The value of mathematics teams in junior high schools · 2020. 4. 2. · Mathematics Contest Rules...

The value of mathematics teams in junior high schools

Item Type text; Thesis-Reproduction (electronic)

Authors Kessler, Rollo Virgil, 1900-

Publisher The University of Arizona.

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THE VALUE OF MATHEMATICS TEAMS IN JUNIOR HIGH SCHOOLS.

BYROLLO VIRGIL KESSLER

---------- ^

Submitted in partial fulfillment of the requirements for the degree of

Master of Artsin the College of Education of the

UNIVERSITY OF ARIZONA

1933

Approved:yfajor a&v1aer

, |9 3 3Bate

ACKHOYiLEDGMEHT

The author wishes to acknowledge the fine cooperative spirit of the mathematics students of Mansfeld Junior High School itiilch has played-no little part in the developing of the mathematics teams.

Although the author originated the mathematics team idea with the aid of his students, he must admit that other Mansfeld teachers deserve the credit for the develop ment of the idea. Although the author was in charge of the first mathematics tournament, the interest which made that tournament a success was developed in the mathematics classes after the author wag teaching general science.

The cooperative spirit of the executives of the Tucson school system has made it possible to develop the mathematics team idea. This system gives the teachers freedom of thought and method, which encourages new ideas.

The author also feels indebted to the faculty of the Educational Department of the University of Arizona for their encouragement, inspiration, and help.

After all, there is very little that one man can do without the cooperation of others. The author has recognized the value of this cooperation from others and in this humble way wishes to thank those who have aided in the development of the mathematics team idea, as well as those whose cooperation made this experiment possible.

90735 R. V. K.

TABLE OF CONTENTH

Chapter Page....... . ■

I. Introduction ................................... 1\ . ■ : ■ " - : : ' '........ ■ ; . ; .

Statement of Problem............................ 2Procedure................ 3History......................... .......... 4

II. The Experiment............................. 6Equating of the Groups..........................12

III. Results......................... ................25

IV. Conclusion ............................... ....34Suggested Studies........... ,35

Bibliography.................... ...............36

Appendix.................. ...........^ , IMathematics Contest Rules Compass Diagnostic Test No. XVIII Courtis Standard Test, Series MB*.

1

CHAPTER IIHTRODUCTION

All junior hl^h school mathematics teachers realize the need of the drill in the four fundamentals of arithmetic, The hardest thing to teach any person is something which he thinks he already knows. The hardest thing in which to drill a class is something in which they think they need no drill. The attitude in which the class attacks its work will determine the results more than the content of the material used. If other factors are relatively equal, the spirit in which we do anything will determine the results which will aeerue from our. efforts.

Junior high school teachers must motivate their drill work in the fundamentals# As the students have had charts, graphs, and records used in arithmetic classes since the third grade to motivate their drill work, one feels the need of a new technique for the motivation of this work in the junior high school. The author decided to form mathematics teams to motivate the drill in arithmetical fundamentals.

After using the mathematics teams in his classesand seeing the other mathematics teachers in Mansfeld Junior High SohooP^use teams in their classes the ques-1. All junior high schools referred to in this thesis are located at Tucson, Arizona.

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tton arose as to whether or not the increased motivation oooaeioned "by the use of these teams resulted in any significant improvement in pupil achievement. The author and the other mathematics teachers have felt since the teams were started that they were of definite value to the drill work and to the general work of the mathematic s classes. This feeling has so far "been based only on subjective data, since there has been no attempt to get objective data to determine their value.

STATEMENT OF PROBLEM

It is the purpose of this study to determine through objective data the value of mathematics teams as a means of motivation in speed, accuracy, and reasoning in the junior high school mathematics.

The words in this statement are self explanatory, probably with the exception of the "mathematics team". The mathematics teams consist of five or six members. The first team of a class was under the charge of the captain who had been chosen by the class. This team was chosen by three persons; the captain, a student chosen by the captain to aid him, and the mathematics teacher of that class. The other teams in the elaee were picked by the teacher who had the students "tryout" for places on the second, third, fourth, and fifth teams. The members of these teams chose the captain of their team.

3.

PROCEDURETo make a study of this problem, the following

procedure was used:1. Two groups of one hundred students were formed,

one of which was called the control group, and the other which was known as the experimental group.

2. The following factors were made as constant aspossible for both groups: (a) the quality of teachingor the abilities of the teachers for the groups, (b) the time of the class recitations, and (c) the attitudes of the teachers toward the various classes.

3. An attempt was made to equate the groups for other factors which are variable in nature.

4. Both groups used the traditional techniques of motivation. The experimental group used in addition the mathematics teams as a technique of motivation.

5. Mathematics contests were used in the experimental group to motivate the work of the mathematics teams.

6. Mathematics team leagues and tournaments were also used to motivate the contests. These indirectly motivated the work of Individuals.

7. Two final tests were given at the end of the experiment to determine the difference in achievement or gain between the experimental and the control groups.

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HISTORY

A careful study of the history of motivation inmathematics shows that the early teachers of arithematictaught the children to count on their fingers to make the

(1)work "more real" to them. This developed, into the counting of objects such as stones, beads and blocks, and later we find^numbers upon the blocks. The early histories of mathematics show us the development of content and mathematical processes but there is no mention of techniques of motivation.

One has to go back only a few decades into the history of mathematics to find contests between individuals being used to motivate the work in fundamentals. In the modern mathematics classes the teacher does not have time for contests between individuals as the classes are too large.The mathematics team contest is but a modified form of the old contests between individuals. In the modern mathematics classes one does not have time for contests between individuals but without a doubt contents between groups of individuals can be used efficiently.

1. Monoe, Paul. "Encyclopedia of Education." Arithmetic, The History of. The MacMillan Co., Sew York, 1911.2. Ball, W. Vi. Rouse. "A Short History of Mathematics." The MacMillan Co., London, (1915).Cajori, FIorian. "A History of Elementary Mathematics." The MacMillan Co., lew York, 1896.Fink, Karl. "History of Mathematics." The Open Court Publishing Co., Chicago, 111., 1900.

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If one makes a study of recent mathematical tech-(1) (2)

nitines, he will find projects and socialized recitationshave been extensively used as forms of motivation. One of the criticisms of the project is that it does not furnish drill. In a study of the articles in our currentmathematical magazines, there can be found many articles

(3)on the content of drill, but the author has failed to find an article on the motivation of the drill work. No doubt many teachers use teams in various ways in mathematics classes, but it is difficult to find reports of attempts to use teams in an organized manner comparable to that followed at Manofeld Junior High School.

1. Jablonower, Joseph. "The Project Method and Socialized Recitation." The Mathematics Teacher 21: 431-41, 1928.

Smith, Donald P. "A Project in Mathematics." The Mathematics Teacher 18: 97-101, 1925.2. Jablonower, Joseph, op. oit.3. Lee, Dorris Hay and J. Murray. "Maintenance Drills in the Junior High School." The Mathematics Teacher 24: 448-52, 1951.Blaisdell, Walter H. "Daily Testing." The Mathematics Teacher 26: 337-44, 1933.

6.

CHAPTER II* »

In September, 1932, the author Aooldtd to perform an experiment for the purpose of determining to what extent significant differences in speed and accuracy in arithmetical fundamentals could be obtained when mathematics teams were used as compared with other forms of motivation.

It was decided to organize an experimental group of one hundred junior high mathematics students whose work would be motivated by mathematics team contests. To measure accurately the achievement of this group it would also be necessary to have a control group of the same number and, relatively, of the same ability.

After careful consideration it was decided to use only students in this experiment who had never been in any classes where mathematics teams had been used. The reason for this is obvious since one would not expect the students to show a high degree of improvement in a skill in which they had previously become very efficient by the same technique. There were only four seventh grade mathematics classes in Mansfeld Junior High School which could be considered as all of the other classes had had mathematics teams the year before. Since only two of these seven B classes were taught by the same teacher and were therefore suitable for the experiment, it was thought advisable to go to the Roskruge Junior High

7.

Sohool to find, additional classes suitable for the experiment. At Roskrugo were found two seven B classes, two eight B classes, and two eight A classes that eould he used in this experiment. The seven B and eight B classes were taught hy one teacher and the eight A classes were taught hy another teacher.

On Wednesday and Thursday of the sixth week of the first semester tests were administered to 240 students in the eight mathematics classes chosen for the experiment. The tests given were "The Courtis Standard Test, Series B^Form I".and "The Compass Diagnostic, ITo.ZVIII, Form A".

The teacher in the Boskruge Junior High School who taught the two seven B and the two eight B classes was asked to pick the better seventh and the eighth grade classes. The seven B class which she rated the poorer and the eight B class which she rated the better were put into the control group. The teacher of the eight A classes was asked to pick his better class which was put into the experimental and the poorer was put into the control group. The teacher of the classes in the H&ns- feld Junior High School picked her better class which was put into the control group and the poorer class was put into the experimental group. The control group now consisted of four classest two, a seven B and an eight A, being rated below the average, and two, a seven B and an

L. Copies of these tests will be found in the appendix.'"

8.

eight B, being rated above the average by their teachers. The experimental group also eonaisted of four olaaaea: two, a seven B and eight B, being rated below the average, and two, a seven B and an eight A, being rated above the average by the class room teachers. This classification was only tentative; to permit the progression of the experiment until adequate measures for equating the groups could be obtained. A careful study of the time of the different class recitations showed that the tentative classification satisfactorily equated the time of meeting between the experimental and control groups.

The four classes in the control groups recited the second, third, fourth, and fifth periods, while in the experiment group one class recited the third period, two classes recited the fourth, and one the fifth period.There are six class periods of one hour each in the day. Some who do experimentation consider this factor so small that it is of no importance. Although this factor is of little importance, the author believes all factors should be given consideration When possible in order to make the experiment more accurate.

