
 
 3 
 
 9 times 3 are 27, 
 
 3 times 9 are 27 ; 
 
 3 in 27 9", 
 
 9 in 27 
 
 3 
 
 10 times 3 are 30, 
 
 3 times 10 are 30 ; 
 
 3 in 30 10", 
 
 10 in 30 
 
 3 
 
 4. 
 
 1 time 4 is 4, 
 
 4 times 
 
 1 are 4 
 
 4 in 4 1 |, 
 
 ; M in 8 2-1, 
 
 41»42 3", 
 
 lin 4 
 
 4| 
 
 4.9 
 
 2 times 4 are 8, 
 
 4 times 
 
 2 are 8 
 
 2 in 8 
 
 3 times 4 are 12, 
 
 4 times 
 
 3 are 12 
 
 3 in 12 
 
 4 " 
 
 4 times 4 are 16 
 
 } 
 
 4M^16 
 
 4 times. 
 
 
 5 times 4 are 20, 
 
 4 times 
 
 5 are 20 
 
 4 in 20 ^^^^ 
 4 in 24 6",^ 
 
 5 in 20 
 
 4 " 
 
 6 times 4 are 24, 
 
 4 times 
 
 6 are 24 
 
 ^6in24 
 
 4 " 
 
 7 times 4 are 28, 
 
 4 times 
 
 7 are 28 
 
 ; 4in28 7", 
 
 Xm 28 
 
 4 " 
 
 8 times 4 are 32, 
 
 4 times 
 
 8 are 32 
 
 4 in 32 8", 
 
 8 In 32 
 
 4 " 
 
 9 times 4 are 36, 
 
 4 times 
 
 9 are 36 
 
 4 in 36 9", 
 
 9 in 36 
 
 4 " 
 
 LO times 4 are 40, 
 
 4 times 
 
 10 are 40 
 
 4 in 40 10 " , 
 
 10 in 40 
 
 4 " 
 
IN NUMBERS. 
 
 105 
 
 5. 
 
 1 time 5 is 5, 
 
 5 times 1 are 5 
 
 ; 5 in 5 1 |, 
 5 in 10 2|, 
 
 lin 5 
 
 5o 
 5-1 
 
 2 times 5 are 10, 
 
 5 times 2 are 10 
 
 2 in 10 
 
 3 times 5 are 15, 
 
 5 times 3 are- 15 
 
 5 in 15 3", 
 
 3 in 15 
 
 5 " 
 
 4 times 5 are 20, 
 
 5 times 4 are 20 
 
 5 in 20 4", 
 
 4 in 20 
 
 5 " 
 
 5 times 5 are 25 ; 
 
 5 in 25 
 
 5 times, 
 
 
 6 times 5 are 30, 
 
 5 times 6 are 30 
 
 5 in 30 6", 
 
 6 in 30 
 
 5 " 
 
 7 times 5 are 35, 
 
 5 times 7 are 35 
 
 5 in 35 7", 
 
 7 in 35 
 
 5 " 
 
 8 times 5 are 40, 
 
 5 times 8 are 40 
 
 5 in 40 8", 
 
 8 in 40 
 
 5 " 
 
 9 times 5 are 45, 
 
 5 times 9 a»B'45 
 
 5 in 45 9", 
 
 9 in 45 
 
 5 " 
 
 iO times 5 are 50, 
 
 5 times 10 are 50 
 
 5 in 50 10 " , 
 
 10 in 50 
 
 5 " 
 
 6. 
 
 1 time 6 is 6, 
 
 6 times 1 are 6 
 
 • 6 in 6 1 §, 
 6 in 12 2 1, 
 
 lin 6 
 
 6 
 
 2 times 6 are 12, 
 
 6 times 2 are 12 
 
 2 in 12 
 
 6 
 
 3 times 6 are 18, 
 
 6 times 3 are 18 
 
 6 in 18 3", 
 
 3 in 18 
 
 6 
 
 4 times 6 are 24, 
 
 6 times 4 are 24 
 
 ; 6 in 24 4", 
 
 4 in 24 
 
 6 
 
 5 times 6 are 30, 
 
 6 times 5 are 30 
 
 6 in 30 5", 
 
 5 in 30 
 
 6 
 
 6 times 6 are 36 ; 
 
 6 in 36 
 
 6 times. 
 
 
 7 times 6 are 42, 
 
 6 times 7 are 42 
 
 6 in 42 7", 
 
 7 in 42 
 
 6 
 
 8 times 6 are 48, 
 
 6 times 8are48 
 
 6 in 48 8", 
 
 8 in 48 
 
 6 
 
 9 times 6 are 54, 
 
 6 times 9 are 54 
 
 6 in 54 9", 
 
 9 in 54 
 
 6 
 
 times 6 are 60, 
 
 6 times 10 are 60 
 
 6 in 60 10 " , 
 
 10 in 60 
 
 6 
 
 7. 
 
 1 time 7 is 7, 
 
 7 times 1 are 7 
 
 7 in' 7 1 o, 
 7 in 14 2-1, 
 
 lin 7 
 
 7 o 
 
 2 times 7 are 14, 
 
 7 times 2 are 14 
 
 2 in 14 
 
 7| 
 
 3 times 7 are 21, 
 
 7 times 3 are 21 
 
 7 in 21 3", 
 
 3 in 21 
 
 7I; 
 
 4 times 7 are 28, 
 
 7 times 4 are 28 
 
 7 in 28 4", 
 
 4 in 28 
 
 7 " 
 
 5 times 7 are 35, 
 
 7 times 5 are 35 
 
 7 in 35 5", 
 
 5 in 35 
 
 7 " 
 
 6 times 7 are 42, 
 
 7 times 6 are 42 
 
 7 in 42 6", 
 
 6 in 42 
 
 7 '♦ 
 
 7 times 7 are 49 ; 
 
 7 in 49 
 
 7 times, 
 
 
 8 times 7 are 56, 
 
 7 times 8 are 56 
 
 7 in 56 8", 
 
 8 in 56 
 
 7 " 
 
 9 times 7 a're 63, 
 
 7 times 9 are 63 
 
 ; 7 in 63 9", 
 
 9 in 63 
 
 7 " 
 
 10 times 7 are 70, 
 
 7 times 10 are 70 
 9 
 
 ; 7 in 70 10 « , 
 
 10 in 70 
 
 7 '* 
 
106 
 
 FIRST LESSONS 
 
 a 
 
 1 time 8 is 8, 
 
 8 times 1 are 8 
 
 , 8iii 8 1 §, 
 8 in 16 2|, 
 
 lin 8 
 
 8| 
 
 2 times 8 are 16, 
 
 8 times 2 are 16 
 
 2 in 16 
 
 8| 
 
 3 times 8 are 24, 
 
 8 times 3 are 24 
 
 8 in 24 3", 
 
 3 in 24 
 
 8 " 
 
 4 times 8 are 32, 
 
 8 times 4 are 32 
 
 8 in 32 4", 
 
 4 in 32 
 
 8 " 
 
 5 times 8 are 40, 
 
 8 times 5 are 40 
 
 8 in 40 5", 
 
 5 in 40 
 
 8 " 
 
 6 times 8 are 48, 
 
 8 times 6 are 48 
 
 8 in 48 6", 
 
 6 in 48 
 
 8 " 
 
 7 times 8 are 56, 
 
 8 times 7 are 56 
 
 8 in 56 7", 
 
 7 in 56 
 
 8 " 
 
 8 times 8 are 64 ; 
 
 8 in 64 
 
 8 times. 
 
