275 101 15MB
English Pages [100] Year 1965
$1.29
MATHEMATICS"-^
0, GOLDEN
Mastering Arabic Numerals A Workbook with Self-Teaching Text and
Learning Exercises
by IRVING ADLER, Ph.D.
• •• l|l|l
1 |
1
f
I
t
1
I
I
I |
1
j
']
•
m
n
*
i
i
il
t
1
1
i
1 i
l|l|l|l|l|l|l|
1
|
1
III
TO THE PARENT AND TEACHER MATHEMATICS — GRADE 3 matics both tion for skill.
in this
is
based on a careful study of the methods used
country and abroad. The aim
is
to
to teach
mathe-
develop understanding as a founda-
The book includes the best practices found anywhere and has the freshness
originality that are characteristic of all the author's books.
and
book, the third
In this
numbers, and the
first
in
a series of
steps
in
six
,
addition and subtraction are extended to larger
multiplication
and division are introduced. The book begins
with a quick review of the basic addition and subtraction facts, proceeds with several
methods
of thinking out
more advanced sums and
based on the place-value concept. Multiplication times three, ten times four, and ten times is
five.
is
differences,
developed through ten times two, ten
The concept
applied to division into groups of two, three, four, and
form
of
games, are provided, with verbal problems and
Other concepts and
skills
and ends with examples
of division into equal
five. Drill exercises,
groups
often
in
tests.
developed include: fourths, thirds, multiplication by one,
counting money, making change, use of the dollar sign, the calendar, telling time at
minute
intervals, the
To strengthen of objects in the this
his
thermometer, and measurement with a
five-
ruler.
understanding of number ideas, each child should work with groups
ways suggested by the exercises
in
the book.
A
kit of
suitable objects for
purpose should include: several strings of beads, with ten beads on each
board squares, and strips containing ten squares
and
the
half-dollars; checkers, buttons,
in
string; card-
a row; pennies, nickels, dimes, quarters,
and dominoes.
ABOUT THE AUTHOR Irving Adler received his Ph.D. in pure
teacher
in
the
New
mathematics
at
Columbia University. He was a
York schools for twenty years, including six years as chairman of a high-
school mathematics department. Dr. Adler has taught at Columbia University and Benning-
ton College, and was the keynote speaker at the Washington conference of state supervisors of mathematics, called by the U. S. Office of Education in June, 1961. of about fifty
He
books on mathematics, science, and education, and co-author
is
the author
of thirty
more.
MATHEMATICS-GRADE 3 Mastering Arabic Numerals A Workbook
with Self-Teaching Text
and Learning Exercises
by IRVING ADLER, Ph.D. Author of The Giant Golden Book of Mathematics,
The New Mathematics, and Magic House of Numbers
Illustrated
by Dick Martin
Copyright ©1965 Western Publishing All rights
Company,
Inc.
reserved.
GOLDEN®. GOLDEN® & DESIGN, and A GOLDEN BOOK® are trademarks of Western Publishing Company, Inc.
A GOLDEN® BOOK Western Publishing Company, Racine, Wisconsin 53404
Inc.
No part ot this book may be reproduced or copied in any form without written permission from the publisher. Produced in U.S.A. Thirty-eighth Printing, 1983
One
One Hundred
to
Write the numbers from one to one hundred on the beads of this frame.
n
\t~
n
6
i
M)GO€ *
.
i
r~
Woods
John
Is
find his in
lost In
the woods. Help him
way home.
Start in the box
the middle where the
number
1 is.
Continue
in
this way,
box at a time, to until
moving one
3, 4, 5,
and so on,
you reach 35 on the road home.
or right or
When you have found the path out of
left
or through a corner to a box with
the woods, draw a line from box to
the
number
Move one box up or down
2.
ox to show
it.
page 3
Counting by Twos, Write the numbers you say
Fives,
and Tens
when you In
count by tens up to 100. Then put circles
around the numbers you say when you int
•••••—••••• ••••• •
by twenties.
the
the
first
square write
number shown on the
frame. Then count by twos
up to 60.
Count by
fives
up to 100.
In
••••> >• >• • «> M> • ••••
the
the
first
square write
number shown on the
frame. Then count by fives
up to 100.
Write the
number shown by the beads
on each frame.
•••••
In
••••• ••••• •••••—••
the
the
first
square write
number shown on the
frame. Then count by tens
up to 95.
page 4
Counting \
One dime
is
One penny
To
worth
is
dime, 5 for each nickel, and This
is
called counting
A
1
One
$.
1
worth
find the value in cents of a
Money nickel
is
One quarter
*.
group of coins, add 25
for
worth
is
worth
*.
u
each quarter, 10 for each
for each penny.
money.
Example
10
Count the money shown
in this picture.
Write under the coins the numbers you say as you count. Value:
^W 2S Count by
fives until
One quarter as
IT
is
W
S
Itj
you have 25$. Cross out the coins
worth the same
left
One quarter
nickels.
You can exchange dime.
il
*
over.
is
worth
dimes and a
nickel.
