Margaret M Campbell. # Suggestive lessons in numbering arranged for individual work, fifth grade online

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How much longer is the longest line than the shortest?

(h) Find the sum of the three short lines.

LESSON VIII.

1. What is the easiest way of finding how many seats

there are in your schoolroom? How many seats are there

in a row? How many rows? There are seats in

this room.

2. (a) What would be an easy way of finding how

many trees could be planted on a rectangular piece of

ground? (b) How could we easily find out how many

boy scouts there are in a group in regular formation T

(c) What is the best way to get the number of squares

on a checkerboard?

3. Secure two pieces of pasteboard of different sizes,

(a) Take one of these, and measure its length in inches;

its width in inches, (b) Put dots one inch apart on all of

the edges of this pasteboard, (c) Draw lines one inch

26 SUGGESTIVE LESSONS IN NUMBERING

apart (1) from top to bottom, (2) from side to side,

(d) How many squares are there in the first row? (e) How

many rows are there? (f) How many square inches are

there on this pasteboard? (g) Name two ways that you

had of answering this last question.

4. (a) Take the second piece of pasteboard. Find the

number of square inches in the first row. (b) Find the

number of rows, (c) Find the number of square inches on

this pasteboard.

5. Exchange pieces of pasteboard with two of your

friends, trying to get some that look different from yours.

(a) Using the clean side of one of these, show how many

square inches there are in the first row. (b) Show how

many rows, (c) How many square inches are there in the

whole pasteboard? (d) Did you add, subtract, multiply

or divide to find out?

6. (a) Find the number of square inches in the first

row on the second piece of pasteboard, (b) Find the

number of rows, (c) Find the number of square inches on

this pasteboard.

7. (a) Measure the top of your desk, using only inches

and half inches, (b) If you do not see immediately how

many square inches there are in the first row, us.e chalk

to make one row of one-inch squares at the top of the desk,

(c) Then use lines to mark off the number of rows, (d)

Find the number of square inches on the top of your desk.

8. (a) Find the number of square inches on the top of

your book, (b) Find the number of square inches on one

sheet of your tablet paper.

9. (a) Measure one section of the blackboard in feet.

(b) At the bottom make one row of foot squares, (c) How

many rows of these squares are there? (d) How many

square feet are there in a section of the blackboard?

ARRANGED FOR INDIVIDUAL WORK 27

10. (a) At one end of the floor, make one row of foot

squares, (b) How many rows are there? (c) Find num-

ber of square feet in the floor.

11. (a) Find the number of square feet on the top of

the table, (b) Find the number of square feet on the

door; (c) in one-half of the window.

DKILL SHEET SUBTEACTION I.

1111111111

1111111111

5 /8 % % VlO %0 %0 %0 % %2 T/12

y 2

DRILL SHEET SUBTRACTION II.

1% 1% 1% 1% 1% 1% 1% 1% 1% 1%

28 SUGGESTIVE LESSONS IN NUMBERING

11/8 11/6 ll/ 6 ll/ 8 11/8 11/3 1% 1% 1%

% % % % 7 /8 % % % %

1% 1% 1% 1% 1% 1% 1%

% %o % %o % %o %

1% 1% 1% 1% 1% l%o 1% 1%

% 9io % %o % % % %

iHo 1% iHo 1% 1% i x /2 1% 1%

1% iy 3 1% 1% 1% 1%

DEILL SHEET SUBTEACTION III.

61/4 71/8 8y 2 53/8 95/8 71/4 6i/8 91/4 81/4 734 934

31/2 41/4 33/4 21/2 434 3% 534 51/2 37/8 3y 2 47s

81/3 71/6 91/2 71/3 81/6 71/3 91/3 13 92/3 151/2 111/2

52/3 31/3 42/3 4y 2 42/3 5% 2% 81/3 5y 2 91/3 75/ 6

ARRANGED FOR INDIVIDUAL WORK 29

9% 8% 73/5 91/5 73/ 5 112/ 5 8 y 2 1334 lll/ 6 121/ 3

4% 37 8 32/ 5 5% 4%o 5% 5y 2 43/ 5 77/ 8 91/4 83,4

11% 75/ 6 91/6 123/ 8 51/ 16 9% 2 125/ 8 131/ 6 92/3

81/3 7V 2 31/4 61/3 2% 6% 52/3 83,4 43/4 72/ 3 62/3

DEILL SHEET SUBTEACTION IV.

25% 341/3 4iy 2 621/4 281/6 76y 2 40y 3 54% 27%

19y 2 262/ 3 273,4 383/s 19% 475/ 8 255/ 6 365/ 8 19%

365/s 49i/ 10 64i/ 2 9334 45?4 26i/ 6 7 i % 6 3% 2 34%

21T/8 263/ 5 452/3 377/ 8 392/3 191/4 361/3 363,4 16%

521/s 52i/ 6 3 i3/ 8 i63/ 5 42% 2 89% 51%

29?4 3734 161/3 9% 26?4 52% 372/ 3 16% 483/ 5

2134 40 742/ 5 1091/3 62% 2 1213,

197/8 1334 39y 2 765/6 383,4 87%

782/g 663,4 901/3 74y 2 36

292/s 36% 195/8 113^ 1013/5

30 SUGGESTIVE LESSONS IN NUMBERING

LESSON IX.

1. (a) How many hours are there in a day? (b) In

drawing a line to represent a day, if you let ^2 i nc h stand

for an hour, how long should the line be? (c) If % inch

stands for an hour, how long should the line be?

2. (a) John goes to bed at 8 p. m. and gets up at

7 a. m. How many hours does he sleep? (b) Mary goes

to bed at 9 p. m. and gets up at 6 :30 a. m. How long does

she have for sleep? (c) How many hours does their father

spend in bed if he retires at 10:30 p. m. and arises at

6:15 a. m.?

3. (a) What time do you go to bed? What time do

you get up? How many hours of sleep do you have?

(b) What time do you usually have your breakfast? What

time do you have lunch? How long is it between these

two meals? (c) How long is it between your lunch and

your dinner? (d) How long after you have eaten your

dinner is it till bedtime?

4. (a) What time does your school take up in the

morning? At what time do you have recess? How long

must you be in school before recess time? (b) How long

is it from recess until noon? How long is school in session

in the forenoon? (c) What time does school take up in

the afternoon? What time does it close? How long is the

afternoon session? (f) Which is the longer, the morning

session or the afternoon session? How much longer?