The reason for giving this factor careful consideration is obvious since the physical conditions of the students and teachers change from period to period, and it is possible that this might affect the achievement of the students. It should be noticed that the teacher

9.

faster is constant since each of the three teachers has the same trasher of classes in each of the two gronps. All teachers were experienced teachers, highly recommended hy their principals to aid with the experiment.It should also he noted that only the Mansfeld teacher had had experience with mathematics teams. The two Roekruge teachers and their principal were entirely free from bias with reference to the mathematics team idea.

During the progress of experiment the author kept in close contact with all the teachers. Each teacher wa® to teach both the experimental and the control classes the same material in the class recitations. All students were to bo given daily drill in the fundamentals. Charts, graphs, and records were to be used by ; all teachers as forms of motivation as they saw fit. The teachers were to use all the traditional teohniqjies for the motivation of the drill work in both groups but wore to confine the use of mathematics teams to the experimental groups. On two or three days each week the drill periods of the classes in the experimental groups were to be used for team practice and the selection of first, seeond, third, and fourth teams.

Each of the teachers was given a copy of the mathematics contest rules which are to be found in the appendix, and was to organise teams consisting of five or six individuals in each team. The teachers organized first,

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aeoond, third, fourth, and fifth teams hy having the children MtryoutM for places on the various teams. The students often came into the class rooms at noon to practice. The mathematics contests did take more of the teacher’s time at noon and after school, but the teachers became Interested in the work and did not seem to mind the extra work which was necessary.

The contest was between two mathematics teams. There were twelve problems in each contest, three each of the four fundamental arithmetic processes. The problems were sufficiently difficult that the time required for the solution would permit judging which of the contestants finished first, second, and third. Two contestants from each team went to the blackboard for each type of problem,1. e., two pupils for a problem in addition, two other pupils for a problem in division, et cetera. As the contestants finished a problem, they turned and faced the Judges with their writing hands and chalk above their heads. No contestant was permitted to work or change the problem after this gesture had been made. The first contestant who obtained the correct answer received five points score for his team; the second, three points, and the third, one point. No contestant was permitted to work more than six problems. , There was a teacher in charge whose duties were to read the problems and to announce the score which was based upon the decisions of

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the Judges. The contests were usually judged ty three persons whose duties were to determine which contestants finished first, second, and third.

The author was well pleased with the response from the teachers and the experimental classes. The teachers "became very much interested in the experiment, and the students apparently enjoyed the mathematics contests.Many students came into the class rooms "before school and at noon to practice. Contests were held by some teachers at noon, "but the maj ority were held after school. The teachers became so interested that they seemed to enjoy them as much as did the students.

At Mansfeld Junior High School the teacher formed a league which provided that each team engage in the same number of contests. At Roskruge Junior High School the teachers organized a mathematics tournament which was quite successful in motivating the contests. One teacher, whose chief duty was to set the handicaps so that the fourth and fifth teams would be given an equal ohanoe in the contests with the better teams, was put in charge of the tournament.

Often the teachers reported that students in the control groups wanted to know why they could not have mathematics teams. Students of the control group were kept out of tho rooms while mathematics contests were being held.

18.I

There was one inter-Junior high school oonteet which was won hy the eight B first team of the Roskruge Junior High School. At the end of the experiment, on Wednesday and Thursday of the last week of the semester, the "Courtis Standard Test, Series B, Form II” and the "Compass Diagnostic, No. XVIII, Form A" tests were administered.

SQUATIHG THE GROUPS

Three factors which would influence the results have already been taken into consideration and made as constant as possible. They are the time of recitation, ability of teachers, and the attitude of the teachers towards the various classes.

The other factors which enter into the equating of the groups are the mathematical ability of the students in speed, accuracy, and reasoning, an effort which is due to the attitude of the student towards mathematics, and the intelligence quotient or degree of brightness.In order to give the above factors adequate consideration, the groups were equated for each of the following five variables:(1) the individual scores of the first Courtis Standard

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Test,(2) the individual scores on the first Diagnostic Test,(3) the previous estimate of the students in mathematics as shown by the marks in that subject,(4) the estimates of the teachers who taught the other "solid subjects", and(5) the chronological ages of the students.

To determine the value of the motivation in speed and accuracy the results from "The Courtis Standard Test, Series B" were used. The Courtis test was used because it is one of the best tests of.its type, being carefully and uniformly constructed. Its problems are not too long but long enough to make a good test of the pupil*s ability in accuracy. There are enough problems in each unit to permit measurement of the rate of speed of the students.

To determine the ability of the pupils in mathematical reasoning, the results from "The Compass Diagnostic Test, Mo. XVIII" were used. This test is based on written problems. The test is based on five written parts. Parts I, III, IV, and V are composed of five statements. The correct one in each part is to be checked. Part II contains more than one correct statement, all of which should be checked.

The last three variables were Included because there had been no Intelligence tests given in the school system

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in reoent year9. The mathematics teacher* s grade v/ae given separate consideration since there was a possibility of some student having had better previous training and motivation in mathematics than in other "solid subjects", while the reverse might be true with other pupils. The chronological ages were reversed, that is, the oldest child being scored the lowest, while the youngest was scored the highest. The ages in number of months were used. Since there were eighth-grade and seventh-grade students in the experiment, it was decided to subtract twelve months from the eight B students and seventeen months from the eight A students so that their ages would be comparable to the seven B students.

Many recent studies show that the chronological ages and the teachers* previous estimates are of definite value to determine the general intelligence of a childwhen intelligence test results are not available. Dr.

(1 )F . D. Brooks, of John Hopkins University, states the following conclusions in a recent article:

Conclusion 5. "Sectioning by chronological age results in 57 per cent correct classification, 39.8 per cent displacement by one section and 3.2 per cent displacement by two sections.

1. Brooks, F. D. "Accuracy of Group Test Mental Ages and Intelligence Quotient of the Junior High School Students." School Review, XXXIV (1926) 333-42.

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6. Sixth-grade school marks give more accurate classification by intelligence than does the chronological age. 60.7 per cent being correctly classified,34.2 per cent being displaced by one section and 5.1 per cent being displaced by two sections.

7. Combining the sixth-grade marks and chronological age gives almost as accurate classification by intelligence as does the average group intelligence test, 63 per cent being correctly classified, 35.2 per cent being displaced by one section and 1.8 per cent being displaced by two sections.n

When the experiment was completed and all tests were graded by the author, there were complete data on ninety-six students in the experimental group and ninety- four in the control group. The data of two students picked at random were removed from the experimental group which made ninety-four in each group.

In order to get the data into such shape so that it could be easily handled, cards were printed, which had a total of twenty blanks to be filled in for each student. One hundred cards were printed on salmon color placard material which were used for the control group, and the same number were printed on blue material which were to be used for the experimental group. Examples of the cards which were made out for each student are shown on the following page.

The raw score of the first Courtis Tests was placed on the cards in a space marked for that score. The means and standard deviations of the experimental group and control group were figured separately. The raw score on each

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Cards used for the experimental and control groups.Pain g 7B3K

...................Rank J L 3 1

................... Points

Aver. T. Score ' - ; 1

Total D iff.......................

Courtis Diff.

................... .Diagnostic Diff.T. Score

T. Score

.....J..... Courtis Form '....2 .

Courtis Form II

Diff.

1...... First Diagnostic.A7

Second Diagnostic.(Blue shows gain, red shows loss.)

,301.i-f V (. . . . . . . . • •

Age. / J - / /

Teacher’s previous estim ate in Math

Average mark in other solids............

Diff. from Average D.

,/J\r

/^<JV ' f O .30 A

rln

gain

loss

gain

loss

vL...........J2.

Clark b 7B2M.......... Rank

................... Points

Aver. T. Score

Diff. fromScore

n iCourtis Form I ....................... x

Diff. Average D.

gain

^ ^ ^ Courtis Form I I ..................... >1 O’ 2 - ' b jc loss

First D iagnostic.................... 4 gain

^ *7........Second Diagnostic.................. « £ / loss(Blue shows gain, red shows loss.)

.....d..... ..............Teacher’s previous estim ate in Math. ...........................................................................

■i................... Average mark in other solids / ................ ......................................

...Age. / / - S 5

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card was turned into a standard deviation score by the following method. The mean of the group was subtracted algebraically from the individual’s raw score. It should be noted that approximately one-half of the remainders were negative numbers. The remainder was divided by the standard deviation of that group. The quotient obtained was multiplied by one hundred. This product was algebraically added to five hundred for the purpose of eliminating negative numbere. Whenever there is reference made to the standard deviation score of an individual, it shall mean a score derived by this method.

After the raw scores and the standard deviation scores of the first Oourtis test were placed on the cards, like scores were computed for the first Compass Diagnostic feet, the mathematics teacher*e estimates, the other teachers1 estimates, and the chronological ages. These were all entered in the appropriate blanks on the cards. With these ten scores upon the card the task of balancing the groups was made much easier. It should be remembered that the scores of the experimental and control groups were figured separately or from different distributions. There are five variables being considered.

The next problem was to get each of the five variables of the experimental group nearly equal to the corresponding

variable of the control group. To compare these variables an attempt made to equate the groups so that the differences

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between the experimental and control groups would become so small as to be only a matter of mere chance. The fol-

tlowing formulas were used to determine the significance of differences between the means for each variable.

The first formula is of the same mathematical value as that stated by Garreti but is in a more convenient form. This formula could be stated in words in this way: thedeviation of the difference between the two groups is equal to the square root of the sum of the standard deviation of the experimental group squared, divided by the number of cages in the distribution from which it was derived, and, the standard deviation of the control group squared, divided by the number of cases in the distribution from which it was derived. The second formula may be expressed as the difference between the mean of the experimental group and the mean of the control group divided by the standard deviation of the difference between the means of the two groups which equals the difference quotient. Garrett has a table 1

c-o-ntrolH d q -

1. Garrett, Henry E. Pg 137-134. *Statistics inpsychology and Education*. New York; Longmans Green and Go., 1926.

to show the degree to whteh the difference quotient is ofCDsignificant value.

It ehotiid he noted that the deviation of the difference and the difference quotient had to he computed for each of the five variables. The latter was the only one of value when the variables were being compared.

