g.1313914129913129142423191929991321282626148829232916151917191922————————
Woody ['16] has constructed his well-known tests on this principle, though he uses only one example at each step of difficulty instead of eight or ten as suggested above. His test, so far as addition of integers goes, is:—
SERIES A. ADDITION SCALE (in part)
By Clifford Woody
(1)(2)(3)(4)(5)(6)(7)(8)(9)23—243—172—5345—7226—6037—3 + 1 =2 + 5 + 1 =201023025—(10)(11)(12)(13)(14)(15)(16)(17)(18)213335—325917—431213—232516—25 + 42 =100334520146—924121519—199194295156——2563138749542065——(19)(20)(21)(22)$ .751.25.49——$12.5016.7515.75——$8.005.752.334.16.946.32——547197685678456393525240152——
In his original report, Woody gives no scheme for scoring an individual, wisely assuming that, with so few samples at each degree of difficulty, a pupil's score would be too unreliable for individual diagnosis. The test is reliable for a class; and for a class Woody used the degree of difficulty such that a stated fraction of the class can do the work correctly, if twenty minutes is allowed for the thirty-eight examples of the entire test.
The measurement of even so simple a matter as the efficiency of a pupil's responses to these tests in adding integers is really rather complex. There is first of all the problem of combining speed and accuracy into some single estimate. Stone gives no credit for a column unless it is correctly added. Courtis evades the difficulty by reporting both number done and number correct. The author's scheme, which gives specified weights to speed and accuracy at each step of the series, involves a rather intricate computation.
This difficulty of equating speed and accuracy in adding means precisely that we have inadequate notions of what the ability is that the elementary school should improve. Until, for example, we have decided whether, for a given group of pupils, fifteen Courtis attempts with ten right, is or is not a better achievement than ten Courtis attempts with nine right, we have not decided just what the business of the teacher of addition is, in the case of that group of pupils.
There is also the difficulty of comparing results when short and long columns are used. Correctness with a short column, say of five figures, testifies to knowledge of the process and to the power to do four successive single additions without error. Correctness with a long column, say of ten digits, testifies to knowledge of the process and to the power to do nine successive single additions without error. Now if a pupil's precision was such that on the average hemade one mistake in eight single additions, he would get about half of his five-digit columns right and almost none of his ten-digit columns right. (He would do this, that is, if he added in the customary way. If he were taught to check results by repeated addition, by adding in half-columns and the like, his percentages of accurate answers might be greatly increased in both cases and be made approximately equal.) Length of column in a test of addition under ordinary conditions thus automatically overweights precision in the single additions as compared with knowledge of the process, and ability at carrying.
Further, in the case of a column of whatever size, the result as ordinarily scored does not distinguish between one, two, three, or more (up to the limit) errors in the single additions. Yet, obviously, a pupil who, adding with ten-digit columns, has half of his answer-figures wrong, probably often makes two or more errors within a column, whereas a pupil who has only one column-answer in ten wrong, probably almost never makes more than one error within a column. A short-column test is then advisable as a means of interpreting the results of a long-column test.
Finally, the choice of a short-column or of a long-column test is indicative of the measurer's notion of the kind of efficiency the world properly demands of the school. Twenty years ago the author would have been readier to accept a long-column test than he now is. In the world at large, long-column addition is being more and more done by machine, though it persists still in great frequency in the bookkeeping of weekly and monthly accounts in local groceries, butcher shops, and the like.
The search for a measure of ability to add thus puts the problem of speedversusprecision, and of short-columnversuslong-column additions clearly before us. The latterproblem has hardly been realized at all by the ordinary definitions of ability to add.
It may be said further that the measurement of ability to add gives the scientific student a shock by the lack of precision found everywhere in schools. Of what value is it to a graduate of the elementary school to be able to add with examples like those of the Courtis test, getting only eight out of ten right? Nobody would pay a computer for that ability. The pupil could not keep his own accounts with it. The supposed disciplinary value of habits of precision runs the risk of turning negative in such a case. It appears, at least to the author, imperative that checking should be taught and required until a pupil can add single columns of ten digits with not over one wrong answer in twenty columns. Speed is useful, especially indirectly as an indication of control of the separate higher-decade additions, but the social demand for addition below a certain standard of precision isnil, and its disciplinary value isnilor negative. This will be made a matter of further study later.