 
 9 times 8 are 72, 
 
 8 times 9 are 72 
 
 8 in 72 9", 
 
 9 in 72 
 
 8 " 
 
 10 times 8 are 80, 
 
 8 times 10 are 80 
 
 ; 8 in 80 10", 
 
 10 in 80 
 
 8 " 
 
 9. 
 
 1 time 9 is 9, 
 
 9 times 1 are 9 
 
 9 in 9 
 
 2-1, 
 
 lin 9 
 
 9 
 
 2 times 9 are 18, 
 
 9 times 2 are 18 
 
 9 in 18 
 
 2 in 18 
 
 9 
 
 3 times 9 are 27, 
 
 9 times 3 are 27 
 
 9 in 27 
 
 3", 
 
 3 in 27 
 
 9 
 
 4 times 9 are 36, 
 
 9 times 4 are 36 
 
 9 in 36 
 
 4", 
 
 4 in 36 
 
 9 
 
 5 times 9 are 45, 
 
 9 times 5 are 45 
 
 ; 9 in 45 
 
 5", 
 
 5 in 45 
 
 9 
 
 6 times 9 are 54, 
 
 9 times 6 are 54 
 
 9 in 54 
 
 6", 
 
 6 in 54 
 
 9 
 
 7 times 9 are 63, 
 
 9 times 7 are 63 
 
 ; 9 in 63 
 
 7", 
 
 7 in 63 
 
 9 
 
 8 times 9 are 72, 
 
 9 times 8 are 72 
 
 9 in 72 
 
 8", 
 
 8 in 72 
 
 9 
 
 9 times 9 are 81 ; 
 
 9 in 81 
 
 9 times, 
 
 
 times 9 are 90, 
 
 9 times 10 are 90 
 
 9 in 90 10 " , 
 
 10 in 90 
 
 9 
 
 10. 
 
 1 time 10 is 10, 
 
 10 times 1 are 10 
 
 10 in 10 
 
 2|, 
 
 lin 10 
 
 10 
 
 2 times 10 are 20, 
 
 10 times 2 are 20 
 
 10 in 20 
 
 2 in 20 
 
 10 
 
 3 times 10 are 30, 
 
 10 times 3 are 30 
 
 10 in 30 
 
 3", 
 
 3 in 30 
 
 10 
 
 4 times 10 are 40, 
 
 10 times 4 are 40 
 
 10 in 40 
 
 4", 
 
 4 in 40 
 
 10 
 
 5 times 10 are 50, 
 
 10 times 5 are 50 
 
 10 in 50 
 
 5", 
 
 5 in 50 
 
 10 
 
 6 times 10 are 60, 
 
 10 times 6 are 60 
 
 10 in 60 
 
 6", 
 
 6 in 60 
 
 10 
 
 7 times 10 are 70, 
 
 10 times 7 are 70 , 
 
 10 in 70 
 
 7", 
 
 7 in 70 
 
 10 
 
 8 times 10 are 80, 
 
 10 times 8 are 80 
 
 10 in 80 
 
 8", 
 
 8 in 80 
 
 10 
 
 9 times 10 are 90, 
 
 10 times 9 are 90 
 
 10 in 90 
 
 9", 
 
 9 in 90 
 
 10 
 
 10 times 10 are 100 ; 
 
 10 in 
 
 100 
 
 10 times. 
 
IN NUMBERS. 
 
 107 
 
 c. 
 
 FACTOR OR DIVISIOS TABLE. 
 
 4 is 2 times 2 ; 
 
 6 is 3 times 2, or 2 times 3 ; 
 
 8 is 4 times 2, or 2 times 4 ; 
 
 is 3 times 3 ; 
 10 is 5 times 2, or 2 times 5 ; 
 12 *s ^ ^ times 2, or 2 times 6 ; 
 \ 4 times 3, or 3 times 4 ; 
 
 14 is 7 times 2, or 2 times 7 ; 
 
 15 is 5 times 3, or 3 times 5 ; 
 
 16 is 8 times 2, or 2 times 8, or 
 
 4 times 4 ; 
 
 18 is 
 
 20 is 
 
 \ 9 times 2, or 2 times 9 ; 
 / 6 times 3, or 3 times 6 ; 
 ^10 times 2, or 2 times 10 ; 
 ( 5 times 4, or 4 times 5 ; 
 21 is 7 times 3, or 3 times 7 ; 
 
 -. . . ^8 times 3, or 3 times 8 : 
 
 24 isK ^ . ' ^ . ^' 
 
 f 6 times 4, or 4 times 6 ; 
 
 25 is 5 times 5 ; 
 
 27 is 9 times 3, or 3 times 9 ; 
 
 28 is 7 times 4, or 4 times 7 ; 
 oQ . ^10 times 3, or 3 times 10 ; 
 
 ( 6 times 5, or 5 times 6 ; 
 
 32 is 8 times 4, or 4 times 8 ; 
 
 35 is 7 times 5, or 5 times 7 ; 
 
 36 is 9 times 4, or 4 times 9, or 
 
 6 times 6 ; 
 40 is \ ^^ tinies 4, or 4 times 10; 
 ( 8 times 5, or 5 times 8 ; 
 42 is 6 times 7, or 7 times 6 ; 
 45 is 9 times 5, or 5 times 9 ; 
 
 48 is 8 times 6, or 6 times 8 ; 
 
 49 is 7 times 7 ; 
 
 50 is 10 times 5, or 5 times 10 ; 
 54 is 9 times 6, or 6 times 9 ; 
 56 is 8 times 7, or 7 times 8 ; 
 60 is 10 times 6, or 6 times 10 ; 
 
 63 is 9 times 7, or 7 times 9 ; 
 
 64 is 8 times 8 ; 
 
 70 is 10 times 7, or 7 times 10 ; 
 72 is 9 times 8, or 8 times 9 ; 
 
 80 is 10 times 8, or 8 times 10 ; 
 
 81 is 9 times 9 ; 
 
 90 is 10 times 9, or 9 tim^ 10 ; 
 100 is 10 times 10. 
 (See Manual, page 120.) 
 
