A COURSE OP STUDY FOR BASIC MATHEMATICS IN HIGH SCHOOLS A Project Presented to the Faculty of the School of Education The University of Southern California In Partial Fulfillment of the Requirements for the Degree Master of Science in Education By Jesse Clintoh Davis, Jr June, 1950 UMI Number: EP45791 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. IJM I' Dissertation Publishing UMI EP45791 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 bi 'SO f This project report, written under the direction of the candidate’s adviser and approved by him, has been presented to and accepted by the Faculty of the School of Education in partial fulfillment of the requirements for the degree of Master of Science in Education. J, / ■ y j - p ........ Adviser Dean i i TABLE OP CONTENTS CHAPTER PAGE PART I HOW TO DO THE FUNDAMENTAL OPERATIONS 1. How to add......................... *2 2. How to subtract ........... 12 3. How to multiply .............................23 4. How to divide................... . . . . 3 5 PART II HOW TO FIGURE PERCENTAGE 5. How to save your money.............................50 6. How to buy insurance....................- , . . . . 55 7. How to bank your money............................ qO 8. How to buy on the installment plan ............64 PART III HOW TO MEASURE THINGS YOU USE 9. How to buy rugs for your floors. . . . . . . . . . 5 0 10. How to buy fencing......... 71 11. How to paint your home .......................... 74 12. How to measure time and distance . . . . . . . . . . 7 8 13. How to make a circular graph....................... .. i i i PREFACE This course of study is a remedial course in arith­ metic for slow learners. It is a course designed for high school students who place below eighth grade on placement tests designed to ascertain their competency in handling numbers. Since the abilities of students enrolled in basic mathematics classes will vary greatly the course is adapted to individual abilities. Students are expected to achieve a real proficiency in the major content of the fundamental processes, problem solving, percentage and its applications, measurement and graphs. Each area is presented in a simple and practical manner with emphasis on use and understanding. Therefore, the problems here presented are of interest to all adoles­ cents and are designed to make the individual more effective personally and socially. This course of study may be used for grades eight and.nine of the junior high school. This course of study is to be used in conjunction with a good textbook in arithmetic suitable to pupils for which the course is used. 1 PART I HO?/ TO DO THE FUNDAMENTAL OPERATIONS Before you begin to repair your car you should have some tools to work with and before you begin a study of basic mathematics you will need some facts to build the larger structures on. A solid foundation is the first consideration of a good structure. A mastery of the funda­ mental skills of arithmetic is essential to a better, more meaningful and more lasting course of study in basic arith­ metic. 2 CHAPTER 1 HOW TO ADD A. MOTIVATION: Advantages of learning to add correctly and, rapidly. 1. SUCCESS IN COMPUTATION: You will know how to add correctly. 2. EASE IN LATER PROCESSES; You will have little trouble transferring the idea of "putting together" to other processes. 3. MORE TIME SAVED; You will know how to get a sura quickly. 4. FEATHER IN YOUR CAP; Most jobs require a knowledge of addition. You will Increase your qualifications for a job. 5. FEWER GYPS; The person who adds correctly and i rapidly catches clerks who short change him. B. DIRECTIOHS; How to do the mechanics of addition. 1. SINGLE COLUMNS OF TWO NUMBERS; How to add two numbers each less than ten. a. Write the numbers down one under the other. b. Begin with top number and total the two numbers. c. ?/rite this total down under the column you are adding with units in answer directly under the column. d. Example: Find the sum of 7 and 8. Write the numbers down as shown 7 here. Add 7 to 8 and get 15. 8 lb Write the 5 of 15 under the column and then put the one down to the left of the 5. The 5 is put down under the column of units and the 1 is in the tens place. The sum of 7 and 8 is 15. SINGLE COLUMN OP MOKE THAN TWO NUMBERS: Hoy; to total more than two numbers each of which is less than ten. a. Write the numbers down in one column. b. Begin at the top of the column and total the first two numbers. c. Add the first total to the third number and get another total. d. Continue this process until you have summed up all of the numbers in the column. e. Example: To sum up 5 plus 8 plus 7 plus 4 write the numbers down as shown here. 5 Add 5 to 8 and get 13. Now add 13 8 7 7 and get 20. Add 20 to 4 and get 4 5>4 24. Write the 4 of 24 under the 4 in the column you are adding. Put the 2 of 24 to the left of the 4 and you have a sum 24 correctly written. DOUBLE COLUMNS OP TWO NUMBERS: How to add a double column of numbers. a. Write the numbers down one above the other with unit in one over unit in the other. b. Get the sum of the right most column and write this down under column 1. c. Get sum of next column and write this sum down under this column. d. Example: Add 35 and 51. Writ© the 35 numbers down as shown here. In the 51 86 right most column we have 5 over 1. Siam this column up and you have a total of 6. In the next column you have 3 over 5. Sum this column up and you get 8 for a total. Write this 8 under the column you ;Just totaled. You have now completed the problem and 35 plus 51 is 86. DOUBLE COLUMN WHERE YOU MUST CARRY: How to carry when adding. a. Write the numbers down as In adding a double column of two numbers. (See the above sections.) b. When you sum up the first column you will get a two digit umber. Write the number in the ■units place of this sum down right under the first column and write the other number down in the next column above the column. c. Add the next column including the new number you wrote in it, (This is the number you carried from the first column.) d. Write this sum down under the column you just summed up* e. Example: Add 67 and 96. Write the numbers down as shown here. Add 7 and 6 1 -67 and get 13. Write the 3 down under 9.6 the first column and put 1 over the next column. Row sum up the next column in­ cluding the 1 you carried and you have 1 plus 6 plus 9 is 16. Write the 16 down with the 6 right under the second column. The sum of 67 and 96 is 163. SUM OP A COLUMN OP NUMBERS; How to add any column of whole numbers. a. Write the column of figures down in any order so long as you have units under units, tens under tens, hundreds under hundreds and so on. If a number has no hundreds or tens and such, just write all of its digits under proper digits of the other numbers as above. b. Get total of first column by adding from top to bottom and write sum down. If you have a sum that is greater than ten carry everything but the number in the units place, to the next column. c. Add the next column, the column of numbers in the tens place, Including what you carried from the first column, and write down the last number