When the five difference quotients were completed, it was found that difference between the control and experimental groups of two of the variables were great enough to admit the probability that they were not due to chance alone. Three of the variables showed no significant difference between their means. The two variables showing a significant difference between their means were chronological egee and arithmetical reasoning. It was interesting to note that the control group, the means of which indicated an excess of older pupils, ranked low on the Diagnostic Test which was being used to test reasoning ability. This might be interpeted to indicate a negative correlation between reasoning ability in arithmetic and chronological age within a grade*

The next step was to change the groups by eliminating certain pupils so that these two differences would become smaller. The big question was which pupils should

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1. Op. Oit. Page 134.

The differences between the experimental and control groups before the equating process was started. There were 9% oases in each group.

TABLE I

Variable

MTAMS STANDARD DEVIATION DIFFERENCESExperimental dontrol Experi

mental Control 0 or Difference between means «$(aiff.) D

6(diff)

Courtis 35-64 35-53 13.53 14.31 .11 2 .0 5 4 0535Diagnostic 26.3 2 9 .064 10.181 11.42 2-764 1 .5 4 9 1.784

Math Teacher 3-043 3-138 1.053 1.058 095 .1 5 4 .617

Teachers* Eet. 3-126 3-195 .7674 •7785 .067 .1198 •559Agee 156-277 152.341 15.065 10.555 3 936 1.897 2 .0 7 5

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*be taken from the groups. It was decided to eliminate the same number of pupils from each group to keep the groups equal in number of cases. This was done only for convenience in statistical treatment. At this time the individual deviation scores were of definite value. By glancing at the deviation scores one could tell if the pupil ranked high, low, or near the middle on the curve of each variable. It was necessary to find individuals in the control group who had low deviation scores in chronological age and on the Diagnostic Test, while in the experiment group high scores in these two variables were chosen. It was necessary that consideration be given the other three variables, since every individual eliminated from a group would affect the means of all five of the variables’. Deviation scores near five hundred would not affect these other means to any great extent.

Four individuals, after careful consideration, were eliminated from each group, which made ninety pupils in the control and ninety in the experimental group. Ten new means and ten new standard deviations were now computed since all means had been changed. The difference deviations and quotients were again computed.

Although the significant of the differences had been greatly reduced, it was decided to eliminate five more

TABLE IIThe differences between the experimental and control groups after four Individuals had been eliminated leaving 90 oaeea in each group.

VariableMEANS STANDARD DEVIATION DliiSRElOIS

Experimental Control Experimental Control D or Differencebetween means DJTHfT)Courtis 35.276 3 5 .6 0 9 14.53 13.41 •333 2.084 .1599Diagnostic 28.571 2 6 .7 1 1 IO.7 6 10.133 1 .8 6 0 1.558 1 .1 9 4

Math Teacher 3.100 3 .07s 1.044 1 .0 1 9 .022 .1521 .1 4 5 1

Teachers' Eet. 3-159 3 .1 6 7 .7782 .7556 .008 .1306 .0 617

Agee 152.94 15*.6l IO.3 2 12.97 1 .6 6 7 1.881 .8864

S3.

pupils from e&oh group and again compute the means and standard deviations. This time, with eighty-five pupils in each group, none of the five variables showed a difference between the means of the experimental and control groups great enough to be considered significant. This meant that the groups represent by the eighty-five remaining Individuals were so near alike or equivalent that it was improbable that the difference between the means of the two groups could be due to other than chance.

Table III shows how nearly equal the two groups were on the five variables being considered.

the final grouping showing the differences between the experimental and control groups with 85 eases in each group.

TABLE III

Variable

HEAI1S STANDARD DEVlATIOIi DIFFERENCESExperimental Control Experi

mental Control D or Difference between means <$ (diff.) DS (diff)

Courtis 35-5 3 6 .0 8 8 14.80 13.41 • 588 2 .1 6 6 .2715Diagnostic 2 7 6 2 % 27.53 IO. 5 5 9 .8 0 6 .094 1.543 .0609Math Teacher 3.012 3.071 .988 1 .0 3 2 .059 .1187 .4969Teachers' Eet 3-l%5 3-204 .7695 7568 .059 .1 1 6 6 .5059

Ages 153-382 1 5 3.97c 1 0 .3 8 1 3 .0 0 .588 1-942 • 3028

25.

CmPTBR IIITHE RESULTS

Although all the tests had ‘been, graded before the equating of the groups was started, the raw scores of the final Courtis and Diagnostic test were not put on to the cards until after the groups were balanced. The reason for this is obvious, since the cards of certain individuals were to be withdrawn from both groups, there would be no possible tendency to withdraw cards which were known to influence the results in any certain way. The cards which were withdrawn during the equating process had only data which showed the pupils ratings at the start of the experiment. It was not possible to equate the groups before the final tests were given as there was no way to tell which pupils would take the final tests, since some would move and others would be absent. The teachers were asked to keep the final tests of the pupils whom they thought had been absent to snoh an extent that the absence would affect the results. Although over two hundred and twenty-five pupils took each set of tests, there were only complete data on one hundred and ninety pupils when the experiment was finished. Ho attempt was made to have those pupils who had missed only one or two tests to take the tests at some other

£6

time as the eonditlons would not "be quite the same. The results are "based upon data which were taken from tests administered under the regular elaee room conditions.

After the equating of the groups had heen fini tiled, the raw scores of the final Courtis and Diagnostio tests were placed upon the cards. Then the means and standard deviations of "both the tests were computed for the experimental and control groups. From the standard deviations and the mean®,the standard error of the difference "between the means and the difference quotients for each test were computed. ■

The results show there was a slight difference in the results of "both tests in favor of the experimental group, 1.53 on the tests of speed and accuracy and .659 on the test of arithmetical reasoning, "but it should he noted that the difference is so small that it can not he considered as a true superiority in performance by the experimental group hut may instead he due purely to chance.

When one notes the mean score of these pupils on the first Courtis test and the second Courtis test, it is evident there has been production of definite improvement in speed and accuracy. This, however, is practically the same for the experimental and control groups. The improve ment is merely indicative of the quality of instruction. One other factor should he noted, that is, the same Diagnostic test form was given both times. There should be

Difference in achievement between the experimental and control gronpe me indicated by the teete administrated at the close of the experiment.

TABLE HO. IV.

mss SfAITDARD DEVIATIONS DIFFERENCES

Variable Experimental

Control Experimental

Control D or Difference between Means jtdiff.) tdiff.)

Courtis 44.677 43.147 16.53 14.59 1.530 2.391 .6398Diagnostic 35.671 35.012 11.72 1153 .659 1.784^ .3695

28.

some gain shown the second time, hut this gain "because of the practice effect would he the same for both the experimental and the control group.

It would not he fair to consider the results of this experiment or to compare it to any other similar group experiments without considering the teacher fastor. This experiment was carried on in classes under well trained experienced teachers. The fine spirit in which these teachers responded to the experiment has already been mentioned. But these teachers were not the enthusiastic originators of the technique as we often find to he the case in experiments of this type. The results are, therefore, such that one would expect from any teacher who would carefully plan and work out mathematics teams as a technique of motivation. Too frequently we note a tendency to accept uncritically the conclusion® of experiments performed in the classes of some enthusiastic teacher who would have shown definite and apparently significant results with any technique had that person used his enthusiasm in a similar way. The three teachers who aided with the experiment all thought that the mathematics teams had been of value as a motivating force to their classes, hut we must remember these opinions were based upon subjective data. The results of this experiment again show "That all is not gold which glitters,w. Too often a new technique appeals to the teachers and to the students through its

29.

novelty which overshadows the real results.(1)

Messick in an experiment designed to investigate the relative desirability of drills for speed as compared with drills conducted for the purpose of improving accuracy in mathematical computations used one hundred thirty-six students in one group in which the teachers continually stressed speed as they were taking the daily arithmetic drills. In another group of the same size the teachers put special emphasis on accuracy.

Messick in his conclusions states that the accuracy group exceeded the speed group "by 2.6 per cent in speed and hy 32.5 per cent in accuracy, that 4.7 per cent gained more in speed than accuracy and 7.4 per cent loss more in speed when drilled for speed. ’

Messick*s-final statements were as follows:"Accuracy is more important than speed.1. From the standpoint of speed it makes little dif

ference as to whether drill is for speed or accuracy.2. From the standpoint of accuracy it is much better

to emphasize accuracy.3. It is better to emphasize accuracy rather than

speed." .Since the mathematics teams do emphasize speed, it

was decided to make a careful check to compare the speed of the experimental and control groups. The difference in speed between the two groups is shown by the data in Table Ho. V. The experimental group has a slight gain in speed, but this gain may be due to mere chance since the

T~. Messick, A. I. "Effect of 'Certain Type of Speed Drills in Arithmetic." Mathematics Teacher 19: 104-11, Feb., 1926.

TA3LS HO. VDiffer mice In speed between the experimental and control group a as Indi

cated by the number of problems, attempted on the Courtis Teste.

m i s 3TAM>AHD D39TATI0KS DIFFEREHCE3

Variable Experimental Control Experimental Control D or Differencebetween means i(dlff.] D _n t i H )Beginning of Experiment 46 M 46.36 13-79 IS-93 .06 2 .0 5 .0293Close of Experiment 55*57 53*03 1 6 -0 1 15-11 2-53 2.367 1.(^0

31 .

difference is not sufficiently great to eoneidered significant.

To compare the accuracy of the experimental and the control groups, it was thought advisable to compare the efficiency in computation of the two groups. The efficiency is computed by the division of the number of problems correct by the number of problems attempted.This computation gives the percentage of correct solutions.

From the average number of problems correct in Table No. -Ill and from the average number of problems attempted in Table No. V, there was an efficiency of 77.44 per cent for the experimental group at the beginning of the experiment. This number is derived by comparing 35.5 with 46.44. By comparing 44.677 with 65.57, one finds an efficiency of 80.40 per cent for the experimental group at the close of the experiment, which was a gain of 3.96 per cent in efficiency for the experimental group.

