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Suggestive Lessons in
Numbering

Arranged for Individual Work

FIFTH GRADE



BY



MARGARET M. CAMPBELL, M.A.

Department of Mathematics, Junior High School

University of California, Southern Branch

Los Angeles



1922

HARR WAGNER PUBLISHING CO.

San Francisco
California



miiiiiiiiiiiim



SUGGESTIVE LESSONS IN NUMBERING



Arranged for Individual Work



FIFTH GRADE



BY



MARGARET M. CAMPBELL

Department of Mathematics, Junior High School

University of California, Southern Branch,

Los Angeles



February 15, 1922



1922

HARR WAGNER PUBLISHING CO.

San Francisco

California



Copyright 1922
By Harr Wagner Publishing Co.

1900




PREFACE.

These lessons are planned to use with the California
State Series, and so are not complete in themselves, but
they show possibilities of securing material from other
divisions of the curricula. So close is the relation between
arithmetic and the other branches of knowledge, that it
might be said that only the mastery of the fundamental
processes should be designated arithmetic, for the appli-
cation belongs wherever quantitative thinking is desirable.
The importance of finding favorable opportunities for this
kind of thinking cannot be over-emphasized, and nowhere
are they more auspicious than along the lines of the pupils'
present interests and needs.

In consideration of the pupils' individual abilities and
differences, the arrangement as well as the graded steps,
both in the separate lessons and the series as a whole,
is such that they may progress, each at his own rate of
speed and with his own degree of doing. The essential
points are, that each pupil feels an inner urge to do, and
that he develops his own power by such activity.

M. M. C.

February 15, 1922.



492236



*

' .*





TABLE OF CONTENTS



Lesson

Measuring.

I. Estimating and measuring with a ruler

II. Keeping a record of arithmetic lessons

III. Keeping a record of other school work

IV. Making a checkerboard

Common Fractions.

V. Lines

VI. Circle; square

Addition and subtraction of fractions

Drill sheets Addition of fractions

VII. Checking addition of fractions

VIII. Measuring squares

Drill sheets Subtraction of fractions

Working With Time.

IX. Counting time

X. Picturing time

XI. Saving money

Miscellaneous.
XII. Working a puzzle

XIII. How to read the time table

Project Children's Book Week.

XIV. Making a picture of a bookcase

XV. Making a pasteboard model of a bookcase,

Drill Sheets Multiplication of fractions . .

XVI. Learning to read scale drawing

XVII. Making bookcase ,

XVIII. Buying books

Football

XIX. Drawing the field

XX. Scoring the game

Being Well and Strong.
XXI. How to read the table of heights



ii



CONTENTS



Lesson Page

XXII. Beading table of weights 58

XXm. Figuring heights and weights 60

XXIV. Making a table of heights and weights for the

class 62

XXV. Keeping a monthly record of an individual's

height and weight 63

Drill sheets Division of fractions 66

XXVI. Being a checker at cafeteria 67

Selecting Proper Food.

XXVII. Suitable foods for boys and girls 69

XXVIII. Suitable foods 72

XXTX r Helping to use a fireless cooker 73

Working With Money.

XXX. Counting money 75

XXXI. Figuring costs and making change 77

Making Christmas Presents.

XXXII. Problems of the sewing class 78

XXXHZ Sailboats 80

XXXIV. Envelopes 81

XXXV. Holder for pictures and kodak films 84

Blocking Patterns.

XXXVI. Toy pig 86

XXXVII. Toy pig 87

XXXVIII. Sketching human figure 89

XXXIX. Comparative studies of human figure 91

XL. Sketching figures of children 92



SUGGESTIVE LESSONS IN NUMBERING

ARRANGED FOR INDIVIDUAL WORK.



FIFTH GRADE.



LESSON I.

1. (a) Draw a line that you think is one inch long.
Measure with a ruler, (b) Draw another line that you
think is one inch long. Use your ruler to draw an inch
line just below this, (c) Practice drawing inch lines
without the ruler until you can make them look as though
they had been drawn with a ruler.