(e) What is the length of your school day?

5. (a) Our school begins at 8:35 a. m. At 10 a. m. we

have our arithmetic. How long are we in school before

we have our arithmetic? (b) The boys work in the shop

from 10 :45 a. m. till 12 :20 p. m. How much time do they

ARRANGED FOR INDIVIDUAL WORK 31

spend in the shop? (c) The girls have cooking from 1:40

p. m. till 2:23 p. m. How long does their cooking period

last?

6. (a) How long is it from the time school opens in

the morning till the end of your geography recitation?

(b) How long is it from the beginning of your arithmetic

recitation until you have physical education? (c) What is

your favorite class during the day? How long is it from

the time school opens until this recitation begins? How

long is it from the time this recitation ends until school

closes at night?

7. What is your longest recitation during the day?

Which is the shortest? How much longer is the first one?

This is what part of an hour?

LESSON X.

1. (a) How long does it take you to get washed and

dressed in the morning? This is what part of an hour?

(b) Do you help your mother in the morning? For how

long? This is what part of an hour? (c) What time do

you leave home to come to school? What time do you

reach school? This is what part of an hour? (d) How

long is it from the time you get up until you are at school?

2. (a) What time do you get home from school in the

evening? How long do you have for play before dinner

time? (b) Do you take any kind of lesson after school?

How long does it take you to go for your lesson, have the

lesson, and to come home afterwards? (c) If a line

V 2 inch represents 1 hour, how long would a line be that

represented the time you spent on a lesson that was taken

outside of school?

3. Do you study or practice any of the time you are

32 SUGGESTIVE LESSONS IN NUMBERING

home? How long? This is what part of an hour?

4. (a) Draw a line to represent a day. If % inch rep-

resents 1 hour, how long should this line be? (b) Use this

line to make a rectangle 1 inch wide. How long will the

two end lines be? The other side line?

5. (a) How much time do you spend in sleep? Mark

off a box in this rectangle that just represents this

time, (b) How long is it from the time you get up until

school opens? Make another box to represent this length

of time, (c) How many hours do you stay at school?

Show this on the rectangle you have made, (d) How long

is it from the time you leave school until you go to bed?

If ^4 i nc h represents 1 hour, how long should the line be

that represents this time? (e) Measure the part of the

rectangle that you have not used to see if it is this length.

If so, you have made no mistake in your work.

6. (a) Draw a circle 2 inches in diameter, (b) How

can you find one-half of this circle? One-fourth of it?

One-third of it? One-eighth of it? Three-eighths of it?

7. (a) Shade in the part of this circle that would show

how much time you spend in sleep, (b) Use fine lines to

show the part of the day you spend at school. (c)

Show in some other way the part of the remaining time

that you spend in play? (d) What part of the circle has

not been used?

LESSON XI.

Some boys and girls were talking about things they

would like to buy. The question of saving money came up.

They asked how they could find out how long it would

take them to save certain amounts of money. In answer-

ing their questions this lesson was worked out.

ARRANGED FOR INDIVIDUAL WORK

33

1. (a) How many months are there in a year? (b) How

many weeks in a year? (c) How many days in a year?

SAVINGS.

Amount

Each month

Each week

Each day

$ 50.00

$4.17

$0.96

$0.14

60.00

75.00

80.00

85.00

87.50

90.00

100.00

105.00

115.00

125.00

135.00

140.00

150.00

160.00

175.00

200.00

2. (a) To save $50.00 a year, one should save of

it each month: that is $50.00-7- equals

(b) $50.00-r- shows how much should be saved each

week. $50.00-r- equals (c) $50.00-f-365

equals , or the amount that should be saved each day.

3. Write answers in the table given above.

34 SUGGESTIVE LESSONS IN NUMBERING

4. If Mary saves 5 cents a day, how much can she save

in the month of January? February? March? April?

May? June? July? August? September? October?

November? December? How much is saved for the

entire year?

5. (a) If George saves a penny a day, how much will

he have in a week? In a year? (b) If John can manage

to save 15 cents a week, how much will he have at the

end of a year?

6. Mary and Jean are paid for helping at home. They

receive 20 cents for doing the dinner dishes on school

days. Whenever one does the work alone, she receives all

the money. Jean failed to help two evenings. How much

did Mary receive for that week? How much did Jean

receive ?

7. (a) The one who is ready first helps with the break-

fast, for which she receives 10 cents on school mornings.

Jean helped three mornings, and Mary the rest of the time.

How much did each receive? (b) How much did Mary

make for the week? Jean? How much did it cost their

mother ?

ARRANGED FOR INDIVIDUAL WORK 35

LESSON XII.

This is a copy of a puzzle printed by a Los Angeles

newspaper.

1. How many sides to a triangle? How many corners

in it? TRIangle means THREE CORNERS.

2. How many sides to a diamond? How is it different

from a square?

3. (a) In the part marked B, how many small squares

in a row? How many rows? How many small squares

in all? (b) How many middle-sized squares in a row? How

many rows? How many of these squares in all? (c) How

many of the large squares in a row? How many rows?

How many of the large squares? (d) How many squares

have you counted?

4. In the part marked C, how many of the middle-

sized squares in a row? How many rows? How many

of these squares?

5. (a) In part marked D, count the small triangles in

36 SUGGESTIVE LESSONS IN NUMBERING

each row. Find the sum. (b) Why can't we find the

number of triangles by finding the number in each row,

and then counting the rows as we did with the squares?

6. (a) Can you see the middle-sized triangles that are

formed by using two rows of the small triangles? How

many of these are there? (b) How many that are formed

with three rows of small ones?

7. Now look for the triangles that are formed by using

four rows of the small ones. How many of these are there ?

How many of the still larger ones are formed by using five

rows of the small ones? Six rows? Seven rows?

8. How many triangles in the part marked A? Look

for the small, middle-sized and large. How many triangles

have you found of all kinds?

9. (a) Look for the diamonds that touch the line marked

X Y. How many are there? How many in the row next

to this? In the third row? Fourth? Fifth? Sixth?

Seventh ?

10. Now take two rows together and count the diamonds

that you find in them? How many are there in the first

and second rows? In the third and fourth rows? In the

fifth and sixth rows?