By comparing 36.088 with 46.38, one finds an efficiency of 77.81 per eent for the control group at the beginning of the experiment. By comparing 43.147 with 53.03, one finds an efficiency of 81.56 per cent for the control group at the end of the experiment which is a gain of 3.55 for the control group during the experiment. If one subtracts the gain of the control from the gain of the experiment, there is a difference of .41 of one per cent. This gain is too small to be given any consideration.

32

These data from Table Ho. Ill and Table Ho. V tend to show that there has been no gain in speed or accuracy because of the motivation of the mathematics teams. The data further indicate that although the mathematics teams have emphasized speed, that speed is not being developed to any extent. One should note that this is simi-

(1)lar to Xessieks1 conclusions. It is possible that if the mathematics team contests were changed to emphasize accuracy instead of speed, one might find a significant difference in the efficiency. If such results should be obtained, they would confirm the findings, of Messiok.

The efficiency was computed by comparing the average number of problems right with the average number attempted.

It should be noted that during the compiling of this data there were a total thirty-eight means and thirty- eight standard deviations figured. There were nineteen difference deviations and nineteen difference quotients figured besides the nine hundred and forty individual deviation scores which were computed on a total of ten distributions. All the statistical work was done with five- place logarithms, and often the sixth-place was taken into consideration. The author always anticipates his answer, which aids a great deal in eliminating mistakes. Logarithms are very satisfactory for this work because when a mistake is made in the logarithms, it is nearly always so large that it is easily detected. Logarithms were carried

hod dick, A'. i." "op. citV 1

33.

straight through the work with the antilogarithms for which they stood, to eliminate the dropping of fractionalparts as much as possible.

34.

SHA.IfSR IfOOHOLTTSIOH

The experiment has been so conducted that if there had been a significant difference between the groups at the end of the experiment, it would hare shown that the mathematics teams were a valuable addition to the techniques now in common usage. It should be bourne in mind, however, that there has been no attempt to compare this technique with any other technique or group techniques. The data compiled in this experiment seem to warrant the following conclusions:

1. Mathematics teams are of little value, if any, in the motivation of speed and accuracy or reasoning in junior high school mathematics when used with other techniques. In a comparison of results between the experimental and control groups there was a difference quotient of .6398 on the Courtis test and .3695 on the Diagnostic test.

2. There was a slight gain for the experimental group over the control group in favor of the mathematics teams, but this gain was not sufficiently great to insure that it was not due to mere chance.

3. There was nothing in the results of the tests to show that the mathematics teams had decrease the effioien ey of the instruction. On the final test the means of the experimental group were slightly higher than the

35

means of the eontrol group.4. The results of this study are not to he Inter

pet ed as Indicating that mathematics teams are either superior or Inferior to other techniques, since all other techniques were used in both the experimental and control groups while the experiment was in progress and the mathematics teams were introduced as merely an additional factor in the experimental groups.

6. The probability of desirable ooneomitant and associate learnings because of the use of mathematicsteams might be worthy of some consideration* That there

■

is a possibility of their existance is indicated subjectively by the attitudes of the students and teachers towards mathematics teams.

BOGOESTBD STUDIESIt should be noted that throughout this study the

author has not attempted to compare the use of mathematics teams as a technique with the other traditional techniques. It has been the purpose of this thesis to study the value of the mathematics teams as a mean for the increasing present achievement in arithmetical fundamentals. It appears that a study to compare the value of mathematics teams with the value of charts, graphs,and records as means of motivation would be worth while. If mathematics teams are to be used in the junior high schools, their relative value in comparison with the traditional forms of motivations should be known.

36

BimosHAEmr

!• B/iIiL, VI. Yf. ROUSE* nA Short History of llathematios.0 The MacMillan Co., Hew York, several editions.

2. BMISDELL, HALTER Yf* "Daily Testing." The Mathematics Teacher 26$227-34, 1933.

3. BROOKS, F. D. "Accuracy of Croup Test Mental Ages and Intelligence Quotient of the Junior High School Students." School Review 34:333-42, 1926.

4. CAJORI, FLORIAH. "A History of Elementary Mathematics.” The MacMillan Co., lew York, 1896.

5. KDWVtRDS, HERBERT. "Iced for Testing Practices in Curriculum Revision." The Mathematics Teacher 22:320- 23, 1928.

6. TAWDRY, R. C. "Reform in Mathematics Teaching." The Mathematics Teacher 17:65-72, 1922,

7. FIHK, KARL. "History of Mathematics." The Open Court Puhliahing Co., Chicago, 111., 1900.

8. GARRETT, H U R T E. "Statistics in Psychology and Education. ® Longmans, Green and Co., Hew York, 1926.

9. GOODRICH, MERTOH TAYLOR. "Should the Mathematics Teacher Seek to Know the Heeds of Society." The Mathematics Teacher 26$ 241-43, 1933.

10. HAHSOH, LERA 3. "Creating Interest in Mathematics through Special Topics". The Mathematics Teacher 23:1- 8, 1931.

11. HEDRICK, E. R. "Formalism in Mathematics Teaching." The Mathematics Teacher 25:441-50, 1932.

12. JABLOHOWER, JOSEPH. "The Project Method and SocializedRecitation". The Mathematics Teacher 21:431-41, 1928.

13. KLOPP, Yf. J. "Socialized Mathematics". The Mathematics Teacher 23:161-65, 1930.

14. LBFEVER, WBLTY D. "Dangers and Values in the Teacher- Made Test." Education 53:409-14, March, 1933.

15. MCCALL, YfILLIAH A. "How to Measure in Education." The MacMillan Co., Hew York, 1922,

16. MCCALL, WILLIAM A. "How to Experiment in Education."The MacMillan Co., Hew York, 1923.

17. MESSICK, A. I. "Effect of Certain Type of Speed Drills in Arithmetic." The Mathematics Teacher 19: 104-11,

37

Feb. 1926.18. MOHHOE, PAUL, "Ermyolopedia of Ednoatlon." Hao-

Millaa Co., lev; York, 1911.19. ( OTIS, ARTHUR S. “Visual Method of Solving Arithmetic

^Problems.“ The Mathematics Teacher 21:483-90, 1928.20. POTTER, MARY. “An Attempt to Improve Computation.“

The Mathematics Teacher 20*381-90, 1927.21. RABOURH, SARii B. F. “Room Devices for Stimulating

Interest in Mathematical The Mathematics Teacher 20:328-34, 1927.

22. SMITH, D02TALD P. “A Project in Mathematics." The Mathematics Teacher 18:97-101, 1985.

23. SYMOHDS, PERCIVAL M. “Measurement in Secondary Education." The MacMillan Co., Hew York, 1928.

I

APPJSIBIX

Mansfeld Mathematics Contest Roles.

ARTICLE I.(the team)

Each team shall have a captain chosen fcy their class.The team shall he chosen hy the captain, one member of the class chosen by the captain %o aid him and by the teacher of that class.Each team shall consist of five members including the captain.The captain shall have complete charge of the team during the contest.The teacher may give suggestions to the captain at any time.

ARTICLE II.(the contest)

Each contest shall consist of three problems of each of the four fundamentals.The problems in addition shall consist of three digits in the number and nine numbers in the problem.The subtraction problems shall be in the hundred millions. The multiplicand shall be.four digits and the multiplier three digits.The divisor shall have three digits and the quotient three digits. There shall be no fractions nor decimals (quotient must be even.)Two members shall go up from each team for every kind of a problem, making four at the blackboard at one time.Ho member of either team shall be permitted to work more than six problems.The contest shall be judged by three persons, at least one of whom should be a teacher.The teacher in charge shall read the problems and declare the score which must be based on the decision of the judges. The teacher in charge must be the teacher of both teams or of neither team.

II.

ARTICLE III (the soore)

When the problem is finished, the contestant mast turn and face the judges with his writing hand and chalk above his head. After this gesture the contestant will not be permitted to work nor change the problem.The first contestant finished with the correct answer shall count five points for his team, the second three points, and the third one point. The judges shall decide who was first, second and third.If every contestant has an incorrect answer, another similar problem shall be given for that problem.If the soore is tied at the end of the contest, the teacher in charge shall ask each captain which kind of a problem his team prefers to work to decide the contest. If both captains decide they want the same kind, one problem shall be given to decide the contest. If each captain wants a different kind of problem, one of each kind asked for shall be given. If the contest is still tied after two problems have been worked, the teacher in charge shall give two more problems, one each of the other two fundamentals.The following handicap shall be placed on the scores of the first teams before each contest: 8A3-0; 8A2; 8A1;8B1-10; 7A1-5; 7A2-25; 7A3-35; 7A4-40 mid 7B1-30. Every second team in each class shall add 15 points to its first teams handicap to get its handicap and every third team shall add 25 points to its first teams handicap to get its handicap. The 7A1 second and third teams shall add an additional 5 points to get their handicap.

Measure the efficiency, of the entire school, not the individual ability of the few.

BUREAU EDUCATIONAL RESEARCH & SERVICES T A T E U N IV E R S IT Y O F IO W A

Extenmion DIvialonResearch Tests in Arithmetic

TEST N o. 1. ADDITIONSeries B Form 1

SCOREHe. Attmetri---No. Ri*k-------

You . will be given eight minutes to find the answers to as many of these sddition 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.