2. (a) Draw a two-inch line without the ruler. Measure
it. Is it too short or too long? Can you make another
that is about right? (b) Make two points on your paper
that are three inches apart. Do this by guess. Now meas-
ure the distance between them to see if you are right.
Just below these points draw a three-inch line.

3. (a) How long is your paper? Measure it to see if
you made a good guess. How wide is it? Measure its
width. How many inches were you "off" in your guess?
(b) How long is your book? How wide is it? How many
inches did you miss in the length? How many in the
width?

4. (a) How far is it from the end of your first finger



a SUGGESTIVE LESSONS IN NUMBERING

to the second joint? Measure to see if you are a good
guesser. How far is it from the end of your first finger
to the knuckle? (b) How much longer is your second
finger than your first? What is the length of your thumb?

5. (a) Measure the distance from the end of your
thumb to the end of your first finger when your hand is
opened out wide; from the end of your thumb to the end
of your second finger; from the end of your thumb to the
end of your little finger.

6. (a) Measure the width of your hand, (b) Measure the
distance from the end of your second finger to your elbow,
(c) Stretch your hands out wide and place the ends of
the thumbs together. Now make points with the ends
of the little fingers. Measure the distance between these
points, (d) Who in your class can stretch their little
fingers farther apart than you can? How much farther?
(e) Who cannot stretch as far? How much less?

7. (a) Draw a line nine inches long. One-half inch
below this draw another of the same length. Join the
ends, (b) What is the length of this rectangle? What is
its width?

8. (a) Mark off quarter inches at the top and bottom
of this rectangle, (b) Connect these points, making^ as
many little rectangles as you can. How many did you
make? (c) In the middle of the big rectangle draw a line
from side to side. How many squares have you made?
What is the size of each square?

9. You have made this so as to keep a record of your
lessons. After you have finished it, fasten it to your book
in some way so that you will not lose it. (a) In the upper
row of squares number from 1 to 40. (b) Each time you
have handed your teacher a lesson, mark off the square?



ARRANGED FOR INDIVIDUAL WORK 9

under the number of the lesson, thus |/|. When you have
corrected your mistakes in the lessons, mark it |X|.

10. Get a piece of heavy cardboard, 20 inches long,
(a) Leave a two-inch space at the left, (b) Mark off
half -inches along the rest of the top. (c) After leaving a
two-inch space at the left, mark off half-inches along the
rest of the bottom line, (d) How many pupils are there
in your class? Mark off one more than that many half-
inches along both sides, (e) Now draw all the lines to
make the little squares, (f) In the top row write num-
bers 1 to 40. (g) On the lines in the two-inch space
write the names of the pupils in your class. The teacher
will select the best chart for the class record. Keep this
up on the wall where everyone can see it.

LESSON II.

An easy way of keeping a record of your work.

1. (a) Make a three-inch square, (b) Mark off each
half -inch with a little dot in both the top and bottom lines.
(c) Draw a line from the dot in the top line to the one
just below it in the bottom line, (d) Mark off the sides
of the square into quarter inches, (e) Draw a line from
the dot in the left side to the one just across from it in
the right side, (f) Make double lines around the big
square by drawing lines one-sixteenth of an inch below
each of the outside lines, (g) In the little boxes at the
top of the square, write the abbreviations for the days
of the week, beginning with the second one from the left,
(Write Mon. for Monday, Tues. for Tuesday, etc.) (h) Use
the boxes at the left of the square for numbers. In the
one at the bottom write "o"; in the one above, "10"; the
next one, "20," and so on, counting by 10s until you have
reached 100.



10 SUGGESTIVE LESSONS IN NUMBERING

2. (a) The first inside line at the bottom is the 10 line.
Which is the 40 line? The 90 line? The 30 line? The
70 line? (b) Where would you show 75? 45? 95? 25? 85?

3. These were John's grades for a week in his arith-
metic drill: Monday, 60; Tuesday, 50; Wednesday, 80;
Thursday, 75; Friday, 90. (a) Put the grade for Monday
on the 60 line in the middle of the column marked Mon.
(b) Show with your finger where you will put the grade
for Tuesday. Put a point there, (c) Find the place for
Wednesday's grade. Make a point, (d) Where should
Thursday's grade be placed? Mark it. (e) On which lin.e
shall you place the grade for Friday? Locate this point,
(f) Now draw a line through all these points, beginning
with the first one located, then the second, third, etc.

