Math 3

See, feel and do.

1. Put > or < or = sign in the boxes:

98,405 98,505 64,902 64,903
24,820
49,801 59,801 24,810 34,820
45,850
60,100 60,100 34,810 98,400

73,125 73,129 35,850
99,801 99,811 99,400

The greatest and smallest numbers made up of certain
number of digits

See, feel and learn.

Could you form the greatest
and smallest number of
digits 1, 0, 3, 4?

Sorry sir, I don’t know.
Could you help me
properly?

To form the greatest number,
Let’s keep the digits in descending order i.e.
4310. So, 4310 is the greatest number formed

by the digits 1, 0, 3 and 4.

Similarly, to form the smallest number, let's arrange the digits in increasing order
i.e. 0134. But it is a number of three digits. So, if there is 0, we have to take it
as second digit. So, the smallest number is 1034 formed by the four digits 1, 0, 3
and 4.

Mathematics 3 Approved by CDC 51

See, feel and do.

1. Form the greatest number and the smallest number of the given
digits.

Greatest number Smallest number

4, 3, 5, 7 7543 3457

6, 0, 1, 9

1, 2, 0, 5

9, 1, 6, 7

2, 3, 4, 8

8, 6, 5, 0

2. Form the greatest number and the smallest number of the following
digits.

Greatest number Smallest number

3, 1, 0, 4, 8 84310 10348

9, 3, 2, 1, 4

4, 0, 1, 3, 7

1, 2, 3, 4, 5

6, 4, 2, 8, 0

3. Form the greatest number and the smallest number of the following
digits.

Greatest number Smallest number

0, 2, 4, 6, 8, 9 986420 204689

1, 0, 3, 5, 7, 9

2, 4, 5, 7, 8, 1

3, 4, 6, 7, 8, 9

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2.6 Formation of numbers using
four digits

See, feel and learn.

Let’s take four digits 3, 2, 4, 6.
How many numbers can be made by

using these four digits?

24 I can’t say.
36

3246 , 3264 , 3462 , 3426 , 3624 , 3642

First let’s pick up the digit 3, then 2, then
4 and at last 6.That means running in the
direction of the hand of a watch, the number
formed is 3246 and so on 3264, 3462,
3426, 3624, 3642

Now let’s start from 2, then 4, then 6 and at last 3.The number formed is 2463 and so on
2436, 2634, 2643, 2346, 2364.

Similarly, start from 4, then 6, then 3 and at last 2. 24
The number formed is 4632. In this way four numbers 36
are formed and they are 4632,4326,4362,4263,4236. 3246 , 3264 , 3462 ,
3426 , 3624 , 3642
Similarly, let start from 6, then the numbers will be
6324, 6342, 6243, 6234, 6432, 6423. Again again let
start from 3 and the number will be 3246, 3264, 3462,
3426, 3624, 3642.

Thus, the 24 numbers formed by using the digits 3, 2, 4 and 6. Which are 3246,
3264, 3462, 3426, 3624, 3642, 2463, 2436, 2634, 2643, 2346, 2364, 4632 , 4632,
4326, 4362, 4263, 4236, 6324, 6342, 6243, 6234, 6432, 6423, 3246, 3264, 3462,
3426, 3624, 3642.

Mathematics 3 Approved by CDC 53

See, feel and do.

Make all 24 numbers using the given four digits. Also, circle the
greatest number among them and cross the smallest one.

Digits Numbers

7 2795 2759 2957 2975 2579 2597
259 5279 5297 5792 5729 5972 5927
7952 7925 7529 7592 7295 7259
9527 9572 9725 9752 9275 9257

6
437

8
529

6
189

2
579

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145

54

Use of comma while writing numbers

See, feel and learn.

Do you know where to put commas
in the number 245639?

Yes, sir, I know. We have to
put comma after counting 3 digits from the

right and the another comma
after 2 digits from the first comma and so on.

That means we write the
number in the form: 2,45,639.