 D. TABLE OF ALIQUOT OR FRACTIONAL PARTS* 
 
 1 is 1 of 2 
 
 lislof 3 
 
 lis! of 4 
 
 2 is 1 of 4 
 
 2 is i of 6 
 
 2 is 1 of 8 
 
 3 is ^ of 6 
 
 3 is 1 of 9 
 
 3 is 1 of 12 
 
 4 is 1 of 8 
 
 4 is 1 of 12 
 
 4 is \ of 16 
 
 5 is 1 of 10 
 
 5 is ^ of 15 
 
 5 is 1 of 20 
 
 6 is I of 12 
 
 6 is 1 of 18 
 
 6 is 1 ot 24 
 
 7 is I of 14 
 
 7 is ^ of 21 
 
 7 is 1 of 28 
 
 8 is 1 of 16 
 
 8 is 1 of 24 
 
 8 is 1 of 32 
 
 9 is 1 of 18 
 
 9 is 1 of 27 
 
 9 is \ of 36 
 
 10 is 1 of 20 
 
 10 is i of 30 
 
 10 is I of 40 
 
M AIsTU AL 
 
 OF 
 
 METHODS AND SUGGESTIONS. 
 
 Oral Instruction. — Very much of your success as a primary 
 teacher -will depend upon the kind of oral instruction you impart, 
 and the manner in which you conduct your classes. 
 
 If you make judicious use of the methods, hints, and suggestions 
 contained in this Manual ; if you enter into the work of oral instruc- 
 tion with earnestness and zeal, using proper discretion and judgment, 
 you will find that your pupils will soon partake of your spirit, and 
 your efforts will he rewarded with the most satisfactory results. 
 
 In attempting to be energetic, you must not forget to be per- 
 severing also. Do not pass too rapidly over a subject or lesson. 
 Endeavor to fix every point in the mind of the pupil so thoroughly 
 that he can readily recall it at any future time. To do this, you must 
 dwell upon the point until you are sure the pupil understands it. And 
 here you are cautioned not to confound memory with understanding. 
 The learning of Tables and Combinations is an act of memory ; the 
 solving of problems or examples intelligently, necessarily involves 
 understanding, or reason and judgment. It is not enough that the 
 pupil repeats your words, or the language of the book ; you must 
 extemporize questions, as tests of his understanding of the lesson or 
 subject. The suggestions on teaching children to count (page 110) 
 will indicate to you a course that you may pursue with any section or 
 exercise in which the pupil encounters obstacles. 
 
 Incidental Instruction. — Ton will add much interest to this 
 study, by familiar conversations with the pupils about the pictures in 
 the lessons, and the various objects represented in them. Many of 
 the pictures represent mechanical, manufacturing, and other business 
 operations and industrial pursuits, about which children should be 
 instructed. Encourage them to visit factories, shops, and other 
 places of business of the kinds represented in the pictures, or sug- 
 gested by them or by the examples, for the purpose of obtaining 
 information. When either pictures or examples contain objects or 
 terms with which a child is unacquainted, explain them to him, con- 
 sulting a dictionary whenever you do not understand the object to be 
 explained, or the term to be defined. 
 
 Use of Books in Class. — The mere memorizing of the language 
 of a problem or example, is no part of the true object for which 
 
MANUAL FOR TEACHERS. 109 
 
 Mental Aritlimetic should be studied. The attempt to memorize and 
 reproduce problems or concrete examples, verbatim, occupies and 
 confines the mind, and thus prevents its free exercise in forming the 
 combinations and discovering the reasons for them. Therefore, gener- 
 ally, let the pupil use his book during recitation, unless the lesson is 
 one upon abstract combinations. 
 
 Forms of Answer,— Abundant experience has fully established 
 the fact that young children are not generally capable of understand- 
 ingly making a rigid application of the principles of logical analysis, 
 in the solution of arithmetical problems. 
 
 In most cases, children who have had no previous instruction or 
 training in numbers, will give the result of a problem first, and the 
 because afterward. So generally is this the case, that it may be 
 regarded as the natural order of development of mind in its first steps 
 in concrete numbers. Hence, while several forms of answer or solu- 
 tion are given to one or more concrete examples in each of the differ- 
 ent classes of combinations in this book, the first answer given, in 
 any case, conforms to this view. 
 
 You should require only very brief answers from young children, 
 and you should not insist upon, or exact from them, formulated 
 analyses logically stated. But you should always require pupils to 
 give answers that are correct in language, and to form complete sen- 
 tences, introducing the numbers contained in the question. For 
 example: Sarah has 3 roses, and Eliza has 5. How many roses have 
 the two girls ? 
 
 Answers. (1.) The two girls Jiave 8 roses; becaicse 8 roses and 5 roses 
 are 8 roses. Or, 
 
 (2.) JTie two girls have 3 roses and 5 roses^ which are 8 roses. Or, 
 
 (3.) 3 roses and 5 roses are 8 roses. Therefore, the two girls have 8 roses. 
 
 Any question involving but a single combination of abstract num- 
 bers, admits of only a brief answer. For example : 
 
 How many are 7 and 4 ? Ans. 7 and 4 are 11. 
 
 What is the difference between 12 and 5? Ans. The difference 
 between 12 and 5 is 7. 
 
 How many are 3 times 8 ? Ans. 3 times 8 are 24. 
 
 How many times is 4 contained in 24 ? Ans. 4 is contained in 24 6 
 times. 
 
 Any attempt at a because, or to give a reason, in the answer to ques- 
 tions of this kind, is evidently worse than useless. 
 
 You are again reminded that you are not expected in all cases to 
 adopt the forms of answer given as models in this Manual. When- 
 ever a better form can ^e given for any particular class of questions, 
 adopt it. But before doing this, be sure that it is better, 1st. For the 
 particular class of problems ; and 2d. For the pupil or class under 
 instruction. 
 
110 MANUAL FOR T JE A C H E K S . 
 
 Answers in Review Artlcles.—In the review of each section 
 — ^which is the last article, or the one preceding the last — encourage the 
 pupils to solve the questions in various ways. Thus, after an example 
 has been solved by one of the class, asli who can give a different solu- 
 tion ; or, who can obtain the answer by a different process, or in a 
 different way. Continue this method, till you have fully tested both 
 the ingenuity of the class and their understanding of the examples. 
 
 Slate and Blackboard Exercises.— Make daily use of black- 
 board and slates. Upon the former place combinations, tables, etc., 
 as models for the pnpils ; and require the pupils to use the latter in 
 copying your work. For particular suggestions upon this subject, 
 see directions for teaching the tables, pages 118-120. 
 
 We will now pass to suggestions to which references are made in 
 various parts of the book. 
 
