Table Of ContentA 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
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UMI EP45791
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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
