A course outline for eighth grade mathematics as applied to home expenditures

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A COURSE OUTLINE FOR EIGHTH GRADE MATHEMATICS AS APPLIED TO HOME EXPENDITURES

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 Homer L. Hendricks August 1950

UMI Number: EP46356

All rights reserved INFO RM A TIO N 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.

D issertate Publishing

UMI EP46356 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 4 8 1 0 6 - 1346

ts't T his project report, w ritten under the direction of the candidate’s adviser and ap p ro ved by him , has been presented to and accepted by the F a c u lty o f the School o f E d ucatio n in p a r t ia l f u lf illm e n t of the requirements f o r the degree

of M a s t e r of

Science in Education.

D ate

:

djktsls..... A d v is e r

Dean

ii INTRODUCTION Statement of need.

It is generally recognized, in

varying degrees, by teachers of mathematics in our junior high schools that there is a great need for making their subject matter more "alive," more applicable to life problems. The formal division of subject matter into fractions, decimals, per cents, etc., and the mechanical manipulation of numbers is not a way of using mathematics to the best advantage in solving problems of daily living nor is it even a good method of learning. Statement of problem.

This course outline for eighth

grade mathematics is being written, actually, with two problems in mind.

First, there is the general problem of

making mathematics meaningful by "functional!zing" it.

That

is, making realistic application of the subject matter to the needs of the student as they exist now and insofar as the student is able to comprehend such needs.

In other words,

the viewpoint taken herein is that mathematics is not in it­ self purposeful, but rather, that it becomes purposeful only to the extent that it becomes functional and is used as a tool for meeting real life problems. This leads to the second, more specific problem with which this course outline in mathematics is concerned:

that

of meeting those financial needs and problems that arise in

iii the home whose solutions are better insured through the use of mathematical understandings. It is generally accepted practice in teaching mathe­ matics to put the tail before the house; to begin with numbers, processes, and manipulations involved and assume that application will ’’naturally’* follow.

This is actually

a carry-over of the erroneous "faculty discipline" theory of transfer which simply required the pupil to redigest the reasoning of others, and which in no way contributed to the development of the pupil’s ability to think. Point of view.

This course outline for eighth grade

mathematics is an attempt to avoid the fallacious assumption that the study of mathematics per se in the classroom results in an automatic application of the "learned"techniques to real life problems outside of the classroom.

The point of

view taken herein is that understandings and applications must go hand in hand; that a separation of the two kills both.

Mathematics has meaning only when applied to real

life problems and these problems should be brought directly to the classroom. Method of attack.

This course outline in mathematics

is directed toward the student.

The basic assumption is that

each student would like to see his or her family get more in return for the money that is spent in the home.

It follows

then that the area under consideration is home spending, with the chapters being laid out in terms of how the money is spent.

Each chapter is divided into sections titled "re­

wards,” "investigations," "over-all activities," and "testing programs.”

It is intended that the "rewards” section provide

motivation.

The "investigations" section has a dual purpose:

first, to provide direction for the inquiries that are to be made, this being done by means of statements in "how to" form with questions following; and, second, to slant these directions in such a way that most of the answers can only be obtained by the use of mathematics.

Mathematics is,

therefore, being brought into the picture through the "back door."

The student is not studying mathematics in its

purity but is using it as a tool to solve life problems, during which process he gains a better understanding of those problems and certainly an ability to apply mathe­ matics in a way that is useful to him.

The "over-all activi­

ties" section puts into one action those directions given in the "investigations" section and the last section, "testing program," is an evaluation check-up for the student on what he or she has learned and accomplished through a participation in and a carrying out of these courses of action listed in the "over-all activities" section. As a means of combating the need for diagnosis of and practice on the basic operations in mathematics, the

teacher is provided with a series of four minute tests in the appendix that are especially designed to bring to light the students* computation difficulties as well as furnish whatever drill that may be necessary.

Further information

on how these tests should be incorporated into the curriculum is given in the appendix. Materials for this course outline in mathematics were gathered from students (two hundred strong), teachers, books and articles.

Contributions from students and teachers were

in the form of statements concerning those problems of home spending that they were most interested in knowing more about. These replies were grouped according to problem content and form the basis of the chapter divisions.

Consideration is

given to the individual problems within the ’’investigations1’ section of each chapter.

The writings' of Brueckner and

Grossnickle, Fay Adams, Claude C. Crawford, and others as is indicated in the bibliography, are recommended for giving additional support and information on the point of view and method of attack used herein.

vi PREFACE TO STUDENTS Is mathematics one of your poor subjects? easy for you but just a little boring?

Or is it

How would you like

to have it changed into a course that is neither of these— a course that is new and different and full of ulife"?

If

this doesn’t sell you, how about considering the next point: there are ways and means by which you can help your family save money that you have never heard of— methods and techniques of buying that, when used, result in savings never before thought possible. If you want your family to get the most out of Its Income, and if you want to learn a few things yourself that many adults don’t even know, then make an honest effort to follow the directions given herein and you will not be disappointed.

vii

TABLE OP CONTENTS CHAPTER

PAGE PART I. THE TWO ESSENTIALS HOW TO AUDIT EXPENSES ON POOD AND CLOTHING

1 . PURCHASING POOD:

How to evaluate the wisdom of ................... your parents' food expenditures

2.

3

BUYING CLOTHING: How to help your parents save money on buying clothes . ............................ 10 PART II. YOUR CASTLE AND SURROUNDINGS HOW TO GET MORE VALUE OUT OP THE SHELTERING DOLLAR

3«

BUYING A HOME: How to help your parents save money on buying a h o m e .......................................17

1}..

PAYING FOR RENT AND UTILITIES: How to help your parents save money on houserent and utility costs .

23

5 . PAYING FOR UPKEEP OP HOUSE AND YARD:

How to help your parents save money on furniture and appliance expenditures ........................................

6.

29

BUYING FURNITURE AND APPLIANCES: How to help your parents save money on furniture and appliance ex­ penditures ............................................. 36 PART III. THE THREE MUSTS HOW TO BE FREE FROM PEAR, KEEP UNCLE SAM HAPPY, AND STILL GET AROUND

7. 8.

9-

BUYING A CAR: How to help your parents save money when buying a c a r ...................

lj.3

PAYING INCOME TAXES: How to help your parents save money on income taxes . . . . . . . . .............

$0

INVESTING IN INSURANCE: How to help your parents save money by the proper use of i n s u r a n c e ........

B I B LIOGRAPHY............................................... 6l APPENDIX

63

1

PART I. THE TWO ESSENTIALS HOW TO AUDIT EXPENSES ON POOD AND CLOTHING There are two things in life that you are always going to have a need for, namely, food for your stomach and clothing for your body. The following two chapters will help you, and through you, your parents to provide for these two essentials at greater savings. Make an honest effort to follow the directions provided for you herein, and you will not be disappointed. You will notice that these directions are given in terms of questions and you are asked to find the answers in "everyday life" by means of investigation, inquiry, search, quest, and explo­ ration. Your teacher, of course, will provide all the help and guidance that you will need.

PURCHASING- POOD

3 CHAPTER 1 . PURCHASING FOOD HOW TO EVALUATE THE WISDOM OF YOUR PARENTS' FOOD EXPENDITURES A.

REWARDS:

Advantages of being able to help your parents

be more discriminate in their grocery buying.

1.

IMMEDIATE REWARDS: a.

Extra money:

Benefits that will be yours now. You can share in the money saved

at the grocery store. b.

Take part in responsibilities:

Your knowledge of

grocery store economy will cause your parents to depend upon you more.

2 . FUTURE REWARDS:

Benefits that you will realize fully

at a later date. a.

Compound savings:

Your "grocery store horse-

sense" will save you money all through life. b.

Marriage:

Your capable handling of the grocery

bill will be a big contribution to your future home's budget. B.

PROCEDURES:

Suggestions that will enable you to check

how wise your parents are in food purchases.

1 . How to choose the grocery store to patronize. a.

Does a chain grocery store undersell an inde­ pendent grocery store in all items?

b.

Is there, any relation between prices of "on sale" items in different stores?

c.

Is it necessarily true that the larger the store the cheaper the prices?

d.

What are the advantages and disadvantages of always buying your groceries in the same store?

How to get more value in return for being known. a.

Do you have to know the butcher to get good meat

b.

Do independent grocery stores offer savings to their "regular11 customers?

c.

Are there any advantages in being a regular customer?

d.

Do you have to be known in order to open a grocery charge account?

How to get more vegetables at less cost out of your own yard. a.

Do you have enough space for a garden in your yard?

b.

How much does it cost to raise a vegetable garden?

c.

How many hours of work are necessary to produce an adequate supply?

d.

How many tomato plants are necessary to supply a family of four?

e.

What vegetables can be supplied at what times of the year?

How to compare cost and size.

a.

Does the price of laundry soap per ounce vary with the size of the package?

b.

Is canned fruit cheaper by the large can or the small?

c.

How much saving, if any, is there in buying a

25^ Hershey bar instead of a 5/ one? d.