 SECTION I. — Page 8.— Exercise the class upon the objects repre- 
 sented in the pictures, and then with other objects or counters, until 
 all of them can count ten. Then name familiar objects not in sight, 
 as men, animals, birds, fruit, flowers, houses, trees, etc., and require 
 the class to count them or tell the number. This may be done by ask- 
 ing familiar questions relating to tlie objects, and involving definite 
 numbers not exceeding ten. Tims : How many apples must I have 
 to give one to each girl in this class ? How many peaches to give one 
 to each boy ? How many cherries to give one to each pupil ? How 
 many horses has your father ? How many cows ? How many birds 
 has your sister ? How many houses on this street ? When the class 
 can associate the numbers with concrete objects, and not before they 
 can do so, exercise them in counting abstractly. You may vary the 
 following model exercises, according to circumstances : 
 
 I. Children Naming the Numbers, — One. How many heads have 
 you? How many nocks? How many bodies? How many right 
 hands ? How many left hands ? How many right feet ? 
 
 Two. How many eyes have you ? How many hands ? How many 
 feet ? How many ears has a horse ? How many feet has a bird ? 
 Count two. Commence at two and count down to nothing. 
 
 Three. How many children do you see in the picture on the first 
 page of this book ? How many heads have they all together ? How 
 many faces ? Count three. Count from three down to nothing. 
 
 Four. How many hands have two boys ? How many feet ? How 
 many arms ? How many eyes ? How many fingers on your ri^ht hand ? 
 How many feet has a horse? A dog? A cow? A kitten? Count 
 four. Count from four down to nothing. 
 
 Mve. Count the thumb and all the fingers on the right hand ; how 
 many are there ? How many on the left hand ? In the last picture on 
 
MANUAL FOR TEACHERS. Ill 
 
 page 24 how many bags do you see in the pile on the floor ? Count 
 five. Count from five down to nothing. 
 
 Six. (Place 3 girls before the class.) How many hands have these 
 girls ? How many arms ? How many eyes ? How many feet ? How 
 many books in this pile? (Six books.) How many marks have I 
 made on the blackboard ? (Six marks.) How many feet have a man 
 and a horse ? A man and a dog ? A cat and a bird ? An ox and a 
 chicken ? Count from to 6 and back again. 
 
 Pursue the same course with 7, 8, 9, and 10. 
 
 n. Teacher Naming the Numbers.— 1. Hold up 3 fingers. Hold 
 up 7 fingers. 1 finger. 9 fingers. 5 fingers. 2 fingers, etc. 
 
 2. On the blackboard (or your slate) make 4 marks in a row. 
 (Thus, ////.) In another row, below this one, make 7 marks. In ^ 
 other rows, below these, make 2 marks ; 5 marks ; 8 marks, etc. 
 
 3. Clap your hands 6 times. (Let these exercises first be accom- 
 panied with oral counting, and then with mental or silent counting, 
 by the class. Sometimes count for the class, and test their knowledge 
 by making mistakes.) Clap your hands 4 times. 3 times. 8 times. 
 Take 5 steps across the room. Take 9 steps. 7 steps. 10 steps. step. 
 
 4. Tell me the names of 4 girls whom you know. The names of 6 
 boys. Of 8 men. Of 3 kinds of fiowers. Of 5 kinds of animals. 
 
 5. Which is the first day of the week ? Which is the second day ? 
 The third day ? &c. Put 8 books in a pile and count them. Number 
 them, commencing at the top of the pile : thus, first hook^ second book^ 
 and so on. Number them from the bottom of the pile. (In a similar 
 manner, teach the ordinals of 9 and 10.) 
 
 6. Show me 9 things of the same kind — as 9 apples, 9 slates, 9 mar- 
 bles, or any other objects. Name 10 kinds of fruit. 
 
 7. Count, 8, 5, 10, 3, 7, 4, 1, 6, 9, 2. Count down to 0, commencing 
 at 8, 5, 10, 3, 7, 4, 1, 6, 9, 2. Give the class similar exercises, from time 
 to time, in counting to 20, 30, 40, 50, and so on to 100. 
 
 SECTION II. — ^Before leaving Article A the class should learn and 
 be thoroughly exercised upon the addition and subtraction table 1, 
 page 100 ; before leaving Article B they should learn table 2, page 100 ; 
 and before leaving Article C, table 3 page 101. For methods of teach- 
 ing these tables, see pages 118-120. 
 
 (Forms or models of answers and solutions are in italics.) 
 
 Page 1 1 • — ^Ex. 1. One girl and one girl are two girls. 
 
 Ex. 6. One girl from two girls leaves one girl. 
 
 Ex. 7. (1.) There are 3 kittens in the picture; becaiise% kittens and 1 
 izitten are 3 kittens. Or, 
 
 (2.) In the picture are 2 kittens and 1 kitten^ which are three kittens. Or, 
 
 (3.) 2 kittens and 1 kit^n are 3 kittens. Ther^ore^ tliere are 3 kittens 
 in the picture. 
 
112 MANUAL FOR TEACHERS. 
 
 Page 12. — Ex. 9. (1.) 2 of t/ie chairs are withxmt a:'ms; because 1 
 chair from 3 chairs leaves 2 chairs. Or, 
 
 (2.) 2 chairs from 3 chairs leave 1 chair. Therefore^ 1 chair is wiOtxmt 
 arms. Or, 
 
 (3.) As many of th£ chairs are without arms as will he left after taking 
 2 chairs from 3 chairs^ which is 1 chair. 
 
 Page 19.— Tables 1, 2, 3, pages 100, 101, should be thoroughly 
 reviewed by the class, before they commence Article E. 
 
 SECTION Til. — In connection with Article A, require the class to 
 learn table 4, page 101 ; in connection with Ai'ticle B, table 5 ; and in 
 connection with Article C, table 6, page 103. 
 
 Page 22. — Ex. 1. (1.) There are 7 boys in thxit company; because 4 
 ■» boys and 3 boys are 7 boys. Or, 
 
 (2.) Tn that company are 4 boys and 3 boys, or 7 boys. Or, 
 
 (3.) 4 boys and 3 boys are 7 boys. Therefore, there are 7 boys, etc. 
 
 Ex. 2. (1.) There is one more boy standing ; because Z boys from 4 boys 
 leave 1 boy. Or, 
 
 (2. ) 3 boys from 4 boys leave 1 boy. Therefore, 1 mxyre boy is standing. Or, 
 
 (3.) As many more boys are standing as will be left after taking 3 boys 
 from 4 boys, which is 1 boy. 
 
 Page 25. — Ex. 14. Give the pupils clear and distinct ideas of the 
 terms 77iore and less. 
 