9 2 7 2 9 7 1 3 6 4 8 63 7 9 9 2 5 3 4 0 7 6 57 5 6 4 7 3 9 8 8 5 2 48 3 7 9 8 3 3 8 6 1 4 09 2 4 3 1 5 3 5 3 8 1 21 1 0 6 6 1 9 0 4 4 6 68 5 4 7 9 4 5 4 7 3 5 59 6 5 1 7 7 1 9 2 8 3 43 4 4 1 2 4 4 3 9 5 6 7

3 8 4 1 7 6 2 7 7 8 3 74 7 7 7 8 3 4 4 5 8 8 28 8 1 6 9 7 6 8 2 9 5 92 6 6 2 0 0 5 9 4 6 0 36 7 9 3 6 6 4 8 1 1 1 82 4 1 8 5 1 7 7 8 7 8 17 9 6 5 3 5 8 4 9 7 5 68 5 0 3 2 3 1 5 7 2 2 27 3 3 2 2 9 9 5 3 5 2 5

5 3 7 6 6 4 6 9 5 2 7 8 4 7 1 3 4 5 9 1 3 9 2 1 5 6 4 7 8 7 9 3 2 6 4 6 5 5 9 4 3 3 1 0 6 4 6 4 2 2 8 4 4 9

6 3 4 5 7 2 1 6 8 2 5 3 7 1 7 9 4 8 1 4 2 5 2 9 4 4 9 9 3 6 4 5 3 2 2 3 9 2 4 3 5 8 6 5 9 6 7 6 4 3 2 1 2 2

2 2 6 3 5 1 8 8 0 7 8 8 6 6 3 7 0 5 8 1 9 1 7 4 7 7 9 4 2 6 1 2 3 6 4 9 3 3 8 7 5 5 9 9 6 1 4 0 3 0 3 2 4 6

4 2 8 8 6 2 9 7 5 1 5 9 4 5 0 3 8 3 1 9 4 4 5 1 6 6 6 9 3 8 7 4 2 4 3 3 2 9 5 5 9 9 1 8 7 1 7 2 2 8 1 1 5 2

6 7 7 2 2 3 1 8 6 2 7 54 6 4 8 7 8 4 7 8 5 2 12 3 4 6 8 2 9 2 7 8 5 47 1 8 3 9 9 5 1 6 9 3 98 3 8 9 0 4 9 2 3 5 8 22 9 3 3 5 3 5 5 3 5 6 64 2 3 4 1 9 2 1 6 9 3 69 5 5 7 5 6 6 6 9 4 7 25 1 9 3 1 4 4 0 9 2 6 4

Name_____________________

School------------------------------

City-------------------------- State.

4 3 2 6 3 4 5 4 7 5 8 88 7 6 3 2 7 1 9 7 2 5 65 7 1 3 2 7 6 8 5 7 1 99 1 7 3 9 4 6 7 8 5 2 47 4 9 8 0 7 4 5 6 9 6 94 9 5 1 6 9 3 9 3 7 6 12 5 0 4 9 1 5 2 5 1 1 38 3 3 8 8 5 2 4 0 4 4 93 1 8 4 0 3 1 5 2 1 2 2

--- --------, Ate last birthday.#OY O* *I*LGrade— --------------- Room------------- -

---------------- D ate__________________26925 Printed In U. S. A.

M fgjar* f/;* o / enffr* jcA oot nof fAe aAW^p 0 / (Ae /e w .

Arithmetic. Test No. 2. Subtraction.Series B Form 1

SCOREM#. A**#m#W ..No. Right ... .

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 ftre 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 you* answers right than to try a great many examples.

1 0 7 7 9 5 4 9 17 7 1 9 7 0 2 9

1 6 0 6 2 0 9 7 18 0 3 6 1 8 3 7

1 1 5 3 6 4 7 4 18 0 1 9 5 2 6 1

6 4 5 4 7 3 2 94 8 8 1 3 1 3 9

7 5 0 8 8 8 2 45 7 4 0 6 3 9 4

5 1 2 7 4 3 8 72 5 8 4 2 7 0 8

6 7 2 0 8 1 2 52 9 S 4 6 8 6 1

1 2 1 9 6 1 7 8 39 0 4 9 2 7 2 6

9 1 5 0 0 0 5 31 9 9 0 1 5 6 3

1 1 7 3 5 9 2 0 83 6 9 5 5 5 2 3

9 2 0 5 7 3 5 24 2 6 8 9 0 3 7

1 0 9 5 1 4 6 3 28 1 2 6 8 6 1 5

8 7 9 3 9 9 8 37 2 2 0 7 3 1 6

4 7 2 2 2 9 7 01 7 5 0 4 9 4 3

1 1 3 3 8 0 9 3 64 2 5 5 6 8 4 0

1 2 5 7 7 8 9 7 23 0 3 9 3 0 6 0

9 2 9 7 1 9 0 06 2 2 0 7 0 3 2

1 0 4 3 3 9 4 0 97 4 8 3 5 9 3 8

6 0 4 7 2 9 6 05 0 1 9 6 5 2 1

1 1 9 8 1 1 8 6 43 4 3 7 9 8 4 6

1 3 7 7 6 9 1 5 3 1 4 4 6 9 4 8 3 5 1 2 3 8 2 2 7 9 0 8 0 8 3 6 4 6 57 0 1 7 6 8 3 5 7 4 1 9 9 2 2 5 4 0 5 6 8 8 1 4 4 9 1 7 8 0 3 6

I9 !"M #a#er# f&# e#Kc#em<y of tA# *mf&* #*Aoo& mo# fA# AWMdagf «&#*(? o f fA# A**."

. BUREAU OF EDUCATIONAL RESEARCH & SERVICEUNIVERSITY OF IOWA I----- -------------

Iowa City, Iowa ^ ...|„ J ____Research Tests in Arithmetic *y»____

TEST N o . 1 . ADDITIO N -----------------------Series B Form 2

_ 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.1 2 7 9 9 6 2 3 7 3 8 6 1 8 6 4 7 4 8 7 7 5 3 73 7 5 3 2 0 9 4 9 4 6 3 7 7 5 7 8 7 8 4 5 6 8 59 5 3 7 7 8 4 8 6 8 2 7 6 8 4 5 9 1 9 8 1 4 5 23 3 3 8 8 6 9 8 7 2 4 0 2 6 0 1 0 6 6 9 3 9 0 43 2 5 9 1 3 3 5 4 6 1 6 3 7 2 8 6 9 1 8 4 5 1 19 1 1 1 6 4 6 0 0 2 6 1 8 4 6 4 5 1 7 7 2 9 8 S5 5 4 8 9 7 7 4 4 7 5 5 5 9 5 3 3 6 7 4 9 5 5 91 6 7 9,72 1 9 5 8 3 3 2 5 4 8 2 0 2 5 6 1 2 75 5 4 1 1 9 2 3 4 9 5 9 1 3 7 5 3 3 2 5 8 3 2 3

2 3 7 5 6 4 6 3 2 6 7 4 4 2 1 2 5 8 3 2 6 2 6 74 9 2 2 7 8 2 6 3 1 5 8 9 8 8 8 8 5 7 7 0 8 5 46 7 9 9 4 7 3 1 8 7 4 5 4 6 5 6 0 0 7 5 3 6 8 45 1 3 5 2 2 9 4 9 1 2 1 1 1 4 8 7 4 1 9 9 3 5 84 6 8 9 8 9 7 4 6 4 3 7 6 7 6 7 2 6 4 6 9 9 3 87 3 1 2 4 3 6 5 3 4 2 6 7 2 9 1 4 2 6 4 3 3 3 38 5 6 3 3 4 4 2 8 9 5 3 2 3 5 3 5 5 6 9 8 4 9 33 0 2 6 6 9 4 5 6 6 7 4 1 9 0 9 4 7 1 8 6 7 7 59 2 5 1 4 2 5 3 2 3 2 9 4 0 6 3 5 1 1 7 3 2 3 9

8 7 3 6 2 2 4 8 5 1 7 2 2 3 6 5 3 7 6 4 8 5 8 41 6 8 4 7 9 8 7 1 4 2 6 5 7 8 2 2 7 3 9 6 1 5 73 3 2 2 8 3 5 2 4 9 5 1 8 7 7 7 2 5 3 8 9 6 1 74 1 9 7 9 1 9 1 9 5 3 7 9 1 6 5 9 8 3 7 4 6 2 49 3 4 8 0 8 7 2 2 9 8 9 5 4 3 9 0 6 8 5 9 4 6 74 9 3 2 5 3 4 5 6 5 6 5 5 9 3 7 6 3 1 9 1 3 6 95 2 9 4 1 9 2 1 6 2 3 0 9 5 6 1 9 5 4 2 3 5 1 11 5 6 9 5 2 8 6 2 6 7 3 4 3 9 4 8 0 8 4 9 2 4 52 2 4 5 2 2 4 2 4 2 5 8 3 0 9 1 0 2 3 4 2 2 3 3

Name------ ---- ---------— ---------------------------- ,------------ , Age last birthday.BOY OR OIRL

School_ -------

City - - State_____________ . Date_________________

SCORE

*#.*** -----

Printed In U. S, A, 26613

f&e q f fA# ac&oo& mo# *6# fmdfWdao# *Af###c/f*#/ipW .* .

Arithmetic. T est No. 2 . SubtractionSeries B» . Fora 2

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 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.

1 1 4 9 5 7 1 8 7 9 4 7 5 2 8 0 8 1 0 6 0 8 9 4 4 9 9 9 8 3 3 9 7 89 0 2 7 1 7 9 7 6 7 3 4 9 6 4 0 1 6 9 1 5 3 9 0 7 3 1 6 0 2 2 7

SCORE He. AnemebiRfcfcB *********w*mra

1 1 5 1 7 1 7 0 0 8 2 4 8 4 7 4 0 1 1 5 9 1 6 9 1 3 7 2 2 2 9 4 7 06 3 0 8 7 3 8 1 4 8 2 0 7 8 2 5 5 5 5 3 6 3 2 9 4 5 0 4 9 1 7 3

1 4 6 2 4 6 2 5 25 2 1 6 0 8 9 1

8 0 6 3 0 2 6 66 8 1 6 4 3 2 9

1 2 4 4 8 5 0 1 87 3 0 9 8 6 2 4

1 0 7 4 1 9 3 7 36 5 3 4 8 4 0 5

3 7 9 5 3 6 3 52 3 9 1 3 8 8 4

1 3 7 8 2 5 9 2 16 2 7 2 9 4 9 0

1 5 2 6 9 5 0 3 08 5 6 1 2 8 1 6

1 7 8 9 7 6 2 2 69 3 0 6 0 3 0 3

9 7 0 8 9 3 0 12 0 2 0 3 2 6 7

1 6 8 3 5 4 1 8 67 0 5 3 7 8 6 1

• 9 3 9 9 4 4 1 35 4 7 8 3 9 3 8

1 8 8 5 4 5 3 6 49 2 4 7 1 2 5 9

1 0 8 0 5 1 8 6 17 3 4 6 3 8 4 9

1 2 0 9 8 1 4 2 76 4 1 8 8 0 4 5

1 6 3 1 3 0 5 6 99 1 0 6 1 2 5 5

1 0 5 7 5 5 7 8 29 0 8 6 3 1 4 7

*6* 0/ #6# *nffr# jc^ooL no# #Ao fndfWdnof ehW#p 0/ #Ao

Arithmetic. T est No. 3 . MultiplicationSeries B Form 2

SCORENo. Attempted „ He. eye ..