1
nickels for
one
One dime and
*C
is
worth a nickel
pennies. page 5
Dollars
and Half
Dollars
Count the money shown by each group of coins.
Under the coins
write the
bers you say as you count.
The value
of each quarter
shown
is
by the dimes and nickels at the
right.
Count the dimes and nickels by tens and fives to
answer these questions:
One quarter
is
Two quarters
worth
are worth
Three quarters are worth
A
dollar
is
worth the same as four
quarters.
A
dollar
is
worth
This coin
is
worth half
A of a dollar. It is
or
page 6
worth quarters.
dollar
is
worth the same as
dimes. $,
A
half dollar
dimes.
is
worth the
same as
num-
$1.00 means
1
dollar
Using a Dollar Sign and no cents. $4.75 means
dollars
and
cents.
$1.15 means
dollar
and 15 cents.
$3.48 means
dollars
and
cents.
$2.34 means
dollars
and
cents.
$7.29 means
dollars
and
cents.
means
dollars
and
cents.
$8.56 means
dollars
and
cents.
l$5.62
Change John bought a book
for 28*.
He
for
paid for
a Half Dollar it
out these coins for change, starting at the
with a half dollar.
The storekeeper put
left.
Under the coins are the numbers he said as he
made change.
Count the change. Each of the purchases shown below was paid for with a half the coins shown with each purchase to the
make change.
It
is
dollar.
worth
$.
Use some
of
Write under the coins you use
numbers you say as you make change. Next cross out the coins you do not
use.
Then count the change.
page 7
Each purchase below was paid
for with a half dollar. Follow the directions
on page
7 for making change.
The change itself is
worth
Price:
420
//
The change V
itself is
tMM
worth
i
Price:
170
Put
five pennies,
change
for
Price:
240
There
is
Price: 3€ *
There
There page 8
is
nickels,
and two dimes on your desk. Use the coins
each purchase. Then count the change to see how much
A
half dollar
in
A
A
paid.
was
paid.
was
change.
Price:
11*
There
is
Price: 16 *
There
change.
half dollar
in
was
change.
half dollar
in
is
Price: 3C H
two
paid.
is
Price: 12 If
There
is
A
is
quarter was paid.
in
A
it
to
change.
quarter was paid.
in
change.
A quarter was in
change.
paid.
make
worth.
Counting Backwards Count backwards by twos from 60
Count backwards by tens, from 100.
to 22.
60
[100
I
Count backwards by
fives,
from 100.
100 Count backwards by twos from
19.
19
Places in Line
The people are standing tickets for the zoo.
beginning of the
If
line to
in
buy
you count from the
line,
person whose number
you say that the is
21
rule
is
used
the thirties,
in
the forties, and so on. Here are the numbers of
some people
in
line.
To show
their places in line, write after the
is in
the twenty-first (21st) place.
The next places are
The same
ber the correct ending:
st,
num-
nd, rd, or th.
called
twenty-second (22nd),
35
42
51
33
61
27
82
73
76
43
80
38
52
60
81
twenty-third (23rd),
and twenty-fourth (24th). In
the twenties you use the st ending for
the place where the numeral ends
nd where the numeral ends
in 2;
and rd where the numeral ends You use the th ending for
all
in 1;
in 3.
the rest
page 9
Numbers Write each set of five numbers
in
order,
in
Order
Write the missing numbers.
starting with the smallest.
35
31
39
32
36
78
28
48
38
58
21
19
42
63
80
After each of the numbers, write the
This candy was paid for with a dollar.
next higher number.
Use some
of the coins
make change. 39
25
shown below
Write under the coins you
use the numbers you say. Then count the change.
52
19
gZggm
99
61
Before each of the numbers, write the next lower number.
I
page 10
to
20
30
50
31
46
29
58
75
45
61
19
44
100
The change
itself is
worth
Fourths
Sue cut her sandwich
Then she cut each Half of a half
is
fourths of a sandwich
a whole sandwich.
There are in
half in half.
called a fourth.
There are in
in half.
fourths of a sandwich
I
I
Put a circle
half a sandwich.
If 1
fourth of a sandwich
sandwich are
and
who
1
half
full.
Put a star is
taken away
from a whole sandwich, then| of a
is
left. 1
half a
1 fourths
sandwich
is
in
one fourth
Put a cross is
the box under the jar that
in
the box under the jar that full.
in
the box under the jar that
three fourths
full.
fourths of a sandwich equal a
e sandwich.
To cut something cut
it
into fourths,
pieces,
into
you must
and the pieces
must be equal.
Draw Draw
circles
around the sandwiches
that are cut into fourths.
lines that
cut this pie
r
into fourths. First cut
it
in half.
Then cut each
half
in half.
Here
is
t a picture of a piece of cloth.
Draw if
lines that cut
it
1
1
into fourths.
_LL
,
page
11
Odd and
Even
Draw a
Sam
John
circle
around each even number.
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Half of an Even
Number
® Divide the checkers equally between
John and Sam. Cross out one checker
and draw
it
under John. Cross out an-
other and draw
under Sam. Do
it
this
over and over again as often as you can.