 Page 28. — Do not permit the class to pass to Article D until they 
 have thoroughly reviewed tables 4, 5, 6, pages 101, 102. 
 
 Page 29. — The combinations in Ex. 6, 7, 8 refer to the picture on 
 page 30 ; and Ex. 10, 13, 17, 18, page 30, refer to the picture on page 29. 
 
 Page 31. — Practice the class in these counting exercises, both in 
 concert and singly, until they can count rapidly, both forward and 
 backward. See page 110. 
 
 SECTION IV. — In connection with Articles A, B, C, and D, respect- 
 ively, the pupils should learn tables 7, 8, 9, 10, pages 102, 103. 
 
 Page 33. — Instruct the pupils to make figures of good form and 
 proportions ; and when they print or write tables of combinations 
 upon the slate or blackboard, (as directed on page 118,) require them 
 to arrange the numbers in good order in columns and lines. Com- 
 mend every preceptible improvement, however little it may be. 
 
 Page 37. — The class should be masters of tables 7, 8, 9, 10, pages 
 1C2, 103, before passing to the next section. 
 
 SECTION v.— Page 38.— Require the class to review the addition 
 and subtraction tables, pages 100-103, while upon this section. 
 
 Each combination in this section occurs twice, — 1st, with concrete 
 numbers ; 2d, with abstract numbers. The lessons should be recited 
 without the aid of visible objects. In some cases it may be found 
 profitable for the class to pass over this section a second time, without 
 
MANUAL FOR TEACHERS. 113 
 
 using the book at recitation; the teacher reading the example or 
 question slowly and distinctly, and then requiring a pupil to repro- 
 duce it from memory, and give the solution or answer. 
 
 Page 40. — Before commencing Article B, give the class 
 
 ORAii Exercises: — Addition. Name all the pairs of numbers that 
 can be added to form 9. Thus, 8 and lorl and 8 are 9; 7 and 2 or 2 and 
 7 are 9 ; and so on. In the same manner name all the pairs of numbers 
 that can be added to form 10; to form 11 ; to form 12 ; and so on, to 20. 
 
 Subtraction. Name all the numbers that can be taken from 9, and 
 also the numbers that will be left. Thus, 1 from 9 leaves 8, 2 from 9 
 leave 7, and so on, to 9 from 9 leave 0. What numbers can be taken 
 from 10, and what numbers will be left ? And so on, to 20. 
 
 Page 41. — Article B. In the same manner teach the pupils to ex- 
 press by figures all the numbers to 100 inclusive. — Article C. Give the 
 class thorough drills in these counting exercises, in the manner indi- 
 cated on page 98. Before passing to Section VI, review all the 
 addition and subtraction tables, pages 100-103, as directed on page 119. 
 
 SECTION VI. — Page 42. — Before assigning lessons in this section 
 to the class, spend the time of one or two recitations in giving oral 
 instruction, with the aid of counters or other visible objects to repre- 
 sent the same combinations as those in Article A. Pursue the same 
 plan, on commencing Article B. 
 
 Ex. 1, last question. 2 times 1 camel are 2 camels. 
 
 Page 45. — ^Require the pupils to memorize the multiplication 
 table of 2, page 104, before passing to Article B. For methods of 
 teaching these multiplication and division tables, see page 118-120. 
 
 Ex. 15, first question. (1.) ToutoillJiave IS chestnuts; because 2 times 
 9 chestnuts are 18 chestnuts. Or, 
 
 (2.) You will have 2 times 9 chestnuts, or 18 chestnuts. Or, 
 
 (3.) 2 times 9 chestnuts are 18 chestnuts. Therefore, you will have 18 
 chestnuts. Or, 
 
 (4.) In 2 hands you will have 2 tim^s as many chestnuts as you have m 1 
 hand, and 2 times 9 chestnuts are 18 chestnuts. Therefore, you will have 
 IS chestnuts. (Or, omit the last sentence.) 
 
 Page 46. — Ex. 6, first question. 8 marbles are 4 times 2 marble^. 
 
 Ex. 8. (1.) You can Imy 5 peaches ; because 2 cents are contained m 10 
 cents 5 times. Or, 
 
 (2.) 2 cents are contained in 10 cents 5 times. Therefore, you can buy 5 
 peaches. Or, 
 
 (3.) Since you pay 2 cents for 1 peach, for 10 cents you can buy as many 
 peaches as the times 2 is contained in 10, which is 5 times. Therefore, you 
 can buy 5 peaches. (Or, omit the last sentence.) Never use the ex- 
 pression "as many as 2 is contained times in 10." 
 
 Page 48.— The division table 2, page 104, is to be learned before 
 passing to Article B. The multiplication and division* table 2 should 
 be recited as one table, across the page. See page 118. 
 
114 MANUAL FOR TEACHERS. 
 
 Page 49.— At Ex. 6 the process of addition to obtain a product is 
 dropped. Be sure that the manner of obtaining products by repeated 
 additions is fully understood by the pupils. If necessary, continue 
 the method by addition through several more lessons. 
 
 Page 52, — Table 3, page 104, is to be learned before passing to the 
 next section. 
 
 SECTION VII.— Tables 4 and 5, pages 104, 105, are to be learned 
 in the following order : after Art. A, page 56, multiplication of 4 ; 
 after Art. B, page 58, division by 4; after Art. C, page 59, multi- 
 plication of 5 ; after Art. D, page 61, division by 5 ; and with Art. E, 
 pages 61, 62, a thorough review of the tables of 4 and 5, both separ- 
 ately (i. e., multiplication and division each by itself) and conversely 
 (i. e., across the page.) 
 
 Page 55. — Make all necessary explanations to the class about the 
 objects mentioned in the examples. 
 
 Page 61, — Wherever practicable, exhibit to the class the objects 
 named in the examples. "Where this can not be done, make use of 
 counters, and require the pupils to form the combinations. 
 
 Page 62. Ex. 17. — Upon the blackboard draw a picture of a bar- 
 rel. Also, ask the children to look at a flour barrel at home, and see 
 if it has 10 hoops. 
 
 SECTION VIII. — Page 63. — Pursue the same course in teaching 
 tables 6 and 7, page 105, as you were directed to pursue with tables 
 4 and 5, above. 
 
 SECTION IX. — Page 68.— All the combinations in the examples 
 upon this page may be made from the three pictures, by counting the 
 objects named in any example as many times as there are units in the 
 multiplier. 
 
 Page 70.— Require the class to thoroughly review the tables of 
 multiplication and division, pages 103-106, both separately and con- 
 versely, before leaving this section. Also practice them till they can 
 answer any question of the kind suggested by the following 
 
 Oral Exercises. — (1.) Name all the pairs of factors of 12. Thus, 
 6 times 2, or 2 times 6 are 12 ; 4 times 3, or 3 times 4 are 12. Name all the 
 pairs of factors of 15. Of 16. Of 18. Of 20. And so on, with all the 
 composite numbers to 100 inclusive, requiring only those factors that 
 do not exceed 10. 
 