How many items in the store come in "economy sizes?”

e.

Is there any saving in buying fresh vegetables in larger quantities?

f.

Will a dollar buy more canned corn than fresh corn?

g.

Are canned weiners cheaper in the grocery de­ partment than the packaged ones at the meat counter?

h.

Is Pepsi-Cola cheaper in the quart size or the regular size?

i.

How does the price per ounce of packaged cheese compare with that of fresh cut cheese?

j.

Is milk cheaper by the half gallon than by the quart?

k.

Are “economy size" breakfast cereals cheaper by the ounce?

5 . How to check the farmers1 "road-side market" offerings. a.

Are a lug of apricots from the farmer’s orchard

cheaper than those sold in the grocery store? b.

How do the prices of olives, oranges, and apples in the road-side stand compare with those in the grocery store?

c.

Do prices at road-side markets vary and if so why?

d.

Considering time, travel expense, etc., could your parents save any money by shopping at road­ side markets?

e.

How many miles away are various road-side stands from your home?

C.

OVER-ALL ACTIVITIES:

Some learning experiences that will

help you evaluate the wisdom of your parents’ food ex­ penditures.

1.

Talk your parents into allowing you to purchase a full week1s supply of groceries and show them exactly where you saved money and how much.

Present this

information to the class.

2. Take over the grocery buying when your parents go on their vacation or are away from home for several days and give an account of your results to the class.

3 . Visit a road-side stand and compare its prices with those of your neighborhood grocery.

D.

TESTING PROGRAM:

Assignments that will help you evaluate

your money saving techniques in grocery store shopping*

1.

TRUE-FALSE:

Place an

X

in the correct space for

true or false. T a.

F

( ) ( ) If you buy a 1 l/l|_ lb. can of corn for 27/, is it more expensive than a 2 lb. 6 oz. can for 53/?

b.

( ) ( ) You should buy canned vegetables in preference to fresh vegetables because they are cheaper.

2.

BEST ANSWER:

Place the number of the best answer in

the parenthesis. a.

( ) If you buy-hand soap that is regularly priced at 3 for 25/ and is available at Ip for 30/, the saving per each is: (3 ) 14-/5/

b.

(

(1) 6/5/

(2) 2/3/

(if) .75/-

) The difference between 5 lb* 8 oz. and Iplb. 10 oz. is:

(1) lip oz.

(2) l6 oz.

(3) l/2 lb.

(ip) 1 lb. 2 oz.

3 . COMPUTATION PROBLEMS:

Place answer in front of each

problem: a.

A 2 lb. 3 oz. can of tomatoes cost 19/ and fresh tomatoes sell for 30/ a pound.

How

much more per ounce does one cost you than the other?

b.

If the nearest road-side vegetable stand to your house is 10 miles away and you usually save about $2.00 each time you go there, what is the difference between your saving and gas expense round trip if car gets 15 miles to the gallon of gas at 25/ per gallon?

4 . RATING SCALE FOR THE ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score. Total the results.

Factors to be Rated

Weak Fair Superior 1 2 - 3 k 5-6 7 8

Wt. Score x 3 =

b.

Size of undertaking involved.

x 2 =

c.

Resulting personal benefits.

K

d.

Resulting family benefits

x 1 =

COMMENTS:

11

Amo tint of money saved.

H

a.

TOTAL a

SAVE-

10 •

A.

CHAPTER 2 . BUYING CLOTHING HOW TO HELP YOUR PARENTS SAVE MONEY ON BUYING CLOTHES REWARDS:

Benefits of being able to help your parents

buy clothes for the family less expensively.

1 . SELF-ESTEEM:

Your personal pride will be given a

shot in the arm when you get that

"extra" coat or

pair of shoes that Mom and Dad were able to afford through your advice.

2 . ON YOUR OWN: clothes when

You can do your own shopping for you know ’'what goes" and gain your

parents confidence. B.

INVESTIGATIONS:

Directions for checking on the expenses

involved in keeping up the family wardrobe.

1. How to find out about reduction sales in clothing. a. What information does your newspaper give you on sales? b. What stores in your neighborhood specialize in clothing sales? c. What clothing stores specialize in telling their charge account customers first about coming sales?

2 . How to buy clothes during seasonal sales-. a. At what times- of the year do clothing stores have their seasonal sales. b. What per cent reductions can be expected during these sales?

11

3.

How

to buy clothes at marked discounts.

a. What does " 2 0 % off” mean? b. What does " 2 0 %, reduction” mean? c.

What is the relation between ”amount reduced” and ”per cent saving”?

If.

How

to buy clothes at sources other than retail

clothing stores. a.

Do you get more than what you pay for at ’’factory outlet” clothing stores?

b.

(Consider quality)

Can independent salesmen offer you legitimate prices on clothes that are substancially less * than regular retail prices?

5>. How to use charge accounts. a.

Do you sometimes pay for a carrying charge when using charge accounts?

b.

Is it correct to think that the use of a charge account is a means of saving money?

6;

How to make use of organizational membership for legiti­ mate reductions on clothes. a.

What organizations do you know of that make it possible for their members to save money on clothes?

b.

Does either your father or mother make use of such an affiliation?

7. How to buy in terms of quality. a.

Do more expensive shoes last longer for you

than less expensive ones? b.

What is the relationship between the quality and the price of clothing and the length of time that it will last?

8.

How to buy in terms of color combinations. a.

Is it possible to have more varied outfits at less cost if the colors of your clothing harmonize?

b.

What color combinations do you now have in your clothing?

9*

How

a.

to buy in terms of style combinations. Is using good style combinations in your dress a means of saving money?

b. C.

What style combinations best fit you?

OVER-ALL ACTIVITIES:

Projects that you can do to increase

your abilities at saving money on clothes.

1 . Talk your parents into allowing you to buy your own clothes for a period of time and show the various ways that you were able to save money.

Present your

results to the class.

2.

Do some shopping for your baby brothers and sisters and help them save money and get more value.

Show

your results to your parents and bring them to class for presentation.

3 . Look in the newspapers and stores for sales and help your parents save on items of clothing that they need to buy.

13 D.

TESTING PROGRAM:

Check-ups that will help you to evaluate

your abilities at discriminate shopping for clothes.,

1.

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) ( ) You should shop for clothes in terms of quality as well as in terms of price.

b.

( ) ( ) Reductions on clothes that you buy may be indicated in terms of per cent and in terms of dollars.

2 . COMPUTATION PROBLEMS:

Write the answer on the blanks

ahead of each item. a.

_______ What is the sale price that you would have to pay on a coat regularly priced at $ 16.95 and marked down 1$%.

b.

_______ What per cent reduction would you be getting on a dress regularly priced at $9*95 and reduced 20$.

3 . RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score.

Total the results.

34

Weak Fair Superior Factors to Rate a. b. c. d.

1 2 - 345-6 7 8

Wt. Score

Amount of savings realized

x 3 =

Increased wearing ap­ parel resulting

x 3 =

Resulting personal benefits

X

1

a

X

1

=

Resulting family benefits ,

COMMENTS:

TOTAL -

15

PART II. YOUR CASTLE AND SURROUNDINGS HOW TO GET MORE VALUE OUT OP THE SHELTERING DOLLAR If you are interested in having a better roof over your head with more underneath and around it then read the next four chapters and see how your family's income can be stretched into providing more of these needs for you.

16

BUYING A HOME

17 CHAPTER 3 . BUYING A HOME HOW TO HELP YOUR PARENTS SAVE MONEY ON BUYING A HOME A.

REWARDS;

Advantages of being able to help your parents

save money on buying a home.

1 . HOME OF YOUR OWN:

If your parents can see how they

will save money by buying a home they will do so and the whole family will be happier.

2 . LARGE DIVIDENDS:

Money saved is always appreciated

and the best place to save money is probably on the home because of the siz© of the investment.

3 . PRIDE IN UPKEEP:

Living in your own home is always

a source of inspiration for making it look nice. B.

INVESTIGATIONS:

Directions for checking on ways and

means of saving money when buying a home.

1 . How to check the interest rates. a.

What is the rate of interest?

b.

How much of the monthly payment goes on interest?

c.

How does the down payment affect the interest charge s ?

d.

Including interest charges, what is the total cost of the house?

2 . How to check on the builder. a.

Inspect other houses built by the contractor.

b.

What kind of a reputation does the contractor have?

c.

Find out how satisfied the other persons are that the contractor has built for#

How to check tract home values. a.

Are homes in tracts less expensive?

b.

Do homes in tracts generally have smaller down payments?

c.

Why?

Why?

-Are materials and workmanship in tract homes generally up to standards?

d.

Do tract homes always look alike?

e.

How do the rates of interest on tract homes com­ pare with those of non-tract homes?

How to check the use of rent as a down payment. a.

Who has the option of applying back-paid rent onto a down payment?

b.

Does this buying feature afford a saving to the prospective buyer?

c.

For how long a time is the option in effect?

How to check location. a.

How accessible are shopping centers?

b.

How far away is your father’s job?

c.

What kind of people live in the neighborhood?

d.

How beautiful are the surroundings?

e.

