oe Prep the od: sereres #: THRE HAH Lut iy, it Wer HM setae iit Bot, F CHibhy ah . giuer eee ditt iy " jeepney yay my rit ! un pris) AH aster stre HE Rsiarteet att: iad 53 +4: hata re BH SH FUT Ate Digitized by the Internet Archive in 2022 with funding from University of Illinois Urbana-Champaign https ://archive.org/details/childrensarithme01 chan Su if “std ah aAYyS cepqayyicon EMO AE ad enna CHILDREN’S ARITHMETICS BY GRADES GLOBE SERIES Meio i) b OOK NUMBERS BY WILLIAM E> CHANCELLOR, M.A. SUPERINTENDENT OF SCHOOLS, BLOOMFIELD, N.J.- & GLOBE SCHOOL BOOK COMPANY NEW YORK AND CHICAGO Copyright, 1901, by GLOBE SCHOOL BOOK COMPANY. Morea. “Tf a child learns how to use the text-book, he learns how to make use of the experience of mankind. The text-book enables the child to do individual work for himself, and helps him to become independent of oral teaching.” Wate wR RIS, United States Commissioner of Education. MANHATTAN PRESS 474 WEST BROADWAY NEW YORK eS ees eet MATHEMATICS LIBRARY mer PREFACE For boys and girls who know the numbers from one to ten thor- oughly, there is here about a year and a half’s work. When should boys and girls begin to study numbers in books? As soon as books can help them forward to the mastery of numbers. This time comes as soon as children can read. How should boys and girls study numbers? The interrelations of number-facts and of number-principles are such as to make progress very slow and very difficult through their intricate maze. Is there any Ariadne’s thread to follow through the labyrinth of numbers? Is number ratio or counting? Is it comparison, or magnitude, or multitude? Is it a logic of thought, which can be analyzed after the topical style, — addition, subtraction, multiplication, division, rule of three, and so forth,—of which we may complete one part before beginning the next? Shall we learn every discoverable fact about twenty before taking up twenty-one, or every conceivable fact about 4 of § of 3 of 42 before taking up liquid measure? ‘This book is neither “topical” nor “spiral” in plan. Its substance is neither ratio nor counting. Its purpose is to conform numbers in their facts and principles to the usual processes and powers and interests of children’s minds. The graded reader has opened the way for the graded arithmetic. Grading all books is part and parcel of the new education, which means to discover and to obey the facts of the child-mind, its methods, nascent periods, and order of growth. The core of the concentric theory is recognition of the value of finding something that is known even in the mass of the unknown. Let us not hesitate in schoolbooks as we do not hesitate in life to branch out into the new and to return again to the old. Because comparing is the root and numbering is the top, let us not forget reasoning which is the main trunk of arithmetic. _The child’s knowl- edge of arithmetic should grow as evenly in all directions as the most careful and the most open-minded education can secure. 5 4642433 6 Progress in education is largely a matter of progress in power to understand books. Oral instruction may be continued too long as the sole medium for imparting knowledge. ‘This book is rather for reading and study than for the setting of many exercises in writing figures. It calls for oral expression far more than for written work ; but it is meant to call most for the quiet, studious effort of the child to think through the number-processes for himself in the light of the instruction of the teacher and of these pages. Many minds, of adults as well as of children, cannot at once comprehend principles and facts explained orally. We often need to see the printed words, and slowly and patiently to think out their truth and meaning for ourselves. We remember with more than twofold certainty what we have verified for ourselves after hearing from others. The value of numbers in real life is such as to warrant illustra- tions in the pages of text-books, both in topics, such as the clock, thermometer, calendar, and house address, and in pictures, which add to number the same interest they add to reading. Children are not alone in their frequent inability to realize in imagination a word-picture. Teachers are entirely justified in asking for their endeavor to awaken children to vigorous mental life the attraction of illustrations, and ought to seize every opportunity offered by arith- metic for training them to see, to image, to compare, and to represent the visible realities of the world. Author and publishers desire to acknowledge the valuable sugges- tions of Principal W. B. Gunnison, Ph.D., of Erasmus Hall High School, Brooklyn, N.Y., in reviewing the proofs of these pages. Wo BC: BLOOMFIELD, N.J., March 25, 1901. ai 2. | —_— -_ SUGGESTIONS TO TEACHERS 1. The preface explains the general purpose of the book. 2. Read the book itself. The purposes of certain special features will appear only when seen in relation to other features. 3. Do not hesitate to use in advance of the order in the book facts which appear later in these pages. 4. While the purpose of number-study is to learn numbers, oral language expression needs to be encouraged. Develop the number- story features of early primary work as much as time permits. The speaking of English sentences tends to promote that rational under- standing of number-processes which is the end of Arithmetic as a science. 5. See that the children do study this book, but do not ask them to study quietly over a quarter of an hour at any one time. Children tire quickly and recover even more quickly. 6. Drill for the sake of instant accuracy; but do not follow any drill to the point of over-fatigue. Take great care not to drill upon things not essential. 7. This book is only a collection of suggestions; it is not an en- eyclopedia of devices. Seek great variety in methods and devices. There are children who will not learn things in our ways. Try to find their ways of understanding number-facts and number-principles. Since historically our decimal system of counting by tens has grown from our having ten fingers, and since the authority of modern mathe- matical philosophy distinctly asserts the naturalness of counting upon the fingers, such counting should be permitted as a helpful stage in number-progress, but not to the extent of establishing a physical automatism. 8. Every child has peculiar interests. Find them. For number- stories use facts which interest the various children. Remember that children have their “good” and their “bad” days. On their good days children sometimes learn an amazing amount of new matter. 9. A boy or girl may be ready to undertake harder work than this book offers before knowing this book from cover to cover. Yet we should not forget that doing easy things over and over begets confi- dence, which supports us in our attacks upon new and harder problems. 10. Neatness in writing tends to accuracy in all number-operations. od ( LESSONS READING NUMBERS AT SIGHT Sizes, Forms, ANGLES Numsers 1 To 10, REVIEW READING NumBers, 10 To 100. FRACTIONS. Facts or NumsBers, 11 To 20 Money DIVIDING AND MULTIPLYING AND PARTING TABLE OF Twos, AND HALVES TABLE OF THREES, AND THIRDS TELLING QUANTITIES Days OF THE WEEK RaTIos TABLE OF Fours, AND FourRTHS TELLING WEIGHTS NumBeERrs, 21-29, 30-99 TELLING LENGTHS HunpREbDS, THOUSANDS ADDITION, SUBTRACTION House NuMBERS Fives anp Tens, Firras anp TENTHS SIxES AND TwELves, SrxTHs AND TWELFTHS. DATES AND CALENDAR TELLING TIME . TreLtinc HEAT anp CoLp Music Notes NuMBER TABLES AND TESTS 96, 101-102, 105 PAGES . 9, 60 10, 20, 113 fi 15-18 22-27, 86-87 28-67 , 81, 43, 98 . 82-36, 56 - 88-39, 45 46-47 48-49 Ant 66-69 eye MET 74-82 91 . 65, 85, 97 108 106-107 108-109 114-115 116-119 120-121 . 122 126-128 HOW MANY ? TELLING NUMBERS AT SIGHT Number always means number of ones. ; How many ones? @@@ How many ones ? ee Fay. me @ @ Find twos and How many twos‘ ® es J ee threes. AAG How many ones? Find five and one. eee How many threes? Look across. How many twos ? Look up and down. eeee low many twos? Find threes and two. @@@@ How many fours? Find five and three. How many threes? Find two fours and one. ee0@ ; eae eee Find six andthree. Find seven and two. @@@ Find five and four. Find eight and one. eceee@ ow many twos? e ms eo @ . e eeee@ 7 many fives ? 2 How many fives ! ©eee | '@ @/\'|@6' & How eo. e600 ee many ? | @®@ e dnd x =< e ee J e@ 8 @8e @ Counting adds ones, or puts units together. Adding finds what new number tells all the ones in other numbers taken together. Subtracting takes a number from another number. Multiplying adds one number once or several times to itself. Dividing finds how many times a number contains another. 9 WHAT KIND? 10 HOW MUCH? COMPARISONS / Count these dots @ @ @ @ @ and crosses X X X. - We cannot add dots and crosses together because they are | not the same kind of ones or things. Count these circles O O O O andsquaresO OOOO. , Can we add circles and squares together? Why not? TS — Number always means number of ones of the same kind. This picture shows one inch square of I oleae Draw one EACH SIDE IS ONE square inch on paper. INCH LONG el But this picture shows two inches square of paper. Draw one square inch on paper, then on the blackboard. How many square inches do you find in this two- inch square picture ? When Mary would like two pieces of red paper, she should tell how large she wishes the pieces to be. Telling the size or amount or weight is called measuring. We find How many? by counting; and How much? by measuring. ov. 11 STUDY ORAL * ALL FACTS OF 1 TO 10, IN REVIEW Additions : 1+1=2 14+6= 7 24+38=5 24+8=10 38+7=10 1+2=383 1+7= 8 24+4=6 8+38= 6 44+4= 8 14+38=4 14+8= 9 24+5=7 384+4= 7 445= 9 144=5 149=10 246=8 845= 8 4+46=10 145=6 242= 4 24+7=9 384+6= 9 5+5=10 Subtractions : 10—9=1 9-8=1 8-6=2 [7-—4=38 9—3=2 10—8=2 9-7=2 8-5=3 6-5=1 4—3=1 10-—7=3 9-6=3 8-—4=4 6-4=2 4—2=2 10—6=4 9-5=4 . 7T-6=1 6-—38=3 38—2=1 10—5=5 8-—T=1 7—d=2 5-—4=1 2—l1=1 Multiplications : Bete ee comb 2X de 8 Ko 10) ox a=9 Divisions : 10+5=2 8+4=2 9+3=3 6+3=2 4+2=2 QUESTIONS 1. How many are 545? 6. How many 3’s in 9? 2. How many are 10—5? 7. How many are 8—4? 3. How many 5’s in 10? 8. How many 4’s in 8? 4. How many 2’s in 10? 9. How many are 247? 5. How many are 9—6? 10. How many 3’s in 6? + means and, — means less, x means times, 9+3 means, How many 3’s are there in 9? 4+, —, x, and + are called Signs. WRITING 12 PRACTICE BLACKBOARD With thumb and fingers, hold the chalk crayon under the palm of the hand, and use free arm movements only. Blackboard figures should be three inches high. These figures are three inches high. » COMMA eed » PERIOD ONE INCH Se ee be ee ee eee 0 1 2 3 THREE INCHES Write on the blackboard five times with commas and Pe ic| Re2ee 3) ek evans Mama AEC! ~ 13 WRITING PRACTICE PAPER WITH PENCIL Write with a soft lead pencil. BOO 11640 Pencil figures should be at least one half inch high like these. Each side of this square measures one half inch. We call this a half inch square. There are only ten signs for numbers, and each sign is written by itself. Most children, if asked to try, soon make figures both clear and beautiful. Mayrite |, 2, 3, U, 5, 6 1, & Gd, 0 meric Od. |, 6, 5, U, 3, 2, 1. ere Oth (913 (15, Losi] 161g erent 20, 21,.22,23, 21 95,2621, 2890. 5. Write 30, 31, 32,33, 34,35, 3b, 37,38 3d. 6. Write UO,U/,U2,U3, UUU5,4b,U7,48,4q. SPELLING OF THE NUMBER-NAMES 7 Lone. 92. two. -o, turee. 