Thank you! You are absolutely correct. But it is Devanagari or Hindi Arabic or
Local system. There is Hindu Arabic of English or international system too. In
Hindu Arabic System we put comma after counting three digits from right and
next comma after next three digits and we put comma in between the digits 5 and
6. So, we read it as two hundred and forty five thousand six hundred and thirty
nine. In Hindu Arabic System there is no lakh.

See, feel and do.

1. Use comma:

International System Local System International System Local System

573491 573491 704578 704578

24560 24560 8194 8194

674951 674951 34589 34589

9650 9650 123456 123456

53270 53270 598976 598976

Mathematics 3 Approved by CDC 55

Odd and even numbers

See, feel and learn.

Do you remember how to find
the given number is an odd or

an even number?
Sir, I have

studied in class 2 but I have
forgotten. So, could you
repeat once again?

To find the given number is an odd or an even,
we have to observe the digit in ones place. If the digit in
ones place is 0, 2, 4, 6 or 8, then the number is an even number.

If the digit in ones place is 1, 3, 5, 7 or 9 then the
number is an odd number.

Natural and Whole Numbers

a. Natural Numbers.
Number like 1,2,3,4,5, ... etc are used to count the number of things or object.
Such numbers are called counting numbers. The counting numbers are also
called natural number. Guess which is the least natural number and the
greatest natural number.

b. Whole Numbers.

How many 2 years There are no 2 years old
old students are there in your students in my class.

class ?

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It means there are 0 Oh, whole number
number of 2 years students. are also natural number

0,1,2,3,.. etc. are called including 0 (zero)
whole number.

0 is the smallest whole number.
The set of whole number is denoted by W = {0,1,2,3,4...}

See, feel and do.

1. Find whether the given numbers are even or odd.

Ones digit Type Ones digit Type

1,23,456 6 Even 7,64,902

2,45,769 8,09,408

4,56,710 9,45,675

6,97,841 3,49,609

2. Answer the following questions : ___________
___________
a) What is the smallest natural number ? ___________
b) What is the smallest whole number ? ___________
c) What is the smallest natural odd number ? ___________
d) What is the smallest natural even number ? ___________
e) What is the even number between 3 and 5 ?
f) What is the odd number between 20 and 22 ?

3. List the even number between 25 and 35.

4. List the odd number between 14 and 22.

Mathematics 3 Approved by CDC 57

2.7 Structure of numbers

See, feel and learn.

Study the following examples to know the structure.
1. The natural numbers are written as 1, 2, 3, 4, 5, .........

Here, each and every numbers are written as increased by 1.
1, 1 + 1, 2 + 1, 3 + 1, 4 + 1, ........ etc.

2. Pranav, Pnanisha, Prashun, Pratik, Pralika and Madhav has got Rs 100, Rs.
200, Rs. 300, Rs. 400, Rs. 500 and Rs. 600 according to their ages given by
parents in dashain after tika.
Here,
Rs. 100, Rs. 200, Rs. 300, Rs. 400, Rs. 500, Rs. 600

+ 100 + 100 + 100 + 100 + 100
Every person are given Rs. 100 more than the first according to their ages.

3. Number of dots used to patterns.

13 6 10 15

Here,

The no. of dots goes on incresing by 2, 3, 4 and 5 respectivly.

4. Blocks used to represents numbers.

5 10 15 20 25
+5
+5 +5 +5
58 Mathematics 3
Approved by CDC

See, feel and do.

1. A shopkeeper sells good in a week as :

Sunday Monday Tuesday Wednesday
Rs. 1100 Rs. 1200 Rs. 1300 Rs. 1400

Thursday Friday Saturday
Rs. 1500 Rs. 1600 Rs. 1700

He sold every day by Rs. in the week.

2.

100 120 140 160 180 200
Abacus shows the numbers increased by in each steps.