Measurements of these abilities may be of two sorts—(1) of the speed and accuracy shown in doing one same sort of task, as illustrated by the Courtis test for addition shown on page 28; and (2) of how hard a task can be done perfectly (or with some specified precision) within a certain assigned time or less, as illustrated by the author's rough test for addition shown on pages 28 and 29, and by the Woody tests, when extended to include alternative forms.
The Courtis tests, originated as an improvement on the Stone tests and since elaborated by the persistent devotion of their author, are a standard instrument of the first sort for measuring the so-called 'fundamental' arithmeticalabilities with integers. They are shown on this and the following page.
Tests of the second sort are the Woody tests, which include operations with integers, common and decimal fractions, and denominate numbers, the Ballou test for common fractions ['16], and the "Ladder" exercises of the Thorndike arithmetics. Some of these are shown on pages 36 to 41.
Courtis Test
Arithmetic. Test No. 1. Addition
Series B
You will be given eight minutes to find the answers to as many of these addition examples as possible. Write the answers on this paper directly underneath the examples. You are not expected to be able to do them all. You will be marked for both speed and accuracy, but it is more important to have your answers right than to try a great many examples.
You will be given eight minutes to find the answers to as many of these addition examples as possible. Write the answers on this paper directly underneath the examples. You are not expected to be able to do them all. You will be marked for both speed and accuracy, but it is more important to have your answers right than to try a great many examples.
927297136486384176277837379925340765477783445882756473988524881697682959837983386140266200594603924315353812679366481118110661904466241851778781854794547355796535849756965177192834850323157222344124439567733229953525————————————————
and sixteen more addition examples of nine three-place numbers.
and sixteen more addition examples of nine three-place numbers.
Courtis Test
Arithmetic. Test No. 2. Subtraction
Series B
You will be given four minutes to find the answers to as many of these subtraction examples as possible. Write the answers on this paper directly underneath the examples. You are notexpected to be able to do them all. You will be marked for both speed and accuracy, but it is more important to have your answers right than to try a great many examples.
You will be given four minutes to find the answers to as many of these subtraction examples as possible. Write the answers on this paper directly underneath the examples. You are notexpected to be able to do them all. You will be marked for both speed and accuracy, but it is more important to have your answers right than to try a great many examples.
10779549175088824915000538793998377197029574063941990156372207316————————————————————
and twenty more tasks of the same sort.
and twenty more tasks of the same sort.
Courtis Test
Arithmetic. Test No. 3. Multiplication
Series B
You will be given six minutes to work as many of these multiplication examples as possible. You are not expected to be able to do them all. Do your work directly on this paper; use no other. You will be marked for both speed and accuracy, but it is more important to get correct answers than to try a large number of examples.
You will be given six minutes to work as many of these multiplication examples as possible. You are not expected to be able to do them all. Do your work directly on this paper; use no other. You will be marked for both speed and accuracy, but it is more important to get correct answers than to try a large number of examples.
8246784348373478648229702831546——————————
and twenty more multiplication examples of the same sort.
and twenty more multiplication examples of the same sort.
Courtis Test
Arithmetic. Test No. 4. Division
Series B
You will be given eight minutes to work as many of these division examples as possible. You are not expected to be able to do them all. Do your work directly on this paper; use no other. You will be marked for both speed and accuracy, but it is more important to get correct answers than to try a large number of examples.
You will be given eight minutes to work as many of these division examples as possible. You are not expected to be able to do them all. Do your work directly on this paper; use no other. You will be marked for both speed and accuracy, but it is more important to get correct answers than to try a large number of examples.
25) 677594) 8535237) 999086) 80066
and twenty more division examples of the same sort.
and twenty more division examples of the same sort.
SERIES B. MULTIPLICATION SCALE
By Clifford Woody
(1)(3)(4)(5)3 × 7 =2 × 3 =4 × 8 =233—(8)(9)(11)(12)503—2546—10368—50966—(13)(16)(18)(20)87548——78989——24234——287.05——(24)(26)(27)(29)1625⁄8——974259——6.253.2——1⁄8× 2 =(33)(35)(37)(38)2½ × 3½ =987¾25———2¼ × 4½ × 1½ =.09631⁄8.084——
SERIES B. DIVISION SCALEBy Clifford Woody
(1)(2)(7)(8)3 )69 )274 ÷ 2 =9 )0(11)(14)(15)(17)2 )138 )5856¼ of 128 =50 ÷ 7 =(19)(23)(27)(28)248 ÷ 7 =23 )4697⁄8of 624 =.003 ).0936(30)(34)(36)3⁄4÷ 5 =62.50 ÷ 1¼ =9 )69 lbs. 9 oz.