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 have your answers right than to try a great many examples.

3 4 6 7 4 6 3 79 3 8 2

8 2 5 92 8

5 2 8 9 ' 6 4 7 3___3 9 7 4 0

8 5 2 95 6

8 6 3 22 0 6

5 9 4 76 2

3 2 6 89 5

4 7 9 58 3

7 9 5 47 4

2 3 8 63 8

9 7 4 55 9

6 2 8 34 7

9 6 2 45 0 3

7 8 5 33 5

4 9 2 66 2 0

5 8 7 34 9

2 9 6 49 4

8 3 5 78 7

6 2 4 97 8

3 7 8 53 5

4 9 6 519

Measure the afficiencg of the entire school, not the individual ability of the few, R V

Arithmetic. Test No. 4 . DivisionSeries B Form 2

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 have your answers right than to try a great many examples.' .

2 4 ) 6 9 8 4 9 5 ) 8 5 8 8 0 3 6 ) 1 0 4 4 0 8 7 ) 8 1 8 6 ^

SCORE*#. ---Me.#** —___

7 8 ) 6 2 8 6 8 4 2 ) 1 7 6 8 2 6 3 ) 2 6 4 6 0 5 9 ) 5 0 7 9 9

3 6 ) 1 6 2 3 6 8 7 ) 6 1 1 6 1 9 5 ) 6 9 3 5 0 2 4 ) 1 0 8 0 0

6 3 ) 4 2 9 0 3 4 2 ) 2 8 5 6 0 5 9 ) 2 9 9 1 3 7 8 ) 4 4 5 3 8

2 9 ) 2 4 6 7 9 5 7 ) 5 1 6 4 2 3 8 ) 3 2 3 0 0 6 4 ) 6 1 5 0 4

4 6 ) 3 4 0 8 6 7 5 ) 5 5 5 0 0 9 2 ) 2 7 7 8 4 8 3 ) 2 6 6 4 3

j t ta s a n tb» efficiency of the entire echoot. not the individual ability of the fem. •l

Arithmetic. Test No. 3 . MultiplicationSeries B Form 1

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 have your answers right than to try a great many examples.

SCORE He ___He. Kith-- *_

8 2 4 62 9

3 5 9 77 3

5 7 3 98 5

2 6 4 84 6

9 5 3 79 2

4 2 6 83 7

78936 4 0

6 4 2 8 _ 5 8

8 5 6 32 0 7

2 9 4 76 3

3 8 7 69 3

9 2 4 586 7 3 6 87 4

2 5 9 42 5

6 4 9 51 9

Measure the efficiency o f the entire school, not the in dividual ab ility o f the feVO.R

Arithmetic. Test No. 4. Division

Series B Form 1

SCORENo. Attempted --------

No. Rif lit ...................

You will be given eight minutes to work as many of these division examples %m 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 have your answers right than to try # great many examples.

2 5 ) 6 7 7 5

7 3 ) 5 8 7 6 5

3 7 ) 1 4 4 6 7

-•gfifc

# 8 ) 3 9 5 0 8

2 8 ) 2 3 5 4 8

9 4 ) 8 5 3 5 2

4 9 ) 3 1 4 0 9

8 6 ) 6 0 3 7 26 #

____4 9 ) 2 8 4 2 0

5 4 ) 4 8 7 0 8

3 7 ) 9 9 9 0

VO6 8 ) 4 3 5 2 0

— '■"kV n

9 4 ) 6 7 7 7 4

5 2 ) 2 1 1 1 2

3 9 ) 3 2 7 6 0

8 6 ) 8 0 0 6 6

5 2 ) 4 4 2 5 2

_______2 5 ) 9 7 5 0

7 3 ) 3 3 6 5 3

6 7 ) 6 1 7 0 7

4 5 ) 3 3 7 9 5 7 6 ) 5 7 0 0 0 9 3 ) 2 8 4 5 8 8 2 ) 2 9 6 0 2

I Standard Mathematical Service

COMPASS DIAGNOSTIC TESTS IN ARITHMETIC Ruch— Knight— Greene— Stodbbakeb

edited bt a. w. mters

TEST XVm: PROBLEM ANALYSIS: ADVANCED:

Name........................................................................... Grade....................Boy or girl?.............................

Age_____ When is your next birthday?.................................................... How old will you be then?.

School................................................................................................................ Date________________(Name) (City) (State)

Summary of P upil’s Score Pa b t I . Part 2 Pa bt3 Part 4 Pa rts Total

Scores on Parts of Test

Educational Age Equivalent

Grade Equivalent of Score

FORM A

Do Not Turn the Page until Told to Do So.

#Copyright, 1925, by Scott, Foreman and Company

PROBLEMS PART 1—COMPREHENSION PART 2—WHAT IS GIVEN

AbdeMApmMMikbw, TAenwort ocroaa (Aafioo/acimg yog# (o (&e rigAf, (&%%# 00 Pork /or o%4 fMYd&em 6gfbre pofmp fof&e %a%f. Do %of po &oc& omdwork on a Part after you have completed the one following.

Read the Sample below.

Put a cram (X) on the line before the

problem.

Pid a cro&a (X) 0% (Ad 6d/W

(Ae proAbm.

Sample[PeoJ (Ae proWem]

M y reading book has 124 bages. I have read 72 pages. How many pages do I have left to read?

.......■>

Sample

I have read all my reader.I have read less than half

my book.____I have the most of my

book to read.X I have read a little more

than half my book.I should add to get the

answer to this problem.».- ..>

Sample

[CAect (X) wAaf w pwen]Number of pages to read.

X Number pages in book.X Number of pages I have

read.Number of stories I have

read.Number of pages with p ic

tures on them.

Remember: Work across the page to the right.

[Read the problem]

Problem 1A girl gave i of her apple

to her brother and % of it to her pet rabbit. How much of the apple did she give away?

».... .>

[Check true statement]

The girl gave all of her apple away.

The girl gave away more of her apple than she kept.

The girl gave away exactly two-thirds of her apple.

The girl kept all of her apple.

The girl kept most of her apple.

».—.>

Part of apple girl kept.Part of apple girl gave to

rabbit.Part of apple girl gave to

brother.Part of apple given to

both brother and rabbit.Part of apple the girl

threw away.

[Read the problem]

Problem 2A boy worked three evenings

after school, working a toted of 13% hours at 52% cents per hour. How much did he earn altogether?


The boy worked for more than 24 hours.

The boy worked as many hours as he received dollars.

____The amount the boy earnedwill be found by using multiplication.

____The boy worked threewhole days for me.

The boy received one dollar per hour.

[Check what is given]

Number of hours boy worked daily.

The days of the week on which he worked.

Total amount the boy earned.

____Amount paid the boy perhour.

__ _ Total number of hoursworked altogether.

----------- ------------------------—------- -

PART &--WHAT IS CALLED FOR PART 4—PROBABLE ARSWRR PART5--CORRECT SOLUTION

Fw( a crow (x) on ^K nafw ^bra#* onedaWwm* Wow toAtcA kfb wW (a cofkd/br %n (Ag proMam.

JPwf a <yo## (X) on (A* Nno &gforo Me on*aWe%wmf Wow wAtcA pwwa Abe new#* pro&o&k onauwr (o Mo pro&km. Do no( (ok Kmo (o wort Mo proMem.

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Sample

[CAocA (X) wW w caBod/or]

___Number of pages in book.X Number of pages yet to

read.___ Number of pages I have

read.___ Number of stories I have

read.___Number of pages with pic

tures. m..>

Sample

[Check probable answer]

__ _ One book.___ About 124 pages.___About 72 stories.X About 50 pages.

____About 196 pages.

Sample

[Check correct solution]

___ 124 +72 = 196___/124+72 = 196

1196-5- 2 = 98(124 —62 = 62

----- 62+72 = 1341134-5- 2= 52

___ 1 2 4 -7 2 = 7 2X 1 2 4 -7 2 = 5 2

Remember: Work across the page to the right.

[Check what is called for]

Part of the apple given to brother

Part of apple given to rabbit.

Part of apple girl gave to both.

Part of apple girl kept.Part of apple girl threw

away.


One-half.About two-thirds. All.About three-fourths. One-third.


m = f '

x —i = t or $2 + 4 = 4 + 3 = 1 or 11 — I — 4 = 4

Now Start Problem 2.


____Number of hours boyworked on any one day.

____Total amount earned byboy.

___ _ Number of days boyworked.

____Amount paid boy per hour.____Number of hours boyI worked altogether.


About 13 dollars.52 cents.About 7 dollars.13 hours.About 7 | hours.


13* X.52J =$6.76(1 3 1 = # hrs. 5 2 * = - ^ l V X ^ = =7.09.5 2 # X 13* = $ 6 .7 6 - .061 =$6.82

(131X3 =401. 401=81/2 - 521 =$1.05/2. V- hrs. X 1 ^ = 8 5 .0 5 /4 =$21.26 •

____/131+.521 = 65+ 1166X3 = 1.98


[Read the problem]

P ro b lem 3

A b o y scou t h ik e d to a cam p 11.7 m ile s d is ta n t; H e w a lked 6.3 m ile s in th e foren oon . H o w fa r d id h e h a ve to w a lk in th e afternoon?


Boy walked total distance to camp in morning.

____ Boy walked exactly one-half the distance to camp in the forenoon.

Boy walked all the way in the afternoon.