How accessible is public transportation?

f.

How does the location affect transportation costs

How to check upkeep expenses.

a.

How high are water rates?

b.

What would it cost to paint the outside of the house?

c»

the inside?

How long can the type of roofing used be expected to last?

d.

How much would it cost to put in flowers and shrubbery?

e.

How much would termite disinfestation cost?

7 . How to check on utility expenses. a.

What

are water rates?

b.

What

are electricity rates?

c.

What

are gas rates?

d.

Are these rates acceptable?

8 . How to check property taxes. a.

Is the house in the city or county?

b.

How much are the property taxes each year?

c.

Are the property taxes acceptable?

9 . How to check accomodations. a.

Are there enough bedrooms to provide for possible future additions to the family size?

b.

Is there enough room in the backyard for

a bar-

be cue ? c.

Is the yard fenced in?

d.

Are the various rooms large enough for the family furniture?

20 C.

OVER-ALL ACTIVITIES;

Some learning experiences that

will help you in finding ways and means of saving money on buying a home.

1. Make inquiries and collect information on homes for sale in your neighborhood.

2. Write to real estate agencies and ask for information. 3.

Check with your local banks and finance companies on loan requirements and methods of payment.

I|..

If your parents are buying their own home now, collect all pertinent information from them. Ask your friends, neighbors, and relatives about the contracts on their homes.

6. D.

Present all the information collected to the class.

TESTING PROGRAM:

Assignments that will help you evaluate

your familiarity with the saving techniques of buying a home.

1.

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) ( ) You should include interest charges when considering the over-all expense of a house.

b.

( ) ( ) Your interest charges will be smaller when you pay more on a down payment.

21

2.

COMPUTATION PROBLEMS:

Write the answer in the

blank ahead of each item. a.

_______ What per cent interest would you be paying if $22.50 of a $>60.00 payment goes on interest?

b.

_______

If you were going to use a rent option to buy and your rent had been $>lj.5 a month for two years, how much of a down payment would you automatically have?

3.

RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score.

Total the results.

Factors to Rate

Weak Fair Superior 1 2 -3 lj.5-6 7 8

Wt. Score

a.

Quality of class report

x 2 =

b.

Amount of information collected

x 3 =

Resulting personal benefits

x 1 =

Resulting family benefits

X 1 ■

c. d.

COMMENTS:

TOTAL =

PAYING FOR RENT AND UTILITIES

23 CHAPTER 4 . PAYING FOR RENT AND UTILITIES HOW TO HELP YOUR PARENTS SAVE MONEY ON HOUSE RENT AND UTILITY COSTS A.

REWARDS:

Benefits of being able to inform your parents

on all factors related to rent and utility costs.

1.

A ROOM OF YOUR OWN:

Your family's housing needs

will be better supplied when your parents' rent dollar yields greater returns.

2 . A NICER LOCATION: at home will

More satisfying surroundings

be yours when wiser methods of rental

shopping are employed by your parents. B.

INVESTIGATIONS:

Directions for checking on the ways and

means of saving money on rent and utility costs,

1 . How to compare rent to family income. a.

The rent amounts to what per cent of the family income?

b.

What fraction of the family income can be spent on rent?

2 . How to check on utility rates. a.

Are utilities included in the rent?

b.

Where is information available on utility rates?

c.

What would you normally expect to pay a month on lights, gas, and electricity?

d.

Is there a water shortage factor to be considered?

e.

What is the unit charge for water? electricity?

for gas?

for

How to read the water, gas and electricity meters. a.

Where are these meters located?

b.

What kind of units is water measured in terms of?

c.

What kind of units is natural gas measured in terms of?

d.

What kind of units is electricity measured in terms of?

e.

What are the place values of the numbers indi­ cated on the various dials in each meter?

f.

Is it possible to check your utility bills by reading these meters monthly?

How to check on maintenance costs. a.

Does the landlord pay for all maintenance costs?

b.

What upkeep expenses should be considered?

How to check on local school facilities. a.

How much will it cost to get to and from school?

b.

What are the tuitions at the nearest junior college and university?

c.

How good are the facilities in the local grammar school and high school?

d.

What kind of a reputation does the local school district have?

How to check the furniture

(if house is furnished).

a*

What condition is the furniture in?

b.

Are any improvements necessary?

7. How to check the cost of furnishing (if house is un­ furnished) . a.

Will the rugs you now own fit into the different rooms?

b.

Will your stove and refrigerator fit into the kitchen?

c.

Is there enough space for your dining room set?

d.

Are the bedrooms large enough for your bedroom furniture?

e*

Is it necessary to buy any additional furniture to furnish the house?

8 . How to check transportation a.

How much will it cost? costs.

How far away is Dad's work?

How much will it

cost him a week to get to and from work?

C.

b.

How far away is the nearest shopping district?

c*

How close are the nearest bus lines?

OVER-ALL ACTIVITIES:

Projects that will help you and

your family save money in renting your home.

1 . Go out and look for a house more of your needs than the

to rent that will fit one you are'now living

in, and at no extra cost.

2 . Talk to your landlord and see if he can offer you any more in return for your rental dollar.

3.

Find out what people you know are looking for a place to rent and be on the look-out for a suitable residence for them.

26 D.

TESTING PROGRAM;

Assignments that will help you check

your familiarity with money-saving considerations in renting.

1 . TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

P

( ) ( ) You should never expect utilities to be included in your family*s rent.

b.

( ) ( ) You can rent a furnished house for less than an unfurnished one.

2.

COMPUTATION PROBLEMS:

Place the answer on the line

in front of each item. a.

_______ How much would you have to cut off a rug 15* x 20* to fit a room 12* x 1 5 ’?

b.

_______ If your family income is §200 a month how much can be spent for rent on the basis of l/ij. the monthly income?

3 . RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score.

Total the result.

27

Factors to Rate a. b. c. d.

Weak Pair Superior 1 2 -3 if 5-6 7 8

Wt. Score

Amount of savings realized

x 2=

Results of search for house to rent

x 3=

Resulting personal benefits

x 1=

Resulting family benefits

x 1z

28

V(r Y W ,

»k - ta. A w ~ PAYING FOR UPKEEP OF HOUSE AND YARD

29 CHAPTER 5 - KEEPING UP THE HOUSE AND YARD HOW TO HELP YOUR PARENTS SAVE MONEY ON HOME MAINTENANCE A.

REWARDS;

Advantages of being able to help your parents

afford, an attractive and well-cared for house and yard.

1.

PRIDE:

You will be anxious to show your friends

improvements that you shared in obtaining.

2 . A JOB:

The experiences gained here in setting up

improvements in and about the house, will open up avenues to part-time jobs.

3 . GOOD WILL:

Your parents* respect for your newly

attained ’’maintenance saving” abilities will cause them to ask for your advice more often. B.

INVESTIGATIONS: expense

1.

Directions for checking on the upkeep

of your house and yard.

How to figure the cost of painting

the outside of

the house. a.

How much surface area will a gallon of paint cover?

b.

What are the differences in cost in the kinds of paint that can be used?

c . ■ How many gallons of paint does it take to paint the outside of your house? d.

How much would it cost to have a painter paint the outside of your house?

e.

How much would it cost to paint the roof of your house?

How to figure the cost of painting the inside of the house. a.

What is the cost of various indoor paints?

b.

What is the cost of paint brushes?

c.

How many quarts of paint would be needed to paint your kitchen?

d.

What would be the total cost of painting your kitchen yourself?

e.

What would be the cost of painting the different rooms in your house?

f.

How much can you hire a painter for doing the inside work?

g.

Would it be cheaper for you or the painter to furnish the paint?

How to control termites in the house. a.

How much does it cost for a termite inspection?

b.

Is termite inspection a necessary expense when selling your house?

c.

What are the advantages of having termite in­ spection regularly?

d.

Is termite disinfestation costly?

How to figure the cost of roofing the house. a.

How much would It cost to replace the kind of roof you have on your house?

b.

How much would it cost to repair a part of the

roof that may need fixing?

5 . How to figure the cost of sanding the floors. a.

How much does it cost to rent a sanding machine? (Consider the length of time that the machine would be needed.)

b.

How much would it cost for other materials needed to finish the floors with?

c.

Would it be cheaper to hire a man to sand and finish your floors?

6.

How to figure the cost of papering the walls. a.

How much does wallpaper cost by the yard?

b.

Would it be cheaper to hire someone to paper your walls or buy the materials and do it your­ self?

(Consider all factors.)

7 . How to figure the cost of filling in wall cracks. a.

How much would the necessary materials cost?

b.

What would the total expense be if you did

this

job yourself? 8.

How to figure the cost of opening up stopped-up plumbing. a.

What would the total expense be if you did this job yourself?

b.

(Consider materials needed.)

How much does a plumber charge per hour?

9 . How to figure the cost of improving the lawn. a.

How much does lawn seed cost?

b*

How much seed is necessary to put in a new lawn?

(Consider area to be seeded.) c.

What is the cost of fertilizer?

d.

What would be the total cost of doing this job yourself?

e.

