How much longer is the longest line than the shortest?
(h) Find the sum of the three short lines.
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
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
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
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.
5 /8 % % VlO %0 %0 %0 % %2 T/12
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
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
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?
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?
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
1. (a) How many months are there in a year? (b) How
many weeks in a year? (c) How many days in a year?
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
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
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
ARRANGED FOR INDIVIDUAL WORK 35
This is a copy of a puzzle printed by a Los Angeles
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?
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
HOW TO BEAD THE TIME TABLE.
Los Angeles and San Diego*
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
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
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
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 ?
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
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
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?
ta Thomas Railey ft Id rich gook QSC
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
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
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 -
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
% x %=
% X %-
DRILL SHEET MULTIPLICATION IV.
%x2y 5 = 3i/ 3 xiy5=
3i/ 2 X43/4= 101/2X8%=
3i/ 2 X
iy 6 x
3i/ 3 X 9 =
6 Xl2i/ 2 =
iy4X3i/ 2 = 2%X1%=
iy 2 =
3i/ 2 X
iy3xiy4= 3%x2i/ 2 =
iy 2 x
2y 2 xiy6= 4y 2 x3y3= 5 x 121/2=
iy 2 x2
DEILL SHEET MULTIPLICATION V.
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%
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?
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
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?
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