WORK AND WITH NUMBERS WENTWORTH - SMITH £fout $ork £>tate (^allege uf Agriculture .At Qfornell IniuetBttB Cornell University Library QA 135.W47 Work and play with numbers. 3 1924 002 956 575 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924002956575 WORK AND PLAY WIT NUMBERS GINN AND COMPANY BOSTON • NEW YORK • CHICAGO ■ LONDON COPYRIGHT, 1912, BY GEORGE WENTWORTH AND DAVID EUGENE SMITH ENTERED AT STATIONERS' HALL ALL RIGHTS RESERVED 521.1 (.INN AND COMPANY- PRO- PRIETORS • BOSTON • U.S.A. PREFACE It has been recognized ever since the days of Pestalozzi that children when they first enter school have a taste for number work and also a considerable knowledge of numer- ical forms. They use numbers in their games, they talk about them, they like to count, and they enjoy a little work and play with numbers within their mental grasp. On the other hand, children of this age are not ready for such a study of arithmetic as the formal textbook offers. A textbook of that kind would take away their love for number and would jdace upon them a burden heavier than they could carry. Not to begin the study of the subject when the child enters school, however, is to say that the child's natural tastes should not be fostered. What we need is to intro- duce, in an informal and attractive fashion, such number work as is within his grasp at this time. Experience shows that children can easily learn the combinations in addition, and part of those in multipli- cation, before taking up a formal study of the subject; in other words, they can cover the work included in this little book. Since the entire multiplication table is some- times required, it is given at the end of the book, to be developed in the usual manner if necessary. 4 PREFACE To meet the need which the experience of teachers has justified, the authors have set forth, informally and in simple language, the number facts that should be mastered. They have not attempted to prepare a textbook of the conventional type, nor yet a mere book of devices to im- pose upon the teacher certain methods that she cannot profitably use. They have sought to offer to the schools a book that shall serve as a guide and helper both to the teacher and to the pupil, one that shall save labor, furnish a list of reading exercises, and suggest a basis for some- what informal work with beginners.: It will be observed that the type has been selected with greatest care. A child at this time heeds to train the eye to see number relations, and that he may do this without undue visual exertion, a large and heavy type is used. He also needs to write numbers, and when asked to do this the numbers have been put in script. He also needs to read the ordinary printed numerals, and when these appear in sentences they are in the usual printed form. In this way, with a minimum of eye strain, he accom- plishes the important results mentioned. The authors desire to express their appreciation of the artistic work of Miss Hope Dunlap, whose illustrations