Are any checkers
left
over?
no
yes
How many checkers does John get? When 2 people share things equally, with none If
one
left,
is left,
the
The number 8 John has
the
number
number
is
even.
odd. odd.
even.
is
is
half the checkers.
Look at the Half of
Write the stars.
8
is
even number.
circle
Then
write
answers.
number shown by each
Then draw a
tree.
Half of 2
is
>
set of
around each
because Half of
4
is
i
because Half of 6
8
are 4.
ar id is
»
because Half of
are 2.
ar id
are 6.
ar id is
f
because
ar id
are 8.
ar id
are 10.
1
Half of
1( 3 is
because page 12
your
Counting by Twos, Threes, and Fours Count by twos from 6
Count the milk cartons by twos.
to 28.
6
28 Count by twos from 7 to 29. There are
cartons here.
7
29
Count the stars by threes.
•••••• *•••••• • •••••• •
Count by threes up to 36.
There are
Count by threes from
1 to
stars here.
34.
Count the children by
fours.
1
Count by threes from 2 to 35. 2
Two
steps of counting by twos
There are is
children dancing here.
like
one step of counting by fours. Count the cherries by threes.
Count by fours up
to 20.
Count by fours from
1 to
II III 17
There are
cherries here.
page 13
Counting by Mixed Groups It
saves time to count by groups, even when the groups are not equal,
These marbles were counted from
As each group was counted, the new
8 Count these groups from groups, as
in
left
total
10 to right.
left
was
13
to right.
written under
15
it.
17
As you count, write the
19 totals
under the
the example above.
page 14
.
Adding a You can add by adding a
little
Little
at a
Time
at a time.
9+3+3+3
9+9 Example Since 5
= 3 + 2,
8 + 5 = 8 + 3 + 2:=
11 + 2 =
+3+3 13.
+3 Add a
little
at a time.
8
+4=8+2+2
7+4=7+2+2 =
9
+2
+2 = 8
+7=8+4+3
8+6=8+2+2+2 +
2
8
+4+4
+2
+4=
8+6=8+3+3
9+4=9+2+2 +
3:
+6=9+3+3
9+8=9+3+3+2 +3+2
=n +2 = 9+7=9+3+3+1
9+5=9+2+
=
+3 + 1 +1
=
page 15
Completing Ten Write the to
number needed
8+5
complete 10.
7
+D =
8
+
= 10
6
+
= 10 = 10
3+n
4+
10
9
+
5
+
2
=
first
Here 7
8
is
Add by
+
7
=8+2+5 = 10 + 5 = 15
written as 2
was needed
first
+
=
10
6+6=
6-f
=
5 because 2
to complete 10.
+ 4 = 9+
10
6+9 = 6+
completing ten.
10 7
two steps, by
+ 9=9+
=
10
+
+ 8 = 9+
9
7
+ +
+8= 6+ 10
+
page 16
10
-
+
+ 6 = 7+
=
+ +
~>n +
=
+
+ 7 = 7+
10
6
=
+
+
+ 5=
9
+ 10
9
J+U
completing ten.
Example
9
in
=
+
+ 9
Sometimes you add
10
+ +
J+Q +
=
Doubles and Near Doubles
••••••••
Double5
=5+5=
Double 6
=6+6=
Double7
=7+7=
Double8
=8+8=
Double9
=9+9=
Double 10
Some sums
Add.
1
!
1
|
=10 +10 =
are easy to find because
they are near doubles.
5
+ 6is 1
more than 5
+ 5.
+1 =
505 + 6 =
in
Fill
8+Q8+
6
+ 7 Is
1 less
than 7
506 + 7 =
8
+
=
4
8
+
= 15
12
+
5
9
+
= 11
9
+
4
9
+
= 13
7
+
2
7
+ [j=13
7
+
6
7+Q-15
+ 9isllessthan9 + 9.
So8 + 9= 5
Q
3
9
-1 =
So7 + 8= 8
+ 7.
-1 =
the blank spaces.
+ 6 is 1
les sthar
So5 + 6 =
-1
|
1
6
=
Draw
a circle around the correct sum.
+ 6.
-1 =
12
6
+8
13
[14 7
+7
ll
8
+5
12
.4 6
+ 7 is 1
more than 6
So6 + 7 = 7
+1=
+ 8islmc)rethcin 7 + 7.
So7 + 8 = 8
+ 6.
13
+1= 13
+ 9islmc)rethein 8 + 8.
So8 + 9 =
+1=
9
+3
12
15 page 17
Subtracting in
Two In
Steps by Stopping at Ten
each exercise take away the number of circles
you are subtracting by
Take away
11-1
1
from
Take away 2 from
11-1 =
1
=
9.
Take away 3 from first step,
11
11-3 Do each
—
1
=
of these subtraction exercises in
—
11. 11
1
=
10
You can do
11.
with purple.
in
in
it
two steps:
10
-
Then 10
11-2
them
filling
So 11 11.
