Mathematics - Grade 3 Workbook : Mastering Arabic Numbers : A Workbook with Self-Teaching Text and Learning Exercises 0307059731, 9780307059734

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MATHEMATICS"-^

0, GOLDEN

Mastering Arabic Numerals A Workbook with Self-Teaching Text and

Learning Exercises

by IRVING ADLER, Ph.D.

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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