will, they feel sure, bring delight to thousands of children. GEORGE WENT WORTH DAVID EUGENE SMITH CONTEXTS CHAPTER 1'AGE I. NUMBER WORK TO 10. COUNTING TO "LOO 7 II. ADDITION TABLE COMPLETED 80 III. PRACTICE ON THE ADDITION TABLE 73 IV. NUMBERS TO 1U00. MULTIPLICATION Ill WORK AND PLAY WITH NUMBERS CHAPTER I NUMBER WORK TO 10. COUNTING TO 100 Hickory, dickoryv dock, The mouse ran up the clock, The clock struck one, And down he ran, Hickory, dickory, dock. 1 one • / o^ruis The clock struck one. I see one clock. I see one _^^1$ I see one # and one (^ I write one like this : /. TWO [ace: and Jill went up the hill To get a pail of water. Jack fell down and broke his crown, And Jill came tumbling after. two ~2 ttAM}- I see two Jack and Jill have one TWO One and one arc two. 1 + 1 =2 Two hands hold the One ^ and one ^ are two ^ S 1 +1 2 Two less one is one. 2-1=1 Two less two is none. 2-2 = Write : 1 + 1=2 I- 1 = 2-1=/ 2-2=0 2 1 / + = I 2 + 0=2 10 THREE aa, baa, black sheep. Have you any wool ? Yes sir, master, three bags full. three 3 tA/i veso I see three I see three (3^ and £> are (^ J *§fiy and 1^* are I see one tree. I see two trees. THREE 11 One Q and one Q> are two Q> ^A One and one and one $> are three ^ ^ Read: Two and one are three. One and two are three. Three less one is two. Three less two is one. Three less none is three. Write: 1 1 2 3 3 3 + / +2 + / -/ -2 -3 2 3 3 2 / / + / = -2 3- 1 =2 3 + = 3 2+ / • -3 3-3 = 2-0=2 1+2- = 3 3-2= 1 ■ 3-0 = 3 12 FOUR &^? Two legs sat upon three le&'S With one leg in his lap. In comes four legs And runs away with one leg Up jumps two legs, Catches up three legs, Throws it after four le^s & ij ? And makes him bring back one leg. four U- Oli/U ® and <$#<» are %«*## FOUR ' 13 Read : Two and two are four. Three and one are four. One and three are four. Four less three is one. Four less two is two. Four less one is three. Two legs and two legs are four legs. Four is one more than three. Write : / 3 2 4 4 4 + 3 + / +2 -3 -2 - / 4 4 4 / 2 3 1+3- = 4 4-3=1 4+0 = 4 3+ / - -4 4-1=3 4-0 = 4 2+2- -4 4-2=2 4-4=0 14 FIVE his little pig went to market; This little pig stayed at home; This little pig had roast beef; This little pig had none ; This little pig said, "Wee, wee! I can't find my way home." 5 five ••• S FIVE and flfltiltdgf arc I see that gj, Q, 0> @> and Q| are^)C>^3€)© Four and one are five. One and four are five. Three and two are five. Two and three are five. Write : / 4 3 2 £ + £ + / +2 + 3 + £ £ £ £ £ £ £ £ £ £ -4- - / -2 -3 -£ I 4 3 2 1 love a sixpence, Jolly little sixpence, I love a sixpence As I love my life; I spent a penny of it, I lent a penny of it, I took a fonrpence home to my wife. G six 6 &iz> Read : Five and one are six. One and five are six. Four and two are six. OOOO and 00 are OO060® SIX 17 I see that ^J and fUS are lElEsfes We see that MMMUk. and are We see that £ and £££££ are ££££££ /fa/d : 6 + = = 6 4 + 2 = 6 2 + 4 = 6 5+1 = = 6 3 + 3 = = 6 1 + 5 -6 WWfe : / 2 3 ^ S b +s + 4 + 3 +2 + / + ~b '~b ~b ~~b 6 b 6 b b b b b - / -2 -3 -4 -s -b s 4 3 2 i 18 SEVEN .S I was going to St. Ives I met a group of seven wives; Each wife had seven sacks, Each sack held seven cats, Each cat had seven kits. Kits, cats, sacks, and wives, How many were going to St. Ives ? seven • •• 7 6ytyU^71y SEVEN 19 I see I see C%(3H Read : 6 cats and 1 cat are 7 cats. 5 sacks and 2 sacks are 7 sacks. Four and three are seven. 