Do
-
2
it
in
=
9.
two steps.
In
the
take away enough to leave 10. 10,
and 10
two steps.
-
2
First
= 8.
So 11
-
3
= 8.
take away enough to
leave 10.
11-4
11-5
To take away 4, take away
ii-o=io
To take away
(and |
|
5,
take away
|
Soil
take away
To take away
(and
7,
take away
[
|
io-Q=n
ii-n=io
10-
Soil
-7 = |
11-8
|
11-9
To take away 8, take away
To take away
i J
n-Q=io io-QSoll-8=|
(and |
Soll-6 =
page 18
|
11-7 |
—0]= 10
|
|
|
11-6
11
|
-5 =
|
6,
|
io-[>n
Soll-4=|
To take away
[and |
|
9,
take away
|and
J
n-Q=io io-n=n Soll-9 = |
|
Subtract
in
two steps. Stop
at
10 on the way.
12-3 Takeaway
12-
12-5 Takeaway
and
=
10
10
12-3 =
12-1
-n-
and
on
10-
1=10
12-5 = L
12-6
12-7 Takeaway
Takeaway
and
12-Q.lO 10-Q
12-7-Q
D
12-
10
13
Takeaway
and
i3-Q=io
lo-Q-Q
=
13-
13-4 =
14
Takeaway
and
141
14-6^Q
Takeaway
15-
10
—
1
1=
—
1
1=
and 10
[=10
14-5=Q
n
15-6
7
Takeaway
and
'
=
10
14-5
--io 10-Q
15-
D D = D
and
13-6
14-6 Takeaway
10
12-6 =
13-4 Takeaway
and
and
«
— 15-
10
K 7 =
D-D
15-1
[=10
15-6
H
1
10
page 19
Sub
ract in
two steps. Stop at 10 on the way.
2-4:
2-
6-7:
=10
10-
= 10
=
12-4 =
10
16-7 = -5:
3-8:
3- n=io
io
-n
13-8=[] 3- 7: 3-
= 10
10
-
13-7 = -8:
-8:
D
=10
10
-Q
.7-8-n 4-8:
4-
2-9:
=10
10-
=
2-
=10
10-
=
12-9 =
14-8 4-7:
5-9:
4-q=io lo-n-n 14-7-n
*-n-io io-n-n
3-9:
4-9:
3_
=10
10-
13-9 = page 20
=
15-9 =
4-
=10
D
10-
14-9 =
=
Complete each family of four number
Fill in
6 8
the missing
num bers.
H
I
+
8
=
-6 =
6
stories.
1
+
1
=
-7 =
7
I
-8 = 8
9+9=
-9=9 page 21
Half of an Even 12
O O O O O O
Here are
o o o o o o
12
that
circles
have been put down two at a
A
time.
group of twelve
= 20 + 6 Half of 26 = half of 20 +
26
two equal groups.
J
28
= 20 + 8
Half of
28=half
number
circles as the
down two
tells
you
circles at a time, with
each side of the
of
20
=
each chart below, draw as many Put
to.
16
8
half of
=
=
20 + 10 Half of 30 = half
30
+
+ of
20
+
half of
10
one on
+
line.
14
a-
+
10
circles into
Half of 12 equals
In
6
half of
the
divides
line
Number
18 Half of
40
=
20
+
20
20
=
Half of 60
Half of 80
Half of
24
= +
100=
=100
22 20
Half of 14
Half of 16 [
Half of page 22
22
|
Half of |
20
|
24
70
=
+
90
=
+
46
10
Half of
50
=
Half of
70
=
Half of
90
=
= 40 + 6
Half of
46
=
62
= 60 + 2
Half of
62
=
84
=
Half of
84
=
Half of
44
=
10
10
|
=
|
Half of
= 40 +
=
|
Half of 18
50
=
[
44
Ji
n
Fourths Here are some groups of things arranged
group
is
printed at the
left.
in pairs.
The number
of things in each
Count by twos to check each number.
^f ^k ^^^^r^^^ 12
•rRT
16
r
20
^
a*-
In
^S ^8
«nl
jl
h^hzAzheh; htz$mhzhi
\lt\ 28
^r »rl
w*
w w W
\\\\\
Lf jBL
w
&
far 7\
xt
44444444444444
each group above, draw a
Then draw a
line
line
from
left
to right that divides the
from the top down that divides each half
in half.
group
in half.
One
fourth of
8
is
One
fourth of 12
is
One
fourth of 16
is
One
fourth of
20
is
One
fourth of
24
is
One
fourth of
28
is
Four groups of
each make one group of
Four groups of
each make one group of 12.
Four groups of
each make one group of 16.
Four groups of
each make one group of 20.
8.
page 23
Calendars Put
in
numbers
to complete the calendar for these two months.
March has 31 days. June has 30 days.