How much would a gardener charge you for this job?

f.

Vfttieh would be cheaper, doing this job yourself or having someone else do it?

10. How to figure the cost of putting in flowers and shrubbery. a.

How much do plants, flower seeds, and bulbs cost (Consider the kind that you want.)

b.

What would be the cost of doing this planting yourself?

11. How to decide between doing yardwork yourself and having a gardener do it. a.

How much would the essential yard tools cost?

b.

Would it be cheaper in the long run to hire a gardener?

Q.

OVER-ALL ACTIVITIES:

Projects that you can do to help

your parents save money on home maintenance.

1 . Save a part of your allowance each week and, when you have enough, do one of the maintenance jobs around the house that you think is in most need of

being done.

Show your parents the results obtained

and the costs involved.

Present to the class the

considerations and problems you encountered.

2 . Ask your neighbors and friends if there are any odd jobs involving maintenance that you could help them out with.

Bring to class for discussion the problems

that give you trouble. D.

TESTING- PROGRAM;

Check-ups that will help you evaluate

your abilities in saving money on home maintenance.

1*

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) (

)You should always do maintenance work yourself rather than hire it out.

b.

( ) (

)In considering the cost of maintenance work that you do yourself, you should consider your own labor a part of it.

2.

COMPUTATION PROBLEMS:

Write the answer in the blank

ahead of each item. a.

________ The outside area of a rectangular shaped house SO ft. by 30 t t ,

and 15 ft. high is

how many square feet? b.

_______

How many gallons of paint would you need, in problem "a", to paint the house if a quart of paint covers 225 sq. ft.?

3 . RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score.

Factors to Rate a. b. c. d.

Total the results. Weak Fair Superior 1 2 - 3 10-6 7 8

Wt. Score

Per cent savings realized

x

3 =

Size of undertaking involved

X

1 s

Resulting personal benefits

X

2 »

Resulting family benefits

x 2 r

COMMENTS:

TOTAL =

35

CASH DOWN / 1 IK

\n BUYING FURNITURE AND APPLIANCES

36 CHAPTER 6. BUYING FURNITURE AND APPLIANCES HOW TO HELP YOUR PARENTS SAVE MONEY ON FURNITURE AND APPLIANCE EXPENDITURES A.

REWARDS:

Benefits of being able to help your parents

buy furniture and appliances less expensively.

1 . MORE INSIDE:

When you show how the furniture dollar

can buy more your family will enjoy more of the con­ veniences of modern housekeeping.

2 . LESS HOUSEKEEPING DRUDGERY:

You, your mother, and

the whole family will find housekeeping easier and more fun when even just a few labor-saving devices are provided. B.

INVESTIGATIONS:

Directions for checking on ways and means

of saving money on furniture and appliance purchases.

1* How to open a charge account. a.

Whom do you see to open the account?

b*

What information are you required to give?

2 . How to use a charge account. a.

Is there any relation between making your pay­ ments on time and your credit standing?

b.

Should creditors be informed of a change of address?

3 . How to buy in accordance with your housekeeping needs. a.

What are your family needs?

b.

How much of the family income can be directed

toward meeting these needs? c.

What future needs should be considered?

1).. How to plan a program for future purchases. a.

What relations are there between present buying and future buying?

b.

Should possible changes in needs, tastes, and surroundings be considered?

5 . How to figure carrying charges. a.

What are carrying charges?

b.

What relationship exists between carrying charges and interest charges?

c.

Why is there a difference between installment price and cash price?

6.

How to buy at marked discounts. a.

What does "10$ off" mean?

b.

What does "15$ reduction" mean?

c.

What relation is there between "amount reduced" and "per cent saving"?

7. How to locate clearance sales. a.

What information do your newspapers give you?

b.

What information will your radio give you? (evaluate)

c.

What stores in your neighborhood specialize in furniture and appliances?

8.

How to check your newspaper want ad section.

a.

Is there a division listed for furniture and appliances?

b. 9.

Can used furniture be bought at great savings?

How to buy at auctions. a.

Where are regular auction sales held?

b.

What advantages do some auction houses have over others?

c.

What do these auctions have to offer in the way of savings?

10.

How to make use of organizational membership for savings. a.

What organizations make it possible for their members to buy, among other things, furniture and appliances at a discount?

b.

Is it possible for either of your parents to belong to such an organization?

C.

OVER-ALL ACTIVITIES:

Some learning experiences that will

help you find ways and means of saving money on furniture and appliance buying. 1.

Plan a house'furnishing program for your family*s present and future needs.

2.

Demonstrate how savings can be made on your house furnishing program by visiting furniture stores, attending auctions, locating clearance sales,

39 checking your newspaper want ad section, and by whatever other means that may occur to you. D.

TESTING PROGRAM:

Assignments that will help you evaluate

your abilities at discriminate buying for furniture and appliances. 1.

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) (

)You should consider future needs when buying for present needs.

b.

( ) (

}Your credit standing does not effect your ability to open a charge account.

2.

COMPUTATION PROBLEMS:

Write the answer on the blank

ahead of each item. a.

_______

If your family bought a washing machine on time for $225 and the cash price was $20Q, how much was the carrying charges?

b.

______

If your family’s income were $200 per month and furniture payments totaled $ 37*50 what per cent of the income is being spent on furniture?

3.

RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score.

Total the results.

ij-0

Factors to Rate

b. c. d.

Wt. Score

Per cent savings realized

x 2 =

Benefits resulting from planned program

x 3 =

Resulting personal benefits

x 1 s

Resulting family benefits

COMMENTS:

X H II

a.

Weak Fair Superior 1 2 - 3 ^ 5-6 7 8

TOTAL =

PART III. THE THREE MUSTS HOW TO BE FREE FROM FEAR, KEEP UNCLE SAM HAPPY, AND STILL GET AROUND If you and your family are going to have your share of the joys of living there are three indispensables that must be accounted for, namely, income taxes, a car, and insurance. Read the next three chapters and see how this can be done at greater savings with larger returns.

h o o l i g a n 's

BUYING A CAR

k-3 CHAPTER 7. BUYING A CAR HOW TO HELP YOUR PARENTS SAVE MONEY WHEN BUYING A CAR A,

REWARDS:

Benefits that result from your ability to Inform

your parents on how to provide transportation at less expense. 1.

A BETTER CAR:

Showing your parents the many ways that

money can be saved when buying a car makes it possible for the family to have a nicer car. 2.

TRAVEL:

Your family will enjoy week-end trips and

vacation travels much more often when the family car is a pleasure to ride in. 3.

A VEHICLE OP YOUR OWN:

Your parents may find it

possible to provide you with a bicycle or motor scooter if you can show them how to save money on their own transportation. B.

INVESTIGATIONS:

Problems for you to consider in helping

your parents save money on buying a car. 1.

How to figure interest. a.

What is the formula for finding interest?

b.

What per cent rate is being used?

c.

How much is the money owed?

d.

For how long of a time are the pa^yments going to be made?

e.

Is the interest rate an annual, a semi-annual, or a monthly rate?

1*4 2.

How to decide upon the down payment. a.

What effect does the down payment have on interest charges?

b.

How does the down payment affect the number of payments to be made?

c.

How does the down payment affect the size of each monthly payment? (1) How large a monthly payment can the family income afford? (2) What relation is there between the size of the monthly payments and the interest charges?

3.

How to figure sales tax. a.

What is the

state sales tax rate?

b.

What is the

city sales tax rate?

c.

Where are the sales tax rate cards obtained?

d.

How do you determine a certain per cent of so many dollars?

If* How to

5*

figure license fees.

a.

On

b.

Where is information available on these fees?

How to a.

what basis are license fees determined?

figure insurance costs.

How is your car classified on the rate scale?

b.

What is the

liability rate?

c.

What is the

collision rate?

d.

What does "full coverage" mean?

*1-5

e.

What does "$>50 deduetable" mean?

f.

What is the rate for "fire, theft and compre­ hensive" ?

g.

What does the term "comprehensive" mean?

h.

What is the total cost for insurance coverage on your car?

6.

How to figure depreciation. a.

Why does the resale value on a new car drop at least $>200 as soon as it leaves the showroom floor?

b.

What makes of cars have the highest depreciation?

c.

What does "blue book" price mean?.

d.

Who makes up "blue book" prices on cars?

e.

Under what conditions do prices on used cars go up instead of go down?

f.

g»

What

relation is there between

prices of cars on

used

car lots and the resale value of cars?

What

relation is there between

resale value and

depreciation? h.

Does the treatment a car receives have any effect on depreciation?

7.

How to estimate upkeep expenses. a.

What general relationship is there between car size and repair cost?

b.

What general relationship is there between

ij.6 horsepower and gas consumption? c.

What general relationship is there between the number of moving parts in a transmission and repair costs?

d.

Which of the following parts on a car would cost the most to replace,

the next to the most,

so on down to the least: mission, 8.

and

Valves, piston, trans­

clutch, axle, differential, and hub cap?

How to judge condition when buying a used car. a.

Is there any relation between oil consumption and motor condition?

b.