6+1 =7 5 + 2=7 4 + 3=7 Write : 6 s ^ + I +2+3 1 +6=7 2 + 5=7 3 + 4=7 3 + u 2 + S I 6 +/ 7 7 7 7 7 7 7 7 7 7 7 7 7 7 I -2 b S 3 ~4 ^ 3 o 2 6 1 o 20 RIGHT J^ittle Bo-Peep lias lost her sheep And can't tell where to find them; Leave them alone, and they will come home And bring their tails behind them. 8 eight t 7 sheep and 1 sheep are 8 sheep. I see that ^^ ^ ^ ^ and t^t^iT are ^ ^ ^ ^ ^ EIGHT and $ arc "g 21 I see that I see that are Read : 7 sheep and 1 sheep are 8 sheep. 6 trees and 2 trees are 8 trees. 5 boys and 3 boys are 8 boys. 4 girls and 4 girls are 8 girls. Write : / 2 3 v s 6 7 ®® and <§) are ig^O®^®® ^@><©© i?e«c? : 9 and 1 are 10. 9 + 1 = 10 8 and 2 are 10. 8 + 2 = 10 7 and 3 are 10. 7 + 3 = 10 6 and 4 are 10. 6 + 4 = 10 FFWfe : Twenty-two 20 + 3 = 23 20 + 7 = = 27 20 + 4 = 24 20 + 8 = = 28 20 + 5 = 25 20 + 9 = = 29 20 + 6 = 26 20 + - 10 = = 30 30+1 =31 Tliirty -one 40 + 3 = 43 > „7 Forty- 1 thr ee lead : 11 12 15 17 19 21 22 25 27 29 31 32 36 38 39 41 42 43 44 47 51 52 55 57 58 61 62 60 66 67 71 72 73 75 77 81 82 80 88 86 91 92 95 97 99 28 COUNTING Read : 20 10 6 9 17 31 90 30 42 60 63 80 54 75 40 50 86 62 70 92 55 88 98 77 99 56 89 74 79 100 Write : 30+2 = -32 40 + 8' = 48' Write : 20 + 6 = 30 + 5= so +7 6o + / = 8*0+2 = 40 + 3 ]0 + S= 30+2 = qo + q 20+7 = S'O+b- 40 + 4 so+s= 70 + f= 60+ 7 COUNTING Head : I saw 30 tr ees. Wc saw 42 cars. We saw 14 birds. Mary lias 20 books. The boy lias 12 apples. The man has 25 hor. ses. Read : 17 23 41 19 36 52 82 18 43 68 87 60 29 70 54 Write : 30 + o/ca^ cLoMl c&. SUBTRACTING 3 How many roses are 7 roses and 3 roses ? How many roses are 10 roses less 3 roses? How many are 4 + 3 ? How many are 7 - 3 ? How many are 7 - 4 ? 51 Read and learn : 3-3 = 7-3 = 4 11 -3= 8 4-3=1 8-3 = 5 12-3= 9 5-3 = 2 9-3 = 6 13-3=10 6-3 = 3 10-3=7 14-3=11 Write: 7 4 3 6 s // 3 -3 ■ -3 -3 -3 -3 -3 -J / / + 3 = 12-2 Cs ~ c*£s ' " e-O' c^ <=*~s o<> <= See how Ave multiply 3 22 by 3. 66 w rite an id multiply : 10 II 12 13 14 20 21 22 2 2 2 2 2 2 2 2 23 24 30 31 32 33 34 40 2 2 2 2 2 2 2 2 41 42 43 44 II 12 13 20 2 2 2 2 3 3 3 3 21 23 30 31 32 33 II 12 3 3 3 3 3 3 4 4 MULTIPLYING 135 How much is 3x3? How much is 3x4? 3* 40? How much is 3 x 43 ? „ See how we multiply 3 43 by 3. T29 Write and multiply : SO SI S2 S3 40 41 42 SO 2 2 2 2 3 3 3 3 20 21 22 30 31 32 40 41 4^444444 10 II 20 21 30 31 40 41 ssssssss 10 II 20 21 41 SI SI SI b b 6 6 6 7 f <7 136 MULTIPLYING How much is 2 x 3 ? 2 x 30 ? How much is 2 x 30 and 2x3? How much is 2 x 33 ? 2 x 32 ? How much is 3x1? 