4four. 95, five. © 6.'six, 8. T,seven. 8, eight. 9, nine. 10, ten. 0, cipher or zero. 9. ll,eleven. 12,twelve. 13, thirteen. 14, fourteen. 15, fifteen. 16, sixteen. 10. 17, seventeen. 18, eighteen. 19, nineteen. 20, twenty. 30, thirty. 40, forty. 11. 50, fifty. 60, sixty. 70, seventy. 80, eighty. 90, ninety. 100, one hundred. ORAL 14 TEACHING TEN, 10 We always count by ones. We say that one and one are two, two and one are three, ten and one are eleven, twenty and one are twenty-one. If we would like to add three apples and two apples, we must know that we are counting three ones and two ones; we must know that three and one are four, four and one are five. eee-+trteeee~=>->-eeee e@ 3 2 MYA GP wc 1) Until we reach the number ten, each number has one figure as its sign. ‘The sign of one is 1, of five is 5, of nine is 9. But when we reach the number ten, we find a number which has two figures as its sign. The sign of ten is 10. In this sign 10 are the figure 1 and the fig- ure 0, called zero. ‘This 0, or zero, with a figure before it at the left as we look at it, shows that the figure means ten times the number of ones for which it stands when it has no 0, or zero, before it. 10 means 1 ten, 20 means 2 tens, 50 means 5 tens. yf 9 e eee are | ten, ee oe ee ee are 2 tens, or ONO 195 OT Or LOS tell Woke ene On ae enO man Osu \vn Te All these dots together are 8 tens, or 30, thirty. Whenever a number has two figures, the figure to the left of the zero tells how many tens are meant. AGC aL eee Add 10 eeee eoe e + 6 eee 6 @eee8 eee | sixteen 16 15 ORAL TEACHING STUDY NUMBER-NAMES ABOVE TEN We call ten and one, eleven; ten and two, twelve. Most number-names for more than twelve things are names made of the single number-names from one to twelve. We call ten and three, thirteen, which is very much like three-ten. Four and ten are fourteen; five and ten, fifteen; six and ten, sixteen; seven and ten, seventeen ; eight and ten, eighteen; and nine and ten are nineteen. Read these numbers: 10, 11, 12, 18, 14, 15, 16, 17, 18, 19. @©eee# eee 0@2@080 @ e ie are ten. e ie ee are two tens. e@eeee @eeeoe @808280 @ Two fives we call ten. Two tens we call twenty. A great many years ago people called two tens, twain tens; then they used to call two twain. Twenty and one we call twenty-one; twenty and two, twenty-two; twenty and three, twenty-three; then we have twenty-four, twenty-five, twenty-six, twenty-seven, twenty-eight, and twenty-nine. Give the names for these numbers: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Read these numbers: 25, 24, 26, 28, 22, 27, 21, 29, 20. Three tens we call thirty. ‘Three tens and one we call thirty-one. Four tens we call forty. Fifty means five tens. Sixty, six tens. Seventy, seven tens. Kighty, eight tens. Ninety means nine tens. We have another name for ten tens, one hundred. 10 ten 16 sixteen 30 thirty 90 ninety lleleven 17seventeen 40 forty 90 +1= 91 12 twelve 18 eighteen 50 fifty 90 ++ 3 = 93 13 thirteen 19 nineteen 60 sixty 90 +5 = 95 14 fourteen 20 twenty 70 seventy 90+ 8= 98 15 fifteen 21 twenty-one 80 eighty 100 one hundred READING 16 WRITING COUNTING : sae ot ere Count by twos, beginning at 2. 2 + 6 Br SheeO ci. tL 2ae ea LO ames 20 BP) UDA) QOV (2B SU) 9-320 parte anes ne 40 BF, AL: 946): 4B OO) 8b2e sate hob ee 60 Bee GG4 yi 60°: OBR 0°) Tizai aid tee wes 80 62984: 86) 1884-90. 9270 Os) §O6" Sos eee These are called the even numbers. 2 divides each number without a one left. Count backwards, beginning at 100. Count by twos, beginning at 1. = 1 3 5) T cel dn] OS 99) 1 See 19 Ble 23-225) 7 2 295 eh eae eed eee 39 Al} AS. 450° AD SON Ole, (0375 dary aoe 59 Bie 6o: ~ + Oo 00 et OO eT Lai Fo gee ee 79 Bo) 8S yhoo Ly ASO) weele, 905 Sao 99 These. are called the odd numbers. 2 divides no num- ber evenly. One is always left over. Count backwards, beginning at 99. Count by threes, beginning at 3: then backwards. BY 6. (Qo), 12) Loe BLS peel eee, oe 386 39 42 45 48 S51 54 ST 60 638 #42466 12) 1) 7°18 Sde sh84 2 87,190) 195 eee 5 10 °° 15 20 925) 30 35) 40 ae 5d 60.1 .65.-_.10 © 1x 80'S SS ee OOls as ere Count by sevens, beginning at 7: then backwards. 7 14 21 28 35 42 49... a 56 63 70 TT 84 91 98 17 COUNTING THINGS TO DO 1. Count all the boys in the room, giving them odd numbers, and all the girls, giving them even numbers. How many are there in all? Can each boy and girl remember the number given to him or to her? 2. Cut out about thirty squares of paper. Write the numbers to thirty, one number on each square. 3. Cut each square into two pieces, and using the vther side of the paper, number each of the pieces. 4. Draw lines like these, but longer, so as to make more squares, and number each of the squares. Cut _ the squares apart. 5. Count the number of panes of glass in all the window sashes of the classroom. 6. Count the number of desks in the room, and then the number of chairs. Write each number for the desks upon a piece of paper, and place it on the desk to which it belongs. : 7. Count marbles, shoes, hands, fingers, hats, caps, pencils, splints, blocks, and other objects, as far as one hundred. 8. Read the numbers of the pages of this book as far as one hundred. ) 9. Count the number of lines of print upon this page. 10. Write the number of the house where you live. 11. How many chickens, or sparrows, or ducks, or cows, or horses, did you ever count together at one time ? WRITING Sri PRACTICE 6. NUMBER TABLE mann CMH. 1p ames ete) 19) Dh 19. DD SOMO! 5 Db Oe cece (3? 238 Ses 5B Sree ae eda Paola Bree Mb RMS MED oy WE PLE ck 1) 8 PeyeMonsi an Ulayiotsieor fs. wo ci Ib 2636 Ub5bbb7b &b Gb F129 37) 4] SiOet See Sale 16 2838 US 58 bE 18 FE G8 Id 2434 44596414 8q qq [0 20°30 05.050 | 06/6 ad Onnore Write ten, eleven, twelve, thirteen, fourteen, fifteen. BO OV la Ome eae GU Write sixteen, seventeen, eighteen, nineteen, twenty. Write twenty-one, twenty-two, twenty-three, twenty-four. 21 22 23 24 Write twenty-five, twenty-six, twenty-seven, twenty-eight. 25 26 27 28 Write twenty-nine, thirty, forty, fifty, sixty, seventy. 29 30 40 50 60 70 Write eighty, ninety, one hundred, one hundred one. 80 90 100 e GLOd 19 BUSY WORK THINGS TO DO We can use instead of dots: eececee5aeeee Deere et ee. Se circles like this O, or eceoeoeveaeee0e crosses like this x, or Barer ne: 22. @ 6.0 © signs like this +, or @®eeeee?3d?s8 ee . : R triangles like this A, or eeeeeeee?ees © 5 : ] wate e@e6eee¢e squares like this UO, or eee oer, © © any forms, such as these, — @eeeeee?e?e? ee @ee7eee%ees8es ee OHRVOG 1. Make 100 dots on paper or on blackboard. 2. Number these dots or squares 1, .2, 3, etc., like this e or this [. 1 l 3. Make lines around every 2 dots like this, @ e) 4. Make lines around every 3 dots, G3) or @ +) 5. Make lines around every 4 dots, every 5 dots, every 6 dots, every 7 dots, every 8 dots, every 9 dots. 6. Connect every dot with all the dots next to it, like this, — 7. Use red chalk or pencil and mark every alternate dot which has an even number, like this @ or this @). 8. Use blue chalk or pencil and mark every alternate dot which has an odd number, like this e or this @). 9. Mark with blue, or yellow, or red chalk every third, every fourth, every fifth, every sixth dot, ete. Use new sets of e, or (, or + tables except for 1 and 2. DRAWING 20 FORM With a stick, or a splint, or a pencil, we can rep- resent a line across, or}| up and down, or slanting up to the right, or down to the right. With two ea pero we can make & CTOSS ora T or an angle like this sticks we can make a form like this It is called a triangle because it oN has three angles. With four sticks each of the same length, we can make squares like this If we have a pair of sticks of the same length, ae and another pair of sticks longer than the others, three or P| or this Try and see. With two like: these ean two like these ———————==,, we can make a_-rectangle like this If we draw a line through our rectangle eee to opposite corners, we have two triangles inside the rectangle. If we have the longer sides twice as long as the shorter sides, then inside our rec- tangle we have two squares. AAT ORAL TEACHING STUDY PARTS OF FORMS How many little squares do you find in this large square? This square is two inches wide and two inches high. ‘ When things are exactly like each other in size, we call them equal. If you find inside of the square A four squares each of the same size, then all four parts of A are equal parts. MEASURE MARKED IN INCHES Is this square as large as the square marked A? Is it as large as any part of A square ? Measure this square B, using a ruler marked with inches; cut a square out of paper of the same size as B, and : see how many little squares as large as B you find in A square. If you find that square A is four times as large as the square marked #, then it is right to say that B is one fourth as large as A. If A is four times B, then BP is one fourth of A. If A is 4 x B, then B is } of A. ORAL TEACHING 99 STUDY EQUAL PARTS OR FRACTIONS A number is always a number of ones of the same kind. A fraction is always one or more of the equal parts of some one thing. eC Co Ee Here are four forms, A, B, C, and D. Each is of a different size from the others. A is divided into five parts. Bis divided into four parts. Cis divided into two parts. JD is not divided. Each part of A, each part of B, and each part of C is the exact size of D. There are 5 D’s in A. Count and see. There are 4 D’s in B, and 2 D’s in C. Each part of A is equal to every other part. The five parts are equal. Each part of B is equal to every other part. The four parts are equal. One part of Cis equal to the other part. We ¢all equal parts fractions. Each part of A is a fraction of A. There are five parts. Each part of A is one part of A. We print this, 4. The 1 above the 5 means that we are taking one part. The 5 means that there are five equal parts in A. Each part of B is a fraction of B. There are four parts. Each part of B is one fourth of 6. We print this, 4. The 1 above the 4 means that we are taking one part. The 4 means that there are four equal parts in B. Each part of Cis a fraction of C. There are two parts. Each part of Cis one half of C. We print this, 4. 23 ORAL WRITTEN REVIEW Can you tell what number separates the numbers in these abs 10. questions, 1 to 9, below ? Bote 14. re eae 7, 10-20-3040; p—Ve1G—1 7; Beli, ere . 8-12-16-20.. 6. 10-17-24-31. 9. 5-13-21-29. Write on the blackboard five times without commas and period : aL. nbs Ee BS voMyeSnsO: 4S" 5 U3) O | Write on the blackboard five times these numbers: 10, 12, 28, 34, 45, 5b, by, 18, 89, 90. 12. 35, Write on the blackboard five times these numbers: Db, 579, 680, 258, 813, 4490, __. SE The rectangle is not divided into equal parts. The rectangle is divided into two equal parts. Each part is one half the whole rectangle. _ ae ee The rectangle is now divided into three equal parts. Each part is one third the whole rectangle. O is 3, one half, of M, for there are 2 O's in M. Sis 4, one third, of M. Why? ORAL TEACHING 94 STUDY PARTS OF NUMBERS What part of A is a? B= a, [ie] B is one half of A. A equals 2 B’s. A B jf ee ») fod falala| What part of Cisa? C=3 B’s. B is one third of C. a= of C. C ke How many dots do you find in B? How many dots do you find in A? A B 4=2x2. 