Is the amount of wear on foot peddles an indi­ cation of mileage?

e.

Does tire wear have more meaning on later model cars?

d.

What defects can be determined by

driving a car?

e.

Is there any relation between the

condition of

a car's paint job, upholstery, floor mats, etc. and the condition of the motor?

9*

How to make comparisons when buying a a.

new car.

How do the cars under consideration compare in terms of depreciation, upkeep costs, insurance costs, license fees, and necessary down payment.

b.

What kind of a trade-in will the different agencies give you on your old car?

k-7 c.

What has to be kept in mind when making com­ parisons between cars in different price fields?

C.

OVER-ALL ACTIVITIES;

Some learning experiences that you

can do to help your parents save money when buying a car. 1.

Go through all the procedures

of buying a car yourself.

Visit used car lots and automobile agencies making appraisals, comparisons, and estimates of total cost. 2.

Find a friend, neighbor, or relative who is in the market for a car and help them gather all information pertinent to costs and values mind his needs and ability to *

D.

TESTING PROGRAM:

received, keeping in pay.

Check-ups that will help you evaluate

your ability to save money on buying a car. 1.

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) ( ) Immediate depreciation after your purchase is greater on a new car than on a used car.

b.

( ) ( ) You should take note of oil consumption when buying a used car.

2.

COMPUTATION PROBLEMS:

Write the answer in the blank

ahead of each item. a . _______ What are the carrying charges on a car you buy if the interest rate is 6 per cent

48 semi-annually and the principal is #l 600? b.

If you buy a car on time for $1500 and your monthly payments total $2000, what interest rate are you paying?

3.

RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting weighted score.

Factors to Rate a. b. c. d.

Total the results.

Weak Fair Superior 1 2 -3 if5-6 7 8

Wt. Score

Savings methods discovered

x 3 =

Per cent savings realized

x 2 =

Resulting personal benefits

x 1 =

Resulting family benefits

X 1

COMMENTS:

S

TOTAL =

PAYING INCOME TAXES

5o CHAPTER 8. PAYING INCOME TAXES HOW TO HELP YOUR PARENTS SAVE MONEY ON INCOME TAXES A.

REWARDS:

Advantages of being able to help your

parents

keep more for themselves when paying income taxes. 1.

A REAL CONTRIBUTION:

Uncle Sam only wants what is

rightfully his and your f a m i l y ^ ’’net” income will be larger through your informative suggestions. 2.

SUCCESS WHERE ADULTS PAIL:

You can realize accom­

plishment at a task that many adults are unwilling or unable to do for themselves. B.

INVESTIGATIONS:

Directions for checking on the preparation

of your family's income tax return for resulting minimum costs. 1;

How to locate the sources for income tax information. a.

Who puts out the information on the preparation of income tax returns?

b.

What sources for information are located nearest your home?

2.

How to file your return. a.

Who is required to file a return?

b.

When must the return be filed?

c.

Why must your family file a return?

d.

Where must the return be filed?

e.

What are your rights of appeal?

How to choose your return for simplicity and lowest tax. a.

What three types of returns are used?

b.

What forms are used for a family income less than $ 5000?

c.

What forms are used for incomes over $5000?

How to choose between a joint and a separate return. a.

Does one or do both of your parents work?

b.

What are the advantages and disadvantages of a joint return?

c.

What are the advantages and disadvantages of a separate return?

d.

How is the joint tax and refund figured?

How to claim your family exemptions. a.

What is an exemption?

b.

Can your father claim an exemption for himself?

c.

Can your father claim an exemption for your mother?

d.

What is

a dependent?

e.

How

are exemptions for dependents determined?

f.

How

are claims for exemptions made?

How to report your family income tax. a.

What income is taxed?

b.

How

are wages and salaries reported?

(1) Are total wages reported before payroll deductions?

52

(2) Can deductions be made for tips and gratuities? (3) Can deductions be made for payment in mer­ chandise? (Ij.) What allowances can be made for on the job meals and living quarters? (5) Can deductions be made for travel expenses of employees? (6) What is the ruling on reimbursed expenses other than travel? (7) What deductions can be made for going to and 'from work?

7.

c.

How are dividends reported?

d.

How is interest income reported?

e.

How is the sale and exchange

f.

How is depreciation figured?

of property reported?

How to claim non-business deductions. a.

Can contributions be deducted?

b.

Can

interest expenses be deducted?

c.

Can

taxes be deducted?

d.

Can

casualty losses and thefts be deducted?

e.

What are the

limitations on medical

and dental

expenses? 8.

How to figure your tax. a.

What tax table is being used?

b.

Which of the forms is being used, the Form 10ij-0A,

53 the Short Form lOlf.0, or the Long Form IOI4.O? c. . C.

How is the form your family is using filled out?

OVER-ALL ACTIVITIES;

Some learning experiences that will

help you assist your parents in paying only what income tax is necessary. 1.

Make out your family's income tax return yourself. Get help by writing to the "Superintendent of Docu­ ments, Government Printing Office, Washington 25# D.

2.

G." and asking for information.

Get one of your relatives or friends to let you work out their income tax return just to see if you can save them money.

D.

TESTING PROGRAM:

Assignments that will help you evaluate

your abilities to save money on income tax returns. 1.

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) ( ) There are no advantages to filing a joint return.

b.

( ) ( ) Your father cannot use himself as an exemption.

2.

COMPUTATION PROBLEMS:

Write the answer in the blank

ahead of each item. a.

If there were 3 children in your family

51]. how many dollars could be exempted

from

gross income for them? b.

If your father’s business travel expenses amounted to f>10 per week, how much could be exempt from his gross income?

3.

RATING SCALE FOR ACTIVITY ASSIGNMENT: number for the rated factor,

Choose a

then multiply this

number by the weight and record the resulting weighted score.

Factors to Rate a. b. c. d.

Total the results.

Weak Fair Superior l 2 — 3 24. 5 - 6 7 8

Wt. Score

Amount of savings realized

x 3 =

Amount of information collected

x 2 =

Resulting personal benefits

x 1 =

11

COMMENTS:

-■

H K

Resulting family benefits

TOTAL =

55

\>

S

^

U

*

-i—

A**C

r — ,

\»

n

^ -------- I

INVESTING IN INSURANCE

56

CHAPTER 9. INVESTING IN INSURANCE HOW TO HELP YOUR PARENTS SAVE MONEY BY THE PROPER USE OP INSURANCE A.

REWARDS:

Advantages of being able to help your parents

use Insurance, wisely. 1.

INCREASED PROTECTION:

You and your family will be

free from fear because of greater security. 2.

A COLLEGE EDUCATION:

By causing your parents to be

more aware of insurance benefits, they may see fit to buy you a "college education" policy. 3*

OLD AGE DEPENDENCE:

By making your parents aware of

retirement possibilities through insurance, you can avoid their later dependence upon you. B.

INVESTIGATIONS:

Directions for checking on the amount of

money spent on family insurance as compared to the values received in return. 1.

How to check on death benefit policies. •a.

How much death benefit protection does your family have?

b.

What are the premiums being paid for this pro­ tection?

c.

What is the saving if these premiums are paid annually or semi-annually?

d.

For how long of a time can these benefits be expected to take care of the family needs?

How to check on retirement benefit policies. a.

How much endowment insurance do your parents carry for themselves?

b.

At what age does this insurance become effective (What is the maturity date?)

c.

What mode of settlement is being used?

d.

When the policy or policies mature, how much money will your parents receive?

e.

Will there be enough money to retire on?

How to check

on term insurance policies.

a.

How much term insurance do your parents carry?

b.

How much would it cost for a similar amount

of

permanent insurance? c.

Does term insurance have any cash value?

d.

Is there any term insurance tied up in your permanent insurance policies?

H ow to check on health benefit policies. a.

How much are the monthly premiums?

b.

How much money is allotted to the various kinds of medical treatment?

c.

Is there a time factor condition affecting payments?

d.

Is it possible to get cheaper health insurance policies elsewhere?

How to check on car insurance policies.

a.

How much liability insurance do your parents carry on their car?

b.

How much does it cost?

Is there a liability condition affecting your driving of the car?

c.

What type of collision insurance is carried? How much does it cost?

d.

Is there any fire, theft, and comprehensive in­ surance on the car?

e.

How much does it cost?

Is there any medical payment provision in the insurance policy?

If so, how much are the

payments and what is the premium paid? 6.

How to check on social security. a.

How much does your father put into social security each month?

b.

How much does your mother put into social security each month?

c.

How many years have your parents paid into social security?

d.

How many years will it be before your parents

can

share in the retirement benefits of socialsecurity e.

What income will be provided at age 65 for your parents?

C.

(Check form provided by the teacher.)

OVER-ALL ACTIVITIES?

Projects that you can do to help

your parents save money on insurance. 1.

Make a thorough investigation of the insurance carried

59 by your parents and discover ways whereby money can be saved or more value can be realized.

Present to

the class a final report on the findings of your investigations along with recommendations. 2.

Ask your friends and neighbors how much money they spend on insurance and present this information to the class.