Ballou Test
Addition of Fractions
Test 1Test 2(1)¼¼—(2)3⁄141⁄14—(1)1⁄31⁄6—(2)2⁄73⁄14—Test 3Test 4(1)3⁄511⁄15—(2)5⁄61⁄2—(1)1⁄79⁄10—(2)7⁄91⁄4—Test 5Test 6(1)1⁄101⁄6—(2)4⁄95⁄12—(1)1⁄69⁄10—(2)5⁄63⁄8—
An Addition Ladder [Thorndike, '17, III, 5]
Begin at the bottom of the ladder. See if you can climb to the top without making a mistake. Be sure to copy the numbers correctly.
Step 6.a.Add 11⁄3yd.,7⁄8yd., 1¼ yd.,3⁄4yd.,7⁄8yd., and 1½ yd.b.Add 62½¢, 662⁄3¢, 56¼¢, 60¢, and 62½¢.c.Add 15⁄16, 19⁄32, 13⁄8, 111⁄32, and 17⁄16.d.Add 11⁄3yd., 1¼ yd., 1½ yd., 2 yd.,3⁄4yd., and2⁄3yd.Step 5.a.Add 4 ft. 6½ in., 53¼ in., 5 ft. ½ in., 56¾ in., and 5 ft.b.Add 7 lb., 6 lb. 11 oz., 7½ lb., 6 lb. 4½ oz., and 8½ lb.c.Add 1 hr. 6 min. 20 sec., 58 min. 15 sec., 1 hr. 4 min., and 55 min.d.Add 7 dollars, 13 half dollars, 21 quarters, 17 dimes, and 19 nickels.Step 4.a.Add .05½, .06, .04¾, .02¾, and .05¼.b.Add .331⁄3, .12½, .18, .162⁄3, .081⁄3and .15.c.Add .081⁄3, .06¼, .21, .03¾, and .162⁄3.d.Add .62, .64½, .662⁄3, .10¼, and .68.Step 3.a.Add 7¼, 6½, 83⁄8, 5¾, 95⁄8and 37⁄8.b.Add 45⁄8, 12, 7½, 8¾, 6 and 5¼.c.Add 9¾, 57⁄8, 41⁄8, 6½, 7, 35⁄8.d.Add 12, 8½, 71⁄3, 5, 62⁄3, and 9½.Step 2.a.Add 12.04, .96, 4.7, 9.625, 3.25, and 20.b.Add .58, 6.03, .079, 4.206, 2.75, and 10.4.c.Add 52, 29.8, 41.07, 1.913, 2.6, and 110.d.Add 29.7, 315, 26.75, 19.004, 8.793, and 20.05.Step 1.a.Add 103⁄5, 111⁄5, 104⁄5, 11, 112⁄5, 103⁄5, and 11.b.Add 73⁄8, 65⁄8, 8, 91⁄8, 77⁄8, 53⁄8, and 81⁄8.c.Add 21½, 18¾, 31½, 19¼, 17¼, 22, and 16½.d.Add 145⁄12, 127⁄12, 911⁄12, 61⁄12, and 5.
A Subtraction Ladder [Thorndike, '17, III, 11]
Step 9.a.2.16 mi. − 1¾ mi.c.2 min. 10½ sec. − 93.4 sec.e.10 gal. 2½ qt. − 4.623 gal.b.5.72 ft. − 5 ft. 3 in.d.30.28 A. − 101⁄5A.Step 8.abcde257⁄12123⁄4———101⁄471⁄3———95⁄1663⁄8———57⁄1623⁄4———42⁄313⁄4———Step 7.abcde283⁄4161⁄8———401⁄2143⁄8———101⁄461⁄2———241⁄3111⁄2———371⁄2143⁄4———Step 6.abcde101⁄342⁄3———71⁄423⁄4———151⁄863⁄8———121⁄5114⁄5———41⁄1627⁄16———Step 5.abcde584⁄5521⁄5———662⁄3331⁄3———287⁄875⁄8———62½37½——97⁄1245⁄12——Step 4.a.4 hr. − 2 hr. 17 min.c.1 lb. 5 oz. − 13 oz.e.1 bu. − 1 pk.b.4 lb. 7 oz. − 2 lb. 11 oz.d.7 ft. − 2 ft. 8 in.Step 3.abcde92 mi.84.15 mi.————6735 mi.6689 mi.————$3 − 89¢————28.4 mi.18.04 mi.————$508.40208.62————Step 2.abcde$25.009.36———$100.0071.28———$750.00736.50———6124 sq. mi.2494 sq. mi.—————7846 sq. mi.2789 sq. mi.—————Step 1.abcde$18.647.40———$25.3913.37———$56.7045.60———819.4 mi.209.2 mi.————67.55 mi.36.14 mi.————
An Average Ladder [Thorndike, '17, III, 132]
Find the average of the quantities on each line. Begin withStep 1. Climb to the top without making a mistake. Be sure to copy the numbers correctly. Extend the division to two decimal places if necessary.