11. Can you find any diamonds if you look at three

rows at a time? How many? If you look at four rows

at a time? How many diamonds of all kinds were you

able to find?

ARRANGED FOR INDIVIDUAL WORK

37

LESSON XIII.

HOW TO BEAD THE TIME TABLE.

Read down

Los Angeles and San Diego*

Aaabeta.

Oranga 54

... SantaAaa

...... AlUo...

Qallvan

lmm Ciplitr

Bern

MatooL

...Baa Onofre...%

...... Agr

...La Flore^

Oceazulde 36,37.

Carl

Ponto

EnctnltM

Cardiff

Del Mar

inda Vlsta__

Selwyn .......

Elvira

..Ladrillo _______

San Diego ..... L

Dtogo ..... Af

ZW Street ..... LT

National City... Lv

1. How many trains a day are there from Los Angeles

to San Diego? (Left side.) From San Diego to Los

Angeles? (Right side.) How many leave Los Angeles in

the forenoon? How many arrive at Los Angeles in the

afternoon ?

2. What time does Number 76 leave? Number 72?

What time does Number 71 arrive? Number 73?

3. How long does it take Number 74 to run from Los

Angeles to Fullerton? To run from Santa Ana to Ocean-

side? From Oceanside to San Diego?

38 SUGGESTIVE LESSONS IN NUMBERING

4. How long does it take No. 78 to run from San Diego

to Cardiff? From San Juan Capistrano to Anaheim? From

La Mirada to Los Angeles?

5. What time does No. 72 arrive at Orange? No. 78?

No. 74? No. 76? No. 79?

6. If you lived in Los Angeles and wanted to spend

the day in Santa Ana, which train would be a good one

for you to take? Upon which one would you return?

This would give you how many hours in Santa Ana?

How long would it be from the time you left Los Angeles

until you returned?

7. If you lived in Fullerton, which train should you

take to come into Los Angeles in the morning? Which one

to return to Fullerton in the afternoon? How much time

could you spend in Los Angeles if you took these two

trains ?

8. How far is it from Los Angeles to Orange by the

Santa Fe ? How far from Los Angeles to Oceanside ? How

far from Los Angeles to Del Mar? From Los Angeles to

San Diego?

9. How far is it from Santa Fe Springs to La Mirada?

Do you add or subtract to find this distance? How far

is it from Mateo to Las Flores ? From Ponto to Sorrento ?

LESSON XIV.

Children's Book Week. November 13th to 19th, 1921.

"Thomas Bailey Aldrich, as told in 'The Story of a Bad

Boy/ had a book case over his bed at the old house in

Portsmouth." One like it can be made for any boy's or

girl's own room. It should be stained or painted to match

the wood work in the room. This book case is 26 inches

long and is 26 inches high. It consists of three shelves

ARRANGED FOR INDIVIDUAL WORK 39

and the two side pieces. It has no back and is hung by

cords passing through holes at the top of sides. Two of

the shelves are seven inches wide, and the other is five

inches.

1. (a) How long must each shelf be? (b) What is the

length and what is the width of the bottom shelf? Of the

middle shelf? Of the top shelf?

2. (a) If you should draw a copy of the bottom shelf,

how long would your paper need to be? How wide?

(b) If your copy were only half as large as the real shelf,

what would be the length and the width of the pattern?

(c) If !/4 inch on your copy stood for one whole inch of

the shelf, how long and how wide would your drawing be ?

(d) If you made your drawing % of the real size, how long

and how wide would your drawing be? (e) We call this

"scale drawing." Which one of the above scales do you

think it would be better to use? Why?

3. (a) Use the same scale that you selected for the

bottom shelf in making a picture of the middle shelf,

(b) What is true of the two drawings? Why?

4. (a) If you make a picture of the top shelf, will it

look just like the other two? Can you explain this?

5. (a) How long must the side pieces be? How wide?

(b) Make a rough sketch of the way you think the side

pieces will look, (c) Does this drawing look like your

drawing of one of the shelves? Why not?

6. (a) Shall you use a board with both edges straight

for the side pieces? Why not? (b) In drawing this side

piece to the same scale that you used for the shelves, how

long must your drawing be? (c) How wide shall you have

it at one end? Why? (d) How wide at about the middle?

Why? (e) How wide at a short distance from the other

end? Why? (f) Now make a rough sketch showing how

40

SUGGESTIVE LESSONS IN NUMBERING

the front part of the side pieces will look, (g) Make a

scale drawing for one of the side pieces.

7. (a) How far apart shall you have your bottom and

middle shelves? (b) What will be the distance between the

middle and top shelves? (c) With this arrangement how

far will the top shelf be from the top of the bookcase?

(d) Shall you be able to use the top shelf for books if you

place it where you first said? (c) Should you have the

same distance between the bottom and middle shelves as

there is between the middle and top shelves? Why?

8. How far did you place the bottom shelf from the

middle shelf? The middle shelf from the top shelf? The

top shelf from the top of the bookcase? What is the sum

of these three distances? If the bookcase is made the

right size, what must this sum be?

LESSON XV.

ta Thomas Railey ft Id rich gook QSC

V

ARRANGED FOR INDIVIUAL WORK 41

Get a nice, strong pasteboard box, and make a "model"

of the Thomas Bailey Aldrich Book Case. Cut the box

carefully at the corners so that you will have flat pieces to

work with.

1. Now decide whether you will make your model the

same size as the bookcase or one-half as large, one-fourth

as large, or one-eighth as large. Why did you choose the

one you did?

2. (a) Using the scale you have chosen, see how long

each shelf should be. (b) How wide should each be?

(c) On your paper draw a pattern for each of these shelves.

(d) Find out how long and how wide the side pieces

should be. (e) Make a scale drawing of a side piece.

(f) Now decide how you want the front part of the side

piece shaped.

3. (a) Cut out the patterns you have made, being

careful to follow the lines so as to make the patterns true.

(b) How can you make both side pieces exactly alike?

(c) Make the two side pieces.

4. Place patterns on pasteboard so that you can decide

which will be the most saving and also the best way to

cut each piece.

5. Which do you think would be better to use, the

patterns in cutting the pieces for the "model," or to make

drawings of them on the pasteboard? Why?

6. (a) What shall you need to measure in making these

drawings on the pasteboard? (b) Make a drawing of the

bottom shelf, (c) When you cut it out be careful to use

a sharp knife or large scissors, (d) Draw and cut out

the other two shelves.