D.

TESTING PROGRAM:

Check-ups that will help you evaluate

your ability to help your parents receive more in return for money spent on insurance. 1.

TRUE-FALSE:

Place an X in the correct space for

true or false. T a.

F

( ) (

)Your parents should buy term insurance when they need more protection and cannot afford permanent insurance?

b*.

( ) (

)State law requires that your parents carry liability insurance on their car.

2.

COMPUTATION PROBLEMS:

Write the answer in the blank

ahead of each item. a.

_______ How many months would a $10,000 settle­ ment last for you at the rate of $150 a month?

b.

_______

If your average monthly social security deduction were $3.10, how much would be

paid by you over a period of 20 years and lj_ months. 3*

RATING SCALE FOR ACTIVITY ASSIGNMENT:

Choose a

number for the rated factor, then multiply this number by the weight and record the resulting rated score.

Total the results.

^ eajj. p aj_r superior Factors to Rate________________ 1 2 - 3 4 5-6 7 8 a. b. c. d.

Wt. Score

Amount of saving realized

x 3 =

Increased protection resulting

x 3 =

Resulting personal benefits

x 1 =

Resulting family benefits

X

COMMENTS:

1

a

TOTAL z

BIBLIOGRAPHY

BIBLIOGRAPHY Adams, Pay: Educating Americans Children. Press Co., New York, l9ij-6. 375 PP»

The Roland

Chapter 10 contains a good definition of the role of mathematics in education. Brueekner, Leo J., Grossnickle, Poster E., and Merton, Elda L . : Arithmetic We Use, Book II. The John C. Winston Co., Los Angeles, 19^-7. 217 pp.

Crawford, Claude C.: "Functional Units ,11 Sierra Edu­ cational News, 3^:22 (Sept., 1938). Harap, Henry, and Mapes, Charlotte E . : "The Learning of Fundamentals in an Activity Program," Elementary School Journal, jhri 5 1 5 - 2 5 • Johnson, J. T.: "Economy in Teaching Arithmetic," The Tenth Yearbook of the National Council of Teachers of Mathematics. Bureau of Publications, Teachers College, Columbia University, New York, 1935* PP» 121-56. Mathematics in General Education. Report of the Committee on the Function of Mathematics in General Education for the Commission on the Secondary School Curriculum. D. Appleton-Century Co., New York, I9 I4-O. Part IV. An extensive report that evaluates mathematics in the school curriculum and the curriculum of mathematics itself "The Measurement of Understanding," Forty-fifth Yearbook of the National Society for the Study of Education, Part I University of Chicago Press, Chicago, The chapters on arithmetic and mathematics are very helpful.

63

APPENDIX

Gk SUPPLEMENTAL TESTS FOR TEACHER’S REFERENCE INTRODUCTION You, as a teacher of mathematics, must agree that no phase of your subject can be isolated and presented to a class without the ugly head of computation inability blocking the road of progress. also a challenging one.

This is a disheartening fact, but The situation is further compli­

cated by the fact that classroom conditions in these times are even less conducive to the so-called ideal known as ’’individualized instruction'L-solving each individual’s diffi­ culties as they arise, individually.

You have too many

young faces to look at during the course of the day to ever hope of teaching purely on this kind of a basis.

This fact

alone, not even to mention the voluminous ’’red tape" portion of the teaching load, lack of equipment, facilities, and so on, necessitates what may be termed a "group attack" rather than an "individualized attack."

Mass production

conditions require mass production techniques. Here is a way for both you and the student to meet and subdue the computation difficulties that arise during the study of mathematics in the eighth grade.

The following

tests are to be used in conjunction with the understandings derived as a coverage of the subject matter is made.

In the

teaching of mathematics, experiencing must always run far

65 ahead of drill. point.

Psychology speaks very clearly on this •

Children learn more easily and remember longer

when they are given drill on topics that they understand. Therefore, it is your responsibility to decide on what phase of the basic operations is causing the most diffi-. culty for the students as they cover the preceding chapters and use the following tests accordingly. In using these tests you should make certain that emphasis is on instruction, improvement of skill in the basic operations--not on testing.

You will notice that

the tests are a slight departure from the ordinary, in that all of them have a uniform time limit of four minutes. They are designed to be used in this manner:

at the

beginning of each period the class takes one of the four minute tests that you think is most applicable for that day.

When the four minutes are up the students should be

allowed to correct their own papers, check their mistakes, and record their results on a personal record sheet.

These

record sheets are to be used by you as a guide for correc­ tive measures and not for grades.

You should make this

fact clear to the students so that there will be a mini­ mum of cheating and a maximum of achievement.

This whole

process should be completed within the first seven or eight minutes of each period.

You will soon recognize certain advantages in using this method of attack.

Getting a class started and "in the

mood" at the very beginning of each period is a hard task to accomplish consistently.

These four minute tests set a

keynote for action that carries over for the rest of the period.

Each student knows that pencil, paper, and eraser

must be ready when the bell rings.

The work begins immedi­

ately and the students work like little beavers to get through before time is called.

During these four minutes

you have time to check roll, file away homework that has been turned in, and set up the lesson that has been planned for the day. POUR MINUTE TESTS The following tests are divided into two types, the Difficulty Analysis Tests that cover groups of related skills, and the Practice Tests that follow each difficulty analysis test and deal with one of the unit skills covered.

67 Difficulty Analysis Test.

Addition of Whole Numbers?

If you pass this test, you probably know the addition facts, needed in your business relations, at home and elsewhere. You do not pass if you make more than one error on the first trial.

The last two examples must be correct.

Add?

9 8

6 7

5 8

9 0

5 9

8 8

9 7

6 8

8 3

7 8

5 6

7 7

9 5

7 0

6 9

9 9

7 6

4 9

29 + 8 =

58

9 =

17 + 7 =

36

7 =

44 + 9 =

49 + 7 =

68 + 6 =

47 + 5 =

86

7 =

84 + 9 =

9 7 4 9 8 3 3

5 1 7 6 8 6 9

5 5 9 5 4 7 8

9 5 2 4 5 1 6

6679 765 87 45807 99

Difficulty Analysis Test.

3739 3496 1046 1227 6794

Important Addition Pacts?

In this test you will find the addition facts that are hardest for you.

Often a person knows all but two or three, but those

cause lots of trouble. your "weak spots." 3 8 5 5

7 5

8 7

2 7

8 0

1 9

4 8

3 2

8 9

It is a good plan to make a list of

Add? 7

8

9

7 7

8 6

7 6

9 0

8 4

5 9

9 3

8 4 7

7 8

5 1

2 5

9 7

6 9

0 5

6 5

2 7

4 3

7 5

6 4

7 3

68

Practice Test,

Adding by Endings:

When you see

26 + 6 , you should at once think thirty-two; when you see 36 + 6 , think forty-two without thinking of carrying or counting.

It is helpful to be able to see at once that the

answer lies in the next tens.

Thus 8 6 + 6 equals _____ -two.

25 + 8 25

38 + 5 =

68 + 7 S3

49 + 7 ss

48 + 6 ss

56 + 8

77 + 6 =

78 + 6 as

69 + 9 SB

77 + 9 =S

13 + 9 S3

85 + 8 S3

89 + 7 =

17 + 5 =

48 + 5 S3

82 + 9 =

25 + 7 ss

39 + 4 SS

58 + 8 S3

59 + 7 =

44 + 9 =

57 + 8 ss

79 + 8 S3

68 + 5 S3

86 + 7 =

86 + 6 ss

49 + 5 S3

87 + 4 -

29 + 3 S3

25 + 6 =

56 + 9 =

78 + 7 S3

45 + 8 SS

35 + 9 =

22 + 9 S3

76 + 8 SS

68 + 9 ss

57 + 7 S3

39 + 2 3S

88 + 3 *

16 + 5 ss

79 + 6 S3

49 + 9 33

79 + 9

Practice Test.

SB

Broken-Column Addition:

SS

Pew Everyday

addition examples are more difficult than these.

3 379 6588

865 5967 ___46

595 9966 74

568 8086 76 80 99

8

79 926 48 4577

8 648 3949 __ 96

7798 662 90 984 7576

8338 5359 6677

79

7

5926

6757 70 978

88888 8

69 Difficulty Analysis Test. Numbers:

Multiplication of Whole

If you can pass this test, you probably know the

multiplication needed in everyday affairs.

Multiply;

9 4

6 8

8

0

6

7 8 50 900

9 7

0 2

8 7

6 9

2 0

7

4

6 8

7

309 80

730 70 ■

5

8

5 0

6

8 9

9 4

6

609 40 709 45

Practice Test.

0 1 3

8

4 8 5

7

6 3

708 97

400 900

770 89

7395 87

Multiplication-Two Places:

The

examples in this test are easy though they are of a kind which is often missed.

Multiply:

630 45

720 39

950 30

820 67

806 59

860 72

509 51

601 35

809 45

705 63

403 57

170 90

107 21

904 60

809 11

307 66

803 24

650 33

450 27

708 18

70 Practice Test.

Multiplication--Large Numbers;

Certain investigations have shown that the problems of every­ day life are seldom more difficult than these. 1000 10

100 100

708 10

5983 37

7395 85

26 268

780 10

Numbers:

700 100

6482 64

Difficulty Analysis Test.