1^**^ Sunday
Monday
M^^M
MARCH Tuesday Wednesday Thursday
Sunday
Monday
+-
2
= 40 + 6 + 2
-*+.-
+
3
=
=
52
+
5
74
+
3
=
21
+
7
52
+
3
= page 29
|
Adding Tens Count by tens
one hundred.
to
Use dimes
= 70 + 20 = 60 + 20 = 30 + 30 = 50 + 40 = 30
[
]
CD CD CD CD CD 10+
10
CD
20
30+
10
CD
40+ 10=
50+
10
CD
60
+
10
=CD
70+
10
CD
80
+
10
=
+
10
=
1
I
1
I
+
sums.
to find these
20
+
50
20
=
= 80 + 20 = 40 + 30 = 30 + 40 = +
40
20
Completing the Next Ten 21
+ 9=20 + 1+9 = 20+
32 + 8=30 + 2+8 = 30+
1
|
1
|
=
54 + 6 = 50+4 + 6 = 50+ 67 + 3 = 60 + 7+3 = 60+ Count by tens
3 dimes are worth
4 dimes are worth 5 dimes are worth
more
to
complete 10.
45 needs
more
to
complete 50.
3 needs
more
to
complete 10.
73 needs
more
to
complete 80.
6 needs
more
to
complete 10.
86 needs
more
to
complete 90.
cents.
cents.
8 dimes are worth
cents.
9 dimes are worth
cents.
10 dimes are worth
cents.
30, you
5 needs
cents.
7 dimes are worth
61
may use dimes.
j
j
v.
30*
Together these dimes are worth
page 30
70
46
+ZD = 50 + ^]=50
+C
30
48
27
+
30
33
+
+CH = 60 23 +EH=30 85 +r"1 = 90
+
I
40
1
50
59
X:
20*
So 20
+
24
42 -^—
=f
cents.
cents.
V
l
cents.
6 dimes are worth
+
1
to find the answers.
2 dimes are worth
To add 20
=T =T
+ 30 =
Complete the next
82+ 56+ 43
+
= =
ten. ;n.
64
+
31
+
25
+
= ^zz
Adding by Completing the Next Ten
Example To add 28
number as
number
a
+
3, think of
each
Think out these sums by
68
+
+
3
3
=
28m
1
+
1
= 68 + 2 +
1
48
+ 3=
29
+
39
to
of the last three pennies,
them with the
make 10
cents.
penny
left
So 28
+
We can
Add the 10 cents
3
= 29 + 1 +
1
+
1
= 39 +
1
+
1=[
59
+
+* =
=
[
49
+
3
=
69
+
3
=
=
37
+
4
= 37 + 3+1=}
49
+4=
49
+1+3 =
58
+4=
58
+
38
+
5
= 38 + 2 + 3 =
48
+
5
= 48 + 2 + 3 =
= 67 + 3 + 2
37
+
5
= 37 + 3 + 2 =
-+2-[
47
+
5
= 47 + 3 + 2 =
31.
think out the
sum
too.
+
2
+
1
|
1
without dimes
complete 30.
28
2
= 39 + 1 + 2
3
=
=
+
+
=
3
=
79
3
to
5
+
+
58
|
3
28 needs 2 more
+
39
|
+1=
+
complete 10.
67
2
1
=
59
to
3
+
r—
Add the
8 needs 2 more
+
49
2
to
over to get 31 cents.
and pennies,
28
2
78
and
eight pennies above
the two dimes to get 30 cents.
+
2
+
+
=
join
complet-
ing another ten:
of cents.
78
Take two
first
= 30 + 1 =
31
2
+
2
|
|
|
|
|
|
=
page 31
Add by completing the next ten
= 29 +1+4 = 39 + 5 = 39 + 1+4= 56 + 5 = 56 + 4+1 = 76 + 5 = 76 + 4+1 = 29
+
5
~ |
53
+
8
44
+
8
27
+
8
42
+
9
54
+
9
53
+
+-
54
+
+-
= 26 + 36 + 6 = 36 + 45 + 6 = 45 +
+
10+12=10+10+2=
+2=
+
30+12=30+10+2=
+2
= 85 +
+
50+16=50+10+6=
+6:
= 37 + 47 + 6 = 47 + 58 + 6 = 58 + 68 + 6 = 68 + 29 + 6 = 29 + 39 + 6 = 39 +
+
70
+
15
+
30+
13
+
40+
17
+
40+
15
+
80+
14
+
=
40+
16
=
26
85
37
+
+
+
6
6
6
+
Splitting Off
34
+
7
= 34 +
+
44
+
7
44
+
+
36
+
7
36
+
56
+
7
Q>[ 45 + rj+n =
45
+
7
56
53
+
+
Here
zi
_
+
7
58
+
7
68
+
7
29
+
7
37
+
7
page 32
68
70
+
-
+
5
ZI
=
= \2 40+10 + [~ =
30
+
10
~| |
+
3
60
+
12
70+13 1~
|
20+11
another way of thinking out sums.
+ 8=50 +
3
+ 8=50+
11
=61
=
49+2=40+9+2=40+
44+9=40+4+9=40+
+
5
= 70 +
= 80 + 23 + 9 = 20 + 45 + 9 = 40 +
+n+n
10
66+7=60+6+7=60+
76 85
is
=
Ten
84
+
8
36
+
9
= 30 +
76
+
8
=
70
+
i
Thinking Out Subtraction
To take away 2 from 25, use brown crayon to
fill
in
2 circles
in
the last
line.