4 are twice two. ale 2=40f4. One half of four 1s C two. b= 24 x) 08) OW erlind Ber ees r= . <3 Oe, e @ 2 Z=— 1 01 6. One third Of Six 18 Uw0-. | @2e 6.6 esetnes hese are pictures of the two fractions B 4 and #. We call the picture-fractions 4, one half, when we think that A=2 B's. pe |e! poe Then B is only $ of | | A. pele ie} We call the pic- A B ture-fractions 2, two Be ee fourths, when we think that A’s 4 dots = 2x B’s 2 dots. Bs 2 of A. 4 is the same amount ot value as 4, A 25 ORAL TEACHING STUDY PARTS Cut out of paper a square one inch on each side. Then cut out a rectangle two inches long, one inch high. The square is one half as large as the rectangle. Cut the square into two equal parts, one inch by 3 inch. Cut the rectangle into four equal parts. Do you see that the 2 parts of the square are ? of the rectangle ? There are 5 equal parts in A. falo]elale| Each is } of A. A a+ 6=2 fractions of A = 2 of A. a+b6+c= 8 fractions of A = 3 of A. a+6b+e+d=4 fractions of A= 4 ol A. a+b+e+d+e=5 fractions of A = 32 of A. But as there are only 5 parts in A, 3 of A =all of A Peel cA. A This form-picture is divided into two parts, b+¢e. b=tof A. c=4 of A. Leal The picture of 6 is divided into three parts, d,e,f. d=}ofb. e=} of b. P ; f= of b. If we divide ¢ into three parts, then A will have 6 parts. If A has 6 parts, then d=} of A. d= of 4 of A, because d is $ of 4, which is 4 of A. 9 . 2 4+dthtd=? 9 dthe? 1 i aay Ye ey Sane ac ia ome Cut and fold pieces of paper to show the answers to these six questions. ORAL TEACHING 26 STUDY PARTS OF NUMBERS 5 names 5 |’s 5=I|1111 1=+} of 3 names 3 |’s 3= Ill 1=4 of 4 names 4 |’s 4 = | 1=} of 2 names 2 Is 2= |] 2=1 of 2 When we say one fifth of anything, we mean that the thing is divided into fifth parts, into five equal parts, and that we are talking about one of these parts. When we say one fifth of any number, we mean that the number is divided into fifth parts, into five equal parts, and that we are talking about one of these parts. Here is a picture i . There are 2 rows up and down of the number ten ee of 5dotseach. The 10 is divided seen in dots. * © into 2 equal parts of 5 each. e@¢ There are also 5 rows across of 2 dots each. The 10 dots are divided into 5 equal parts of 2 dots each. We can say that e e are $-®—— of 10 dots, or +. Zidotes ao eat.* 2x — 10 2=10+5 2 is ¢ of 10 2= 10 ee We can say that $e° are *® of 10 Ye Can Say 1at ee are 10 O . Dix 210 5=10+2 5 is 3 of 10 5= 10 Ve Adde8 Atl) CO A ine ieee es 2 ee 1 (14 SS 6 ae 2. Added : Bo A) ee Ae oes V4.2. 8 (27 ORS 0 ee 27 COMPARE STUDY PARTS OF NUMBERS Sometimes we take things apart. We split a piece of wood into separate pieces; we cut an apple in two; we spend a quarter of a dollar, which is a part of a dollar. . When we make two equal parts of anything, we call each part one half. The figures for one half are . When we make three equal parts, we call each part one third: 4. Each part of four equal parts is one Sess or one quarter: }. After these we have one fifth: 4. A igun Maaeed erarrkee or ec A: B has 2 A’s. D A Measure these lines C has 3 A’s. A and see if these stories D has 5 A’s. A are true. We can take parts of form-pictures. & in Ee We can take parts of number-pic- aS] in tures. We can take parts of numbers. I Ct CO|t bo] wah in 4 bo @ @ We can tell parts by figures. When the parts of anything are equal to each other, then we call the equal parts fractions. There are ten onesin ten. There are three ones in three. eas pele [2 Lote], ee a tenths of the whole figure is } inch long, how long are =; of it ? Three are three tenths of ten. 3= to of 10 ORAL TEACHING 98 ANSWER ELEVEN, 11 If we have ten things and add one thing to them, the name of the number of all these things together is eleven. ee @0@ 0C000000000+0 Morph 6 6.7 8 Blow T ae ne cae 4 10 + 1 are eleven. Ten and one are eleven. 11 We write eleven with the figure 1 twice: 11. In the figures 11 for eleven, the unit one, 1, has the place of the zero, 0, in the figures 1 and 0, printed like this: 10, for the number ten. : In the number eleven, printed as 11, the second < 1 shows that the first 1 stands not for one, 1, unit, e but for one ten, or 10. 11 means 1 ten and 1 unit, ; like this group of dots: zi @ @ 8+3=11 7+4=11 6+5=11 11—5=6 1041=11 94141=11 54541=11 24+384541=11 11—1=10 11—2= 9 94+2=I11 7+2+4+2=11 With splints and counters, show each of the above facts. 1. John had five cents and Tom had six cents. How many cents did they have together ? 2. There were ten boys; one of them had two cents, nine of them had each one cent. How many cents did they have together? 3. Mary had eleven cents. She spent four for apples at one cent each. How many cents were left? 4. ‘Tell number-stories about cents, using these number- facts: | 11e— 1515 2 LOS 9 te a eee 5, Add shloms (00.0 sie ea sibtractege Lelie deen 99 ORAL MEANING OF SIGNS The sign of multiplication is x; it means times. The sign of division is +; it means divided by. ? asks a question. It is called the question mark. When we ask 10 + 1 = ?, what does the + mean ? What is the answer to 10 +2=? What does this. mean? What is its name? 1 4 3 4. What is the name of this mark ,? 5. What does this mark + mean? And this —? 6. Read these questions in words: 83x3=? I11=8.x? and how many over? 6+5=? ieee 68-711? «61142? 848 424-14+7=11. ELEVEN 7. Is eleven an odd or an even number? Why? What is the next number after 10? before 10? . . How many more are 11 than 10 things ? 10. George had eleven marbles and Charlie had 8. Which had more than the other? How many more did he have ? | 11. Take 11-splints. Make 2 squares with them and one triangle. 12. How many triangles can you make with eleven splints? How many splints are left over ? a QS Se SSE es ier ae am at en ES oy Teed a A GD. ig ao 14. Can you remember several numbers when written on the board and then quickly erased? ‘Try and see. ORAL TEACHING - 30 ANSWER TWELVE, 12 If we have ten things and add two things to them, the name of the number of all these things together is twelve. +. ee @ @ e 2999999999199 coc ces tie 10 2 10 + 2 are twelve. Ten and two 12 are twelve. We write twelve with the figures 1 and 2: 12. In the figures 12 for twelve, the unit two or figure 2 has the place of the zero, 0, in the figures 10, for the number ten. In the number twelve, printed as 12, the figure 2 shows that the figure 1 stands not for one unit, but for one ten or 10. 12 means 1 ten and 2 units, like this group of dots: In the numbers eleven and twelve, printed 11 and 12, we say that the 1 in each number where it is the first figure, reading from left to right, is in tens’ place and that the second figure in each number is in units’ place. 12 things make one dozen. When we say, “ Mary’s mother who keeps hens sent b] Mary with a dozen eggs to sell to the grocer,” we mean that Mary carried twelve eggs. 10+2=12 9+3=12 8+ 4=12 T7+5=12 !-—6= 6 12= (=o) 12-10] 29 12 ee Show each of these facts with counters and dots. 1. Tell number-stories about cents, or eggs, or marbles. 2. Mary has seven dozen eggs and Susan has five dozen. How many dozen have they together ? a ee 1 copper penny is worth 1 cent. 31 PENNIES, NICKELS, ORAL WRITTEN AND DIMES The sign, | ¢ 1 nickel is worth 5 cents. We can write nickel, 5¢ 1 dime is worth 10 cents. We can write dime, lot 1. Grace bought half a dozen of cookies at 1¢ apiece. She gave the baker a dime. What change did he give her ? 2. I paid a nickel for half a dozen pens. cents would a dozen pens have cost ? How many 3. 10 pennies are worth 1 dime. 2 nickels are worth 1 dime. Why? 4. Which would you rather have, a dozen pennies or a dime ? Why? 5. It usually cost# 5¢ for a man to ride on the street cars, and 3 cents for a boy. How many men can ride for a dime? How many boys ean ride for a dozen pennies ? 6. Did you ever see a pile of a dozen pennies ? 7. Write on the blackboard a story about pennies, nickels, and dimes. OTHER NUMBERS 2+7=? 5+3=? 6+2=—? 7—4=? 3+6=? 3+7=? (—o=? 9—4—" 9—6=? 10—9=? (+3=? 9—2=—? 14+9=? 9—1—? (1+2=? 6+4+4=—? 10—3=? 444—' (—4=? 8—6=? 94+1—? 10—4=—? 4—3= §+5=? 10—2=? 9—5=—? 10—5=? 4—6=? 10—8=? 24-8=? 10—1=? 84+2=? 1+1=? re a 5—2=? STUDY 39 ANSWER : DIVIDING AND MULTIPLYING 12=—6+46 be? = 12 1232 3.6 Add 6 Subtract 12 6 6 How many are4+4+4? 8x4=? How many are 3+3+4+3843? 4x3=? In 1 above how many 4’s do you count ? In 2 above how many 3’s do you count ? Show 1 and 2 by splints, counters, pennies, or dots. Is it true that 8 x 4=12 and 4 x 83=12? When we find how many fours there are in twelve, we count 4’s until we reach 12. 4+4are 8. 844 are 19. There are three fours in twelve. Multiplying, or finding one number times another, is rapidly adding one number to itself. Dividing, or finding how many times one num- ber contains another, is rapidly taking away the same number several times from another number. 12—-4=83. We find three fours in twelve. er NUMBER-STORIES 7. Charlie had twelve apples; and when four boys came to see him, he wanted to give each of them the same number. How many could he give to each? 8. There were two boys who had six marbles each. How many did they have together ? 9. Lulu had an afternoon tea-party. Her mother gave her a dozen tea-biscuits. She and Clara and Mabel ate them all; each ate as many as the others. How many did each eat ? 89 STUDY ANSWER MULTIPLYING AND DIVIDING ask 5x2=?, what does the x mean? And what does the ? mean? 1. When we And what does the = mean ? 2. What is the answer to 5 x 2=? 1+1=2; or there are two l’s in 2; orl x2=2; or 2x1=2 3. 1+1+1=8; or there are three 1’s in 8; orl x $= 8s or 38 x 1= 3: 4. — is the dash or blank mark. Can you fill in the words or numbers that are left out as shown by the dashes ? In 5 there are 4 apples at 1 ¢ apiece will cost — cents. In 6 there : In 7 there are — 1’s; or 7x 1=—. 5 1+1+1+1=4; or four l’s=4; or there are four 1l’s in 4; or 4 times 1 are 4; or4x1=4. 94+2+4+24+2=8: or 4 2’s=8:; or there are four 2’s in &. Bee eas 2x5=? Dea b+-2=7 6+3=? 8+4=—? AM Zee Dor aat 10+2=? 10=5x? 8=2x? aX t=30 9+3=? 9+5=?+? T+38=?+? 6+8=? 12+3=? 12+5=?4+? 12+4=? 11+-3=?+? A dozen cents less a dime = how many cents? 7, 1+1+1= 83; or three l’s=3;3 or 8x1=83. 2+2+2=6; or three 2’s=6; or 3x 2=6. 8+3+3=9; or three 3’s=9; or 3x 3=9. WRITTEN 34 REVIEW 1. Subtract: 5 fp 9 eg ake | ake Hae) eh 5 6 ea 2. subtract : 10 8 10 T 8 10 9 6 Bais lente fr 2) pubdiuracue LU 9 T 4 6 8 6 8 SOTO WEES OD Se 4: Add: 5 6 2 Se ol. 25. Subtract. Zeal ela rf 6 10 3 11 V Gas Pap 3 Gu aL 6. Copy and answer: S—7=) lO 6-e) MOS ae? + ee 6—?=2 o+?=10 10=7+4+? 10=44+? 10—T=? - 10—2=? F842? 2.447210) 93-47-10) 984 "= 10" eee ee UO oe 10—?=7 10-—?=4 2-—?=5 7+?=10 9-—?=4 o—?=2 6=?+4 10—?=4 Write in words your answers to these next two ques- tions: 7. Two boys had 5 pennies each. Another boy had 2 pennies. If they had put them all together, and had then divided them equally, how many would each have had? 8. They did not do this, but when still another boy joined them, they bought for one cent apiece as many doughnuts at the bakery as they had cents, and divided the brown doughnuts equally, as many to one as to an- other. How many doughnuts did each have ? 9. Tell stories about 12 — 6,6+6,44+4+4, and 6 x 2. 35 STUDY ANSWER DIVIDING Often we write division-questions in this way 3 lO This means just the same as 10 + 2=5. 