Such a line is called a graph. It shows at a glance the
progress that is made in a week.

4. The next week John made these grades in his arith-
metic drill: Monday, 90; Tuesday, 75; Wednesday, 80;
Thursday, 60; Friday, 85. (a) Where shall you place
Monday's grade? Locate the point, (b) Show where
Tuesday's grade is to be placed; Wednesday's; Thurs-
day's; Friday's. Connect these points with a broken line
like this: .

5. John's record for the third week in the same work
was as follows : Monday, 65 ; Tuesday, 75 ; Wednesday, 90 ;
Thursday, 85; Friday, 100. (a) Locate the point for Mon-
day; for Tuesday; for Wednesday; for Thursday; for
Friday, (b) Use either a colored pencil or pen and ink
to connect these points, (c) Why did you make the graph
different each time?

6. Make another square as you did in Example 1.

7. Make a graph showing Mary's attendance at school:
Monday she was there all day (100) ; Tuesday, came 10



ARRANGED FOR INDIVIDUAL WORK 11

minutes late (95); Wednesday, all day; Thursday, left
20 minutes early; and Friday, was present a half -day.






LESSON III.



1. Mary made these grades in her arithmetic drill:
Monday, 40; Tuesday, 25; Wednesday, 55; Thursday, 70;
Friday, 0. Make a graph showing the result of the week's
work.

2. Mary's grades the second week were as follows:
Monday, 35; Tuesday, 50; Wednesday, 45; Thursday, 60;
Friday, 75. Make a graph of this record. (Be careful
to make the two graphs for Mary so that both records
will be clear.)

3. Make another square as you did in Example 1 of
last lesson.

4. The fifth-grade spelling was having a review the
entire week. Each day they had twenty words. Here are
the records for eight in the class: (The figures show
words missed.)

Monday Tuesday Wednesday Thursday Friday

Raei 5 2 1 4

Philip 5 8 3 2 2

George 10 5 5 3 1

Frank 5 2 1 3

Paul 4 2 5 1 1

Julia 3 2

Elizabeth 5 2 3 1 2

Vivian 2 4 1 2 3

(a) If there are 20 words in the lesson, how much should
be taken off for each word? (b) What is Rae's grade for
Monday! How much was taken off on Tuesday? What
was her grade for Tuesday? for Wednesday? for Thurs-



12 SUGGESTIVE LESSONS IN NUMBERING

day? for Friday? (b) Find Philip's grade for each day in
the week, (c) What are George's grades for the week?
(d) How much did Frank make each day? (e) What were
Paul's grades for the week? (f) Find Julia's grades.
(g) Elizabeth's grades, (h) Vivian's.

5. (a) What is the sum of all the grades that were
made on Monday? (b) Divide this sum by 8. The answer
is the average for the class that day. (c) Find the sum
of all the grades for Tuesday, (d) What shall you divide
by to get the average? Why? What is the average for
Tuesday? (e) Find average for Wednesday, (f) What is
the average for Thursday? (g) Find average for Friday.

6. Make a graph of the class averages for a week;
graphs for two of the pupils.

7. (a) Make a graph of your attendance at school last
week, (b) Make a graph of your work in arithmetic for
a week, (c) Make a graph of your spelling grades for
a week.

8. (a) If you were to make a graph showing the tem-
perature in your schoolroom for each hour from 9 a. m.
till 3 p. m., how many columns would you need? (b) How
many boxes on the left-hand side would you need? (When
it is the coldest, what is the temperature of your room?
What is the temperature when it is the warmest? The
difference in these two will tell you how many boxes are
needed. Each box represents one degree of temperature.)

9. Make a graph so as to keep the temperature of your
room each hour in the day for five days.

LESSON IV.

Make yourself a checkerboard and join the checker club.