 (2.) Name all the divisions and quotients of 12. Thus, 6 is in 12 
 2 times^ 2 is in 12 6 times ; 4 in 12 3 times, 3 in 12 4 times. Name all 
 the divisors and quotients of 15. Of 16. Of 18. Of 20. And so on, 
 with all the composite numbers to 100 inclusive, requiring only those 
 divisors and quotients that do not exceed 10. 
 
 (3.) Name all the numbers to 20 inclusive that will contain 2. 
 Thus, 2 is contmined in 2, 4, 6, 8, 10, 12, 14, 16, 18, 30. In what num. 
 
MANUAL. FOR TEACHERS. 115 
 
 bers not greater than 80 is 3 contained ? And so on, by lO's, to 100 
 inclusive. 
 
 These oral exercises are preparatory to the Factor table, page 107, 
 the memorizing of which should now be commenced. Give the class 
 short exercises upon it daily, till they have thoroughly mastered it. 
 (See directions, page 120.) This will require several weeks, but it will 
 prove to be time well spent. 
 
 SECTION X.— Page 72.— In these lessons in Fractions, illustrate 
 the first two or three examples in each article by means of objects. 
 After dividing groups of objects — or a single object, as the case may 
 be — ^before the class, according to the conditions of the question, re- 
 quire the pupils to do the same. 
 
 Ex. 1. (1.) He gaveher 1 orange ; because 1 7ialfof2 oranges is 1 orange. Or, 
 
 (2.) 1 half of 2 oranges is 1 orange. Therefore, he gave her 1 orange. 
 
 Page 73. — Ex. 6. — One half of 2 doves is 1 dove. 
 
 Ex. 20. — After this example, review the Division table of 2, using 
 the fractional form of expression. Thus, 1 half of 2 is 1, 1 half of 4 is 
 2, 1 half of 6 is 3, 1 half of 8 is 4, 1 half of 20 is 10. Then in re- 
 verse order, thus, 1 half of 20 is 10, 1 half of 18 is 9, 1 half of 16 is 
 
 8, 1 half of 2 is 1. Practice the class upon it till they become 
 
 familiar with the fractional form of expression. 
 
 Page 74. — ^Illustrate the idea of halves, by dividing an apple, an 
 orange, a peach, a sheet of paper, etc., into two equal parts, before 
 the class, and then fix the idea in the mind of each pupil, by requiring 
 him to perform the division. 
 
 Divide 3, 5, 7, and 9 objects before the class, in the manner indicated 
 in the cut and explanation, Ex. 3 and 5. 
 
 Ex. 4.— (1.) Each child will receive 1\ pears ; because 1 half of Spears is 
 l\ pears; Or, 
 
 (2. ) 1 half of Z pears is 1\ pears. Therefore, each child will receive 1\ pears. 
 
 Page 76.— Ex. 2.— (1.) He has 4 cents; because 2 cents are 1 half of 2 
 times 2 cents, or 4 cents. Or, 
 
 (2.) 2 cents are 1 half of 2 times 2 cents, or 4 cents. Therefore, he has 4 
 cents. 
 
 Ex. 6,-1 inkstand is 1 half of 2 times 1 inkstand, or 2 inkstands. 
 
 Page 77.— Ex. 20. After this example, exercise the class in the 
 formation and memorizing of the first part, i. e., the halves, of the 
 Table of Aliquot, or Fractional Parts, page 107. 
 
 Article D.— Ex. 1. li peaches are 1 half of 2 times 1\ peaches, or 3 
 peaches. 
 
 Illustrate as follows : (1.) 2 times 1 peach are 2 peaches ; 
 
 (2.) 2 times 1 half peach are 2 half peaches; 
 (3.) 2 half-peaches are 1 peach ; 
 (4.) 2 peaches and 1 peach are 3 peaches. 
 ^ Make this illustration with visible objects, changing the word peach 
 for the names of the objects used. Apply the same method of illus- 
 
116 MANUAL FOR TEACHERS. 
 
 tration to developing the idea of 2|, 3|, 4|, and so on, till the child 
 clearly comprehends, 1st, that f=l, in any case; 2d, that 2 times 
 ^=1=1. Make use of this method or process in illustration, but not in 
 a solution, or as any part of the answer to questions in the article. 
 Pupils should be made so familiar with the method of illustration, 
 that they can apply it to any visible objects, or concrete or abstract 
 numbers, whenever called upon to do so. 
 
 Ex. 4 to 9 inclusive. Give the class clear and correct ideas of the 
 denominations foot, yard, and pound, by the aid of visible objects. 
 
 Page 78.— Ex. 1. (1.) There will be 4: halves ; because in 1 melon there 
 are 2 halves^ and 2 times 2 halves are 4 halves. Or, 
 
 (2.) In 1 melon there are 2 halves ^ and in 2 melons there are 2 times 2 
 halves^ or 4 halves. Therefore^ there will "be 4 halves. (Or, omit last sen- 
 tence.) Or, 
 
 (3.) In 2 melons tJiere are 2 tim£s as many halves as in 1 m^lon, and 2 
 times 2 halves are 4 halves. Therefore^ etc., as in (2.) 
 
 Ex. 2. (1.) She had 2 sisters ; because she had as rnmiy sisters as there 
 are halves in an orange^ and in an orange there are 2 halves. Or, 
 
 (2.) She had as mxiny sisters as there are halves in an orojige^ and in an 
 orange there are 2 halves. Therefore^ she had two sisters. 
 
 Ex. 3. (1.) I will divide them among 6 scholars; because I will give 1 
 pencil to 2 scholars^ and 3 pencils to 3 times 2 scholars^ or 6 scholars. Or, 
 
 (2.) I will give 1 pencil to 2 scholars, and 3 pencils to 3 tim>es 2 scholars, 
 or 6 scholars. Therefore, I will divide them among 6 scholars. (Or, omit 
 last sentence.) Or, 
 
 (3.) I will divide them among as many scholars as there are halves in 3 
 pencils. In 1 pencil there are 2 halves, and in 3 pencils there are 3 times 
 2 halves, or 6 halves. Therefore, I will divide them among 6 scholars. (Or, 
 omit the last sentence.) 
 
 Page 79.— Ex. 2. (1.) 4 half -apples are equal to 2 apples; because 2 
 half -apples are equal to 1 apple, and 2 halves (or 2 half apples) are con- 
 tained in 4: halves (or in 4 half apples) 2 times. Or, 
 
 (2.) 2 half -apples are equal to 1 apple, and 2 halves are contained in 4 
 halves 2 times. Therefore, 4 half apples are equal to 2 apples. 
 