5 We may read 9 )| QO either 10 divided by 2 are how many ? or how many 2’s are there in 10? @eeee @eee?e may think of them as divided into 5 x 2 dots or 10 dots + 5 e | e | @ | @ | ® @'e/e@|e@/@ Here are ten dots We can show that we by drawing lines between every 2 dots or as divided into 2 x 5 dots or 10 dots +2 by drawing a line oD between every 5 dots ©9ee8s @ Dividing is the opposite of multiplying. Dividing is taking numbers apart; multiplying is put- ting numbers together. SOMETHING TO DO 1. Take 12 splints or counters. Separate them into one bunch of 6 and another bunch of 6. This is dividing 12 splints by 2. How would you divide 12 splints by 6? 2. Take the 2 bunches, each of 6 splints, and put them together. This is multiplying 6 splints by 2. What would you do to multiply 2 splints by 6? pele oe Ie 8 KAS Ax BS Answer these questions by dots or counters. 4. 2)4 2)6 2)8 2)10 2)12 3)6 3)9 3)12 mS 4)12 5. A grocer sold half a bushel of onions. What part of the bushel did he have left ? 6. One half of 6 splints = how many splints ? STUDY 36 ORAL DIVIDING WITH A NUMBER OVER 1, Find3’sin?. 2x38=6 641=7 7+3=(8x2)+1. 7 divided by 8 are 2 and 1 over. 2. Find 4’s*in 11.92 x 4] 8) “Sse oe eae = (4 x 2) ta 3. 3. How much is 12+5? 12 divided by 5 are 2 and 2 over. 4. 5)1l. Five is found in 11 twice and 1 over. 5)11 41. 5. T)12 "T1246 ‘6. 8)10' 29 49 do ee 7. 12+10=? 8+5=? 9+8=? 124+9=? When you see these marks (_ ), called parenthesis marks, around numbers, they mean that we must do first what the sign inside says: (8 x 2)+2=? means 8 x 2, which are 6, then add 2=? The answer is 8. But the answer to 8 x (2+ 2) is8 x 4=12. REVIEW s. If I owe you 4%, and give you a dime, how many cents must you give me back? 9. A piece of ice weighed 10 pounds in the morning. In the evening it weighed 2 pounds less. What was its weight in the evening ? 10. Harry bought a bottle of ink for 3 ¥, a pencil for 1¥. He gave the clerk a nickel. Should the clerk give him any change ? 11. Make a story about 3 and 4; about 2 and 5; about 6less1; about3andland2; about 12 +6; about ll +5; 10 + 4. 37 ORAL QUESTIONS 1. How many two-cent stamps. can we buy for a dime? How many can we buy for a dozen pennies ? 2. Frank is 10 years old. His brother is 4 years younger. How old is his brother ? 3. Edgar has a dime. Willie has a nickel and 3. How many more cents has Edgar than Willie ? 4. George earned a nickel on Saturday forenoon and another nickel in the afternoon. On Saturday evening he spent 6%. How many cents had he left ? 5. A post was 10 feet high. 2 feet of it were in the ground. How many feet were above the ground? If Tom is 4 feet tall, how much higher is the post ? 6. I buy an orange for 3¢ and hand the fruit-dealer a dime. What change should he give me ? 7. There were 10 plum treesinan orchard. 2 of them died. How many lived? How many more would the farmer need to plant so as to have a dozen in all? 8s. Arthur gave a dime for a flag and atop. The top cost 4¢. How much did the flag cost ? 9. George gave 3 apples to each of 4 boys. How many did he give in all? 10. Alice had 10 pansies. She gave away 3 of them. How many had she left? If she divided the number left among three friends, giving each two, would she then have any pansies for herself ? 11. Her father gave Helen a dime. She bought 5¢ worth of braid. How many cents had she left ? 12. Louis spelled 3 words and James spelled 4. How many words did both boys spell ? STUDY 38 ANSWER TWOS 13, 12% Bly dy WO RGy ih SH BONE LO miilentes 13 14 15 1617 18 19 20 21 22: 93 94 +2=2 6+2= 8 12 2 14 18 + 2= 20 +9=4 §+2=10 144+ 2=16 20 +2= 2? as 2B NG oes Te 16°029'= 18 9949-94 2x1l= 2 2x%.T=14 ees ol Pepa ths eee 2x 9=18 ge 4s 2x10 = 20 2x5=10 2x 11=22 eG eb) 2x 12=94 MULTIPLICATION TABLE OF Twos We read it either this way, 2 2’s are 4, or two times two are four; two 3’s are 6, or two times three are six; and so on. 6-+6— 12. two 6’si= sixiQ’s; ) 2422-6 Qe Do aa 10 + 10 = 20 two 10’s = ten 2’s 24+24242424242424242=20 1. Copy the Table of Twos on paper. 2. Count by 2’s to 24. Write this counting. 3. Show that two 5’s are 10, two 9’s are 18, two 12’s are 24. 4. Show that two 4’s are 8, two T’s are 14, two 11’s are 22. —E———e ——EOe -< 4 39 STUDY ANSWER HALVES When anything is divided into two equal parts, each part is called a half. ‘Two halves make a whole. BAN tectangle in halves Circle in halves Triangle in halves Square in halves When anything is divided into two equal parts, the parts are called halves. Draw a line 2 inches long. Divide it into halves. Draw a square. Divide it into halves. One half is written 4 in figures. 1. How many halves are there in one dollar? 2. How many halves are there ina pie? If a pie cost 10 cents, how much will half a pie cost ? 3. James had one dollar. He spent half a dollar for a ball. How much money had he left? 4. If you bought a cookie and ate half of it, how much of it would be left? Would the part of it left be equal to the part you ate ? 5. One orange is what part of two oranges ? 6. One basket is what part of two baskets ? 7. One half of two cents is how much ? 8. One half of four cents is how many cents ? 9. George earned ten cents by doing errands. He gave half of the money to his sister. How many cents did he give to her? 10. 4 of 10 cents is how many cents ? bole ORAL TEACHING 40 STUDY THIRTEEN, 18 When we have ten things and add three things to them, the name of the number of all these things together is thirteen. 10 (2) e©e2ee¢ e o Php cee ane G Om eaeereysstcs saa | 10 + 3 are thirteen. Ten and three are thirteen. : ] We write thirteen with the figures 1 and 3,13. ° We put 1 in tens’ place, and 3 in units’ place. 13 means 1 ten and 3 units, like these dots : 12 +1=13. > o> $ zo Ze are fractions. So also are , 2, #, 2, 3, o) & & & & 10 10 10 10 10 10° 17 10° Read these. When fractions are written in figures, the number below the line tells into how many parts the thing is divided, and the number above the line tells how many parts we are talking about. °%, means that there are 12 equal parts, and we are taking 5 of them. ESTRELLA a Point out halves and quarters. ae a Point out fifths and tenths. Point out thirds and sixths. el CO Point out halves, quarters and eighths. — CS an I Point out halves, thirds, fourths and twelfths. Point out sevenths. ee nn a er Point out thirds and ninths. RN EE FR Point out twentieths, tenths and, fifths. 1. Draw on the blackboard forms of figures showing halves, thirds, quarters, fifths, sixths, sevenths, eighths, ninths, tenths, twelfths, twentieths, and fortieths. 2. Tell why the larger the number of parts of anything the smaller each part is. rie eee 1a aol 1 1 eee et 19 19 +) What is 3 of 4 4 of 4 of 4 x of 4 4 of +! 1 pL ee “bepe) Coal AOR Fall aes ah 1 aes aby. 4 of 4? 4 of 4 of 4? +4 of 4 x of 3 4 of 3% 1 95 1 39 2 eye 19? 4 of 2: + Of Bt 2 of 3 2 of 4. Fold or cut paper to show the facts on this page. Q7 STUDY ANSWER FRACTIONS The equal parts of numbers are called fractions. Fold or cut paper to show these facts. 1. 3 of 6=8. Six halves are three wholes or units, because two halves equal one whole, and six are three times two. §=3. fof6=3 4x6=$=83. 2 FOLS=s. $=>4. J ors=—4. 4x8=4. 3. dof 6=§. Six thirds are two wholes, or units, because three thirds eines one whole, and six are two times three. § = 2. 4 of 6 = 2. 4 bie oi vi 1 unt aes 1 fe 1 Ae 4 t+o0of9=}2. 2=3. RUC Ie. weet) Ooo. =e ity ea 6.) 4 0f112 ="? 7. of 14=? 8. of l6=? rere Ul Laie lo. dof 1lb6=? v1: tof 18 =? ab 4 of 21 ? 13. 2 of 9 2x 9= 418 because 9 times two thirds are 18 Pigie 18 = 6, eee 18 +3 = 6. 2 ey ae oe um foliam? gxBaae—s COO 1 1 rads wu 15. fof8=? }x8=§=2 ae] 16. Find # of 8, #o0f 12, 20f 16, Coot q of 20. Count and see 17. Find 2 of 10, 2 of 15, 2 of 20, 2 of 25. 1s. Find 2 of 15, 4 of 20, 3 of 80, 2 of 40. 19. What: Breage Diy LB e102? 562 97.210? 2247 20? +30? 20. Find 4 of 20, 10, 15, 5, 25, 30, 35, 40. 21. Find 2, 4, and $ of 18, 6, 12, 24, 30, 36, 42, 48. 22. Find 2, 32, 4, 2, ney, & of 14, 7, 21, 28. 23. ‘ What are 2, 3, 4, 3, $, and { of 16, 8, 24, 32, 40? enloo enh ORAL 88 QUESTIONS 1. If a bushel of corn cost 80%, what will 8 quarts cost? What will a peck cost ? 2. If a quart of onions cost 9%, how many cents will 3 quarts cost ? 3. How many dimes equal 90¢? 4. A man bought 2 rugs at $9 apiece. What change should he get back, if he gave the clerk a twenty-dollar bill ? 5. 45¢ was divided equally among 9 children. How many cents did each child get ? 6. In 2 hours Fred can ride 30 miles on his wheel. How many miles can he ride in 1 hour? in 3 hours? 7. In a school of 84 children there were 12 over 9 years of age. How many children were under 9 years ? What fraction tells the number of children over 9 years old ? 8. Mr. Brown put into his pocketbook 6 ten-dollar bills, 3 five-dollar bills, and 4 two-dollar bills. How many dollars did he put into the pocketbook ? 9. What is the ratio of 10.to 5? 1o. If 5 oranges cost 20%, how many cents will 10 oranges cost ? 11. What is the ratio of 6 to 2? 12. If 2 pencils cost 8%, what will 6 pencils cost ? 13. Henry has 60¢ in nickels. How many car rides can he take at 5¢ a ride? 14. A baker sold 12 loaves of bread a 4% a loaf and a dozen of cookies for 8¢. How much money did he get ? 15. Emma bought 3 paper dolls for 10¢, and Laura bought 2 skeins of thread for a nickel. How many cents did both girls spend ? 89 ORAL QUESTIONS 1. Zof 8=? of 8=? Lof2W=? of 20=? Lof44=? 2o0f44=? Lof28=? of 28=? One half equals how many fourths ? What is the ratio of 4 to 28? of 28 to 4? Compare 4 with 36. 4 is } of 36. Hence the ratio of 4 os 36 is?. What is the site of 36 to 4? 5. What is the ratio of 24 to 4? of 24 to 6? of 24 to 12? 6. Give the ratio of 4 to: Sipe, ow 40). 48) 44. 694. 20. 12, 4. 7. Give the ratio of each of those numbers to 4. oN s. Ifa hat costs $4, what will a dozen hats cost ? 9. Divide 24 pears equally among 6 boys. How many pears will each boy get ? 10. There were 2 dozen eggs in a basket. One third of them were used for breakfast. How many were left ? 11. James had 28%. He spent } of his money. How many cents had he left ? 12. 3 tops cost 18%. What was the price of one top ? 13. Eddie bought 9 apples at 2¢ each. How many cents did he pay for them ? 14. Katie got 4 spools of thread at 3¢ apiece. How many cents did she pay for the 4 spools ? 15. George has 3 nickels. How many cents has he? 16. Alice had 14 cherries. She gave 4 of them to Lucy. How many cherries did Lucy get ? 17. It is 18 miles from Brooklyn to Garden City. I walked } of that distance. How many miles did I walk ? How re miles would be ? of the distance ? ORAL } 90 WRITTEN QUESTIONS 1. How many pints are there in + of 6 gallons? 2. If syrup is 80% a ee hae many cents must be paid for a pint? 3. What is the ratio of 2 to 6? 2 is what part of 6? 4. If 6 boxes of candy weigh 3 pounds, what will 2 boxes weigh ? 5. What will 12 yards of cloth cost at $4 a yard? 6. When 8 pounds of sugar cost 40 ¢, 1 pound of sugar will cost 4 of 40 ¢, or Zs What j is the ratio of 18 to 6? of 24 to 8? 8s. When 7 yards of silk cost $21, a yard will cost + of $21, or dollars. 4 yards will cost 4 x dollars, or dollars. | 9. If 9 bushels of apples cost $18, 1 bushel will cost 4 of $18, or dollars. 4 bushels will cost 4 x dollars. 10. If a dozen oranges cost 60%, what will be the cost of 1 orange? of 3 oranges ? of 5 oranges ? 11. When 5 pounds of meat cost 45%, what will 1 pound cost ? 2 pounds ? 12. When 5 quarts of milk cost 35%, what will 2 quarts cost ? 