3. Fill the boxes to complete the structure of numbers.

a) 10 20 30

b) 2 6 10

Mathematics 3 Approved by CDC 59

c) 100 300 500
d) 100 120 140
e) 2200 2210 2220
f) 3650 3700 3750

4. Color the numbers taking the difference by 5.

1 2 3 4 5 6 7 8 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 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60

5. Circle the numbers taking the difference by 8.

1 2 3 4 5 6 7 8 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 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60

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6. Complete the structure of numbers from the given patterns.
a)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
036

b)

3 5
c)

1 4
d)

1 4
e)

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Mathematics 3

Rounding off to nearest 10 and 100

See, feel and learn.

Shiba had Rs. 125 in the morning. He spent Rs. 35. Suman asked him how much
money he had?

He answered, "About Rs. 100". Here he applied a mathematical process called
rounding off. We round off a number to the nearest 10 or 100 or 1000 etc.

Near to 20

Far from 10

10 11 12 13 14 15 16 17 18 19 20 21 22

18 is in between two tens i.e. 10 and 20. But 18 is farther from 10 than 20. So,
while rounding 18 to nearest ten, we round off as 20.

Let’s round off 24.

Far from 30

Near to 20

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

24 is in between two tens and they are 20 and 30. 24 is nearer to 20 than 30. So,
while rounding off 24 to nearest ten, we round off it as 20.

Round off 55 to nearest ten.

48 50 52 54 55 56 58 60 62

55 is exactly in between 50 and 60. So we round off 55 as 60. Similarly, 45 is
round off as 50.

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See, feel and do.

1. Round off the following numbers to the nearest ten.

76 67 26
44 94 73
55 11 82

2. Represent the following numbers in a number line and round off to
nearest 10.

43 40 41 42 43 44 45 46 47 48 49 50 40
67 60 61 62 63 64 65 66 67 68 69 70

88 80 81 82 83 84 85 86 87 88 89 90

35 30 31 32 33 34 35 36 37 38 39 40

14 10 11 12 13 14 15 16 17 18 19 20

77 70 71 72 73 74 75 76 77 78 79 80

94 90 91 92 93 94 95 96 97 98 99 100

59 50 52 54 56 58 60

Mathematics 3 Approved by CDC 63

See, feel and learn.

Let’s represent 140 in a number line and try
to round off to the nearest 100.

100 110 120 130 140 150 160 170 180 190 200

140 is in between 100 and 200. It is nearer to 100 than 200. So, it is rounded
off as 100.

Let’s round off
270.

200 210 220 230 240 250 260 270 280 290 300
270 is in between 200 and 300. It is nearest to 300 than 200. So it is round off
as 300.

Let’s try to round
off 350.

300 310 320 330 340 350 360 370 380 390 400
350 is exactly in between 300 and 400. So 350 is round off as 400.

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See, feel and do.

A. Round off to nearest 100.

130 680
260 710
390 820
450 940

570 285

B. Represent the given numbers in a number line and round off to
nearest 100.

140 100 110 120 130 140 150 160 170 180 190 200 100
270 200 210 220 230 240 250 260 270 280 290 300

380 300 310 320 330 340 350 360 370 380 390 400

460 400 410 420 430 440 450 460 470 480 490 500

550 500 510 520 530 540 550 560 570 580 590 600

610 600 610 620 630 640 650 660 670 680 690 700

780 700 710 720 730 740 750 760 770 780 790 800

890 800 810 820 830 840 850 860 870 880 890 900

Mathematics 3 Approved by CDC 65

Unit Revision Test

1. Represent the given numerals in place value table and write in words.

a) 4,259 b) 54,908
c) 8,15,210 d) 7,05,213

2. Write in numerals.

a) Five thousand and one hundred.

b) Ninety eight thousand four hundred and ten.

c) One lakh twenty three thousand five hundred and ninety two.

d) Three lakh forty five thousand two hundred and nineteen.