7. (a) Draw the lines that represent the back and bot-

tom of the side pieces, (b) What will be the best way to

get the front of the side pieces to look as you want them

42 SUGGESTIVE LESSONS IN NUMBERING

to? (c) Be careful to place your pattern so that the parts

representing the bottom and back fall on the lines you

have just made, (d) Now shape the front like the pattern.

(e) Cut out the side pieces, (f) Decide where the holes

are to be placed, and use a punch to put them in.

8. How shall you fasten the shelves to the side pieces?

These can either be glued, or, if pasteboard is heavy

enough, small grooves may be made in the side pieces,

or the shelves can be fastened in with pins, (g) Tint

bookcase the color you want, and fix cord to hang it up.

DRILL SHEET MULTIPLICATION I.

8X%= 9X94 -

=

= 7X%

5X 7 /io=

8X 3 /io=

DRILL SHEET MULTIPLICATION II.

1/3 Of 6=

2/3 Of 9=

% of 30=

2/ 3 of 16=

1/4 of 8=

3/4 of 12=

2/ 3 Of 18=

34 of 15=

l/ 5 of 10=

2/5 Of 10=

% of 24=

% of 19=

i/ 6 of 18=

3/ 5 Of 15=

3/8 Of 16=

3/ 8 of 12=

!/ 9 Of 27=

% of 10=

% of 24=

% of 20=

ARRANGED FOR INDIVIDUAL WORK 43

1/4 of 9= % of 18= % of 32= % of 16=

1/3 of 7= % of 27= 1/2 of 49= % of 13=

i/ 6 of 13= 3^ O f 32= 1/3 of 26= % of 16=

Mo of 18= % of 27=

91 of 15= % of 21=

% of 15= % of 28=

% of 22= % of 40=

% of 18= % of 36=

% of 48= V 2 of 126=

% of 64= 1/3 of 98=

1/9 of 36= % of 42=

DRILL SHEET MULTIPLICATION III.

%X%- %X 2 /3 = % X %=

%x% = y 5 of 3/ 8 =

%X% = 2 /3X%=

%x% = %'XT2

%X% = % Of 2/3=

y 2 x%= y 2 x%= ?4x 5 /i2= % x %=

%x%= 2 / 3 x% = % x %=

% x y 2 = %x%x%-

%of 1/8= %x%xy 2 =

1/3 O f iy 2 = %x%xy 2 -

44 SUGGESTIVE LESSONS IN NUMBERING

%of %=

%x %=

% x %=

% X %-

DRILL SHEET MULTIPLICATION IV.

%x2y 5 = 3i/ 3 xiy5=

3i/ 2 X43/4= 101/2X8%=

3i/ 2 X

iy 6 x

2%X

2%=

3%-

11/2X16 =

3i/ 3 X 9 =

6 Xl2i/ 2 =

iy4X3i/ 2 = 2%X1%=

2i/4 X

51/3=

5 X

1%

=

3%X

%- 2%X2%=

5 X

iy 2 =

3i/ 2 X

21/3

=

iy3xiy4= 3%x2i/ 2 =

iy 2 x

i%=

21/2 X

1%

=

2y 2 xiy6= 4y 2 x3y3= 5 x 121/2=

71/4 x

6

=

iy 2 x2

14= 2^X2

|3/4=

8 X

11/4=

1%X

1%

X4=

DEILL SHEET MULTIPLICATION V.

16

9 16%

481/2

1334

16%

27

ny 5

8i/ 2

31/3 15

7

8

12

9%

9

13%

28 19

261/3

45

25

36

40

10

61/4 81/4

18

i3y 5

8%

934

163/5

ARRANGED FOR INDIVIDUAL WORK 45

48 24% 15y 5 36 2iy 2 19 21 45

163/ 8 9 8 17% 9 91/3 142/3 12%

40y 2 42 64 24 49 35 3iy 3 24

24 18% % W2 161/3 15% 24 11%

LESSON XVI.

LEAEN TO READ A SCALE DRAWING.

1. In this drawing of "The Thomas Bailey Aldrich Book

Case," what scale has been used? Where does it tell this!

2. What is the length of the bottom line in the big

drawing? (b) If this line were just 3 inches long, how

long should the bookcase itself be? (c) How long must

we make the real bookcase if this is a true drawing of it?

3. (a) How long is the line that stands for the height

of the bookcase? (b) Is this correct? How do you know?

4. What is the length of the line that represents the

back part of the side piece? What is the length of this

part in the bookcase?

5. (a) What is the length of the line in the bottom part

of the side piece? (b) If % inch of the drawing equals

one inch of the real bookcase, % inch in the drawing

equals inches in the bookcase.

6. Measure the dotted line near the top of the side

piece. This stands for how many inches in the bookcase?

Why?

7. (a) What is the distance between the bottom and

middle shelves in the drawing? In the bookcase? (b) Is

the scale right? Prove it.

46 SUGGESTIVE LESSONS IN NUMBERING

8. What is the distance between the middle and top

shelves in the drawing? With this scale what should be

this distance in the bookcase?

9. What is the length of the line from the top shelf to

the top of the bookcase?

10. (a) What is the distance in the drawing from the

bottom shelf to the top of the bookcase? (b) What is the

distance from the bottom shelf to the top of the case in the

bookcase? (c) Show by this that the scale in the drawing

is i/ 8 " to 1".

11. (a) How far is the hole in the side piece from the

top in the drawing? (b) How far should it be in the real

bookcase?

12. (a) How wide is the side piece at the center of the

hole? (b) What is the measurement from the center of

the hole to the back of the side piece? (c) What is the

measurement from the center of the hole to the front of

the side part? (d) The answer in (b) is what part of the

answer in (c) ?

13. (a) How wide should the bookcase be at the center

of the hole? (b) Where should the hole be placed in the

bookcase? (c) How far from the top? (d) How far from

the back? (e) How far from the front?

LESSON XVII.

1. Lumber is measured by a piece that is 12 inches

long, 12 inches wide and one inch or less thick. This

is called a "board foot." Why was it so named?

2. (a) Make a drawing that represents a "board foot."

(b) If this board were cut in strips each one inch wide,

how many strips would there be? (c) Show this on your

drawing, (d) Now if these strips were placed end to end,

how far would they extend? Why? (e) How wide would

(h) Find the sum of the three short lines.