3x10? How much is 3 x 12 ? Write and multiply : 13 23 33 4-3 14 24 34 44 a2y c^L =^> =<> c*L- <^L- <*£■ ^ 12 22 32 42 S2 13 23 S3 3 3 3 3 3 3 3 3 40 41 SO SI 40 41 SO SI SO SO 40 41 41 44 S3 S4 jqi?i)3222 REVIEW 137 Write and add: 23 34 41 q3 33 S2 6/ 8*2 62 23 S2 4 4/ 32 2b 10 2 I 3 2 4 S 2 b 3 2 3 4 s £> 302 W7 STq bbb 54F 7^2 202 I/O 22 5/ lb How many feet are 125 feet and 42 feet? 342 feet and 135 feet? ADDING 139 See how we add other numbers. How much is 8 + 4 ? 24 How much is 6 + 2? 68 We say: "8 + 4=12," and we write 2. Then we say : " 1 + 6 + 2 = 9," and we write 9. 12 8_ 92 24 68 How much is 24 + 68 ? 92 Write and add : 34 34 34 O 8*7 S't 8*7 3b 25 2b 27 17 IK iq iq 47 24 42 6 8" 57 45 (o3 CX>'J 42q S3b £01 boq 101 101 20S 402 30S 202 S41 b£2 ^3b 43 7 £22 14-2 2b 1 314 20$ 4/0 142 SUBTRACTING From 45 cubes take .30 cubes. How many miles are 65 miles less 60 miles? 265 miles less 160 miles? How many feet are 136 feet less 25 feet? 336 feet less 125 feet? How many pounds are 255 pounds less 140 pounds ? Write and subtract : S2£ 732 bqs* 4qb 321 20 b 302 427 343 20/ 33q 48*C] b8'7 Cj2b SSq 20 b 227 342 5/5 233 57? bq2 gqt 307 558* 227 34/ b20 /Ob 25? ADDITION TABLE 143 The complete addition table is inserted for purposes of review and reference. 2 + = o 3 + = 3 4 + = 4 5 + = 5 2 + 1 = 9 3 + 1 = 4 4 + 1 = 5 5 + 1 = 6 2 + 2 = 4 3 + 2 = 5 4 + 2' = 6 5 + 2 = 7 2 + 3 = 5 3 + 3 = 6 4 + 3 = 7 5 + 3 = 8 2 + 4 = 6 3 + 4 = 7 4 + 4 : = 8 5 + 4 = 9 2 + 5 = 7 3 + 5 = 8 4 + 5 = 9 5 + 5 = 10 2 + 6 = 8 3 + 6 = 9 4 + 6 = 10 5 + 6 = 11 2 + 7 = 9 3 + 7 = 10 4 + 7 = 11 5 + 7 = 12 2 + 8 = 10 3 + 8 = 11 4 + 8 = 12 5 + 8 = 13 2 + 9 = 11 3 + 9 = 12 4 + 9 = 13 5 + 9 = 14 6 + = 6 7 + = 7 8 + = 8 9 + = 9 6 + 1 = 7 7 + 1 = 8 8 + 1 = 9 9 + 1 = 10 6 + 2 = 8 7 + 2 = 9 8 + 2 = = 10 9 + 2 = 11 6 + 3 = 9 7 + 3 = 10 8 + 3 = 11 9 + 3 = 12 6 + 4 = 10 7 + 4 = 11 8 + 4 = 12 9 + 4 = 13 6 + 5 = 11 7 + 5 = 12 8 + 5 = = 13 9 + 5 = 14 6 + 6 = 12 7 + 6 = 13 8 + 6; = = 14 9 + 6 = 15 6 + 7 = 13 7 + 7 = = 14 8 + 7 = = 15 9 + 7 = = 16 6 + 8 = 14 7 + 8 = = 15 8 + 8 = = 16 9 + 8 = = 17 6 + 9 = 15 7 + 9 = = 16 8 + 9 = = 17 9 + 9 = = 18 144 MULTIPLICATION TABLE In schools where the entire multiplication table is taught before taking up a formal textbook, the following table may be used. 1 x2 = 2 1x3=3 1x4 = 4 1x5=5 2x2 = 4 2x3= 6 2x4 = 8 2 x 5 = 10 3x2 = 6 3x3= 9 3x4 = 12 3x5 = 15 4x2 = 8 4 x 3 = 12 4x4 = 16 4 x 5 = 20 5x2 = 10 5x3 = 15 5x4 = 20 5 x 5 = 25 6x2 = 12 6x3 = 18 6x4 = 24 6x5 = 30 7x2 = 14 7 x 3 = 21 7x4 = 28 7 x 5 = 35 8x2 = 16 8 x 3 = 24 8x4 = 32 8 x 5 = 40 9x2 = 18 9 x 3 = 27 9x4 = 36 9 x 5 = 45 10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50 1x6 = 6 1x7=7 1x8 = : 8 1x9=9 2x6 = 12 2 x 7 = 14 2x8 = = 16 2 x9 = 18 3x6 = 18 3 x 7 = 21 3x8 = = 24 3 x 9 = 27 4x6 = = 24 4 x 7 = 28 4x8 = = 32 4 x 9 = 36 5x6 = = 30 5x7 = 35 5x8 = = 40 5 x 9 = 45 6x6 = = 36 6 x 7 = 42 6x8 = = 48 6 x 9 = 54 7x6 = = 42 7 x 7 = 49 7x8 = = 56 7 x 9 = 63 8x6 = = 48 8 x 7 = 56 8x8 = = 64 8 x 9 = 72 9x6 = = 54 9 x 7 = 63 9x8 = = 72 9 x 9 = 81 10 x 6 = = 60 10 x 7 = 70 10 x 8 = SO 10 x 9 = 90 1HV