Boy walked most of the way in the forenoon.

Boy walked over half distance in the afternoon.

; ' . : ' ' ..


Distance camp was away.Distance boy walked in

forenoon.____Distance boy walked in

afternoon.____Distance boy walked in

both forenoon and afternoon.

Distance the boy rode in auto.

[Read the problem]

P ro b lem 4

T w o w e e k s ago I h ad 6 .7 to n s o f coal in m y coal bin. T h e f ir s t w eek w as v e ry cold an d I bu rn ed 1.1 tons. T h e seco n d w e e k w as qu ite w arm an d I bu rned on ly .8 tons. H o w m uch coal h a ve I left?


Burned entire supply of coal the first week.

Burned most of coal I had the first week.

Burned less coal the second week than the first.

Burned more coal the second week than the first.

Burned all the coal the •second week.


___ Amount of coal in mybin at first.

__Amount burned the firstweek.

___ Amount burned the secondweek.

. Amount burned in twoweeks.

'' Amount left in bin.

[Read the problem]

P ro b lem 5

M r. D a y o w n s fo u r 60 fo o t lo ts va lu ed a t $1000 each, lo ca ted on a s tr e e t which is now bein g p a v e d . Curbing co sts h im $75 p e r lo t an d th e to ta l pavin g co st on th e f o u r . lo ts w ill b e $1500. H o w m uch sh ou ld M r. D a y charge to each lo t f o r cu rbin g a n d pa vin g costs?


Value of lots affects the cost of paving per lot.

Curbing and paving cost less than value of lots.

Curbing costs more per lot than the paving.

It is necessary to use multiplication in solving this problem.

Mr. Day decided not to : pave in front of his lots.

. [Check what is given]

The value of each lot. Width of street in front of

lots.Cost of curbing per lot. Cost of curbing for the four

lots. ‘Cost of paving for the four

' lots.

[Read the problem] •

" P ro b lem 6A g ir l h ad tw o hours in which

to r id e 50 m iles on a branch lin e tra in to th e ju n c tio n w h ere sh e w as to ta k e th e O verlan d E xp r e s s f o r Chicago. H e r train w as on tim e an d tra ve led - at th e ra te o f 30 m ile s p e r hour. H o w m any m in u tes d id sh e h ave to w ait a t th e ju n c tio n un til th e O verlan d E x p ress w as due?


Girl traveled two hours on Overland Express.

Overland Express was two hours late.

Train on branch line traveled 50 miles in less than two hours.

The girl waited two hours at the junction.

The branch line was only 30 miles long.


Distance to the junction.Speed of branch line train.Length of time girl had to

wait at junction.Time girl had in which to

• make train connectionat junction.

Time required to make trip to Chicago.

part 8—what is called FOR PART 4—probable answer PART 5—correct solution[Check what is called for] [Check probable answer] [Check correct solution]

Distance boy had to walk to reach camp.

Distance boy walked altogether.

Distance boy walked in forenoon.

Distance boy walked in afternoon.

Difference between what he walked in forenoon and afternoon.

About 18 miles. About 5.3 miles. About 5.3 hours. 1.4 hours.11 miles.

11.7X6.3=73.71 11.7+6.3 = 18.01 1 .7 - 6 .3= 5.31 1 .7 - 6 .3= 5.4 11.7+6.3 = 17.0

[Check what is called for] [Check probable answer] [Check correct solution]

Amount of coal in bin two weeks ago.

Amount of coal burned the first week.

Amount burned the second week.

Amount of coal burned in two weeks.

About 4 f tons. About 8.6 tons.5.6 weeks.About 4§ weeks.6.7 tons.

6 .7 + l . l - .8 = 76 .7 + l.l+ .8 = 8 .61 .1+ .8= 1 .9

.6 .7 -1 .9 =4.81.1+.8 = 1.9

,6.7+2.9 =9.6 +2 =4.86 .7—.8 =7.5 —1.1 =6.4

Amount of coal left bin.


in

[Check probable answer] [Check correct solution]

Number of lots to be paved.

Cost of curbing for each ------ lot.

Cost of paving for all lots. Cost of curbing and paving

to charge to each lot. Value of the four lots.

240 feet.About 4.75 lots. $1425.About 470 dollars. $1575.

$1500 +75 = 1575.0075 X4 = 1800.0015004-4=375 375 +75 =450.00

[1000x4=4000 40004-1500 =2.67% 1500 X2.67% =$400

1400+75=475[10004-4 = 250 1250+75=325.00


Time required to go to Chicago.

Time girl had to wait at junction until Overland Limited was due.

Total distance girl rode on train.

Speed of branch line train.Distance from girl’s home

to Chicago.


30 miles.About 25 minutes. About 50 minutes. 50 miles.About 48 minutes.


50X2 = 100 - 100 +30 = 130 11304-2 =65; 65 - 60 =5

. 50 - 30 =20(50 4-30 = 1#-]2—1§ = # l# =20. 50+30=80; 80 - 6 0 =20.[30 X2 =60; 604-50 = H 12 — !■#=£ = 48

1

PROBLEMS _______ PART 1— COMPREHENSION PART 2— WHAT IS GIVEN j[Read the 'problem]

P ro b lem 7

W hat w as th e to ta l p a id b y our grocer fo r 6 d o zen m elons a t 12% cen ts ap iece an d 5 bu shels o f apples a t $1.25 p e r bushel?


Grocer bought six melons.Grocer paid one dollar for

five bushels of apples.Grocer bought 12 J dozen

apples.Grocer bought six bushels

of apples.Grocer bought melons by

dozen and apples by bushel. .


Cost of five bushels of apples.

Cost of melons apiece.Number of dozens of mel-

ons bought.Number of bushels of ap-

pies bought.Cost of apples per bushel.

[Read the problem]

P r o b le m s

Irv in g so ld 8 ^ d o zen chicks f o r $8.00 an d a greed to p a y th e ex p ress on th em . The exp ress bill w as 56 cen ts. I f th e ch icks cost h im 5% cen ts ap iece to hatch, h ow m uch d id h e m a k e on th e deal?

‘ [Check true statement]

Irving sold one dozen chicks.

Irvine sold the chicks at 5§ cents apiece.

Irvine received 56 cents for the chicks sold.

Irvine sold more than eieht dozen chicks to an out of town buyer.

The chicks cost the buyer 8§ cents apiece.


____Amount of express bill.____Cost of hatching per chick.

Number dozen chicks sold. Cost per dozen chicks. Selling price per chick.

[Read the problem]

P ro b lem 9

John’s garden is a triangular corner o f th e ya rd . O ne s id e is 11 f e e t an d th e o th er is 18

f e e t to th e righ t angle corner. H o w m an y tom ato p la n ts can h e s e t o u t in th is space, a llow ing 1 sq u a re 'ya rd to e a c h plant?


John’s garden is a circle in the center of the yard.

The garden is a small three-sided plot in the comer of the yard.

The garden is a square in the end of the yard.

John planted one tomato plant in his garden.

Addition is necessary to solve this problem.


The shape of the garden.The number of feet in one

square yard.Space required for one

tomato plant.The length of two sides

of the triangular garden.The number of tomato

plants in the garden.

' [Read the problem] ..................

P ro b lem 10

A fter buying h is s to ck o f p a p ers fo r th e d a y a t 2 cen ts each, a n ew sb o y h ad 35 cen ts change le ft. H e earn ed 15 cen ts by running an errand fo r a m an, an d an oth er m an g a ve him a n icke l. W h en all h is p a p ers w ere so ld a t 5 cen ts each, h e h ad $1.30 in cash . H o w m an y p a p ers d id h e sell?


Newsboy made $1.30 by selling papers.

A man gave him 20 cents.He earned more running

errands than he did selling papers.

The papers cost the boy five cents each.

The newsboy made most of his money selling papers.


____Amount made by se llin gpapers.

____Selling price of papers.Amount given to boy.

____ Number of papers sold.___ Amount boy had after

buying papers.

PART 3—WHAT IS CALLED FOR PART 4—PROBABLE ANSWER PART 6—CORRECT SOLUTION


, Cost of melons apiece.____Cost of melons per dozen.__ _ Amount grocer paid for

melons.Amount grocer paid for

apples..-v Amount grocer paid for

both melons and apples.


75 melons.About $6.00.About $15.00. About 7 dozen.6.5 bushels.


/.12*X 6 = .75; 5X1.25 =16.25; .75+6.25=7.50 / 1 2 x . l2 | = 1.50; 1.25X51=6.25; 1.50 +6.25 = 7.75 / .1 2 |X 6 = .75 1.75X12=9.00 L12*X12 = 1.50; 1.50x61 = 9.00+1.25 = 10.25 (.12§X l2 = 1.50; 1.50x6

------ =9.00; 1.25 X 5 =6 .2519.00+6.25 = 15.25


Profit on this sale.Cost of all chicks.

___ _ Profit on each chick.Cost of each chick.Selling price per dozen

;------- chicks.


About 2 dollars. About 6 | dozens. $67.22.$8.56.$6.08.


112X81 =1001100X51 =5.50(12x81 = 100; 8.004-100

------- = .08; .08 - .0 5 1 = .0251.025X100 = 2.50 (12x81= 100; 100 X.051

------- =5.50; 5.50 +56 = 6.0618.00 - 6.06 = 1.94 (8.004-8.33=8.96; 12 X51 = .66; .96—.66 =.30.304-12 = .025; .025x100

l =2.50


The area of our yard.Number of tomato plants

which can be set out in garden.

Number of square feet ’ allowed plant.

Length of third side of ------ garden.

Corner of yard in which garden was located.


About 10 feet.About 22 tomato plants 198 square feet.99 square feet.About 10 tomato plants.

correcf aoZwfwm]

f 1 8 x l l =198; 1984-2=99 1994-9 = 1118+11=29; 294-3=91

/ 18X11 =198; 1984-2 = 99 1994-3=3318X11=198; 1984-9=22 18+11=29; 2 9 + 9 = 3 7


Total cost of newspapers. Amount of money boy had

before buying papers. Amount of money boy re

ceived for papers. Number of papers sold. Profit made on each paper.