LESSON VIII.

1. What is the easiest way of finding how many seats

there are in your schoolroom? How many seats are there

in a row? How many rows? There are seats in

this room.

2. (a) What would be an easy way of finding how

many trees could be planted on a rectangular piece of

ground? (b) How could we easily find out how many

boy scouts there are in a group in regular formation T

(c) What is the best way to get the number of squares

on a checkerboard?

3. Secure two pieces of pasteboard of different sizes,

(a) Take one of these, and measure its length in inches;

its width in inches, (b) Put dots one inch apart on all of

the edges of this pasteboard, (c) Draw lines one inch

26 SUGGESTIVE LESSONS IN NUMBERING

apart (1) from top to bottom, (2) from side to side,

(d) How many squares are there in the first row? (e) How

many rows are there? (f) How many square inches are

there on this pasteboard? (g) Name two ways that you

had of answering this last question.

4. (a) Take the second piece of pasteboard. Find the

number of square inches in the first row. (b) Find the

number of rows, (c) Find the number of square inches on

this pasteboard.

5. Exchange pieces of pasteboard with two of your

friends, trying to get some that look different from yours.

(a) Using the clean side of one of these, show how many

square inches there are in the first row. (b) Show how

many rows, (c) How many square inches are there in the

whole pasteboard? (d) Did you add, subtract, multiply

or divide to find out?

6. (a) Find the number of square inches in the first

row on the second piece of pasteboard, (b) Find the

number of rows, (c) Find the number of square inches on

this pasteboard.

7. (a) Measure the top of your desk, using only inches

and half inches, (b) If you do not see immediately how

many square inches there are in the first row, us.e chalk

to make one row of one-inch squares at the top of the desk,

(c) Then use lines to mark off the number of rows, (d)

Find the number of square inches on the top of your desk.

8. (a) Find the number of square inches on the top of

your book, (b) Find the number of square inches on one

sheet of your tablet paper.

9. (a) Measure one section of the blackboard in feet.

(b) At the bottom make one row of foot squares, (c) How

many rows of these squares are there? (d) How many

square feet are there in a section of the blackboard?

ARRANGED FOR INDIVIDUAL WORK 27

10. (a) At one end of the floor, make one row of foot

squares, (b) How many rows are there? (c) Find num-

ber of square feet in the floor.

11. (a) Find the number of square feet on the top of

the table, (b) Find the number of square feet on the

door; (c) in one-half of the window.

DKILL SHEET SUBTEACTION I.

1111111111

1111111111

5 /8 % % VlO %0 %0 %0 % %2 T/12

y 2

DRILL SHEET SUBTRACTION II.

1% 1% 1% 1% 1% 1% 1% 1% 1% 1%

28 SUGGESTIVE LESSONS IN NUMBERING

11/8 11/6 ll/ 6 ll/ 8 11/8 11/3 1% 1% 1%

% % % % 7 /8 % % % %

1% 1% 1% 1% 1% 1% 1%

% %o % %o % %o %

1% 1% 1% 1% 1% l%o 1% 1%

% 9io % %o % % % %

iHo 1% iHo 1% 1% i x /2 1% 1%

1% iy 3 1% 1% 1% 1%

DEILL SHEET SUBTEACTION III.

61/4 71/8 8y 2 53/8 95/8 71/4 6i/8 91/4 81/4 734 934

31/2 41/4 33/4 21/2 434 3% 534 51/2 37/8 3y 2 47s

81/3 71/6 91/2 71/3 81/6 71/3 91/3 13 92/3 151/2 111/2

52/3 31/3 42/3 4y 2 42/3 5% 2% 81/3 5y 2 91/3 75/ 6

ARRANGED FOR INDIVIDUAL WORK 29

9% 8% 73/5 91/5 73/ 5 112/ 5 8 y 2 1334 lll/ 6 121/ 3

4% 37 8 32/ 5 5% 4%o 5% 5y 2 43/ 5 77/ 8 91/4 83,4

11% 75/ 6 91/6 123/ 8 51/ 16 9% 2 125/ 8 131/ 6 92/3

81/3 7V 2 31/4 61/3 2% 6% 52/3 83,4 43/4 72/ 3 62/3

DEILL SHEET SUBTEACTION IV.

25% 341/3 4iy 2 621/4 281/6 76y 2 40y 3 54% 27%

19y 2 262/ 3 273,4 383/s 19% 475/ 8 255/ 6 365/ 8 19%

365/s 49i/ 10 64i/ 2 9334 45?4 26i/ 6 7 i % 6 3% 2 34%

21T/8 263/ 5 452/3 377/ 8 392/3 191/4 361/3 363,4 16%

521/s 52i/ 6 3 i3/ 8 i63/ 5 42% 2 89% 51%

29?4 3734 161/3 9% 26?4 52% 372/ 3 16% 483/ 5

2134 40 742/ 5 1091/3 62% 2 1213,

197/8 1334 39y 2 765/6 383,4 87%

782/g 663,4 901/3 74y 2 36

292/s 36% 195/8 113^ 1013/5

30 SUGGESTIVE LESSONS IN NUMBERING

LESSON IX.

1. (a) How many hours are there in a day? (b) In

drawing a line to represent a day, if you let ^2 i nc h stand

for an hour, how long should the line be? (c) If % inch

stands for an hour, how long should the line be?

2. (a) John goes to bed at 8 p. m. and gets up at

7 a. m. How many hours does he sleep? (b) Mary goes

to bed at 9 p. m. and gets up at 6 :30 a. m. How long does

she have for sleep? (c) How many hours does their father

spend in bed if he retires at 10:30 p. m. and arises at

6:15 a. m.?

3. (a) What time do you go to bed? What time do

you get up? How many hours of sleep do you have?

(b) What time do you usually have your breakfast? What

time do you have lunch? How long is it between these

two meals? (c) How long is it between your lunch and

your dinner? (d) How long after you have eaten your

dinner is it till bedtime?

4. (a) What time does your school take up in the

morning? At what time do you have recess? How long

must you be in school before recess time? (b) How long

is it from recess until noon? How long is school in session

in the forenoon? (c) What time does school take up in

the afternoon? What time does it close? How long is the

afternoon session? (f) Which is the longer, the morning

session or the afternoon session? How much longer?