13. If 4 lemons cost 8%, what will 1 lemon cost? 2 lemons? What will a dozen lemons cost? A _ half dozen ? 14. If a newspaper costs 2%, how many cents will 7 newspapers cost ? 15. A man had 18 oranges. He divided them equally among 6 children. How many oranges did each child receive ? 91 TELLING LENGTHS 12 inches make 1 foot. Lorine > Tt in. stands for inch or inches. ft. stands for foot or feet. 3 feet make 1 yard. Dive teva. Be sure to place a period after in. for inch, ft. for foot, and yd. for yard. A. foot-rule shows twelve inches. A yard-stick shows three feet. A foot is a very common unit of measure. We buy boards at the lumber yard by the foot. A yard is almost as common a unit of measure. We buy goods for dresses and suits by the yard. An inch is the unit of measure for small things. We tell how wide and how long a photograph is by inches. 1. Measure 2 inches on a piece of paper with a ruler. 2. Cut squares 2 inches on each side. 3. Measure the size of the first picture in this book. 4. What is the size of your desk? Your teacher’s desk ? 5. Ask your mother how many yards of cloth she needs to make a dress. Measure that number of yards on the blackboard. Size means, How long is it? and, How wide is it? sometimes also, How thick is it ? STUDY INCHES FIVE ORAL 99 QUESTIONS 1. A bushel basket is half full of potatoes. How many more pecks of potatoes will it hold? 2. How many quarts are there in a bushel of chest- nuts? in a bushel of corn? in a bushel of apples ? 3. Ifa bushel of wheat weighs 60 pounds, how many pounds does a peck of wheat weigh ? 4. 8 quarts are what part of a bushel? 2 pecks make what part of a bushel ? 5. If 2 bushels of apples cost four dollars, what will 2 pecks cost ? 6. How many bushels are there in 64 quarts ? 7. How many bushels are there in 72 quarts ? 8s. Arthur gathered half a bushel of chestnuts. To how many boys can he give a quart each, after he has sold a peck of the nuts? 9. How many quarts are there in a bushel? in half a bushel? How many quarts are there in a quarter of a bushel? How many quarts in 2 quarters of a bushel? in ? of a bushel ? 10. If you had } of a bushel of berries, how many quarts would you have? 11. Ifa pint of walnuts costs 6 cents, what will 4 quarts cost? What will half a peck cost ? 12. A dish holds 8 pints of berries. How many quarts will 6 such dishes hold ? 13. At 9%aqt., what will a pk. of cranberries cost ? 14. At 5 cents a quart, what will 1 peck of beans cost ? 15. How many pecks are there in 9 bushels? in 6 bushels? in 3 bushels? in 5 bushels ? 93 ORAL REVIEW What are # of 18? 2? 4? $8? §? 2? What part of Vis 1? Bof 9=? of 10=? fy otlO=? dof 20=? {of B=? |, of 100=—? A string was 12 yds. 1 ft. long. 2 yds. 1 ft. were cut off. How many yards were left ? how many feet ? aie od LU os 5. A tank contained 38 gallons of water. 62 gallons more were poured in. Then 47 gallons were pumped out. How many gallons were left ? 6. A milkman has 7 cans, each holding 12 gallons of milk. He sells 48 gallons. How many gallons has he left? 7. James earned 40¢ in one week, and Arthur earned 55¢. How many cents did both boys earn ? 8. If James spent 29%, and Arthur spent 36%, how many cents did each boy have left ? 9. A man having $56 bought a suit of clothes for $28. What part of his money did he spend? How many dol- lars did he have left ? 1o. At 6¢ a quart, how much money will 6 pints of milk cost? 9 pints? 38 gallons? 11. At 4% a pint, how many pints of berries can you buy for 20%? for 80¢ 12. How many inches long is your shoe? How long are your skates ? 13. How many feet or inches wide is the ring you use for marbles ? 14. If a bushel of peaches costs four dollars, how much will a peck cost ? 15. What will a bushel of potatoes cost at 20% a peck ? STUDY 94 ANSWER QUESTIONS 1. How many ee are there in a quarter of a yard? 3 of a yard? in 4 of a yard? 2. Harriet peeant a yard of ribbon. and divided it equally, for dress trimming, among her six dolls. How many inches of ribbon did she cut off for each doll ? 3. If you drew a line a foot long and divided it into 12 equal parts, what would be the name of any of those parts ? 4. George drew a triangle that was } of a foot on each side. How many inches was it around the triangle ? 5. How many inches are there in 2 of a foot? 6. How many inches is it Rae a desk top 2 feet long and 18 inches wide ? 7. A ribbon was 3 feet in length. How many inches long was it? 8. If it takes 7 yards of lace to trim a dress, how many yards will it take to trim 9 dresses ? 9. A log of walnut was 30 feet long, 4 of it was cut off. How many feet were cut off ? 10. Mrs. Smith bought 10 yards of silk at $1 a yard. She used 3 of the silk. How many yards were left? What was the value of the piece of silk she used ? 11. A bench is 12 feet long and 16 feet wide. How many yards is it half way around the bench ? 12. How many feet are there in 28 inches? How many inches over ? 13. A square room has sides 5 yards and 1 foot long. How many feet is it around the room ? 14. A string 1 foot long is to be cut into inch pieces. How many times must it be cut ? 95 STUDY ANSWER QUESTIONS 1. Draw a rectangle 2 inches wide and 4 inches long. Divide it into 1l-inch squares. How many squares are there in the oblong ? 2. A room is 3 yards and 1 foot wide. How many steps will a boy take in crossing the room if he steps 2 feet at each step ? 3. Measure the distance between 2 windows in your room. Measure the length and the width of the room. 4. Inaroom the distance between a door and a window was measured and found to be 3 yards and 1 foot. How many feet were there in that distance ? 5. Louise bought a roll of braid, and, on measuring it, found that there were 9 feet in the roll. How many yards were there in it ? 6. Mrs. Smith bought 9 yards of silk. She used } of it. How many feet were in the piece she used ? 7. Draw a square with sides 5 inches long. Mark the inches on its sides. Divide the square into 9 smaller squares. 8. Draw a rectangle 1 inch wide and 4 inches long. How many 1-inch squares can you make in it ? 9. On the board make 2 dots, 1 foot apart, guessing the distance. Measure the distance between the dots. 1o. Judge a distance of 1 yard, making the distance by putting 2 dots on the board. Measure the distance guessed. 11. Draw a line that you think is 3 inches long. Meas- ure it. 12. Draw a square that you judge to be 3 of a foot in length. Measure the square. ORAL TEACHING 96 STUDY HUNDREDS We call ten tens one hundred. LOSS OF 314) 99 + 1= 100 50 + 50 = 100 We write one hundred in figures, |OQO. We put the 1 in hundreds’ place by setting two zeros, 00, at the right to show that the 1 is neither in units’ place nor in tens’ place. We call twenty tens two hundred, and write two hun- dred in figures with a 2 in hundreds’ place. 1004100 = 0'0 20 x 10 = 200 Two hundred and one hundred are three hundred. 100 + 100 + 100 = 300 200 + 100 = 300 Four hundred, 400. Five hundred, SH OKO}. Six hundred, b Ores Seven hundred, | OO. Eight hundred, SOO. Nine hundred, q OO: Above one hundred we count units and tens as we do below one hundred. We write one hundred eleven in figures, | | |. We write six hundred ninety-two in figures, b q oe 1. 90+11=101. 11=10+1. Nine tens and one ten make ten tens. ‘Ten tens are one hundred. The unit we set in units’ place. 2. 844+ 20=104. 84=80+4. Eight tens and two tens make ten tens. ‘Ten tens are one hundred. The four we set in units’ place. 3. 70:.4+42=112. 42= 30+ 104 2. bo © tee fe Wael cr re ered se. MS. oo: be (Se) bo -1 OC) pa IND _ _ GN ONE aarp PO (otek Bes > (wen o& pet eet DD Oost Qe Os ADDITION 36 28 17 iL a 34 44 ab 6 22 yy 38 18 31 hed 48 BIT 14 24 24 16 14 12 ie 26 Ie 10 aa 19 AA) yh at 2 1 66 31 10 Lis 5 14 3 27 10 16 26 1s 9 5 30 2 Be 2B 10 | Aba toe ey ee bo CO © Se tm co <¢ ae et J] st SS) b — © ours ew Co ee ee Re CO |] CO bo ee ton pas CO WRITTEN ORAL TEACHING 98 STUDY METAL MONEY Size of a quarter dollar. Size of a Size of a dollar. half dollar. Size of Size of a Size of a a dime. nickel. penny. One dollar is equal to one hundred pennies, or cents. $ is the sign for one dollar, or 100 cents. A half dollar is half 100 cents, or 50 cents. A dime is one tenth of one dollar. 100 + 10 = 10. A dime is worth ten pennies. A quarter dollar is equal to a fourth, or quarter, of 100 cents, or 25 cents. # is the sign for cents. The coins for dollars, half dollars, quarter dollars, and dimes are made of nearly pure silver metal by Our Country. ‘That is one im- portant thing Our Country, whose flag we know so well, does for us. A nickel is equal to five pennies, or 5%. The penny is one cent, one hundredth part of one dollar. $1 = 100¢. 100¢ + 100 = 1c. = one penny. Nickels are made of nickel metal. Pennies are made of copper. 99 ANSWER NUMBER-STORIES 1. Mary and Tom are at the grocery. They have three quarters to spend. Mother wishes them to ask the grocer for three pounds of sugar, half a pound of tea, and a dozen egos. Mr. Grocerman tells them that sugar is five cents a pound, tea is forty cents a pound, and eggs are twenty- five cents a dozen. ‘Tom will carry the things home in the basket. Why does the grocer weigh the sugar? When Mary takes the “change,” or money he gives back to her with the packages and the eggs, how many cents does she have to take home to mother ? 3 quarters = three 25¢ pieces of silver. 8 x 25¢=Td#. 3 pounds of sugar at 5¢ a pound cost three times 5f. 8x bf =15¢. 1 pound of tea at 40% a pound costs one half of 40%. 4 of 40¢=20¢. The eggs cost 25%. 15+ 20¢425f=60f T5¢—60f=15¢ Mary has fifteen cents to take back to her mother. Do you see now why we have to learn about numbers ? 2. Tell a number-story about Charlie and Susan. They have fifty cents. They wish to buy two pounds of sugar at five cents a pound, a loaf of bread at eight cents, and a pound of butter at twenty-eight cents. How much will they have left ? 3. Make up a story about Willie and Jennie, who have one hundred cents. ‘They ask Mr. Grocerman for half a dozen eggs, two pounds of butter, and three large loaves of bread. He asks them twenty-eight cents a dozen for his very best eggs and twenty-eight cents a pound for table butter and ten cents for large loaves of bread. They gave him a silver dollar. Was this right ? WRITTEN 100 QUESTIONS 1. What is the ratio of 12 to6? of 6to12? of 36 to 6? of 24 to 6? of 72to6? of 48 to 6? of 54 to 6? of 18 to 6? of 30 to6? of 42 to6? of 6to18? of 6 to 24? of 6 to 42? of 6 to 86? of 6 to 48? of 6 to 54? of 6 to 72? 2. If 6 dozen apples cost 72%, how many cents will 1 dozen cost ? 3. How many minutes past the hour is it when the minute hand points to III? 15 minutes are what part of an hour? 80 minutes are what part of an hour ? 4. A farm of 72 acres is one sixth woodland. How many acres are woodland ? 5. A table is 48 inches long and 36 inches wide. How many inches is it around the table ? 6. What will 6 apples cost, if 4 dozen cost 96¢? 7. The price of a sofa was $66. It was reduced } in price and was then sold. What was the selling price ? s. A woman had 5 ten-dollar bills and 3 two-dollar bills. She bought 8 yards of velvet at $6 a yard and 1 yard of silk for $3. How many dollars did she spend ? How many dollars did she have left ? 9. A grocer paid $60 for 30 barrels of apples. What was the cost a barrel? He sold the apples for $90. How much did he get a barrel? How much did he gain on each barrel? How much did he gain on the 30 barrels? 