3. Put > or < or = sign in the boxes:

a) 4512 4501 b) 59,008 49,008
c) 6,45,123 8,45,123 d) 9,63,459 9,73,459

4. Write the place value and the face value of the underlined digits.

a) 1,298 b) 54,019
c) 6,95,198 d) 9,84,756

5. Form the greatest number and smallest number of the given digits:

a) 5,3,0,1
b) 9,1,8,6

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c) 7,3,4,2
d) 8,4,2,7

6. Use comma in Hindu Arabic System.

a) 4571 b) 64982
c) 794610 d) 859217

7. Find whether the given numbers are even or odd.

a) 4598 b) 64,127
c) 9,48,200 d) 8,45,239

8. Round off the following numbers to the nearest 10.
a) 35

40 41 42 43 44 45 46 47 48 49 50

b) 52

40 41 42 43 44 45 46 47 48 49 50

c) 69

40 41 42 43 44 45 46 47 48 49 50

d) 87

40 41 42 43 44 45 46 47 48 49 50

Mathematics 3 Approved by CDC 67

9. Round off the following numbers to the nearest 100. \
a) 250

40 41 42 43 44 45 46 47 48 49 50

b) 360

40 41 42 43 44 45 46 47 48 49 50

c) 480

40 41 42 43 44 45 46 47 48 49 50

d) 520

40 41 42 43 44 45 46 47 48 49 50

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s_ @%^#$
v_ !)#)%
u_ !%)*
3_ #@$^%
ª_ &%@*@

!!= tnsf ;+VofnfO{ cs+ df n]v
s_ Ps xhf/ rf/ ;o afx |
v_ ;ft xhf/ gf} ;o aof;L
u_ 5};77\ L xhf/ kfrF ;o kt} L;
3_ aofl; xhf/ ;ft ;o aofga ]
ª_ pgfG;o xhf/ cf7 ;o lqrfln;
Mathematics 3
68 Approved by CDC

3Unit

OUR SOCIETY

Estimated periods - 16

Objectives

At the end of this unit, students will be able to:
Write the numbers in ascending or in descending order.
know the local numbering system including roman system.
understand the measurement of length of objects.
know the fraction like fraction, diagramic representation of fraction etc.

Teaching Materials

Abacus, number chart, place value chart, roman number chart, local
number chart, chart of fractions measuring tape, meter scale, ruler etc.

Activities

It is better to:
interprate the numbers in place value table
to know order of the numbers
use local number system and roman number in practice.
show the fractions taking objects which are used in our daily life.
show the measurement of the objects which are in the classroom.

Mathematics 3 Approved by CDC 69

3.1 Ascending and descending order

See, feel and learn.

Pranav,
Do you know about ascending and
descending order of numbers from
1327, 1325, 1326

Yes mam,
Smaller to bigger 1325, 1326, 1327.
Bigger to smaller 1327, 1326, 1325

Absolutely right.
Smaller to bigger order of number is called ascending order
and bigger to smaller is called descending order.

Arrange in ascending and descending in order.
1

Ascending order

Descending order

2 Mathematics 3
Ascending order 3260, 3261, 3262
Descending order 3262, 3261, 3260

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3 2469, 2470, 2468, 2471
Ascending order 2468, 2469, 2470, 2471
Descending order 2471, 2470, 2469, 2468

4 32516, 32520, 32508
Ascending order
Descending order

See, feel and do.

1. Arrange in ascending order.
a) 9100 8200 6400 4500 7120
__________, __________, __________, __________, __________
b) 7240 7340 7570 7119 7941
__________, __________, __________, __________, __________
c) 28912 29920 27634 25349 24614
__________, __________, __________, __________, __________
d) 56720 38900 69990 87800 14530
__________, __________, __________, __________, __________
e) 64750 59845 28940 97670 81260
__________, __________, __________, __________, __________

2. Arrange in descending order:

a) 4140 7814 6709 8950 9140
__________, __________, __________, __________, __________

b) 6940 5496 9450 7980 8267
__________, __________, __________, __________, __________

Mathematics 3 Approved by CDC 71

c) 39190 38645 31240 35685 33490
__________, __________, __________, __________, __________

d) 26240 38747 96350 25695 14660
__________, __________, __________, __________, __________

e) 47850 98845 89840 76780 12608
__________, __________, __________, __________, __________

3.2 Numbering system in our locality

The numbers from 1 to 10 written in our locality according to their
script can be express as given in table.