About 75 cents.30 cents.About 13 papers. About 13 cents.20 papers.


f.35+ .15+ .05= .50;11.30 - .50 = .80; .80 4-2 =40 (.35+2 = .37;.15+.05 = .20; .37+.20 = .57;

U.30+.57=1.87; 1.874-3=29 (.35 X2 = 70; .15+.05 = .20; ( 1.30 +20 = 1.50; ll.50 -.70= .80;.80 4-5 =.15 f .35+ .15+ .05 = .55; ll.30-.55= .75; .754-.05=15 (.35+ .02+ .15+ .05 =.57 1.30+.57 = 1.87;

11.874-5 = .36


[Read the problem]

P ro b lem 11

O ur k itch en is 9 f e e t 6 inches b y 12 f e e t . An adjoin ing hall is 4 f e e t b y 4 f e e t . M o th er w ish es m e to g iv e bo th flo o rs on e coat o f varnish. I f a p in t o f varn ish w ill cover 65 squ are f e e t , h ow m an y qu arts o f varn ish w ill I need?


The kitchen was the same size as the back hall.

The amount of varnish required depends upon the floor area to be varnished.

____Mother wanted two coatsof varnish on the floors.

The hall required more varnish than the kitchen.

• Number of coats has nothing to do with number of quarts of varnish used.


____ Dimensions of kitchen.- v Area of both floors to - .

gether.Dimensions of hall.Area covered by one pint

of varnish.Number of coats of var-

nish to be applied.

[Read the problem]

P ro b lem 12

I f a rea l e s ta te agen t rece ives 5 p e r cen t com m ission on th e first th ou sand a n d 2 p e r cen t on all a b o ve th a t am ount, w h at sh ou ld h e rem it to th e o w n er a fter se llin g a lo t fo r $1850?

r •" . : • _ .


Agent received 5% of sale price of lot.

Agent received 2% on the first thousand.

Agent should remit less than he sold the lot for.

Agent received 2% on first thousand and 5% on the balance.

Agent received 7% of the sale price of the lot.


Per cent agent rece ives on first thousand.

____Amount purchaser paidagent for the lot.

____Amount lot is sold for.____Amount agent should re

mit to owner.Per cent agent receives on

amount above $1000.

[Read the problem]

P ro b lem 13

Four b o ys a g reed to bu ild a radio to co s t $25.00. T h ree o f th e b o ys to g e th er w ere to p ro v id e % o f th e m on ey , w h ile th e fo u rth w as to d o all th e w ork an d fu rn ish th e rem ain der o f th e m on ey . H o w m uch m on ey d id h e sa v e b y do ing th e work?


Boy’s work on radio de- creased amount of money he put in.

Boy who did the work put in as much money as the rest.

____The three boys put in allthe money.

____Three of the boys dividedthe work on the radio.

One boy paid for his share wholly in work.

[CAecfc what is given]

Total cost of radio set,.____Part of money three boys

were to furnish.____Amount saved by boy who

did the work.Portion of money fu rn ish ed .

by fourth boy.Share of radio set each boy

owned.

i

PAST 3—WHAT IS CALLED FOR PARTi-faOBABLBAIMWER PART 8—CORRECT SOLUTION[Check what is called for]

___ Area of kitchen.___ Area covered by one quart

of varnish.___ Number of quarts of var

nish needed.___ Area covered by one pint

of varnish.___ Number of coats of varnish

needed for floor.

9


About 130 square feet. About 1 quart.1 square foot.About 2 quarts!65 square feet. H


9 i+ 1 2 = 2 1 * ; 211X 2=42 4X 4 = 16; 42+ 16= 68 684-65 = 112X9* =114; 4X 4 = 16 114+16 = 130 130 4-65 =2; 2 4-2 = 1 12x9^ = 114; 4X 4 = 16 114-16= 98; 9 8 -6 5 = 3 3 334-8=49^X2 = 18; 12X 2=24 4X4 = 16; 18+ 24+ 16= 68 68 X2 = 130; 130 4-65 =2 2 4-2 = 19§X12=114; 4X 4 = 16 114+16 = 130 13 0 -6 5 = 6 5


___ Selling price of lot.____ Amount agent should re

mit to owner.___ Agent’s commission on lot.___ Per cent owner pays agent

for selling lot.___Per cent of sale price of lot

agent’s commission represents.


About 65 dollars.100% of the sale price. $1500.$1817.About $1780.

H

- 1


1850 X .05 =92.50 .1850-92.50 = 1757.50 1000 X .05 =50 850. X.02 = 17.00 50.00+17.00 = 67.00 .1850 -67.00 = 1783.00 '1000X.05 = 50 850 X.02 = 17.00 50.00-17.00=33.00 .1850 - 33.00 = 1817.00 .05+.02 =.07 1850 X.07 = 129.50

.1850-129.50 = 1720.50 +000.00 X .05 = 500.00 850 X.02 = 170.00 500+170. =670.00

[1850-670 = 1180.00

[Check what is called for]Amount of money each boy

was to furnish.Total cost of radio set.Amount of money three

boys were to furnish.Time required to build

radio set.Amount of money saved by

boy who did the work.

[Check ■probable answer] About 33 cents. $6.67.About 1.7 hours. About $1.65.$1.25. l

[Check correct solution]f* of $25.00 = 20.00 20 4-3 =6.67 2 5 .-2 0 . =5.

[6.67 -5 .0 0 = 1.67 f25. —5. =20.00 120.4-3=6.67

iX$25.00=$5.00 i:X$25.00=$6.25 $6.25-$5.00 = $1.25 > of 25.00 = 20.0020.004- 3 = 6.67

[6.674-4 = 1.6725.00 —5.00 = 20.00 i of 20.00 = 1616.4- 3 =5.33 25.—20. =5.00

[5.33 -5 .0 0 = .33


- T ' ' , T : - . ' 1 '

P ro b lem 14

T h ree w orkm en took th e contract to bu ild a cem en t s id e w alk 3% f e e t w id e an d SO f e e t long fo r $39 .60 .: I t to o k all th ree % o f a d a y each to d o th e w ork. T h ey Had to bu y 2 ? cu. y d . o f sa n d a t $3.00 p e r , cubic ya rd an d 12 sa ck s o f cem en t a t $1.10 p e r sack . A t w hat ra te p e r d a y w ere th e y p a id fo r th e ir labor if each sh a red equally?

[Check true statement] ]

Workmen took the contract by the day.

Workmen each spent a day on the job.

Four workmen were employed on the job.

Three workmen worked I of a day each.

Workmen worked more than three days on the job.

Money paid out for mar tcrials.

Number of square feet of sidewalk to build.

Time taken to complete the work.

Rate per day men were paid for their labor.

Number of workmen employed.

i«

i

[Read th£'problem]

P ro b lem IS

A t h a r v e s t tim e I h ad 9S6 bu sh els o f w h ea t. I h a d on e bin I T 6* long, 6 ’ w ide , and 8 ’ 4" d e e p which h eld 460 bu shels w hen filled . I s to red th e re s t o f it in a bin W long and 7%' w id e . ' H o w high d id it com e in th is bin w hen le v e le doff? . :


____ One bin was large enoughto store all the wheat.

B alance of w heat was hauled to market.

____Space occupied by onebushel of wheat is given in the problem.

____Wheat crop amounted toover one thousand bushels.

____Another bin slightly largerthan the first was required to store the wheat crop.


Number of bushels of wheat raised.

Number of bushels one bin would hold.

All . dimensions of one bin.Space occupied by one

bushel of wheat. .Height of wheat in second

bin after leveling.

Score***No. right*** Score-No. r ia h l+ 8 = .[Total possible score=15 points] [Total possible score = = 15 points]

part8—what is called FOR PART4—probable answer parts—correct solution[Check what is called for]

____Number of workmen employed.

Number of days required to do the work.

____Rate per day workmenwere paid for their labor.

____Amount paid out for sand.___ Amount paid out for ce

ment.


About 7.5 days. $6.90.About $9.50.$8.20.6.3 days.

[Check correct soZutitm]39.60- s-3 = 13.203. X2§ =7.50 12X1.10 = 13.20 7.50+13.20=20.703 9 .6 0 - 20.70 = 18.90

118.90-*-3=6.30[3. X2J=7.00 12X1.10 = 12.10 7.00+12.10 = 19.103 9 .6 0 - 19.10 =20.50

120.50-5-3=6.83[12X1.10 = 13.203 9 .6 0 - 13.20 = 26.40 26.40-5-3=8.80 8.80 -5-2 =4.40

14.40X3 = 13.20

3.00X2* =7.5012X1.10 = 13.207.50+13.20=20.7039.60 -20.70=18.9018.90-5-3=6.306.30-5-2=3.153.15X3=9.45


Number of bushels of wheat left after one bin was full.

____Total number of bushelsof wheat raised.

____Number bushels of wheathauled to market.

Height to which second bin was filled when leveled off.

____Number of bushels percubic foot of bin space.

1!;


About 8 cubic feet. About 8 feet.7.4 feet.6.7 bushels.6.4 f©6t.


f 10X 7| =77*956 -4 6 0 =496

1496-5-77*=6.4

(ll* X 6 x 8 * = 5 7 5 10X 7 |= 77* sq .ft.

1575-5-77* =7.4

[ll* X 6 x 8 * = 5 7 5 460-5-575 = .8 bu.956 -4 6 0 =496 496 -5- .8 = 620 cu. ft. 10X 7|= 77* sq .ft.

1620-5-77* =8

[11*X 6X 8*=575 575 -5-460 = 1.25 cu. ft. per bu. 956 -4 6 0 =490 490X1.25 = 613 7$ X 10 =76.7

1613-5-76.7 = 8 ft.

Score -No. rtpAf" _______________ Score>“No. righ t*__________{Total possible score - 1 5 points] [Total posable score -15 points] [Total possible score "15 points]

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The value of mathematics teams in junior high schools · 2020. 4. 2. · Mathematics Contest Rules...

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