25-2 =
=
21
-
22
- 1=20 +
1
20
+ 2
1
-
-
1
1
=
20
"L
24-1 = 20+4-1=20+
rn=
25-
1
=
-
1
=r
j
26-
1
=
28-
1
=
32-2 = 30 + 2-2 == 30+ crayon to
fill
from 16, use brown
1
in 1 circle in
16-
1
=
the last
20
= 20 + 1 =
23-1=20 + 3-1 = 20+
27
To take away
=
+
=
34-2 =
36-2 =
=
45-2 =
line.
38
-
2
55-2 =
65
-
2
=
86-3 = 80 + 6--3=80+
28-2 =
74-3 =
= 98-3 =
57-3 =
65-3 =
97
4
=
75
4
=
59
5
=
87-5 =
66
5
=
48-5 =
56
6 =
38-6 =
57
6 =
29-6 =
78
7
=
89-7 =
27
7
=
48-8 =
59
8
=
69-8 =
79
9
=
59-9 =
MM MHm
page 33
Taking As you you
fill
will
in
Away
from Tens
the missing numbers,
be dividing these ten stars into
two groups
in all
possible ways:
********** 1+Q=10
2+|
|=10
3+Q]=10
4+|
|=10
5+Q=10 6+| 7+Q=10 8+| 9+0=10
|=10
Subtract by
number of line with
filling in
|=10
20-1 = 10+10-1 = 10 + 9 30-1 = 20 + 10-1 = 20 + 9
the right
40
-
1
=
50-1
60
-
1
=
70-1
80-
1
circles in the last
purple crayon.
90-
1
20-2=10+10-2=10+1
20-2 = page 34
|=[
30-2 =
40-2 =
50-2 =
60-2
70-2
80-2 =
IBHwrnHHUi
30-4 =
=
50
4
70
4
40
5
90
6
50
7
30
8
50
9
.
60-4 =
19
Subtracting in
Two
Steps
Tof nd 46 — 46
Take away 4
brown 2 in
6
in
fill
2 more circles
in
the second
fill
82
-
2
-
2
= 20
20
-
2
=
55
5
in
1 circle in
2 more circles
31
-
1
the last in
the third
in
42
-
2
= 40
in
with
Then
si-
=
708,
take away 5 and
50
6,
take away
i-izd
1
and
-.-.
fill
line.
First
fill
circles in the last line.
3 more circles
take away 6 and
30-2 =
= 30
Take away 5 from 42.
brown 2
fill
line.
9,
= 50
Tof nd 61 —
brown
=
80-
76-6-70
fxxfTTfj First
take away 2 and
line.
Tof nd 55 —
Take away 3 from 31.
4,
= 80
Tof nd 76 — 22
=
40-
with
Then
circles in the last line.
take away 6 and
= 40
Tof nd 82 — from 22. First
8,
in
the fourth
40 - 3
in
Then
line.
=
with
Tof nd 83 —
8,
take away 3 and
Tof nd 28 -
9,
take away 8 and
6,
take away
)"=
28-
fill
Tof nd 54 —
4 and
54-4 = page 35
Separating the Tens
+
You can add 40
12 by using dimes and
pennies.
think «v
40 '
^
/
/*
F
u
\
f)\V
12*
Put
40
rilii'mijii;
'fill! Ill)
it
out this way:
15
=
10
+
10
+
10
= 20
+
11
So 15
you can
11,
5
= 10+1
11
+ 1=6
5
=20 + 6 =
all
+
the dimes together.
12
= 40 +
first
10
+
2
separating the tens.
+6
30
+ 22 = 30 + 20 + 2 =
+2=
50
+ 26 = 50 + 20 + 6 =
+6=
= 40 + 30 + 5 =
+ 5=
60 + 23 = 60 + 20 + 3=
+3 =
+ 44 = 30 + 40 + 4=
+4 =
40 + 35
50+17 = 20
+
33
|
|+7
=
+
3
=
same way:
10
+
2
+
3
=
12
10
+
6
+
2
=
+
23
=
10
+
20
+
5
+
3
=
+
23
=
10
+
20
+4+
3
=
13
16
+
15
14
'
".,>
.'*_;.. '>.
MUM+K
26+31
™
the
in
= 10+ = 10 +
12+
= 50 + 2 = 52
20+16 = 20+10 + 6 =
26.
II
Think out these sums
Add by
30
To add 15 and
42+15=-
|
1
+
1
1
+2 + 5 =r + 1+4 =
21 + 14
[Z>[Z>i+i-[
31 + 11
32+12 =
1
1
14+15 =
|
1
+
1
l
+2 + 2=["
+
1
|
+4 + 5=|"
=
80+18 =
|
+8
65
+
32
=
|
41
+
12
30
+ 51=
|
+1
12
+
21
=
|
15+
12
40
+
24
=
1
+4=
13
+
16
=
|
17
+
11
20
+
38
=
|
|
+8 =
11
+
11
12
+
12
60+
19
=
13
+
13
14
+
14
=
1
+9 =
=
1
+
25
=
[
+5 =
11
+
18
=
16
+
14
=
1
30 page 36
Taking
Away
Tens j
To take away
10, cross out
-
20
10
one row.