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The numbers from 11 to 20 in different scripts.

See, feel and do.

1. Write the following numbers in Newari, Tibeti, Ranjana and
Devanagari Scripts.

4
8
19
15
12
9
10
17

2. Write the numbers 1 to 20 in system of local numbers used in your
locality.

Mathematics 3 Approved by CDC 73

3.3 Roman numerals

See, feel and learn.

Do you remember the Yes, sir there are seven
symbols used in Roman symbols used in Roman
numeral system.They are I, V,
numeral system?
X, L, C, D and M.

Could you tell what those Yes, sir !
symbols stand for? They stand for

Roman Numeral Hindu Arabic Roman Numeral Hindu Arabic
I 1 C 100
V 5 D 500
X 10 M 1000
L 50
1
Let’s write the numbers I 2
from 1 to 10 in Roman II 3
III
Numeral System.

It shows that we can put I together three times.

Could you represent
4 in Roman Numeral

System?

Yes, sir. It is IIII.

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That’s wrong. We can’t write I for four times. 4 is written as IV. Here,

smaller symbol I comes before greater symbol V. So 1 is subtracted

from 5. ∴ 4 = 5 – 1 = IV

But, to represent 6, we write VI

Here, the smaller symbol I comes after the greater symbol V so, we add

them. ∴ 6 = 5 + 1 = VI

Similarly, 7 = 5 + 1 + 1 = VII

8 = 5 + 1 + 1 + 1 = VIII

But 9 is written as IX because I can’t be repeated for four times.
Now, 10 = X
For 10, we can’t write V V. It means V can’t be repeated for two times.
From the examples given above it is clear that
I comes before and after V and X only.

Can you represent 20 Yes, sir! it is XX.
in Roman Numeral

System?

Could you explain The symbol X stands for 10.
it? So, XX means 10 + 10 = 20.

See, feel and do.

1. Write the Roman Numeral for the given numbers.
4 5 20
8 9 12
19 15 13

2. Write the numerals for the given Roman numeral.

XI XX XIX
XIV IX VII
XII XVIII XIV

Mathematics 3 Approved by CDC 75

3.4 Fraction

See, feel and understand.

• Division of a bread into two equal parts.

Full bread Two equal halfs One half
1
1 + 1 1
2 2 2

Numerator = 1 (How many parts are taken?)

Denominator = 2 (How many parts are there altogether?)

Fraction of one part = 1
2

• Division of pizza in four equal parts.

Full pizza Four equal parts One part
1 1
1 + 1 + 1 + 1 4
76 4 4 4 4
Mathematics 3
Approved by CDC

• Division of a ribbon in three equal parts.

Full ribbon Three equal halfs One part
1
1 + 1 + 1 1
3 3 3 3

• A rectangular piece of paper is divided into six

equal parts.Two parts out of six are removed.

The removed parts are two out of six or two
2
sixth and is written as 6 .

• A rectangular is divided into 2 equal parts.

Each part is called half of the whole rectangle.

One half of the rectangle is shaded One half is
1
written as 2 .

• 1 circle is divided into 3 equal parts.
1
• The shaded part is 3 of the whole circle each

part is called one third of the whole circle.
1
One- third is written as 3

The non-shaded part is two third of the whole circle.

Two third parts is written as 2
3

1 circle is divided into 8 equal parts.

3 parts are shaded or taken. The fraction of shaded part = 3
8

The number of taken part = 3 = 3 is numerator
Total number of part 8 8 is denominator

In a fraction 1 , 3 and 2 , where 1, 3 and 2 are numerators (the number written
4 4 6
above is the numerator) which shows the parts taken in consideration and the

total number of parts where 4 and 6 are denominators. Unless we compare with

the whole part, every object or every part is whole (single)

Mathematics 3 Approved by CDC 77

It is a whole/single or 1 It is a whole/single or 1

See, feel and do.