10. A pail holds 12 quarts. How much will it cost to fill it with milk at 6% a quart? After 4 of the milk is used, how many pints are left ? | 11. In one day Mr. Smith rode 80 miles on his wheel. He rode 4 of the distance in half an hour. How many miles did he ride in that time ? aaa 101 ORAL TEACHING STUDY READING AND WRITING HUNDREDS thc Ll ke Hes ep Te Pp 400 900 50 8 0 1 7 451 987 n mM uo) 4°. 2 Sm Q Sa EES EES map Hap 700 4 0 0 T 0 2 0 T 2 (per he di 422 1. Read the numbers: 299, 648, 110, 444, 770, 801, 999. 2. How many more hundreds has 897 than 153? how many more tens has 897? how many more units ? 3. Tell how many hundreds, how many tens, and how many units there are in: 393 406 744 985 112 615 600 401 642 371 350 404 199 878 555 611 225 111 226 414 660 218 922 660 882 630 808 299 681 TO00 400" OO 1P ae Li Suz oto" "60s “187g 901 584 T17 205 961 3821 201 4. Write by figures: One hundred twenty-five. One hundred ninety-nine. One hundred six. Two hundred forty-six. Two hundred eighteen. Two hundred two. Three hundred eleven. Three hundred thirteen. Four hundred twenty-eight. Four hundred eighty-one. Four hundred ninety. 1000 Five hundred five. Five hundred fifty-five. Six hundred ninety. Six hundred eight. Seven hundred seventeen. Seven hundred seven. Eight hundred forty-eight. Eight hundred thirty-six. Nine hundred twenty-one. Nine hundred fifty. Nine hundred ninety-one. ORAL 102 REVIEW OF HUNDREDS 1. Write these numbers in figures: 7 hundreds. 7 hun- 3 hundreds 6 tens 7 units. 4 hun- dreds 2 tens 8 units. dreds 1 ten 1 unit. 1 hundred 4 tens 3 units. 4 units. 9 hundreds 8 tens 6 units. 3 tens 2 units. 6 hundreds 5 tens 2 units. 2. 220=1104? 425 = 200+? 630 = 220 + ? 530 = 130+ ? 840 = 235 4+ ? 545 = 140+? 250 = 404? 610 + ? = 820 115 + ? = 720 200 + ? = 325 8 hundreds 5 tens 5 units. 2 hundreds 5 hundreds 7 tens 3 hundreds 1 unit. 725 + ? = 930 525 + ? = 835 330 + ? = 640 835 + ? = 940 T49 + ? = 957 3. How many 10’s are there in 200? 300? 400? 500? 600? 700? 800? 900? 1000? 2 tens X0=? betens Xf o tensx5o=? 8 x 6 tens=? 4 tens x 8=? 6 tens x 6=? Dj Xen bee 14 4x4 tens=? 0 Tense." oetons <= — 6 tens x 6=? 7 tens xX 2=? 2 tens x 6=? 4 tens x 4=? 5x 5d tens=? 3x9 tens =? -8 tensx 4=? 7x2 tens=? 4. How many figures are needed to express units, or ones ? to express tens? to express hundreds ? 5. Write a 10’s Table to 1000, in ten parts, 1 to 100, 101 to 200, 201 to 300, 301 to 400, 401 to 500, 501 to 600, 601 to 700, 701 to 800, 801 to 900, 901 to 1000. 103 ORAL WRITTEN HOUSE NUMBERS In towns and cities the streets are named, and the houses and lots on the streets are numbered. One side of the street has odd numbers, and the other side has even num- bers. If there is room between houses for more houses, then these lots, sometimes called vacant lots, are numbered. Has your house a number, and your street a name ? If you live in the open country where there is plenty of room, and people do not need names for their roads and numbers for their houses, probably you know where some townspeople have their houses or stores. The name of the street and the number of the house are part of the address. Mr. William Jones, 165 Main Street. Sometimes when there are very many streets, the streets have numbers for names. When we wish to write a letter to a person living in a different place from our own town or city, we write on the envelope what the place is where we wish the letter to go. Master Charles Marshall, 149 Sixth Street, Atlanta, Georgia. If houses were not numbered in large towns and cities, it would take a great deal of time to find people in them. 1. Write your house address or that of some friend. 2. Exchange your paper with its address for that of the boy or girl in front of or behind you. Read that, and copy it. Exchange across the aisle. 3. Has your schoolhouse any address? 4. Where is your town or city hall? Your post office? ORAL TEACHING 104 STUDY THOUSANDS We call ten hundreds thousands. 10 x 100 = 1000 999 + 1 = 1000 500 + 500 = 1000 We write one thousand in figures, |OOQ. We put the 1 in thousands’ place by setting three zeros, 000, at the right to show that the 1 is neither in units’ place nor in tens’ place nor in hundreds’ place. We call twenty hundreds two thousand; and write two thousand in figures with a 2 in thousands’ place. 1000 + 1000 = 2000 20 x 100 = 2000 Two thousand and one thousand are three thousand. 1000 + 1000 + 1000 = 3000 2000 + 1000 = 3000 We write four thousand HOOO, five thousand 50 0 0, six thousand bO O O, seven thousand | OO,03 eight thousand 6 O O 0, nine thousand dO 00. Ten tens we call one hundred. Ten hundreds we call one thousand. Ten thousands we call ten thousands. One hundred thousand we call one hundred thousand. We write one hundred |QQ. We may write one thou- sand!|QQOQO. The comma is to help us see that there are 3 zeros, and to read thousands quickly. We write ten thousand |QOQOQQO. We write one hundred thousand |OOOOO. It is not necessary to use a comma. 1. 900+ 101 =1001. 101=100+4+ 1. Nine hundreds and one hundred are ten hundreds or one thousand. 2. 700 +420= 1120. 420=300+120. Seven hun- dreds and three hundreds are one thousand. ‘The twelve tens we write as one hundred twenty. 105 STUDY ANSWER THOUSANDS 1. One thousand one, 1001. One thousand nine, 1009. One thousand ten, 1010. One thousand eighteen, 1018. One thousand one hundred eighteen, 1118. Two thousand seven hundred four, 2704. Three thousand thirty-six, 3036. Five thousand six hundred sixty, 5660. Seven thousand seven hundred seventy-seven, T7777. Eight thousand one hundred one, 8101. Eight thousand eight hundred fifteen, 8815. Nine thousand four hundred ninety-seven, 9497. 2. Read: 1246, 9223, 4780, 6111, 4644, 8707, 3136, 4598, 9610, 7000, 3688, 2080, 6202, 7100, 8004, 9110, 1338, 9909, 4707, 8118, 7656, 8771, 4919, 7223, 2748, 4339, 4716, 3188, 7007, 3010. 3. Write by figures: one thousand two hundred sixteen; three thousand seven hundred twenty-eight; nine thou- sand four hundred sixty-three; seven thousand seven hundred; eight thousand nine hundred seventy; two thousand seventy-five ; four thousand four; six thousand six hundred sixty-six; nine thousand ten; eight thousand ; three thousand one hundred forty-four; five thousand eight hundred eighty-one. 4. Write in words: 7414, 38602, 8435, 1014, 5005, 2110, 6116, 9711, 4419, 2829, 1990, 3333, 5208. 5. Give the number of thousands, of tens, and of ones in each of the numbers in 2 and 4. 6. Count by hundreds from 1000 to 2000. 7. Count by thousands from 2000 to 9000. 8. What is the greatest number that can be expressed by three figures? by four figures ? ORAL TEACHING STUDY 106 FIVES AND TENS 5 10 15 20 25 30 35 40 45 50 55 60 04+5= 5 5+5= 10 10+5=15 15+ 5= 20 20 + 5 = 25 25 + 5 = 80 380 +5 = 30 35 +5 = 40 40 +5= 45 45+5=50 50 +5 = 55 55 + 5 = 60 oleae 23 XR) te ional) 5x 8=40 5x38=165 5x 9=45- ox4= 20 aim an ANE l0) B16) Sys Sy ah Lee aye 5x 6=30 ox 12=60 MULTIPLICATION TABLE OF FIVES Make a division table, beginning it like this: 5+5=1 10+5=2 ees 74 | eos LO Sol= eb LOS es eee! LOK est) LOK 930 10 x 4= 40 LOS. == D0) LOS LO atu 10x67 60 LO Sce alte 11) LOS 120 MULTIPLICATION TABLE OF TENS 107 ORAL TEACHING STUDY FIFTHS AND TENTHS When anything is divided into five equal parts, we call each part one fifth. Five fifths make one whole. Circle Square Rectangle Pentagon Line Star Rectangle Into how many equal parts is each of these forms divided ? 1. Point out two fifths of each of these forms; three fifths; four fifths. 2. Make drawings like these forms on paper but larger. 3. Make drawings lke these forms on the blackboard. When anything is divided into tenths, it has ten equal parts. Ten tenths make one whole. ® WII & Into how many parts is each of these forms divided? Count and show the parts. Make drawings like these forms both on paper and on blackboard. ORAL TEACHING 108 STUDY SIXES AND TWELVES 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 0+6= 6 6+6=12 12+6=18 18+ 6= 24 24+ 6=30 30 + 6 = 86 36+ 6= 42 42+4+6= 48 48 +6 = 54 o4 + 6 = 60 60 + 6 = 66 66+6= 72 6x 1 =) 6 6x2=12 -6x3=18 6x4= 24 656530 6x 6 = 36 MULTIPLICATION TABLE OF SIXES 12 24 36 48 60 72 84 96 108 120 132 144 O+12= 12 12412= 24 24412= 386 386412= 48 48+12= 60 60412= 72 72412= 84 84412= 96 96+12=108 1084+12=120 1204+12=1382 1382412=—144 Make up bundles of splints, each with twelve splints, and show that these facts are true. 12x%1=12 12x 7= 84 12% 2=24 12x 8= 96 ee 12x 9=108 12x 4=48 12 x 10 = 120 12x 5 =60 12 x 11 = 132 12x 6=72 J nosp 44 MULTIPLICATION TABLE OF TWELVES OR DOZENS 109 STUDY ANSWER SIXTHS AND TWELFTHS When anything is divided into six equal parts, we call the parts sixths. Six sixths make one whole. Circle Rectangle Hexagon 1. Show that each of these forms is divided into halves. 2. Show that each is divided into thirds; into sixths. 3. Make larger drawings of each of these forms on paper; on the blackboard. When anything is divided into twelve equal parts, we call the parts twelfths. ‘I’welve twelfths make one whole. Circle Rectangle Hexagon 1. Show the various halves in the circle and: hexagon. 2. Show thirds of each of these forms. 3 Show fourths of each. 4. Show sixths of each. 5. Make larger drawings of each of these forms on paper; on the blackboard. 6. §=1; 42=1; 3=1; 4=1. Read of these facts. 7 r4? Why? dor ,? Why? 8. Cut out forms to show the answers to 6 and to 7. 9 Which is larger, 3 or 4? #or4? +#or 4? ORAL 110 WRITTEN DIVISION TABLES Make a division table, beginning it like this: 10+10=1/30+10=3 20 +10 = 2/40 + Make a division table, beginning it like this: 6+ 6=1/18+ 6= 196 = 2174 —|— Make a division table, beginning it like this : 12+12=1/86+12=3 24-+-12=2)48+12= QUESTIONS 1. How many school days are there in 4 weeks? How many working days ? 2. How many hours are there in a quarter of a day ? 3. Which is the greater fraction, } or }? 4. A cake is cut into sevenths. Another cake of equal size is cut into tenths. Would one of these sevenths be a larger or smaller piece of cake than a tenth ? 5. How many 10’s are there in 96? how many units ? 6. If a can of peaches cost 25%, how many cans will $1 buy? T5¢? 7. What is the ratio of 6 to 48? s. If 2 yards of tape cost 24%, what will 1 yard cost? what will } of a yard cost ? 9. A strip of carpeting is ? of a yard wide. How many inches wide is the carpeting ? Tt ORAL WRITTEN QUESTIONS 1. If you had a fifty-cent piece, a dime, and 2 nickels, how many cents would you have? How many more cents would you need to make a dollar ? 2. A dealer paid $96 a dozen for lamps. What was the cost of 1 lamp ? 3. A girl bought 8 yd. of braid at 6f a yd. She gave the clerk a 50% coin. What change should she get ? 4. How many nickels are equal to 40¢? 5. How many cents are there in a dollar ? 6. If a blank book cost 7%, how many blank books can you buy with 3 dimes? How many cents would you have left after paying for the books ? 7. Louis bought half a dozen little flags at 12¢ apiece. He gave the clerk a half dollar and a silver quarter. What change should the clerk give Louis? s. A boy works in a garden at 10¢ an hour. How many hours must he work in order to earn $1? 9. What is the ratio of 6 to 12? of 9 to 27? 1o. If a dozen oranges cost 50%, how much will half a dozen cost ? two dozen ? 11. A man bought a pound of cheese for 15%. He ate 4 of it. What was the value of the part he ate ? 