=
* *
P^C
/Jv
/|s
*
^F
*
*
*
*
*
*
*
*
*
3k
*
*
*
*
*
^
^C
PfC
*
*
*
* *
* *
*
* * ^ * * *
*
*
*
*
*-
*
33-20 = *
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*•
*
*
*
*
*
*
* * * * * *
* * * * * *
* * * *
To take away 20, cross out
1
4
* * * * * ^ * * * * *
*
* rows.
26-
40-20=1"
********** ********** ********** *&
^^
"^ ^^
M^
^^
SW
^^
*>i'
^^
^^
*^^
^^
^^
"^K
^^
^^
^^
40
60
10
30
20
70
30
80
40
70
50
80
60
- 70 80 - 80 100 - 90 80
- 30
= = =
= = =
*•
*
* *
*
* *
= 57 - 30 = 74 _ 20 = 52
10
- 70 90 - 80 90 - 90
90
* X
*-
= * * * * *
mam—^nm
rows.
90-40 = 60 - 50 = 90 - 60 =
10
15-10 =
= 50 - 20 = 90 - 30 = -
>|v
^t
= 70
•
^^
32 To take away 30, cross out
*
77 71
&'. 5
-
10
- 10 - 30 - 30
_ 80 95 - 90 77 - 70
20:
42
10
67
- 30
=
= = =
82 - 70 = 64 - 50 = 55 - 30 = 93
64
mm
= = = page 37
Taking
Away
Tens and Units
To take away 12 from 24, you can use dimes and pennies.
••*• Subtract by crossing out the right
number
of
24
-
12
=
23
v-
12
=
32-
11
dimes and pennies.
11
-
Find
You can also think out subtraction without using dimes and pennies.
To
find
42-
Find
40-
10
and
2-
1
so
42-
11
-30,
11.
48
-
= 1, = 31.
=
48 - 12 75
-
,8
56
—
50-
10
and
6-
2
= 40, = 4,
so
56-
12
= 44.
—
j
1
Find
3 \6
-
=
-
1: 2
,5-
2^
=
13.
j
,6- 3 !
36page 38
- 2
12
75-
12,
think
=
=
— find
1
12.
40 - 10
Find
To
11
50-10=f A54- 11 =
11,
think
54-
=
-
1; 3
=
=
3
Subtracting in Three Steps To find 61 Because
and
33, think of
33 as 30 and
3.
of the 1 in 61, think of 3 as 1
2.
- 30
61
-
=
—
}
-2 = To subtract 23 from 42, think
20 and
3. First
42-20 =
of
23 as
take away 20.
To
22
6.
Because of the 2
Do
3. in
42,
it
in
first
-
16, think of
Because of the 5
and
Then take away
45
find
1.
Take away
take away 2.
So 42
- 23
=
20
1.
45-
19
19.
To
find
73
take away
To find 51-14, think of 14 as 10 and
and
3. First
away 51
-
1
and
10
1 in
51, think of
4 as
4. 1
take away 10. Then take 3:
= 41
41
-
40-3 =
1
10, 5,
and
-5
10
imrngmmm
Because of the
45, think of 6 as 5
two steps.
22-2 = 20 Then take away
in
16 as 10 and
= 40
•
-
24,
1.
Find the Hidden Picture
«
• 2
>
1
• 1
•;2
• 6
• 7
•
4
• 5
8
• 9
• 14
•
• 16
•
•
17
• 18
•
15
19
20
•
•
3 •
13
•
•
•
•
•
•
•
•
•
21
22
23
24
25
26
27
28
29
30
•
•
•
•
•
•
•
•
•
•
32
33
34
35
36
37
38
39
40
31 •
•
•
•
•
•
•
•
•
•
41
42
43
44
45
46
47
48
49
50
• 51
• 52
•
•
•
•
•
•
•
•
53
54
55
56
57
58
59
60
•
•
•
•
•
•
•
•
•
•
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
•
•
•
•
•
•
•
•
81
82
88
89
90
•
•
91
v
83
.
n3L
you
If
• a 85
•
•
•
•
•
•
95
96
97
98
99
you
join,
find out
of a dot. Put
which
6
g.
19
69
+
4=
h.
8
55
+
7
i.
1
d.
44
+
8
j.
1+2 =
e.
37
+
5
k.
5
f.
23
+
9
I-
c.
page 40
+
[
17
9
+
Go on
= 7
=[
a.
Then
answer to
to the dot of the next
answer, and so on. You
will find
the pic-
ture by joining the answer dots until you
is
reach the dot of the last answer.
3=
+1=
+
b.