1. Write the fraction for the shaded part.

1
2

2. Shade the parts to represent the given fraction:

13 1 2
38 4 5

3. Write the following fractions in words:

1 = Two fifth 4 =
3 7

7 = 1 =
10 4

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1 = 2 =
2 3

5 = 1 =
7 8

4. Write the following in fraction:

One half = five eight =

one tenth = seven twelfth =

three fourth = two fifth =

Like and unlike fractions:

See, feel and learn.

• In the given figures, the shaded portions are
1 3
represented by the fractions 4 and 4 .

In each fraction denominator is 4. So, 1 and 3
are like fractions. 4 4

• If the denominators of two or more fractions are

same, they are called like fractions.
1 3
Example: 4 and 4

• If the denominators of two or more fractions are
not same, they are called unlike fractions.
1 1
Example: 4 and 6

• Like fractions are fractions of same or identical objects.

12 1 3
44 4 4

Different objects Identical objects
Mathematics 3
Approved by CDC 79

• In like fractions, size of unit fractions are same.

equal
In like fractions, fractions with greater numerators are greater than the other.

= 4 = 3
8 8

3 and 4 are like fractions with denominator 8.
8 8
4 3
Here, 4 > 3 So, 8 > 8

See, feel and do.

1. Tick ( ) the like fractions and cross ( × ) the unlike fractions.

(a) 1 and 2 (b) 41 and 3 (c) 3 and 4
3 3 5 5 5

(d) 3 and 3 (e) 47 and 5 (f) 112 and 11
11 11 8 12

2. Write the fractions for the shaded parts and compare.

3 < 4
5 5

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3. Compare the following (Use > or < or = between them)

(a) 4 5 (b) 2 2 (c) 4 3
6 6 4 5 5 5

(d) 1 7 (e) 27 2 (f) 7 6
8 8 7 10 10

4. Arrange the following in increasing (ascending) order (one is done
for you).

170, 130, 5 4 , 7 and 5
10 8 8 8

Here, 3 < 5 < 7. So, the fractions Here, _____________________
are in ascending order ________________________

∴ 3 , 5 and 7 ∴, and
10 10 10

182, 11 and 1 165, 125, 7 and 4
12 12 15 15

Here, _____________________ Here, _____________________
________________________ ________________________

∴, and ∴, , and

Mathematics 3 Approved by CDC 81

5. Arrange the following fractions in decreasing (descending) order:

161, 1101, 171, 2 145, 185, 155, 9
11 15

Here, 10 > 7 > 6 > 2 Here, _____________________
___________________________
∴ The fractions are in descending ___________________________

order.

121, 161, 7 , 10
11 11

2 , 1 , 5 , 4 2 , 1 , 5 , 4
7 7 7 7 9 9 9 9

Here, _____________________ Here, _____________________
___________________________ ___________________________
___________________________ ___________________________

Addition of fractions having same denominators

See, feel and learn.

A circle is divided into 8 equal parts.

Fraction of shaded part with red is 3 .
8
2
Fraction of shaded part with blue is 8 .

Total shaded part is 5 of the whole.
8
3 2 3+2 5
So, 2 + 8 = 8 = 8

Again a rectangle is divided into 6 equal parts.

Fraction of tss+ohhtaaa26ddleesdd happdaarerttd=wwpii1attrhh+6t rgi2esrde36ei nsoi62fs=t.16h36e. whole.
Fraction
Fraction of
Let’s see
of
1
6

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For adding fractions with same denominators, add the numerators and keep the
denominator common.

Example 1: Add : 1 + 3
5 5
1 3
Solution : 5 + 5

= 1+3
5
4
= 5

Example 2: Add : 3 + 2 + 1
7 7 7
3 2 1
Solution : 7 + 7 + 7 32 1
77 7
= 3+2+1
7 6
6 7
= 7

Note:
Addition of fraction is same as adding shaded parts in the same figure.

See, feel and do.