(e) What is the length of your school day?

5. (a) Our school begins at 8:35 a. m. At 10 a. m. we

have our arithmetic. How long are we in school before

we have our arithmetic? (b) The boys work in the shop

from 10 :45 a. m. till 12 :20 p. m. How much time do they

ARRANGED FOR INDIVIDUAL WORK 31

spend in the shop? (c) The girls have cooking from 1:40

p. m. till 2:23 p. m. How long does their cooking period

last?

6. (a) How long is it from the time school opens in

the morning till the end of your geography recitation?

(b) How long is it from the beginning of your arithmetic

recitation until you have physical education? (c) What is

your favorite class during the day? How long is it from

the time school opens until this recitation begins? How

long is it from the time this recitation ends until school

closes at night?

7. What is your longest recitation during the day?

Which is the shortest? How much longer is the first one?

This is what part of an hour?

LESSON X.

1. (a) How long does it take you to get washed and

dressed in the morning? This is what part of an hour?

(b) Do you help your mother in the morning? For how

long? This is what part of an hour? (c) What time do

you leave home to come to school? What time do you

reach school? This is what part of an hour? (d) How

long is it from the time you get up until you are at school?

2. (a) What time do you get home from school in the

evening? How long do you have for play before dinner

time? (b) Do you take any kind of lesson after school?

How long does it take you to go for your lesson, have the

lesson, and to come home afterwards? (c) If a line

V 2 inch represents 1 hour, how long would a line be that

represented the time you spent on a lesson that was taken

outside of school?

3. Do you study or practice any of the time you are

32 SUGGESTIVE LESSONS IN NUMBERING

home? How long? This is what part of an hour?

4. (a) Draw a line to represent a day. If % inch rep-

resents 1 hour, how long should this line be? (b) Use this

line to make a rectangle 1 inch wide. How long will the

two end lines be? The other side line?

5. (a) How much time do you spend in sleep? Mark

off a box in this rectangle that just represents this

time, (b) How long is it from the time you get up until

school opens? Make another box to represent this length

of time, (c) How many hours do you stay at school?

Show this on the rectangle you have made, (d) How long

is it from the time you leave school until you go to bed?

If ^4 i nc h represents 1 hour, how long should the line be

that represents this time? (e) Measure the part of the

rectangle that you have not used to see if it is this length.

If so, you have made no mistake in your work.

6. (a) Draw a circle 2 inches in diameter, (b) How

can you find one-half of this circle? One-fourth of it?

One-third of it? One-eighth of it? Three-eighths of it?

7. (a) Shade in the part of this circle that would show

how much time you spend in sleep, (b) Use fine lines to

show the part of the day you spend at school. (c)

Show in some other way the part of the remaining time

that you spend in play? (d) What part of the circle has

not been used?

LESSON XI.

Some boys and girls were talking about things they

would like to buy. The question of saving money came up.

They asked how they could find out how long it would

take them to save certain amounts of money. In answer-

ing their questions this lesson was worked out.

ARRANGED FOR INDIVIDUAL WORK

33

1. (a) How many months are there in a year? (b) How

many weeks in a year? (c) How many days in a year?

SAVINGS.

Amount

Each month

Each week

Each day

$ 50.00

$4.17

$0.96

$0.14

60.00

75.00

80.00

85.00

87.50

90.00

100.00

105.00

115.00

125.00

135.00

140.00

150.00

160.00

175.00

200.00

2. (a) To save $50.00 a year, one should save of

it each month: that is $50.00-7- equals

(b) $50.00-r- shows how much should be saved each

week. $50.00-r- equals (c) $50.00-f-365

equals , or the amount that should be saved each day.

3. Write answers in the table given above.

34 SUGGESTIVE LESSONS IN NUMBERING

4. If Mary saves 5 cents a day, how much can she save

in the month of January? February? March? April?

May? June? July? August? September? October?

November? December? How much is saved for the

entire year?

5. (a) If George saves a penny a day, how much will

he have in a week? In a year? (b) If John can manage

to save 15 cents a week, how much will he have at the

end of a year?

6. Mary and Jean are paid for helping at home. They

receive 20 cents for doing the dinner dishes on school

days. Whenever one does the work alone, she receives all

the money. Jean failed to help two evenings. How much

did Mary receive for that week? How much did Jean

receive ?

7. (a) The one who is ready first helps with the break-

fast, for which she receives 10 cents on school mornings.

Jean helped three mornings, and Mary the rest of the time.

How much did each receive? (b) How much did Mary

make for the week? Jean? How much did it cost their

mother ?

ARRANGED FOR INDIVIDUAL WORK 35

LESSON XII.

This is a copy of a puzzle printed by a Los Angeles

newspaper.

1. How many sides to a triangle? How many corners

in it? TRIangle means THREE CORNERS.

2. How many sides to a diamond? How is it different

from a square?

3. (a) In the part marked B, how many small squares

in a row? How many rows? How many small squares

in all? (b) How many middle-sized squares in a row? How

many rows? How many of these squares in all? (c) How

many of the large squares in a row? How many rows?

How many of the large squares? (d) How many squares

have you counted?

4. In the part marked C, how many of the middle-

sized squares in a row? How many rows? How many

of these squares?

5. (a) In part marked D, count the small triangles in

36 SUGGESTIVE LESSONS IN NUMBERING

each row. Find the sum. (b) Why can't we find the

number of triangles by finding the number in each row,

and then counting the rows as we did with the squares?

6. (a) Can you see the middle-sized triangles that are

formed by using two rows of the small triangles? How

many of these are there? (b) How many that are formed

with three rows of small ones?

7. Now look for the triangles that are formed by using

four rows of the small ones. How many of these are there ?

How many of the still larger ones are formed by using five

rows of the small ones? Six rows? Seven rows?

8. How many triangles in the part marked A? Look

for the small, middle-sized and large. How many triangles

have you found of all kinds?

9. (a) Look for the diamonds that touch the line marked

X Y. How many are there? How many in the row next

to this? In the third row? Fourth? Fifth? Sixth?

Seventh ?

10. Now take two rows together and count the diamonds

that you find in them? How many are there in the first

and second rows? In the third and fourth rows? In the

fifth and sixth rows?

11. Can you find any diamonds if you look at three

rows at a time? How many? If you look at four rows

at a time? How many diamonds of all kinds were you

able to find?