 Ex. 4. (1.) 4 pints of inlc can be put into 8 half -pint bottles ; because 2 
 half pint bottles will hold 1 pint, and 2 halves are contained in 8 halves 4 
 times. Or, 
 
 (2.) 2 half -pint bottles will hold 1 pint, and 2 halves are contained in 8 
 Tialves 4 times. Therefore, 4 pints of ink can be put into 8 half-pijit bottles. 
 
 SECTION XL— Page 81.— Ex. 2. (1.) 2 girls are in the street; be- 
 cause 1 third of 6 girls is 2 girls. Or, 
 
 (2.) 1 third of 6 girls is 2 girls. Therefore, 2 girls are in the street. 
 
 Ex. 5. (1.) 4 gi7^ls are in the yard : because 1 third of Q children is 2 chil- 
 dren, and 2 thirds of 6 children are 2 times 2 child?'en, or 4 children. Or, 
 
 (2.) 1 third of 6 children is 2 children, and 2 thirds of 6 children are % 
 times 2 children, or 4 children. Therefore, 4 girls are in the yard. 
 
MANUAL FOR TEACHERS. 117 
 
 Page 83« — Ex. 8. (1.) A harrel costs 18 dollars'^ because 6 dollars is 1 
 third of 3 times 6 dollars^ or 18 dollars. Or, 
 
 (3.) 6 dollars is 1 third of 3 times 6 dollars, or 18 dollars. Therefore, a 
 harrel costs 18 dollars. 
 
 Before passing to Article C, drill the class tliorouglily upon the 
 division table of 3, both forward and backward, using the fractional 
 form of expression. Thus, 1 third of 3 is 1, 1 -third of 6 is 2, 1 third 
 
 of 9 is 3, 1 third of 30 is 10.— 1 third of 30 is 10, 1 third of 27 is 
 
 9, 1 third of 24 is 8, 1 third of 3 is 1. 
 
 Also, require the class to memorize the second part {thirds) of the 
 Table of Aliquot, or Fractional Parts, page 107, before taking up Ai- 
 ticle C, or before passing to the next section. 
 
 Page 84. — Ex. 2. (1.) 2 pies can be cut into 6 thirds; because in 1 pie 
 there are 3 thirds, and in 2 pies there 2 times 3 thirds, or 6 thirds. Or, 
 
 (2.) In 1 pie there are 3 thirds, and in 2 pies there are 2 times 3 thirds, 
 or 6 thirds. Therefore, 2 pies can be cut, etc. 
 
 SECTION XIL— Page 86.— Ex. 13. (1.) There are 2 quarts in If o^trth 
 of a peck ; because 1 fourth of 8 quarts is 2 quarts. Or, 
 
 (2.) \ fourth of 8 quarts is 2 quarts. Therefore, there are 2 quarts, etc. 
 
 Ex. 14. Teach pupils that 2 fourths of any thing =1 of the same 
 thing, using for illustration objects that can readily be divided into 
 halves and fourths. 
 
 Ex. 18. (1.) There are 9 inches in Z fourths of a foot ; because 1 fourth of 
 afoot, or 12 inches^ is 3 inxihes, and Z fourths of afoot are 3 tim^s 3 inches, 
 or 9 inches. Or, 
 
 (2.) In \ fourth of afoot, or 12 inches^ there are 3 inches, and in 3 fourths 
 of afoot there are 3 times 3 inches, or 9 inches. 
 
 Page 88.— Ex. 3. (1.) I pound will cost 8 cents ; because 1 pound will 
 cost 4 times as much as 1 fourth of a pound, and 4 times 2 cents are 8 cents. 
 Or, 
 
 (2.) 1 fourth of a pound costs 2 cents, and 4 fourths, or 1 pound, will cost 
 4 times 2 cents, or 8 cents. 
 
 Before passing to Article C, drill the class upon the division table 
 of 4, both forward and backward, using the fractional form of expres- 
 sion. Thus, 1 fourth of 4 is 1, 1 fourth of 8 is 2, 1 fourth of 12 is 3, 
 
 1 fourth of 40 is 10.— 1 fourth of 40 is 10, 1 fourth of 36 is 9, 1 fourth 
 of 32 is 8, 1 fourth of 4 is 1. 
 
 Also require the class to memorize the third part (fourths) of the 
 Table of Aliquot or Fractional Parts, page 107, and then to review the 
 -whole table, across the page, until they are perfect in it, before passing 
 to Article C. 
 
 Page 89. — Ex. 3. (1.) 12 glasses of lemonade can be made from 3 lem- 
 ons ; because from 1 lemon 4 glasses can be made, and from 3 lemons 3 times 
 4 glasses, or 12 glasses, can be made. Or, 
 
 (2.) From 1 lemon 4 glasses can be made, and from 3 lemons 3 times 4 
 glasses, or 12 glasses, can he made. 
 
^ 
 
 118 MANUAL FOR TEACHERS. 
 
 Page 90# — Ex. 4. (1.) She used 4 yards; because 16 times 1 fourth of 
 a yard are IQ fourths of a yard, or 4 yards. Or, 
 
 (2.) 16 times 1 fourth of a yard are 16 fourths of a yard, or 4 yards. 
 Therefore, she used 4 yards. 
 
 SECTION XIII, page 91; and SECTION XIV, page 97.— 
 
 Require pupils to learn the tables of Sec. XIV, one at a time, while 
 passing through Sec. XIII. Before assigning a table as a lesson to be 
 learned, explain its uses, and the several denominations, using visible 
 objects in every case where it is practicable. Also require each pupil 
 to handle the weights and measures, and to use them in weighing and 
 measuring various kinds of objects. 
 
 SECTION XV.— It is of the first importance to the progress of 
 pupils in a future course of study, that they become perfectly familiar 
 with all the tables contained in this section. To accomplish this, it 
 will be necessary for you to give the class daily exercises upon each 
 table, in order, till they become masters of it, not neglecting frequent 
 reviews of all the tables previously learned. The following course is 
 suggested, as likely to secure the desired result in a manner satisfac- 
 tory to you, and interesting and profitable to your pupils. We will 
 take for our illustrations of methods, the tables of 4, pages 101-104. 
 The first column of the table of 4, page 101, is the addition to 4 of all 
 numbers not exceeding 10; the second column, the addition of 4 to 
 all numbers not exceeding 10 ; the third column, the subtraction of . 
 all numbers not exceeding 10 from numbers that leave a difference of 
 4 ; and the fourth column, the subtraction of 4 from all numbers from 
 4 to 14, both inclusive. 
 