Step 6.a. 22⁄3, 17⁄8, 2¾, 4¼, 35⁄8, 3½b. 62½¢, 662⁄3¢, 40¢, 831⁄3¢, $1.75, $2.25c. 311⁄16, 39⁄32, 33⁄8, 317⁄32, 37⁄16d. .17, 19, .162⁄3, .15½, .23¼, .18Step 5.a. 5 ft. 3½ in., 61¼ in., 58¾ in., 4 ft. 11 in.b. 6 lb. 9 oz., 6 lb. 11 oz., 7¼ lb., 73⁄8lb.c. 1 hr. 4 min. 40 sec., 58 min. 35 sec., 1¼ hr.d. 2.8 miles, 3½ miles, 2.72 milesStep 4.a. .03½, .06, .04¾, .05½, .05¼b. .043, .045, .049, .047, .046, .045c. 2.20, .87½, 1.18, .93¾, 1.2925, .80d. .14½, .12½, .331⁄3, .162⁄3, .15, .17Step 3.a. 5¼, 4½, 83⁄8, 7¾, 65⁄8, 93⁄8b. 95⁄8, 12, 8½, 8¾, 6, 5¼, 9c. 93⁄8, 5¾, 41⁄8, 7½, 6d. 11, 9½, 101⁄3, 13, 162⁄3, 9½Step 2.a.13.05, .97, 4.8, 10.625, 3.37b.1.48, 7.02, .93, 5.307, 4.1, 7, 10.4c.68, 71.4, 59.8, 112, 96.1, 79.8d.2.079, 3.908, 4.165, 2.74Step 1.a.4, 9½, 6, 5, 7½, 8, 10, 9b.6, 5, 3.9, 7.1, 8c.1086, 1141, 1059, 1302, 1284d.$100.82, $206.49, $317.25, $244.73
As such tests are widened to cover the whole task of the elementary school in respect to arithmetic, and accepted by competent authorities as adequate measures of achievement in computing, they will give, as has been said, a working definition of the task. The reader will observe, for example, that work such as the following, though still found in many textbooks and classrooms, does not, in general, appear in the modern tests and scales.
Reduce the following improper fractions to mixed numbers:—
19⁄1343⁄21176⁄25198⁄14
Reduce to integral or mixed numbers:—
61381⁄372134⁄67413⁄413697⁄225
Simplify:—
3⁄4of8⁄9of3⁄5of15⁄22
Reduce to lowest terms:—
357⁄527264⁄312492⁄779418⁄874854⁄176930⁄73544⁄24277⁄84718⁄24396⁄224
Find differences:—
62⁄731⁄14——85⁄1151⁄7——84⁄1337⁄13——51⁄4211⁄14——71⁄821⁄7——
Square:—
2⁄34⁄55⁄76⁄910⁄1112⁄132⁄715⁄1619⁄2017⁄1825⁄3041⁄53
Multiply:—
2⁄11× 33 32 ×3⁄1439 ×2⁄1360 ×11⁄2877 ×4⁄1163 ×2⁄2754 ×8⁄4565 ×3⁄1334416⁄214322⁄7
Stone ['08] measured achievement with the following problems, fifteen minutes being the time allowed.