2468 92

5379 29

2684 73

Subtraction of Whole

Now we start on a new topic.

subtraction.

Multiply:

This is a test in

Subtract:

14 9

11 3

13 4

16 7

8 4

14 5

11 4

17 9

14 9

15 9

7 0

17 8

9 1

15 7

13 9

9 0

13 5

11 2

16 7

11

13 7

15 8

13 8

9 9

14

12 3

14 8

12 5

11 6

18 9

85 7 973 758

897629 458257

77 37

63 59 200 83

6 508 44

305 39

1000 309

222553 98671

575 67 600 267

138725 60969

7

752 309 89160 39069

151651 52705

71 Practice Test* without making errors? 95

Subtractions

Can you “borrow11

Subtract:

6

87 34

92 75

99 49

92 58

57 27

53 49

60 35

302 50

706 33

808 64

497 75

207 29

606

88

996 56

383 48

973 94

535 48

682 209

891 684

644 455

964 658

441 237

981 286

100 72

100 67

100 98

1000 209

200 138

200 44

700 156

400 293

Practice Test,

Subtraction--Very Large Numbers:

Most subtraction problems of life will not be more difficult than these.

Subtract:

92240 20476

169071 89561

148128 81830

166975 85432

82532 27016

138725 60969

222553 98671

103867 33117

80819 52470

130543 97998

89160 39069

94137 25209

151651 52705

13418 8436

897629 458257

192344 39472

861750 27921

843958 52273

629105 86464

193935 16751

72 Difficulty Analysis Test.

Division of Whole Numbers:

All your answers in this test should be in their simplest form. 49 — 7

9 _ 9 “

54 _

6

45 _ 9

27 ^ 3

28 _ 4 “

36 4 *""*

56 _

48 3

54 _

8

6

6

56 a 7 48

8

21 _ 7

18 _ 2

21 _ 3 “

63 _ 9 “

0 = 5

72 9

54 _ 9

0 _ 2

535 _ 3 ~

524 _ 5 “

560 _

760

826 _ 9

392 _ 7

2965 _ 97

6278 _

3404 _ 92

Practice Test.

86

8

8 2184 39

Division--One-Figure Divisors:

605 _ 4

535 _ 3“

643 _ 4 *"

556 ^ 7

618 9

480 _

8

305 _ 2~

906 3 “

810 „ 9 ~

642 _ 6 “

806 ~ *

681 _ 4 “

609 _ •6

803 7

508 „ 5 “

503 , 7 ~

784 _ 6 *“

650 _ 7

760

327

840

408 _ 4 ~

956 _ 9“

827 ^ 9 ~

807 _ 4

8~

8“ 1008

8“

6 “ 809 _ 3 “

392 7

524 _ 5

_ “

954 9“

Practice Teat. trouble.

Long Division:

This often causes

But here are some easy examples which will help

you learn how to do long division.

Copy the examples on

another sheet of paper. 462 „ 11 ~

1092 _ 21 “

1922 _ 31 *

1353 41 *

924 „ 22

1664 32

3066 _ 42

966 _ 23 “

2604 62 “

1820 52 “

2343 _ 71 “

3034 83

... Harder examples:

1824 _ 48 “

6768 _ 72

5963 67 “

4876 53“

8736 _ 91

7209 89

1696 = 32

2688 _ 28

345 _ 23

672 _ 16 “

4590 _ 45

9212 94

4592 _ 56 ~

7548 _ 74 *“

4299 81 “

5916 68 “

1672 _ 19

450 18

4508 _ 49

2987 44

1288 __ 46

9555 65 “

8541 _ 98

3276 52

1332 _ 74 ~

1656 _ 69 “

481 37 “

4895 55 “

2025 _ 81

598 26

4578 _ 42

9920 _ 32 ~

936

68 ~

4914 21 ”

3220 _ 92

7854 77

868 _

8820 _ 63

2407 29 ~

924 84 “

3496 _ 92

2862 95 35

35 6364 _

86

3030 63 “

3672 _ * 51 405 _ 27

659 31 2208 39

7k Practice Test.

Adding Two Fractions:

Can you add

two fractions when they are written side by side?

Write

each answer in its simplest form. .

1 2

*

2 , 3 3 + 5

6

A- + 10

A 5

12 +

1 _ F

+ 7 + IF

IF +

2 _ F

5

I

-

3 4

4 , 5 5 12

I

*

. 11 + IF

3 ¥

1 _ 2 2 F

3 8

2 , 5 F F

1 2

+

15 16

5

4

9

3

I 4

6

1 4

+ JL « 12

3 . 4

8

8

16

A_ + 12 T

2 3

A

2

+ -1 = 16

3

.11 _ +

12

5 F

£ 8

10

1

1

1 4

6

7

1 _ 2

A 4

+ JL T 10

I

*

3 _ 4

3 F

7 _ + 10

A

. 3 4

Jl 4

+

. ss 10

8

5 * 3 6 + 4

I ♦ 1 7 2

7 8

2 3

“

75

Practice Test.

Adding Three Fractions:

Add and write

each answer in its simplest form.

jL +

+ _3 ss

2: + — + .i.=

3 + i + i

+ -± 16

+

5 = 8

I 3

3 + 1 8 2

, 3 4

^

5 _ 12 ~

1

5

8

16

± 2 1 3 2 3

+

16

2

*

2

3

+

_ S ~

1

, 5 _

5 , 1 , 5

+ T2 ~

TS +

£

2

1 . 2

a

1____

_2

,

+ 12 ~

9

+

1

*

-

3 ~

2

Practice Test.

3 1 3 T 5 + 2 + 4

S

6

1

2 3

^

1

4

+

+

,

3 *

6

1

+ -

5 a 6

2

^

1

6

+

4

2 . 1 . 5 _ 3 + 2 + 12 “

4 1

i 4

4

1

,

3 * 3

4

5_

_

6 ~

, 1

.

+

■S

5 * 6 * 3

_

1

8*"

3

-

Subtraction of Fractions:

1

6

-

7

12

In these

examples the two fractions are written side by s i d e . .

2

T 10

5

1 4

1 _ ~ TO ~

5 £

2 3

~

2 5

1 _ "* 5 ~

1 _ 4

5 6 5 8 "

~

5

12

12

3

2

1 _ “

9 1 lS “ 10

2 5

3 " IS

9_ _1 _ 16 “ 16

3 4

_3 " 16

_7 _ “ 12 _5 _ 12“

11 12 "

5 _ 8 “

3__ 10 “

1 4

?6

5 8

“

3 4 "

Practice Test.

Subtraction of Fractions:

3 16“

2 3

_5 _ 16“

21 24 ~

3 8

3 4

"

1 _ 3

13 16 “

1 _ 2 “

7_ “ 1 2 “

3 4

"

2 3

3 5

“

1 _ 3 “

“

5 8

_ “

5 8

5 6

“

4 3 ~ 7 8

_ “

_1 = 12 2 5

5 .8

_ “

_JL _ “ 16

_ “

“

7 8 " 7 8 "

“

2 _ 3 “

1 3

“

1 6

1 _ 3 “

2 3 “

3 8

3 4

1 2

5 “ 12

“

3 4

_3 _ 10“

7 TO "*

1 _ 2 “

1 _ 2 “

13 16 “

1_ 4

15 16 “

3 _ 4 “

answer in its simplest form. 1 Y 3 _ S X 4■

2 Y on — 3 X 20=

1 2

3

4 _ 3 “

2

Y A

4 5 3 5 4 5 5 6

Multiplication of Fractions:

the rule used in multiplying two fractions?

Y A

7 8

__7 _ “ 10 “

2 _ 5 ~

3 _ 16“

Practice Test.

5 3 3 5

7_ _5 _ 12 ” 12 “ 5 6

3 4 “

1 4

— “

“

“

5 12

“

1 2

“

1 3

”

2 5

“

2 3

What is

Write each

Multiply: 2

xY ?5 -_

2 v 5 3 x -g

1 3

Y A

^ 3

3__ 8“

Y 1O

77 4

X 6G =

1

X

3 4

y

2 3

y

*

3 8

X 25 =

* 7 8

i5

1 x

i

2

4 _ 7

*

Practice Test.

4 =

-=

X

2

Multiplication of Mixed Numbers:

Remember to write each answer in its simplest form.

iX9|= l| X 6 =

2§X9=

ifxi= 3§

Xf =

Ix4 =

Practice Test.

4x4 =

4x4

if

4

X 4

=

4x4 =

4

4x4

Division with Mixed Numbers:

examples are quite difficult.

X

These

Can you do them?

ol / 1 _ % / 3 -

/1 !e / 8 “

*1 / «1 52 / 73 *

,1 X3 / 4 *

4 /'3 =

4 / 4 “

Ǥ / 4 =

4 / 4

4 /4 =

4/®=

4/5§

iof/4 =

Practice Test.