1. Draw an 8-inch square, (b) Mark off inch-spaces on

all four sides, (c) Make as many inch-squares in the big



ARRANGED FOR INDIVIDUAL WORK 13

square as you can. (d) How many inch-squares are there
in one row? How many rows are there? (e) How many
inch-squares are there?

2. (a) In the first row at the bottom shade the one to
the left, (b) Now shade every other one in this row.
(c) In the second row from the bottom, shade the second
from the left, (d) Then shade every other one in this row.

3. (a) In the third row from the bottom shade the first
one to the left, and then shade every other one. (b) In
the fourth row shade the second one from the left, and
then shade every other one. (c) In the fifth row shade
the first one, omit the second, shade the next, and then
shade every other one. (d) Which one shall you shade
first in the sixth row? Omit the third, shade the fourth,
omit the fifth, shade the sixth, omit the seventh, shade
the eighth.

4. (a) In the seventh row, shade the first one to the left,
omit the second, shade the third, omit the fourth, and then
shade every other one. (b) In the top row shade the
second one from the left, and then every other one.

5. (a) Name the even-numbered rows. Is the first or
second shaded in these rows? (b) Name the odd-numbered
rows. Is the first or second shaded in these rows? (c) How
many are shaded in the whole square? (d) How many
are not shaded? (e) How many are shaded from one
corner to the one opposite it?

6. (a) In making your checkerboard, if you wanted
your squares to measure 1% inches, how long should yon
make your big square? How wide? (b) If you wanted to
make each square l 1 ^ inches, how long should you make it?
(c) If the small squares measured 1% inches, what would
be the length of the big square? (d) If they measured
1% inches, how long would the big square be?



14 SUGGESTIVE LESSONS IN NUMBERING

7. (a) If your paper measured 16 inches, how large
could you make your small squares? (b) If it measured

14 inches, the small squares would measure inches.

(c) If it measured 13 inches, the small square would

be inches long, (d) If it measured 17 inches, the

small square would be long.

8. (a) How large a checkerboard could you make from
a piece of cardboard that was 18 inches long and 15 inches
wide? What would be the size of the small squares?
(b) How large a checkerboard could you make from a
piece that measured 18 inches by 20 inches? (That means
a piece 20 inches long and 18 inches wide.) How large
would each of the squares be in this checkerboard?

9. A good size for a checkerboard is a 14-inch square.

Each small square would measure inches, (a) Get

a good piece of cardboard a little larger than this, (b)
Draw the big square, (c) How many points shall you
make in each side? How far apart will they be? (d) Draw
the small squares, (e) If you do not remember, it will tell
you in problems 2, 3 and 4 which squares to shade.

10. Your men can be made from empty spools. Saw
off the flat parts. You will need 24 of these parts. Twelve
of them should be painted with ink.

LESSON V.

1. (a) Draw a line six inches long. A half -inch below
this line draw another the same length, (b) Continue to
draw such lines until you have eight of them.

2. (a) Divide the top line into two equal parts, (b)
Each part is , and is inches long.

3. (a) Divide the second line into three equal parts,
(b) Each part is , and is inches long.



ARRANGED FOR INDIVIDUAL WORK 15

4. (a) Divide the third line into four equal parts.
(b) Each part is , and is and inches long.

5. (a) Divide the fourth line into five equal parts.
(b) Each part is , and is _ and inches long.

6. (a) Divide the fifth line into six equal parts, (b)
(b) Each part is , and is inch long.

7. (a) Divide the sixth line into eight equal parts.
(b) Each part is , and is inch long.

8. (a) Divide the seventh line into ten equal parts.
(b) Each part is , and is inch long.

9. (a) Divide the eighth line into twelve equal parts.
(b) Each part is , and is inch long.

10. Write each of the fractions that you have made
in the above problems with figures (%, %, etc.).

11. (a) How many fourths are the same as one-half?
(b) How many sixths? (c) How many eighths? (d) How
many tenths? (e) How many twelfths?

12. (a) How many sixths are the same as one-third?
(b) How many twelfths? (c) How many tenths are the
same as one-fifth?

13. (a) How many eighths are the same as one-fourth?
(b) How many twelfths are the same as one-fourth?