1. Add the following fractions:

(a) 1 + 1 (b) 1 + 2 (c) 3 + 2
3 3 5 5 8 8
7 3 123 4 1 2 6 4 3
(d) 13 + 13 + (e) 9 + 9 + 9 (f) 15 + 15 + 15

2. Add the following fractions. Show the addition in the figure by shading.

(a) 5 + 3 = + =
12 12

(b) 2 + 1 =+=
8 8

Mathematics 3 Approved by CDC 83

(c) 3 + 5 = + =
10 10

(d) 1 + 2 + 3 = + =
8 8 8

Subtraction of fraction having same denominators:

See, feel and learn.

• Fraction of total shaded part = 5 = 5 – 2
8 8 8
2
• Fraction of removed shaded part = 8 = 5–2
8
• Fraction of remaining shaded part 3
= 8
5 2 5–2 3
= 8 – 8 = 8 = 8

• For subtraction of like fraction, the numerator of the smaller fraction is

subtracted from the numerator of the greater fraction,keeping the denominator

common.

See, feel and do.

1. Perform the following task :

(a) 2 − 1 (b) 4 − 3 (c) 5 − 2
3 3 5 5 7 7

(d) 2 − 1 (e) 7 − 3 (f) 13 − 7
9 9 10 10 18 18

(g) 4 − 2 (h) 8 − 3 (i) 8 − 7
8 8 9 9 17 17

2. Subtract:

(a) 2 from 5 (b) 3 from 5 (c) 8 from 13
6 6 8 8 15 15

(d) 1130 from 1123 (e) 5 from 199 (f) 3 from 7
19 17 17

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3. Show the following subtraction in figure:

(a) 3 − 1 = 2
4 4 4

(b) 4 − 1 =
5 5

(c) 4 − 3 =
6 6 =
=
(d) 5 − 3
8 8

(e) 7 − 4
10 10

(f) 9 − 5 =
12 12

Mathematics 3 Approved by CDC 85

3.5 Length

See, feel and learn.

Suresh, Yes, mam!
Do you know the They are ruler, measuring
instruments which are tape, meter scale etc.
used to measure length
of objects.

Ruler

Measuring tape

Meter scale

See, feel and learn.

1.
Draw a straight line and measure its length using ruler.

It is 6 cm long. 6 cm Mathematics 3
Approved by CDC
86

2. What is the length of the following objects?

It is 10 cm long.
3. Measure the length of the edges of your book by using ruler.

Length
Breadth 8 cm
Height

Mathematics 3 Approved by CDC 87

4. Length of the given rope.

The rope is 14 cm long.

5. Measure the distance between two points given below using ruler by joining
them.

AB

AB

The points are 12 cm apart.

Activity : Take the following objects and measure their length.

Length of the objects using meter tape.

• Length of a bamboo piece: • Length of a bench.

It is 2 m long. It is long.
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88

• Length of school building • Length of football ground.

Our school is long. Our football ground is long.

• Length of your class room

Our classroom is long.

See, feel and do.

1. Measure the following line segments and fill in the boxes.
a.
AB

AB = 4 cm Approved by CDC 89
Mathematics 3

b.
CD

CD = cm
D
c.
C

CD = cm

d. D
C

CD = cm

3. Measure the lenght of the following objects and fill in the boxes.
a. b.

A B P Q
AB = cm PQ =
cm

c. d.

D cm E M N
DE = Approved by CDC MN =

cm

90 Mathematics 3

e. f. C D

GH

GH = cm CD = cm

4. Measure the length and breadth of the following objects and write
down in boxes [using ruler] .

a. b. length breadth

breadth

length Length
Breadth
Length
Breadth d.

c.

Length Length 91
Breadth Breadth

Mathematics 3 Approved by CDC

5. Draw the line segments with ruler for the given lengths.

a) 5 cm b) 10 cm c) 12cm
d) 15 cm e) 20 cm f) 24 cm

6. Measure the length of the following objects and write down in
boxes [using meter tape].

a) Length of your school. b) Length of your bed.

Length Length

c) Length of volleyball court of d) Length of wooden log found
your school. by you.

Length Length
e) Length of your sitting room. f) Length of your house.