2- r~l m -29 + 5
+
+
a line to the dot of the
exercise
ybur pencil on
78
b.
draw
will
to each exercise
•
100
the dot of the answer to exercise
to
1
do the exercises
a.
,
94
dots you should
number
A
•
To
the
A*
7
93
join the right dots,
The answer
86
•
find a hidden picture.
below.
a
92
These dots are numbered from 100.
• 10
n.
36
+
8
o.
39
+
6
|
=
s.
37
+
2
=
t.
46
+
3
=
u.
52
+
7
=
v.
64
+
5
w.
69
+
9
+
8
x.
79
|
|
|
|
|
|
|
|
|
|
|
|
= =
=
Find the Hidden Picture
4
3
1
7
8
5
10
11
15
16
17
18
19
20
21
25
26
27
28
29
30
.
31
41
42
44
43
35
36
37
38
39
40
45
46
47
48
49
50
60
92
91
93
94
These dots are numbered from 100.
If
you
join the right dots,
find a hidden picture.
dots you should below.
join,
The answer
To
draw a
will
which
the
number
a.
80--9
g-
20
b.
70--9
h.
9-8=
c.
60--9
i.
d.
50--9
j-
e.
40--9
k.
f.
30--9
1.
of a dot. Put your pencil
-9=
-9= 12--9= 12--8 = 11
-
12--7
=
line to
exercise
89
90
99
100
b.
a.
Then
the dot of the answer to
Go on
to the dot of the next
answer, and so on. You
do the exercises
to each exercise
98
97
70
the dot of the answer to exercise
to
1
you
find out
96
95
69
will find
the pic-
ture by joining the answer dots until you
is
reach the dot of the last answer.
on
1
1
] 1
= 5= 6
= 8= 9= 3= 7
page 41
Adding Three
+ 1+
2
or
More Numbers
2+2+2+2=
2+2+1= 1+2+2= 2+1+2= 3+2+1= 3+2+2=
1
2+2+2= 1+1+2= 3+1+2= 3+1+1=
2+1+2+1=
2+2+2+2+2= 4+3+2+2= 4+4+2+2=
Add these numbers from the top down. Check by adding from the bottom up. 2 3 2 4 3
13
12 2
3
3
3+2+1+1=
2 2
3+3+2+2=
3+3+3+3+3= 5+2+2+3=
4+5+2+2= 5+4+3+2= On each
line of
three addends
ber
in
Cross out the number that
the chart below, pick
whose sum
is
space at the
Addends
3
5
7
16
2
4
2
2
5
3
2
3
1
11 page 42
not used.
Then write the addition problem
the num-
the right hand column.
2
is
right.
in
the
Up
Twos
to Five
Here
is
were
sold.
2
Tom was glass.
lemonade
selling
Each customer paid by putting 2
pennies on the counter. Here
money
Tom
2$ a
for
is
was on the counter
that
the
after
the
money
after
4 glasses
2 and 2 and 2 and 2 are
2
4 twos are
2
Four glasses of lemonade
2
cost
*. I
i
L
sold 2 glasses of lemonade.
How much do
five
glasses of
lemonade cost?
2+2+2+2+2= 5 twos are Five glasses of
2 twos are
2
lemonade cost
*. I
Two
2
cost
glasses of lemonade $.
2 twos
Here
were
is
the
I
money
after
=2+2=
3 glasses 3 twos
sold.
2
+
2
=
+ 2=|
J
4 twos
2
+
2
+
2
+
2
=
3 twos are Three glasses of lemonade cost
5 twos
—
£.
2+2+2+2+2= page 43
Up
to
Ten Twos At a party, 2 couples began to dance.
The number 2
+
2, or
When 3 the
2
+
dancing was
PI
2 twos are
f~J
couples were dancing,
number 2
of people
+
of people
or
2,
rn
dancing was
3 twos are
.
|
When 4 the
+
2
couples were dancing,
number 2
When
+
2
of people
+
2,
or
dancing was
PI
4 twos
are
PI
5 couples were dancing, the number
of people dancing
or
|
was 2
+
2
+
2
+
2
+
5 twos are
I
One
of these
postage stamps costs 2^.
2 stamps cost
*•
2 twos are
7 twos are
3 stamps cost
*
3 twos are
to this
4 stamps cost
*.
4 twos are
So 8 twos are
5 stamps cost
5 twos are
5 twos are
If
,
you add another
to this answer,
to this answer,
you get
So 7 twos are
Count by twos. page 44
you add
.
If
you add 2
you get
So 9 twos are
3 twos
= =
4 twos
==
5 twos
=
2 twos If
you add 2
1
8 twos are
So 6 twos are
,
If
ans wer »y ou get
l«.
2 to this answer, you get
6 twos are
.
2,
6 twos
==
= 8 twos = 9 twos = 7 twos
10 twos
2,
Practice with
Twos
mm
I
r
6 twos are
8 twos are
6 twos are
5 twos are
3 twos are
8 twos are
2 twos are
4 twos are
9 twos are
7 twos are page 45
Up 3
+
to Five Threes
3=D
2 threes are