"Solve as many of the following problems as you have time for; work them in order as numbered:
1. If you buy 2 tablets at 7 cents each and a book for 65 cents, how much change should you receive from a two-dollar bill?2. John sold 4 Saturday Evening Posts at 5 cents each. He kept1⁄2the money and with the other1⁄2he bought Sunday papers at 2 cents each. How many did he buy?3. If James had 4 times as much money as George, he would have $16. How much money has George?4. How many pencils can you buy for 50 cents at the rate of 2 for 5 cents? '5. The uniforms for a baseball nine cost $2.50 each. The shoes cost $2 a pair. What was the total cost of uniforms and shoes for the nine?6. In the schools of a certain city there are 2200 pupils;1⁄2are in the primary grades,1⁄4in the grammar grades,1⁄8in the high school, and the rest in the night school. How many pupils are there in the night school?7. If 3½ tons of coal cost $21, what will 5½ tons cost?8. A news dealer bought some magazines for $1. He sold them for $1.20, gaining 5 cents on each magazine. How many magazines were there?9. A girl spent1⁄8of her money for car fare, and three times as much for clothes. Half of what she had left was 80 cents. How much money did she have at first?10. Two girls receive $2.10 for making buttonholes. One makes 42, the other 28. How shall they divide the money?11. Mr. Brown paid one third of the cost of a building; Mr. Johnson paid1⁄2the cost. Mr. Johnson received $500 more annual rent than Mr. Brown. How much did each receive?12. A freight train left Albany for New York at 6 o'clock. An express left on the same track at 8 o'clock. It went at the rate of 40 miles an hour. At what time of day will it overtake the freight train if the freight train stops after it has gone 56 miles?"
1. If you buy 2 tablets at 7 cents each and a book for 65 cents, how much change should you receive from a two-dollar bill?
2. John sold 4 Saturday Evening Posts at 5 cents each. He kept1⁄2the money and with the other1⁄2he bought Sunday papers at 2 cents each. How many did he buy?
3. If James had 4 times as much money as George, he would have $16. How much money has George?
4. How many pencils can you buy for 50 cents at the rate of 2 for 5 cents? '
5. The uniforms for a baseball nine cost $2.50 each. The shoes cost $2 a pair. What was the total cost of uniforms and shoes for the nine?
6. In the schools of a certain city there are 2200 pupils;1⁄2are in the primary grades,1⁄4in the grammar grades,1⁄8in the high school, and the rest in the night school. How many pupils are there in the night school?
7. If 3½ tons of coal cost $21, what will 5½ tons cost?
8. A news dealer bought some magazines for $1. He sold them for $1.20, gaining 5 cents on each magazine. How many magazines were there?
9. A girl spent1⁄8of her money for car fare, and three times as much for clothes. Half of what she had left was 80 cents. How much money did she have at first?
10. Two girls receive $2.10 for making buttonholes. One makes 42, the other 28. How shall they divide the money?
11. Mr. Brown paid one third of the cost of a building; Mr. Johnson paid1⁄2the cost. Mr. Johnson received $500 more annual rent than Mr. Brown. How much did each receive?
12. A freight train left Albany for New York at 6 o'clock. An express left on the same track at 8 o'clock. It went at the rate of 40 miles an hour. At what time of day will it overtake the freight train if the freight train stops after it has gone 56 miles?"
The criteria he had in mind in selecting the problems were as follows:—
"The main purpose of the reasoning test is the determination of the ability of VI A children to reason in arithmetic. To this end, the problems, as selected and arranged, are meant to embody the following conditions:—
1. Situations equally concrete to all VI A children.2. Graduated difficulties.a.As to arithmetical thinking.b.As to familiarity with the situation presented.3. The omission ofa.Large numbers.b.Particular memory requirements.c.Catch problems.d.All subject matter except whole numbers, fractions, and United States money.
1. Situations equally concrete to all VI A children.
2. Graduated difficulties.a.As to arithmetical thinking.b.As to familiarity with the situation presented.
3. The omission ofa.Large numbers.b.Particular memory requirements.c.Catch problems.d.All subject matter except whole numbers, fractions, and United States money.
The test is purposely so long that only very rarely did any pupil fully complete it in the fifteen minute limit."
Credits were given of 1, for each of the first five problems, 1.4, 1.2, and 1.6 respectively for problems 6, 7, and 8, and of 2 for each of the others.
Courtis sought to improve the Stone test of problem-solving, replacing it by the two tests reproduced below.