Multiplication of Decimals:

You often

need to multiply in the way shown by these exercises. in zeros when necessary. 1.

10 X .83 =

21.

.7 X .01 «

2.

100 X .833 *

22.

15 X .001 «

3.

1000 X .25 a

23.

1000 X 5.25 =

4•

10 X 6.75 =

24.

1.2 X 10 a

5.

10 X 3.1416 =

25.

3.1416 X .1 =

6.

3.75 X .1 =

26.

3 X .01 a

7.

100 X .66 =

27.

1000 X .0625 =

8.

1000 X 1.33 a

28.

100 X .6 =

9.

.6 X 100 =

29.

3.4 X .001 =

10.

.1 X 25 =

30.

.01 X 8.75 =

11.

.01 X 240 =

31.

100

12.

.01 X 18.3 =

32.

1.9 X .01 a

13.

.01 X 8 «

33.

1000 X 2.1816 a

14.

.001 X 62.5 =

34.

.7 X .01 a

15.

.1 X .16 a

35.

10 X .01 a

16.

. I X 3.75 a

36.

.82 X 100 =

17.

.06 X .1 =

37.

2.98 X .01 =

18.

4.25 X .01 a

38.

1000 X .6 a

19.

100 X 2.4 a

39.

1.4 X .1 =

20.

3.1416 X 1000 a

40.

.1 X .1 a

X

.8 a

Put

79 Practice Test*

Division of Decimals:

Watch the

decimal point in these exercises. .9 / .3 a

.9 / 3 a

9 / 30 =

9 / .3 =

.9 / 30 =

.09 / 3 =

.09 / .3 a

9 / 300 a

.9 / 300 =

.9 / 3000 *

.09 / .05 =

9 / .003 a

.09 / 3000 «

.9 / .03 =

.09 / .003 =

9 / 3000 =

9 / .03 =

.9 / .003 =

.09 / 30 =

.09 / 300 a

28.44 / .4 «

13.5 / .5 «

8015 / .7 a

7785 / . 9 a

.308 / .4 =

30.06 / .06 =

91.14 / 7 =.

115.2 / .3 =

50.34 / .2 =

7.05 / .3 =

3.496 / .08 =

25.9 / .05 =

342 / .04 =

56.35 / .7 =

6.25 / 2.5 «

241.6 / .08 a

.8 / 4000 -

.08 / 400 »

.06 / 20 a

6 / .02 a

8 / .04 *

6

.8 / .04 «

.8 / 200 =

.08 / .4 =

9 / .4 =

.8

•08 / .004 a

8341 / .5 =

8433 / 9 =

254.1 / .7 =

32.24 / . 8 a

214.2 / .3 =

82.65 / 5 =

27.36 / .04 =

.344 / . 2 a

30.4

2.345 / .07 =

4.02 / .6 =

89.37 / .9 =

/ .05 =

/

.002

=

/

.2

=

80

Difficulty Analysis Test. Per Cents:

Fractions, Decimals, and

Write each of the following in three forms— as a

common fraction (or as a mixed number), as a decimal fraction, and as a per cent.

Of course, one of these forms is already

given for each. 2/5

25%

0.625

3/4

37 1/2%

0.8

1 /1 0

60%

1.25

7/8

10%

0.9

2/50

l/4%

6 2/5%

7/25

1/2%

0.035

0.5

0.16

Practice Test.

Important Equivalents:

Supply the

missing numbers as suggested by the first row which is given here as a sample.

There are 32 blanks to be filled in; so

32 is a perfect score on this test.

Each blank filled in is

either correct or else counted as an error.

Common Fraction in Lowest Terms ..... I/? ... .....

Common Fraction with 100 as Denominator

As a Decimal .50

50/100

In Per Cent 50%

1/3 2/3________ 1/4 3/4

66/100

2/3 .25 75^

1/5 2/5

40%

81

Common Fraction in Lowest Terms

Common Fraction with 100 as Denominator

In Per Cent

.60

3/5 4/5

As a Decimal

80/100

1/6 .

83 l/3$

5/6 .125

1/8 5/8

37/100

1/2

5/8 87 1/2$

7/8

Practice Test.

Important Equivalents:

Remember, you

may take as much time as you need on practice exercises. Supply the missing numbers Common Fraction Common Fraction with 100 as As a In in Lowest Terms_____ Denominator_________ Decimal_____ Per Cent 1/4____________ 25/100_________________.25__________ 25$ 87 1/2% 1 / 1 0 _________________________________________________________________

■

•

60/100____________________________________ ______________________________ .14 2/7_____________ 5/8_______________________________________________________

.75

Practice Test.

Writing Fractions as Per Centss

Write each of the following as a per cent. 1/2

1/6

.125

3/5

5/8

.002

7/10

3/4

.8

1/3

4/5

1.15

1/8

9/10

.375

1/4

7/8

.54

5/6

.25

3.06

2/3

.14

.46

2/5

.08

.875

3/8

.36

.013

1/5

.05

2.5

1 1/4

.6

1.75

2 1/3

.84

.045

5/6

.35

2 3/4

Writing Fractions as Per Cents i

Practice Test.

Write each of the following as a per cent. 1/10

1/2

1/8

.75

2 1/3

3/4

2.35

1/6

5/4

.003

2/5

7/8

5/6

1.7

3/8

.083

1/7

4/5

7/10

1/3

1/4

.625

1/5

5/8

2.2

.38

.8

2.14

1 1/2

.035

2/3

.05

2 1/5

1.75

.023

.49

1.98

1/12

.375

1/10

2 3/8

.062

Practice Test.

Writing Per Cents in Another Form

Write these per cents as decimal fractions. 32$

2%

124$

4$

.4$

'300$

80$

65$

175$

8.3$

60$

6$

55$

4.5$

35$

12$

.2$

2.25$

83 Write these per cents as common fractions in their simplest forms, or as mixed numbers. 10$

37

83 1/3%

12

320%

40%

125%

87

1/2%

30%

1/2%

62 l/2 % 175%

350%

33

1/3%

110%

80%

16

2/3%

60%

66 2/3%

25%

70%

1/2%

Practice Test.

Writing Per Cents in Another Form:

Write these per cents as decimal fractions. 7$

2.5$

18$

37.5$

200$

15$

96$

6.25$

82$

165$

.3$

10$

150$

3.75$

.05$

32$

5$

1.19$

115%

.8%

Write these per cents as common fractions or as mixed numbers• 10%

87 1/2%

16 2/3$

25%

325%

50%

40%

75%

33 1/3%

80%

150%

62 1/2%

20%

110%

12 1/2%

14 2/7%

Practice Te s t.

37 l/2 %

166 2/3%

Finding a Per Cent of a Number:

One

of the most common problems of everyday affairs is to find 5% or 6% or 10$ or some per cent of a number.

Certain per cents

are used frequently, and you should think of them as common fractions.

Thus, when you have to find 25$ of a number take

1/4 of it.

Perform the following exercises.

25# of 16 =

83 1/3# of 12 =

50# of 42 =

37 1/2# of 32 =

33 1/3# of 24 *

60# of 10 a

12 1/2# of 24 »

87 1/2# of 32 a

40# of 15 «

75# of 20 =

16 2/3# of 18 a

133 1/3# of 18 a

62 1/2# of 16 =

40# of 35 =

80# of 25 a

150# of 8 =

66 2/3# of 30 =

12 1/2# of 16 =

20# of 75 a.

16 2/3# of 48 a

62 1/2# of 24 a

225# of 12 =

180# Of 15 a

66 2/3# of 21 =

75# of 32 =

220# of 80 =

37 1/2# Of 80 =

83 1/3# of 18 =

87 1/2# of 48 a

160# of 15 =

Praotloe Test.

The Meaning of a Per Cent:

Write a

T for each true statement and an N after each statement that is not true. 2 1/2# a 2.5#

25# a .25

2.5# a .025

1/4# = .025

2.5# a 0.25

1/4# = .25

2 1/2# = 0.025

1/4# = 2.5

2 1/2# a .0025

1/4# a 0.025

250# a 2.50

1/5# a 0.0025

85

Practice Test. test that many enjoy. are incorrect.

Recognizing Equivalents:

Here is a

Some of the numbers in parentheses

To get an example right, you must copy all

the correct numbers and no others.

Can you find all of them?

1.

60% equals

(60/100, 0.06, 6/10, 3/4, 3/5)

2.

40^ equals

(40/100, 0.04, 4/100,

3.

75% equals

(75/100, 0.75, 750/1000, 0.7, l/2)

4.

12

1/2% equals (1.25, 0.125, 1 l/8, l/8, .012,1/2)

5.

37

1/2%> equals (3/8, 0.37 l/2, 0.375, 375/1000)

.040, 2/5)

6.

5/8 equals

7.

1/6 equals

8.

7/8 equals

9.

10^i equals (.1, 10/100, lOO/lOOO, l/lO)

10.

14/16,

100 .87, 0.875, 87.5^)

3/2 equals

UNIVERSITY OF SOUTHERN CALIFORNIA LIBRARY