 1. For Additio7i.^V\xt the first part of the addition table of 4 upon 
 the blackboard, and with the first lesson which you assign in Sec. Ill, 
 Art. A, page 22, require the class to print or write this part of the 
 table upon their slates, at their seats, say 5 times. In recitation drill 
 them upon it, in concert and singly, (using the methods suggested 
 under Sight Exercises, next page), for say five minutes, daily, until 
 they have learned it. Then assign the second part of the table, and 
 drill the class upon it in the same manner; after which, combine the 
 two parts, requiring the class to recite them as they stand across the 
 table. Thus, and 3 are 3, 3 and are 3 , 1 a7id 3 are 4, 3 aiid 1 are 4 ; 
 2 and 3 are 5, 3 and 2 are 5 ; 3 and 3 are 6 : 4an<?3are 7; 3 and ^are 7; 
 and so on. 
 
 2. For Subtractio7i.— Pursue the same course with the subtraction 
 table of 4 as above suggested for addition. 
 
 3. For Addition and Subtraction.— Combine the two tables, requiring 
 the class to recite them as one table, as they stand across the page. 
 Thus, 7 and 3 are 10, 3 and 7 are 10 ; 7/rom 10 leave 3, Sfrotn 10 leave 7 ; 
 and so on, of the whole table. 
 
 Keeping pupils employed, for an hour each day, in printing or writ- 
 
MANUAL FOR TEACHERS. 110 
 
 ing these tables upon their slates or the blackboard, will be found a 
 valuable aid in fixing the tables in their memories. 
 
 4. For Multiplicatimi arid Division. — Pursue a similar course to that 
 suggested above, for Addition and Subtraction. 
 
 Sight Exercises.— To test their knowledge of each table, before 
 leaving it give the class a drill in sight exercises, as follows : We will 
 confine our suggestions to the tables of 4, as before stated. 
 
 1. For Addition,— WvliQ numbers in pairs — 4 being one of the num- 
 bers—and call upon the class for their sum. Thus, write ^ |, and so 
 
 on, and ask who can give the sum first. 
 
 2. For Subtraction. —Write numbers in pairs — 4 being either subtra- 
 hend or remainder, as ^ ■^^, and call for their difierence. 
 
 3. For MuUiplicatio7i.— 'Write two numbers — 4 being one of them— 
 as, g ^> and call for their product. 
 
 4. For Divisio7i.---'Wnte two numbers, as divisor and dividend— 4 
 being either divisor or quotient— as, 4)28 9)36, and call for the 
 quotient. 
 
 After some practice in this class of exercises, you should then take 
 up the following 
 
 Tabular DxiXH^ —1, For Addition. Write a column of figures 4 
 upon the blackboard, as here shown. After the table of 4, page ^ 
 101, the figures 0, 1, 2, 3, 4, variously arranged, should make up o 
 the column ; after the table of 5, the column should contain only ^ 
 the figures 0, 1, 2, 3, 4, 5 . and so on, of all the tables. The follow- i 
 ing methods of conducting the exercises will be found valuable : 4 
 
 (1.) Class add in concert, commencing at the foot of the col- 
 umn, and giving results as you point, with an index or pointer, to the 
 numbers . 2, 6, 7, 10, 12, 12, 15, 16, 20. 
 
 (2.) Proceed in the same manner, commencing at the top of the 
 column. 
 
 (3.) Commence at any place in the column, as at 3, and add up to 
 the top of the column, and then from the bottom, or foot, to the place 
 of starting. Thus, 3, 5, 5, 8, 9, 13 (now at the foot of the column), 15, 
 19, 20. 
 
 (4.) Commencing at the same place, add in the opposite direction. 
 
 (5.) Call out a pupil to add before the class, in any of the four meth 
 ods above described, and require the class to correct his errors. 
 
 (6.) Let any pupil, with index in hand, point to the numbers, in any 
 of the orders above enumerated, and the class add in concert. 
 
 (7.) In the same manner, let a pupil point to the numbers, and the 
 other pupils, each in turn, name a result. 
 
 2. For Subtractio7i.— The sum of the column already written is 20. 
 Now, commencing at the foot of the column, and pointing to the 
 numbers, consecutively, require the class to give (in any of the orders 
 
120 MANUAL FOR TEACHKRS. 
 
 named for addition) the difference, first between 20 and the first num- 
 ber, then between that diff"erence and the next number, and so on. 
 Thus, you point to 2, 4, 1, and so on, successively, and the pupils in- 
 stantly answer, 18, 14, 13, 10, 8, 8, 5, 4, 0. 
 
 Practice the subtractions by all of the methods giyen for the addi- 
 tion exercises. 
 
 3. For Multiplication.— Write promiscuously all the numbers from 
 to 10, both inclusive, in a line upon the blackboard. Thus, 
 
 7148036 lOS 29 
 Then, commencing at the left hand, and pointing successively to the 
 numbers from left to right, require the class to give the product of 
 the number pointed to, by 4. Thus, you point to 7, 1, 4, and so on, 
 and the class instantly answer 28, 4, 16, 32, 0, 12, 24, 40, 20, 8, 36. The 
 exercises may be varied as follows ; 
 
 (1 ) Commence at the left hand, and pass toward the right. 
 
 (2.) Commence at the right hand, and pass toward the left. 
 
 (3.) Commence at any place in the line, and pass in either direction 
 to the epd of the line, and then from the opposite end to the place of 
 beginning. 
 
 (4.) Point to any number in the line, and the class instantly name 
 the result. 
 
 The methods of recitation may also be varied, as suggested under 
 the Sight Exercises, page 119. 
 
 4. For Division. — Write promiscuously all the exact dividends of 4, 
 to 40, inclusive, in a line upon the blackboard. Thus, 
 
 28 4 16 40 O 82 12 20 8 24 36 
 Then, commencing at the left hand, and pointing successively to the 
 numbers from left to right, require the class to name the quotients of 
 the several numbers by 4. Thus, you point to 28, 4, 16, and so on, 
 and the class instantly answer 7, 1, 4, 10, 0, 8, 3, 5, 2, 6, 9. 
 
 Vary the exercises as just suggested for the exercises in multiplica- 
 tion. 
 
 Factor or Division Table.— -Assign a portion of this table, 
 say to 20, as a lesson for the pupils to print or write upon their slates, 
 and to memorize at their seats. Then write the numbers in order in 
 a line upon the blackboard, and use them at recitation in any of the 
 methods already described. 
 
 After the class can recite the table readily in the order in which it 
 is arranged, write the numbers in a line or a column upon the black- 
 board, in any order you choose, and drill the class as has already been 
 suggested. ~ 
 
 Table of Aliquot or Fractional Parts.— Pursue the same 
 course with pupils while learning this ^1b%that has been indicated 
 for the other tables in this section. 
 
 usriyEii-iiTi 
 
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 UNIVERSITY OF CALIFORNIA LIBRARY 
 
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