14. (a) How many eighths are the same as three-
fourths? (b) How many twelfths are the same as three-
fourths?

15. (a) How many sixths are the same as two-thirds?
(b) How many twelfths are the same as two-thirds?

16. (a) How many tenths are the same as two-fifths?
(b) How many tenths are the same as three-fifths?

17. One-half equals sixths; one-third equals

sixths. Which is the greater, one-half or one-third? How
much greater?

18. One-third equals twelfths; one-fourth equals



16 SUGGESTIVE LESSONS IN NUMBERING

twelfths. Which is the greater, one-third or one-
fourth? How much greater?

19. Two-thirds equals twelfths ; three-fourths

equals twelfths. Which is the greater, two-thirds

or three-fourths? How much greater?

20. (a) What is the sum of %' and %? i/ 2 and %=

(b) What is the sum of % and *4? 1 / 3 + 1 /4=

(c) What is the sum of % and 3/4? y 2 + 3 /4=
or and

21. (a) What is the sum of % and % ? 2 / 3 + 3 /4= ; or

(b) What is the sum of % and % ? %+% ; or

(c) What is the sum of % and % ? %+%= ; or

(d) What is the sum of % and % 1 %+% 5 or

(e) What is the sum of %, % and % ? %+%+% ;

or

(f ) What is the sum of %, 1/4 and % ? 1 /3+ 1 /4+ye= ;

or

LESSON VI.




1. (a) This circle is divided into how many parts?

(b) Each part is called It may also be

written



ARRANGED FOR INDIVIDUAL WORK 17



2. (a) How many twelfths in % of the circle? In
In 2/ 3 ? In %? In %?

3. (a) How many fourths of the circle in nine of those
parts? (b) How many halves in six parts! (c) How many
thirds in eight parts? (d) How many sixths in ten parts?
(e) How many fourths in three parts? (f) How many
thirds in one part? (g) How many twelfths in eleven parts?

4. (a) One-half is the same as ............... fourths, .._ ........... eighths,

............... sixths, ............... tenths, ............... twelfths, (b) One-third is

the same as ............... sixths, ............... ninths, ........... -..twelfths, (c)

One-fourth is the same as ............... eighths, ........ _____ twelfths.

5. (a) Two-thirds is the same as ............ sixths...... ..... -twelfths,

........ ninths, (b) Three-fourths is the same as ........ -..-eighths,

............... twelfths, ............... sixteenths.

6. (a) Draw a 2-inch square, (b) Divide this square
into four equal squares, (c) Divide each of these smaller
squares into four squares.

7. (a) One of these smallest squares is what part of the
big square? (b) Two of these little squares is what part
of the big square? What other way could you say it?

8. (a) Four of the little squares is what part of the big
square? (b) Ten of the little squares is what part of the
big square? (c) Sixteen of the little squares equals / 32 ,
As, /s, -/, /2, of the big square.

9. (a) Add % inch to a line % inch long. What is the
length of the line? (b) Add % inch to a line % inch long.
length of the line? (b) Add % inch to a line % long.
What is the length of the line? (c) Add % 6 inch to a
line % inch long. What is the length of the line?
(d) Add % 6 inch to a line % inch long. What is the
length of the line?

10. (a) Erase % inch from a line y 2 inch long. What
is the length of the line? (b) Erase % 6 inch from a line



18 SUGGESTIVE LESSONS IN NUMBERING



inches long. What is the length of the line? (c) Erase
% 6 inch from a line 1% inches long. What is the length
of the line? (d) Erase % inch from a line 2% inches long.
What is the length of the line? (e) Erase % inch fr m
a line l%e inches long. What is the length of the line?

11. (a) What length of line equals the sum of 2*4 inches
and 1% inches? (b) What length of line equals the differ-
ence between 2 1 /4 inches and 1% inches?

12. (a) What length of line equals the sum of 3% inches
and 1% inches? (b) What length of line equals the differ-
ence between 3% inches and 1% inches?

13. (a) How many hours are there in a day? (b) How
many hours in % of a day? % of a day? (c) How many
hours in % of a day? In % of a day? (d) How many
hours in % of a day? % 2 of a day? In % of a day?
In % 2 f a day?