ARITHMETIC—Test No. 6. Speed Test—Reasoning
Do not workthe following examples. Read each example through, make up your mind what operation you would use if you were going to work it, then write the name of the operation selected in the blank space after the example. Use the following abbreviations:—"Add." for addition, "Sub." for subtraction, "Mul." for multiplication, and "Div." for division.Operation1. A girl brought a collection of 37 colored postal cards to school one day, and gave away 19 cards to her friends. How many cards did she have left to take home?2. Five boys played marbles. When the game was over, each boy had the same number of marbles. If there were 45 marbles altogether, how many did each boy have?3. A girl, watching from a window, saw 27 automobiles pass the school the first hour, and 33 the second. How many autos passed by the school in the two hours?4. In a certain school there were eight rooms and each room had seats for 50 children. When all the places were taken, how many children were there in the school?5. A club of boys sent their treasurer to buy baseballs. They gave him $3.15 to spend. How many balls did they expect him to buy, if the balls cost 45¢. apiece?6. A teacher weighed all the girls in a certain grade. If one girl weighed 79 pounds and another 110 pounds, how many pounds heavier was one girl than the other?7. A girl wanted to buy a 5-pound box of candy to give as a present to a friend. She decided to get the kind worth 35¢. a pound. What did she pay for the present?8. One day in vacation a boy went on a fishing trip and caught 12 fish in the morning, and 7 in the afternoon. How many fish did he catch altogether?9. A boy lived 15 blocks east of a school; his chum lived on the same street, but 11 blocks west of the school. How many blocks apart were the two boys' houses?10. A girl was 5 times as strong as her small sister. If the little girl could lift a weight of 20 pounds, how large a weight could the older girl lift?11. The children of a school gave a sleigh-ride party. There were 270 children to go on the ride and each sleigh held 30 children. How many sleighs were needed?12. In September there were 43 children in the eighth grade of a certain school; by June there were 59. How many children entered the grade during the year?13. A girl who lived 17 blocks away walked to school and back twice a day. What was the total number of blocks the girl walked each day in going to and from school?14. A boy who made 67¢. a day carrying papers, was hired to run on a long errand for which he received 50¢. What was the total amount the boy earned that day?Total Right(Two more similar problems follow.)Test 6 and Test 8 are from the Courtis Standard Test. Used by permission of S. A. Courtis.
Do not workthe following examples. Read each example through, make up your mind what operation you would use if you were going to work it, then write the name of the operation selected in the blank space after the example. Use the following abbreviations:—"Add." for addition, "Sub." for subtraction, "Mul." for multiplication, and "Div." for division.
Operation1. A girl brought a collection of 37 colored postal cards to school one day, and gave away 19 cards to her friends. How many cards did she have left to take home?2. Five boys played marbles. When the game was over, each boy had the same number of marbles. If there were 45 marbles altogether, how many did each boy have?3. A girl, watching from a window, saw 27 automobiles pass the school the first hour, and 33 the second. How many autos passed by the school in the two hours?4. In a certain school there were eight rooms and each room had seats for 50 children. When all the places were taken, how many children were there in the school?5. A club of boys sent their treasurer to buy baseballs. They gave him $3.15 to spend. How many balls did they expect him to buy, if the balls cost 45¢. apiece?6. A teacher weighed all the girls in a certain grade. If one girl weighed 79 pounds and another 110 pounds, how many pounds heavier was one girl than the other?7. A girl wanted to buy a 5-pound box of candy to give as a present to a friend. She decided to get the kind worth 35¢. a pound. What did she pay for the present?8. One day in vacation a boy went on a fishing trip and caught 12 fish in the morning, and 7 in the afternoon. How many fish did he catch altogether?9. A boy lived 15 blocks east of a school; his chum lived on the same street, but 11 blocks west of the school. How many blocks apart were the two boys' houses?10. A girl was 5 times as strong as her small sister. If the little girl could lift a weight of 20 pounds, how large a weight could the older girl lift?11. The children of a school gave a sleigh-ride party. There were 270 children to go on the ride and each sleigh held 30 children. How many sleighs were needed?12. In September there were 43 children in the eighth grade of a certain school; by June there were 59. How many children entered the grade during the year?13. A girl who lived 17 blocks away walked to school and back twice a day. What was the total number of blocks the girl walked each day in going to and from school?14. A boy who made 67¢. a day carrying papers, was hired to run on a long errand for which he received 50¢. What was the total amount the boy earned that day?Total Right
(Two more similar problems follow.)
Test 6 and Test 8 are from the Courtis Standard Test. Used by permission of S. A. Courtis.
ARITHMETIC—Test No. 8. Reasoning