ARRANGED FOR INDIVIDUAL WORK

37

LESSON XIII.

HOW TO BEAD THE TIME TABLE.

Read down

Los Angeles and San Diego*

Aaabeta.

Oranga 54

... SantaAaa

...... AlUo...

Qallvan

lmm Ciplitr

Bern

MatooL

...Baa Onofre...%

...... Agr

...La Flore^

Oceazulde 36,37.

Carl

Ponto

EnctnltM

Cardiff

Del Mar

inda Vlsta__

Selwyn .......

Elvira

..Ladrillo _______

San Diego ..... L

Dtogo ..... Af

ZW Street ..... LT

National City... Lv

1. How many trains a day are there from Los Angeles

to San Diego? (Left side.) From San Diego to Los

Angeles? (Right side.) How many leave Los Angeles in

the forenoon? How many arrive at Los Angeles in the

afternoon ?

2. What time does Number 76 leave? Number 72?

What time does Number 71 arrive? Number 73?

3. How long does it take Number 74 to run from Los

Angeles to Fullerton? To run from Santa Ana to Ocean-

side? From Oceanside to San Diego?

38 SUGGESTIVE LESSONS IN NUMBERING

4. How long does it take No. 78 to run from San Diego

to Cardiff? From San Juan Capistrano to Anaheim? From

La Mirada to Los Angeles?

5. What time does No. 72 arrive at Orange? No. 78?

No. 74? No. 76? No. 79?

6. If you lived in Los Angeles and wanted to spend

the day in Santa Ana, which train would be a good one

for you to take? Upon which one would you return?

This would give you how many hours in Santa Ana?

How long would it be from the time you left Los Angeles

until you returned?

7. If you lived in Fullerton, which train should you

take to come into Los Angeles in the morning? Which one

to return to Fullerton in the afternoon? How much time

could you spend in Los Angeles if you took these two

trains ?

8. How far is it from Los Angeles to Orange by the

Santa Fe ? How far from Los Angeles to Oceanside ? How

far from Los Angeles to Del Mar? From Los Angeles to

San Diego?

9. How far is it from Santa Fe Springs to La Mirada?

Do you add or subtract to find this distance? How far

is it from Mateo to Las Flores ? From Ponto to Sorrento ?

LESSON XIV.

Children's Book Week. November 13th to 19th, 1921.

"Thomas Bailey Aldrich, as told in 'The Story of a Bad

Boy/ had a book case over his bed at the old house in

Portsmouth." One like it can be made for any boy's or

girl's own room. It should be stained or painted to match

the wood work in the room. This book case is 26 inches

long and is 26 inches high. It consists of three shelves

ARRANGED FOR INDIVIDUAL WORK 39

and the two side pieces. It has no back and is hung by

cords passing through holes at the top of sides. Two of

the shelves are seven inches wide, and the other is five

inches.

1. (a) How long must each shelf be? (b) What is the

length and what is the width of the bottom shelf? Of the

middle shelf? Of the top shelf?

2. (a) If you should draw a copy of the bottom shelf,

how long would your paper need to be? How wide?

(b) If your copy were only half as large as the real shelf,

what would be the length and the width of the pattern?

(c) If !/4 inch on your copy stood for one whole inch of

the shelf, how long and how wide would your drawing be ?

(d) If you made your drawing % of the real size, how long

and how wide would your drawing be? (e) We call this

"scale drawing." Which one of the above scales do you

think it would be better to use? Why?

3. (a) Use the same scale that you selected for the

bottom shelf in making a picture of the middle shelf,

(b) What is true of the two drawings? Why?

4. (a) If you make a picture of the top shelf, will it

look just like the other two? Can you explain this?

5. (a) How long must the side pieces be? How wide?

(b) Make a rough sketch of the way you think the side

pieces will look, (c) Does this drawing look like your

drawing of one of the shelves? Why not?

6. (a) Shall you use a board with both edges straight

for the side pieces? Why not? (b) In drawing this side

piece to the same scale that you used for the shelves, how

long must your drawing be? (c) How wide shall you have

it at one end? Why? (d) How wide at about the middle?

Why? (e) How wide at a short distance from the other

end? Why? (f) Now make a rough sketch showing how

40

SUGGESTIVE LESSONS IN NUMBERING

the front part of the side pieces will look, (g) Make a

scale drawing for one of the side pieces.

7. (a) How far apart shall you have your bottom and

middle shelves? (b) What will be the distance between the

middle and top shelves? (c) With this arrangement how

far will the top shelf be from the top of the bookcase?

(d) Shall you be able to use the top shelf for books if you

place it where you first said? (c) Should you have the

same distance between the bottom and middle shelves as

there is between the middle and top shelves? Why?

8. How far did you place the bottom shelf from the

middle shelf? The middle shelf from the top shelf? The

top shelf from the top of the bookcase? What is the sum

of these three distances? If the bookcase is made the

right size, what must this sum be?

LESSON XV.

ta Thomas Railey ft Id rich gook QSC

V

ARRANGED FOR INDIVIUAL WORK 41

Get a nice, strong pasteboard box, and make a "model"

of the Thomas Bailey Aldrich Book Case. Cut the box

carefully at the corners so that you will have flat pieces to

work with.

1. Now decide whether you will make your model the

same size as the bookcase or one-half as large, one-fourth

as large, or one-eighth as large. Why did you choose the

one you did?

2. (a) Using the scale you have chosen, see how long

each shelf should be. (b) How wide should each be?

(c) On your paper draw a pattern for each of these shelves.

(d) Find out how long and how wide the side pieces

should be. (e) Make a scale drawing of a side piece.

(f) Now decide how you want the front part of the side

piece shaped.

3. (a) Cut out the patterns you have made, being

careful to follow the lines so as to make the patterns true.

(b) How can you make both side pieces exactly alike?

(c) Make the two side pieces.

4. Place patterns on pasteboard so that you can decide

which will be the most saving and also the best way to

cut each piece.

5. Which do you think would be better to use, the

patterns in cutting the pieces for the "model," or to make

drawings of them on the pasteboard? Why?

6. (a) What shall you need to measure in making these

drawings on the pasteboard? (b) Make a drawing of the

bottom shelf, (c) When you cut it out be careful to use

a sharp knife or large scissors, (d) Draw and cut out

the other two shelves.