12. At $6 a ton, how many tons of coal can you buy for $27? What will half a ton cost ? 13. What is the ratio of 18 to 36? of 36 to 18? 14. If 36 crates of peaches cost $40, what will 18 crates cost? How many crates would $80 buy ? 15. Mrs. Brown bought 9 yards of sheeting at 7% a yard and 3 yards of calico at 5¢ a yard. She gave the clerk a dollar bill. What change should she get ? STUDY 112 ANSWER REVIEW ; 1. 700+420=1120. 420=4004+20. Seven hundred and four hundred are eleven hundred. We write twenty in tens’ place. 2. Add: 950 800. 700 -800 900 850 880 990 100 250 600 750 950 600 900 400 3. Write in figures two thousand three hundred fifty- six, four thousand nine hundred ninety, six thousand two hundred sixty-two, eight thousand eight hundred. 4. Which is larger; 4, or 4? <3 or #?. 38.07 # or¢? Show the answers by drawing forms. 5. Can you tell which is larger, one tenth or one twentieth of anything? Do you see that equal parts grow smaller as the number-names grow higher? Ten is higher than four, but one tenth is smaller than one fourth. Why? lly aie dl 1 df Weande 6. Compare 4 and+by drawings. and 4%. 4 and +5 7. Compare 2 and #. How much larger is the ?? Show your answer by a rectangle divided into twelfths. s. What is the ratio of 8to 16? of 12 to 24? 9. If 16 pounds of oatmeal cost 40%, what will 8 pounds cost? 12 pounds? enleo aw) 10. Mr. Brown bought 4 dozen pears. 38 of the pears were bad. ‘The goods ones were divided equally among 9 children. How many pears did each child get ? 11. From a door to a window the distance is 2 yards and 1 foot. How many feet is the distance ? 12. Carrie bought a yard and a quarter of red ribbon and # of a yard of white ribbon. How many yards in all did she buy ? 113 _ WRITTEN QUESTIONS 1. Divide each of these numbers by 6, by 3, and by 2: 18, 12, 42, 36, 54, 48, 6, 84, 96, 72, 24, 60, 30, 66, 90, 78. 2. Find 4, 2, 3, 4, and g of each of the following numbers: 60, 30, 86, 72, 18, 54, 48, 42, 24, 84, 96. 3. 2 of 30=? 43 of 80=? Then 2=what other fraction? Show by a drawing. 4.2 of 18=? 42 of 18=? Then 2= what other fraction? Show by a drawing. 5 fof 12=? go0f12=? Jof12=? sof 12=? Then 3? = what other fraction ? 6. How many sixths of a number equal one third of the number? How many sixths equal one half ? 7. How many fourths and sixths are in two ? SB tof18=? 4of18=? go0f18=? 4 of 18=? 9. ‘Two thirds of 18 equal how many sixths of 18 ? 10. Two thirds of 30 equal how many sixths of 30? 11. dof 24=? 2o0f 24=? One half of 24 equals how many sixths of 24? 12. 2 of 836=? 4 of 836=? How many thirds of 36 equal four sixths of 36? 13. One half of 24 equals how many sixths of 48 ? 14. One third of 42 equals how many sixths of 42? 15. One half of 54 equals how many sixths of 54 ? 16. One third of 54 equals how many sixths of 54? 17. tof 60=? 2 of 60=? 4 of 60=? 2 of 60=? 18. Draw illustrations to show @, 2, 4, 3%- ORAL TEACHING 114 STUDY : DATES There are always seven days in every week. There are always at least four weeks or twenty-eight days in every month. There are twelve months in every -year. “ A hundred years make one century. We are living in the twentieth century, because it is more than 1900 years since Jesus Christ was born. When we write letters we put three facts at the top, called the date. We tell the year, the month, and the day of the month: sometimes we tell also the day of the week. We may write the date, January 1, 1900, or Tuesday, Jan. 1, 1900. The calendar tells us how to know the ‘< = a b> month, the day of the month, ¢ ¢ £ 8 % & F the year, and the day of tl ok me ak Re errs year, and the day or the ee les er eed exer week. | LZ | 3 lt PLO OTe This calendar is true for any | | ——|——_|_} month when the first day of the 8 | 9 10) 11) 12/13/14 month falls on Sunday and when ror oF wi the month has 31 days. This 15 16 | 17,18 19) 20) 21 calendar represents December, | 1901, and March, 1903. If the a ea ae feos He 31st day were omitted, it would represent June, 1902, and No- The Pete pee vember, 1903, also. The names of the months are: January, February, March, April, May, June, July, August, September, October, November, December. The year has 865 days, except “leap year,” which has 366 days. Leap year comes every four years ; then Feb- ruary gains another day. Thirty days hath September, Until the year 2400 every April, June, and November, year we can divide by 4 will All the rest have thirty-one, be leap year. We usually call Excepting February alone. thirty days a month unless Twenty-eight are all its store we know the exact month in Till leap year gives it one day more. question. 115 ORAL TEACHING ANSWER THE CALENDAR 1. Get a calendar for the present year. On what week day did the first day of this month fall? On what week day will the first days of all the rest of the months of the year fall? On what week day did the first days of the past months fall ? 2. Can you find what months of each year usually have the same days of the months on the same days of the week ? Why is this not true in leap year ? | 3. ‘Tell the names of the longest months. 4. How many days are there in seven weeks? in three weeks ? in eleven weeks ? 5. How many weeks are there in thirty-five days? in forty-nine days? in eighty-four days ? 6. Which is the longer time, six weeks or two months ? ten weeks or three months? one hundred days or three months ? 7. Make a rectangle upon a sheet of paper seven inches long, five inches high. Mark the inch spaces on it on each side. Draw lines across and up and down so as to make thirty-five squares, one inch on each side. 8. Cut out thirty-one squares; number them from 1 to 31. 9. Place these squares on the sheet of paper to show the present month. Write at the top of the calendar, § for Sunday, M for Monday, T for Tuesday, W for Wednesday, T for Thursday, F for Friday, 5 for Saturday. 10. Make a large monthly calendar on the blackboard. 11. Make with the squares, as in 1 above, a calendar for the next month; the last month. 12. Make February of this year; of the next leap year. ORAL TEACHING STUDY 116 TELLING TIME i) Si tit I Twenty minutes past eight o’clock. nly There are 24 hours in every day. The first hour begins halfway be- tween sunset and sunrise, when the night is darkest. Wecall the end of one day and the beginning of the next day midnight. Then we count 12 hours, 1, 2, 3, 4, 5, 6, (S.ne, LOU (2s herrea twelve o'clock in the daytime, it is just halfway between sunrise and sunset. ‘Then we begin over again, and count 1, 2, 3, to 12, _when it is midnight again. Noon means 12 o’clock in the daytime. Midnight means 12 o’clock in the night. On the clock face we find Roman figures. Ih feyoter es AES aseaeay IB Zetwo oll S45 eciotitey ELE 3 three III 9 nine £ fours Elie LO ten © five V_ 11 eleven Omsk 1V be 12 twelve cll Dele 90 oa= NL) after V means V+ I. fore X means X — I. On the clock face we do not find any figures to tell us about the minutes. I be- IX xX XI Key to clock face. 60 minutes make 1 hour. Sign for morning hours, A.M. 12 hours make 1 half day. Sign for afternoon and even- 24 hours make 1 day. ing hours, P.M. Ltt ORAL TEACHING STUDY ANSWER TELLING TIME 1 hour o’clock is the same place as 5 min- utes. There are two hands on every clock, the hour hand and the minute hand. The hour hand is always shorter than the minute hand. When we studied the fives’ table, we found that 5 x12=60. There are 60 minutes in every hour, and 12 hours in every day. The hour hand goes from XII to I in one hour, but the minute hand goes all the way around from XII past I, I], II], and so on to XII every hour. The minute hand goes twelve times as fast as the hour hand. There are twelve numbers on the clock face to mark 60 minutes. Each number means in minutes just 5 times as much as it does in hours, on the clock. | I means in hours 1, but in minutes it means 5, 5x 1=5. II means in hours 2, but in minutes it means 10. III means in hours 3, but in minutes it means 15. IIII means in hours 4, but in minutes it means 20. V means in hours 5, but in minutes it means 25. VI means in hours 6, but in minutes it means 30. VII means in hours 7, but in minutes it means 35. When the minute hand points to more than 30, we usually read the number of minutes before the next hour. 6 o’clock and 35 minutes we usually call 25 minutes before 7. 60 minutes less 35 minutes are 25 minutes. Railroads read this time 6 hours 35 minutes. VIII means in hours 8, but in minutes it means 40. 6 hours 40 minutes are twenty minutes before 7 hours. IX means in hours 9, but in minutes it means 45. X means in hours 10, but in minutes it means 50. XI means in hours 11, but in minutes it means 55. XII means 12 hours, or 60 minutes, or 0 (no) minutes. ORAL TEACHING 118 ANSWER TELLING TIME We say, “It is two o'clock.” This means “It is two hours of the clock.” When it is 2 o’clock, we find the minute hand at XII hours or 60 or 0 minutes. 2 o'clock 10:20 o'clock 4:45 o'clock twenty minutes quarter of after ten five o’clock This circle is divided into quarters. When the minute hand reaches 15 minutes after XII or 60, we say it is quar- ter past whatever hour the hour hand (| is nearest. A is at III or 15 minutes. B A When the minute hand reaches 45 min- EY, utes after XII or 15 minutes (60 — 45 = 15) before XII, we say it is quarter one half C one half jefore the hour the hour hand is nearest : : : that is, the hour toward which the hour hand is traveling. When the minute hand is at VI or 30 minutes, we say it is half past. 380=60+2. 30=4 of 60. 1. Where should the hands be to show quarter past 9: quarter to 11; half past 9; quarter to 12; quarter past 10; half past 8; half past 3; half past 7; quarter to 12; quarter past 1; quarter ‘past 6; half past 5? 2. Where is each hand at quarter past 12? at quarter past 2? at quarter to 3? at half past 4? at half past 6? at quarter to 9? at half past 11? at quarter to 8? at half past 3? at 10 minutes after 10 ? 119 BUSY WORK TELLING TIME 1. Make a large clock face on thick paper or cardboard, or on the blackboard. 2. Draw the hands to show 5 minutes past 9 o’clock, 10 minutes past 10 o'clock, 15 minutes past 11 o’clock, 20 minutes past 12 o’clock, 25 minutes past 1 o’clock. 3. Draw the hands to show 25 minutes of 3 o’clock, 20 minutes of 4 o’clock, 15 minutes of 5 o’clock, 10 minutes of 6 o’clock, 5 minutes of 7 o’clock, and 8 o’clock. 4. Draw quarter past nine o’clock, half past ten o’clock, quarter of eleven o’clock, and six o’clock. 5. Draw each one of the hours one o’clock, two, three, four, five, six, seven, eight, nine, ten, eleven. 6. Make out of cardboard a clock face, and hands out of cardboard or wood, and set the time to suit your own ideas. Make all the different times o'clock in 2, 3, 4, and 5 above. 7. Draw a picture of the clock in your schoolroom. What time does it tell? Perhaps it took you quite a long time to draw that picture. Draw another, telling what time it is now. How many minutes apart are the two times on the two clocks ? 8. School begins at o’clock. Recess is at o'clock. Recess is over at o'clock. The morning session ends at o'clock. Draw four clock faces to show these times. 9. Do you have a daily program at school? When did this lesson begin ? When will it end? Make clock faces to show these times. Show the times for other lessons. 