Length Length Mathematics 3
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Unit Revision Test

1. Write five hundredth in fraction.

Write how you read the fraction 3 .
10

2. Write the fraction of the shaded part and write the numerator and
denominator.

Fraction = ,

Numerator = ,

Denominator =

3. Compare the fractions:

(a) 3 1 (b) 5 9
4 4 10 10

4. Add :

(a) 3 and 2 (b) 170 and 2
7 7 10

5. Complete the given subtraction:

7 – 4 = =
12 12

Mathematics 3 Approved by CDC 93

6. Write down the given numbers in ascending and in descending order.
a) 3241, 3258, 3229, 3140
Ascending order =
Descending order =
b) 5872, 4829, 8721, 7322
Ascending order =
Descending order =

7. Write down the following numbers to roman and roman to numbers.

a) 7 = b) XXII =

c) IX = d) 24 =

8. Write down the local numbering system which represents the given
numbers.

a) 5 Ranjana = b) 6 Newari =
c) 8 Kirat = d) 1 Maithili =

9. Measure the length of the following objects using ruler.
a. b.

cm cm

94 Approved by CDC Mathematics 3

4Unit

MY CREATION

Estimated periods - 16

Objectives

At the end of this unit, students will be able to:
identify the straight and curve line and able to draw them.
name the angles and draw angle using ruler.
identify the parts (angles, sides, vertices) of triangles and quadrilaterals.
identify circles, its centre, radius, diameter and circumference.
know the points and line segments and trace the outline of objects which
are tin different geometrical shapes

Teaching Materials

Instrument box, geoboard, models of triangles, quadrilaterals, circles and
solid objects (cubes, cuboids, spheres, cylinder, cones etc)

Activities

It is better to:
demonstrate the process of drawing straight lines and curve lines.
demonstrate the models of triangles, quadrilateral and other shapes to
teach the concept of plane figures.
show the corners of different objects to give the concept of angles and
discuss about the sides, vertices and angles of triangles and quadrilaterals.
demonstrate the models of solid objects and explain the shape of their
faces.

Mathematics 3 Approved by CDC 95

What shows a point?
A dot shows point.

What shows the straight line?
Pencil shows a straight line.

What shows the curve line?
Electric wire shows the curve line.

What shows a triangle?
Sandwitch shows a triangle.

What shows a quadrilateral?
Bread shows a quadrilateral.

What shows geometrical shapes?
Above objects shows geometrical shapes.

96 Approved by CDC Mathematics 3

4.1 Lines

See, feel and learn.

1. Here are three roads between your house and school.
Road (A)

Road (B)

Home School

Road (C)
Which road is used to travel from house to school at shortest time?
Discuss and write in box. B
Which is straight road? B
Which are the curve road ? A and C

2.

Winter Electric Poles

Summer Electric Poles

Which wire is straight ? during Winter
Which wire is curve? during Summer

Mathematics 3 Approved by CDC 97

3.
Trace a line with pencil using your book.

It is straight
line.

4.
Trace a line using handle of bucket.

It is curve line.

Point and line segment

See, feel and learn.

A sheet of paper is given below. Identify corners and edges of it.
AB
Corners A | B | C | D
Edges AB | BC | CD | AD

D C Here,
Corners are taken as points.

Edges are taken as line segments.

98 Approved by CDC Mathematics 3

Consider the followings: Q These are points.
ABP

AB
These are the line
segments.

Q

P

The dot having no any measurement is called point.

ABPQ

A part of a straight line having fixed measurement is called line
segment.

A BS

R

• Line segment can not be extend in any direction.

S
R Line segment

• Ray can be extended in one direction.
ray

• Straight line can be extended in both directions.

Straight line

Mathematics 3 Approved by CDC 99

See, feel and do.

1. Which of the following are straight or curve?

2. Write down the length of following straight lines.

a) b) Q
A

BP

AB = cm PQ = cm

3. Draw the straight lines of given lengths.

a) 12 cm b) 16 cm c) 13 cm d) 8 cm

100 Approved by CDC Mathematics 3