7. (a) Draw the lines that represent the back and bot-

tom of the side pieces, (b) What will be the best way to

get the front of the side pieces to look as you want them

42 SUGGESTIVE LESSONS IN NUMBERING

to? (c) Be careful to place your pattern so that the parts

representing the bottom and back fall on the lines you

have just made, (d) Now shape the front like the pattern.

(e) Cut out the side pieces, (f) Decide where the holes

are to be placed, and use a punch to put them in.

8. How shall you fasten the shelves to the side pieces?

These can either be glued, or, if pasteboard is heavy

enough, small grooves may be made in the side pieces,

or the shelves can be fastened in with pins, (g) Tint

bookcase the color you want, and fix cord to hang it up.

DRILL SHEET MULTIPLICATION I.

8X%= 9X94 -

=

= 7X%

5X 7 /io=

8X 3 /io=

DRILL SHEET MULTIPLICATION II.

1/3 Of 6=

2/3 Of 9=

% of 30=

2/ 3 of 16=

1/4 of 8=

3/4 of 12=

2/ 3 Of 18=

34 of 15=

l/ 5 of 10=

2/5 Of 10=

% of 24=

% of 19=

i/ 6 of 18=

3/ 5 Of 15=

3/8 Of 16=

3/ 8 of 12=

!/ 9 Of 27=

% of 10=

% of 24=

% of 20=

ARRANGED FOR INDIVIDUAL WORK 43

1/4 of 9= % of 18= % of 32= % of 16=

1/3 of 7= % of 27= 1/2 of 49= % of 13=

i/ 6 of 13= 3^ O f 32= 1/3 of 26= % of 16=

Mo of 18= % of 27=

91 of 15= % of 21=

% of 15= % of 28=

% of 22= % of 40=

% of 18= % of 36=

% of 48= V 2 of 126=

% of 64= 1/3 of 98=

1/9 of 36= % of 42=

DRILL SHEET MULTIPLICATION III.

%X%- %X 2 /3 = % X %=

%x% = y 5 of 3/ 8 =

%X% = 2 /3X%=

%x% = %'XT2

%X% = % Of 2/3=

y 2 x%= y 2 x%= ?4x 5 /i2= % x %=

%x%= 2 / 3 x% = % x %=

% x y 2 = %x%x%-

%of 1/8= %x%xy 2 =

1/3 O f iy 2 = %x%xy 2 -

44 SUGGESTIVE LESSONS IN NUMBERING

%of %=

%x %=

% x %=

% X %-

DRILL SHEET MULTIPLICATION IV.

%x2y 5 = 3i/ 3 xiy5=

3i/ 2 X43/4= 101/2X8%=

3i/ 2 X

iy 6 x

2%X

2%=

3%-

11/2X16 =

3i/ 3 X 9 =

6 Xl2i/ 2 =

iy4X3i/ 2 = 2%X1%=

2i/4 X

51/3=

5 X

1%

=

3%X

%- 2%X2%=

5 X

iy 2 =

3i/ 2 X

21/3

=

iy3xiy4= 3%x2i/ 2 =

iy 2 x

i%=

21/2 X

1%

=

2y 2 xiy6= 4y 2 x3y3= 5 x 121/2=

71/4 x

6

=

iy 2 x2

14= 2^X2

|3/4=

8 X

11/4=

1%X

1%

X4=

DEILL SHEET MULTIPLICATION V.

16

9 16%

481/2

1334

16%

27

ny 5

8i/ 2

31/3 15

7

8

12

9%

9

13%

28 19

261/3

45

25

36

40

10

61/4 81/4

18

i3y 5

8%

934

163/5

ARRANGED FOR INDIVIDUAL WORK 45

48 24% 15y 5 36 2iy 2 19 21 45

163/ 8 9 8 17% 9 91/3 142/3 12%

40y 2 42 64 24 49 35 3iy 3 24

24 18% % W2 161/3 15% 24 11%

LESSON XVI.

LEAEN TO READ A SCALE DRAWING.

1. In this drawing of "The Thomas Bailey Aldrich Book

Case," what scale has been used? Where does it tell this!

2. What is the length of the bottom line in the big

drawing? (b) If this line were just 3 inches long, how

long should the bookcase itself be? (c) How long must

we make the real bookcase if this is a true drawing of it?

3. (a) How long is the line that stands for the height

of the bookcase? (b) Is this correct? How do you know?

4. What is the length of the line that represents the

back part of the side piece? What is the length of this

part in the bookcase?

5. (a) What is the length of the line in the bottom part

of the side piece? (b) If % inch of the drawing equals

one inch of the real bookcase, % inch in the drawing

equals inches in the bookcase.

6. Measure the dotted line near the top of the side

piece. This stands for how many inches in the bookcase?

Why?

7. (a) What is the distance between the bottom and

middle shelves in the drawing? In the bookcase? (b) Is

the scale right? Prove it.

46 SUGGESTIVE LESSONS IN NUMBERING

8. What is the distance between the middle and top

shelves in the drawing? With this scale what should be

this distance in the bookcase?

9. What is the length of the line from the top shelf to

the top of the bookcase?

10. (a) What is the distance in the drawing from the

bottom shelf to the top of the bookcase? (b) What is the

distance from the bottom shelf to the top of the case in the

bookcase? (c) Show by this that the scale in the drawing

is i/ 8 " to 1".

11. (a) How far is the hole in the side piece from the

top in the drawing? (b) How far should it be in the real

bookcase?

12. (a) How wide is the side piece at the center of the

hole? (b) What is the measurement from the center of

the hole to the back of the side piece? (c) What is the

measurement from the center of the hole to the front of

the side part? (d) The answer in (b) is what part of the

answer in (c) ?

13. (a) How wide should the bookcase be at the center

of the hole? (b) Where should the hole be placed in the

bookcase? (c) How far from the top? (d) How far from

the back? (e) How far from the front?

LESSON XVII.

1. Lumber is measured by a piece that is 12 inches

long, 12 inches wide and one inch or less thick. This

is called a "board foot." Why was it so named?

2. (a) Make a drawing that represents a "board foot."

(b) If this board were cut in strips each one inch wide,

how many strips would there be? (c) Show this on your

drawing, (d) Now if these strips were placed end to end,

how far would they extend? Why? (e) How wide would

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