10. Make clock faces showing the time when you get up in the morning, when you eat breakfast and other meals, and when you go to bed at night. ORAL TEACHING STUDY 120 TELLING HEAT AND COLD In the winter, when the fire goes out, we feel cold. In the summer we are often very warm. Sometimes in winter the fire is very hot, and our rooms are too warm. 212° Water boils 200 ° 150 100 98 Body warmth 90° Warm bath 70° Pleasant heat 50. 32° Ice melts 0° Zero cold Fahrenheit thermometer. The spaces are called degrees. This means equal parts of space. The sign for degree is a It is hot near bonfires or the fire in the blacksmith’s shop. It is warmer in the sunshine than in the shade. We call the warmth or coldness of the air, the temperature. We have thermometers to tell us how warm or how cold it is. Ther- mometer is from thermo, heat, and meter, measure. Inside the glass of the thermometer is a liquid heavier than water. This is a metal called quicksilver or mercury. It looks ike silver, but it flows quickly. Did you ever see little balls of quicksilver run across a table? This quicksilver needs more room and goes up the tube of the glass, when it is warm, but gets smaller and goes down in the glass when it is cold. If the glass is put in water with broken ice in it, the quicksilver goes to 32°. If we hold the bulb or thick end tight in one hand, the quicksilver goes nearly to 98°. In boiling water the quick- silver marks 212°. Hot weather is when the air is as warm as our bodies, Shek We like to have the air in our rooms at 70°; but in winter, to make the air pleasant at that temperature or warmth, we must have water vapor in it. That is why we put water on our stoves or in our furnaces, or let steam out of the steampipes into our rooms. Cold air has only a little water vapor in it. When we warm the cold air, it needs more moisture to make it pleasant to breathe. 121 ANSWER TELLING HEAT AND COLD 1. How many degrees do you find between melting ice and body warmth? 98° — 32° = 2. How many degrees do you find between melting ice and the warm bath? 90° — 32° = 3. Would you like to go swimming in a river full of floating blocks of ice? Why not? 4. Do you like to drink ice water when warm? Why ? 5. We like to go swimming in salt sea water at 68°. How many degrees is that colder than our bodies ? 6. In lakes there are often springs of cold water at 45°. Swimmers often have chills called “cramps” in fresh water because of these springs. Why? 98° —45°= 7. Cool water, 55°, is very pleasant and good to drink in summer when our bodies become very warm in the hot air. How much cooler is the water than our bodies if our temperature is 99° ? 8. When we are sick, we usually have fever. Over 100° may be a fever. If our body warmth is 104°, our doctor is very anxious. How many degrees too warm is this? 104° — 98° = 9. Sometimes we have a chill. If our body warmth falls three degrees, 3°, how warm:are we? 98° —3°= 10. The temperature inside the mouth is 98° or 99°; that of ice cream is usually 32°. Why does it seem so cold? 11. We warm the air with our body warmth. When the wind blows, it takes the warm air away from the skin fast. This is why we get just as cold in a strong wind when the air is 50° as we do on a quiet day when it is 32°. Compare 98° — 50°= and 98° — 82°= RATIOS 122 STUDY MUSIC FRACTIONS In music we have equal parts or fractions of time. A whole note is the musical unit of time. oO 18a whole note © © are two whole notes. is a half note vie" 4 — 1. } isa quarter note 2 , i ie —) nso hale a an eighth note © “iPass bol papas = OOK ae The space between the two vertical bars in this drawing is one meas- ure. One whole note would take Ic A. | S | all the time in this measure. Two half notes would take all the time. ‘T’'wo quarter notes and one half note would also take all the time. 5 » 1. fg +GH5S 1 i Rae is ti +445 4+g=1 3. ¢+4= 1. Pr eee ee ag Gs tar eae 5. gg te ao ale 123 ORAL TEACHING STUDY TELLING ANGLES B B E F C A G H G D D A circle with 4 quarters A circle with 8 eighths and 4 right angles. and many different angles. > AC isa diameter. It divides the circle into halves be- cause it is a straight line through the center of the circle. BD isa diameter. It divides each of the circle’s halves . by pore fal Wo By hy en Pe into two equal parts: 4 of $= Dee / conse Right Obtuse These are angles: Angles are formed by the meetings of lines. AWB is anangle. ‘Trace it. Two diameters crossing each other so as to divide a circle into quarters make right angles with each other. We say that BW is perpendicular to AW because it forms the right angle AWB. We call angles smaller than right angles acute angles. ANE isan acute angle. Point out other acute angles. We call angles larger than right angles obtuse angles. ANF is an obtuse angle. Point it out. We call this a horizontal line : And this we call a vertical sae ABCD is the perimeter or circumference of the circle. ORAL 124 QUESTIONS 1. What is the ratio of 5 to 50? of 5 to 5? of 5 to 25? of 5 to 40? of 5to 55? of 15 to 5? of 85 to 5? of 45 to 5? of 10 to 5? of 20 to 5? 2. What part of 80 is 5? 6? 12? 18? 24? 3. A mason can build a wall in 30 days. What part of it can he build in 5 days? in 6 days? in 18 days? in 12 days? in 24 days? 4. George can ride 50 miles in 5 hours on his wheel. What part of that distance can he ride in 1 hour? in 3 hours ? in 4 hours ? 5. How many feet are Hie in 25 inches? in 380 inches? in 60 inches? 6. Esther bought 9 yards of braid at 5¢ a yard. She gave the clerk a fifty-cent piece. What change should she get ? 7. How much money will 5 gallons of kerosene cost at 12¢ a gallon? 8. Walter paid 40¢ for 2 quarts of molasses. How much would a pint cost at the same rate ? 9. At 11¢ a quart, how many quarts of berries can pee buy for 55¢? 10. Mr. Brown wishes to divide 40¢ equally among his four children. How many cents must he give to each child ? 11. Ina pond there were 36 lilies. A boy picked 9 of them. What part of the whole number of lilies did he pick ? 12. A florist had 44 roses. - of them were white, =4, were red, and the rest were eas How many roses ihe white? How many were red? How many were yellow? ee 125 BUSY WORK REVIEW 1. With a thermometer take the temperature out of doors at 8.80 A.M., at 12M.,and at 8p.m. Tell the differ- ences. Do this for five school days. 2. Take the temperature in the schoolroom every hour all day. 3. Draw pictures of thermometers, showing the quick- silver at 98°, at 32°, at zero, at 212°, at 70°, at 90°, at 100°: 4. Draw pictures of thermometers, telling when ice melts, when water boils, when the heat is pleasant, how warm the body is when one is well, when one has a fever, when one has a chill, how warm a bath should be, and how low the mercury is when it is very, very cold, below zero. 5. Why are some music notes called whole notes ? half notes? quarter notes? eighth notes ? 6. What time is it at noon? When does 12 o’clock come next ? 7. How many hours do we spend in school each day ? 8. Where are the hands on the clock face at the times when you go to school morning and afternoon ? 9. Edgar raised 48 quarts of strawberries. He sold zy of them early in the season and +; of them later on. How many quarts did he sell at his first sale? How many quarts are. ;%, of 48 quarts? ; of 48 quarts? 4 of 48 quarts? 1o. A bin contains 32 bushels of corn. The owner took out } to be ground into meal and 4 for food for his horses. How many bushels in all did he take out ? 11. Which is the largest angle, an acute, a right, or an obtuse angle ? STUDY COPY REVIEWS Counting by 3’s. A248 (4 6 a7 11612 -15014-15 16) 17, 21 22 23 24 25 26 27 28 2 dl 32 33 34 35 36 37 © 41 42 43 44 45 46 47 51 52 53 54 55 56 57 58 5 61 62 63 64 65 66 67 F1725(3 f4.Id5 16-17 81 82 83 84 85 86 87 91 92 93 94 95 96 97 Counting by 4’s. be oe coy eee LY a ad 1112 °15 14°15 16 17 BT e223 24: 20826 27 31 32 35 34 35 36 41 42 45 44 45 46 47 51 52 53 54 55 56 57 61 62 63 64 65 66 67 TAVIZs OH 1D 7041 81 82 83 84 85 86 87 91 92 93 94 95 96 97 Counting by 5’s. oak Ow Ai; 14 15 16 17 on) LO — i — or) ; oC ht DO bo WM bk WH WL CL LO b PO — oo ws) a _ a H Oo Oo 44 45 46 47 54 55 56 57 64 65 66 67 14.75 76.77 84 85 86 87 93 94 95 96 97 > On _— on On ot) ei lee) C8 | == COCO coOoON OS Co tC C&O OV & 23 24 25 26 27 2 34 35 36 37 126 NUMBER TABLES Counting by 6's. 1 P2e Beate tf OOy 1112 4514515-16 517, 21 Ze eoree 20020 sed 31 32 33 34 35 36 37 41 42 43 44 45 46 47 D1 52 53 54 55 56 57 61 62 63 64 65 66 67 71°72 73 74 75 76 77 81 82 83 84 85 86 87 91 92 93.94 95.96 97 or or Ow GSueCr IOx Lek 2 ted eaters) a Oe, Tiere oat el ogi 21422 25'24°20 #4 27 31 32 35 34 35 36 37 : 41 42 43 44 45 46 47 d1 52 53 54 55 56 57 | 61 62 65 64 65 66 67 71 72 73 74 75 76 77 81 82 85 84 85 86 87 91 92 93 94 95 96 97 Counting by T’s. REC ee neti ge hin A 213814 15 16 17 2 donot ooP eed, 31 32 53 34:35 36 37 41 42 43 44 45 46 47 51 52 53 54 55 56 57 61 62 63 64 65 66 67 11 72 73 (4 75 76 77 81 82 83 84 85 86 87 8 9 18 19 28 29 3.9 18°19 28 29 38 39 48 49 58 59 68 69 78 79 88 89 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 91 92 93 94 95 96 97 98 99 100 The 10’s are always at the ends of the rows. = Counting by 9’s. 73 — 85 97 98 3 15 99 109 110 111 121 122 123 153 134 135 NUMBER TABLES 1 4 100 112 124 136 9) 17 29 6 18 30 42 54 66 78 90 101 102 115 114 125 126 137 138 Counting by 11’s. 1 15 25 37 49 61 73 85 97 9 14 3 15 27 39 51 63 75 87 2h, 109 110 111 121 122 123 133 154 155 4 88 100 Liz 124 136 ov 89 101 102 115 114 125 126 157 138 79 91 103 115 127 159 91 103 115 121, 139 12 20 52 80 92 104 7 93 105 116 117 128 140 80 92 104 116 128 140 129 1: 141 93 105 ise 129 141 46 58 70 82 94 TO 144 59 71 83 95 96 106 107 108 118 119 120 130 131 132 142 143 144 that the 2 figures in each number which contains Notice 3 9 always add together 9, ex- cept 99. 9+9 Notice also that the unit figure of each larger multiple of 9 is always 1 less. 18, 27, 36, and so on. Notice that from 1 to 100 the 2 figures in each multiple of 11 are always the same, and that above 100 the number of tens always in- creases 1, 110, 121, and so on, and the ber of units al- ways increases 1, 121, 182, 148. num- 1. Copy these Number Tables in red and blue pencil on paper, or in red and blue chalk on the blackboard. 2. Read these Tables in class, explaining them. TESTS OF 128 SUCCESS ORAL 1. Count by fours to one hundred. 2. How many are 15—44+8+4943—10—2-7x2=? 3. How many dimes are there in half a dollar ? 4. How much is 4 of 4? dof 4? lof 2? 5. Is 4 more or less than}? } than $? }thand? Why? 6. Give the multiplication table of threes. 7. How many pints are there in a gallon? in a peck? 8. Measure the size of the schoolroom in feet. 9. Read the calendar for to-day. 10. Tell a number-story about 24 cents, 4 boys, and two dozen apples that cost a dime a dozen. WRITTEN Teed see eo eee 2. Subtract: 46 92 T4 eee eee La Lis Eo IBS ein <. oe 3. Write the Number Table of One Hundred, showing very plainly every number containing 7. 4. Draw a clock face, showing 5.20 o’clock. 5. Draw a rectangle divided into sixths. 6. Write in words 2671, 4203, 3081, 1850. 7, Answer 0+(4x2)=? (8x3)+9=? (18+6)4+7=? 8. John had one dollar. He spent a quarter for a cap, forty cents for a bantam hen, and a nickel for chestnuts. How much money did he have left ? 9. What is the ratio of 6 to 9? of 12 to4? of d to 3? 10. 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