I/I 1 1 / I "1 / "I *\/ "I / O1 / ^/

%-%- iy 2 -%= 23/4+ 7/ 8 =

25/ 8 _3/ 8== iy 4 -%= iy 4 +2%=

1%+%= 1%+%- 1%+%-

LESSON VII.

FEACTIONS
DEILL SHEET ADDITION I.

f 1/ O/ O/ O/ I/ "I/ Q/ T/ T/

2 72 % 73 % 72 72 % 78 /10



ARRANGED FOR INDIVIDUAL WORK 19



% y 2 y 2 y 2 y 2 %o %

% % % % %



DBILL SHEET ADDITION H.
% % % y 2 % % V 2 Vs % %



% % X /2 % % V2 % % % %

% y 2 % % % y 2 y 2 % %o y 2

1 / 2/ ^/ i /



20 SUGGESTIVE LESSONS IN NUMBERING

DEILL SHEET ADDITION III.
%%%%%%

% % % % %0 V4



y 2



% %

%0 %

%o y 2



DRILL SHEET ADDITION IV.

6% 9y 2 7y 3 5y 4 9y 2

71/3 834 82/ 3 934 7% 5% 3%

ey 2 4%



ARRANGED FOR INDIVIDUAL WORK 21

31/4 5% 92/3 8y 2 35/ 6 42/3 67/ 8

QO/ rr-i / O"l / ^"1 / m / f\

0/3 '72 072 '% "73 "



8% 9% 7% 92/ 3 4%

72/3 81/3 93,4 9i/ 6
7%



DRILL SHEET ADDITION VI.

16% 723/ 5 39 5/ 6

5434 1834 18/io 48%

16%o



582/ 3 753/ 4 i 5 3/ 8 23%

30*4 182^ 1634 48y 2

ISi/g 19y 2 17%



571/3 ey 2 iey 2 273%

962/3 434 8%



22



SUGGESTIVE LESSONS IN NUMBERING



LESSON VII.



FIG. t

1. (a) Use your ruler to find the length of the bottom
line, (b) Measure the four parts of the top line, (c) Find
their sum. (d) How can you tell if the answer is right?
This is called "checking the answer."



2. (a) What is the length of the bottom line in Fig. 2?
(b) Measure the parts of the top line, (c) Find the sum,
but be sure your answer is correct.



F I G . 3

3. (a) What is the length of the bottom line in Fig. 3?
(b) Measure all the parts of the top line, (c) Find their
sum. Is your work correct?



ARRANGED FOR INDIVIDUAL WORK



23



PIG. 4

4. (a) Measure the bottom line in Fig. 4. Measure the
lines marked 1, 2, 3. (c) Could you find the length of line
marked 4 without measuring it? How? (d) Find the sum
of the lines marked 1, 2, 3. (e) Subtract this sum from
the length of the bottom line, (f) Measure line marked 4
to see if your answer is correct, (g) Measure the three
broken lines, (h) Find their sum. (i) Measure the line
marked b. (j) How much greater is the answer in (h)
than the answer in (i) ?



24 SUGGESTIVE LESSONS IN NUMBERING






-



/>
I - rflfc



PIG. 5

5. (a) Measure lines a, & and c in Fig. 6. Find the
sum of these numbers, (b) What line can you measure
to check your answer? Is your work correct? (c) How
much longer are a and c together than 6?



FIG.6.



ARRANGED FOR INDIVIDUAL WORK 25

6. (a) Measure lines g, h and i. What is the sum of
the three! (b) Which line can you measure to check this
answer? Find out if your answer is correct, (c) How
much greater is the sum of a, b and c than the sum of
g, h and il

7. (a) Measure the five parts of the top line, (b) Find
the sum of these lengths, (c) Which line can you measure
to check the answer? Measure it. (d) How much farther
is it from a to b than it is from & to c? What measure-
ments have you that you can use to find the distance from
a to ft? (c) How much longer must you make the line
bd to reach the bottom line? (f) If this part were added
on to bd, how long would the line be then? (g) Which
is the longest line in this figure? Which is the shortest?


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