Shubharambha Math Book 5 for CTP 2077

Approved by Government of Nepal, Ministry of Education, Curriculum Development
Center(CDC), Sanothimi, Bhaktapur, Nepal

Maths Zone
With 5Grade

Maths for Fun
and

Practice Zone

Authors
Sthir Babu Subedi
Bishnu Prasad Poudel

Shubharambha Publication Pvt.Ltd.

KKaatthhmmaanndduu, NNeeppaall

Published by:

Shubharambha Publication Pvt. Ltd.

Kathmandu, Nepal
URL: www.shubharambhapublication.com.np
E-mail: [email protected]
www.facebook.com/shubharambhapublication

Book : Maths Zone - Grade 5

Authors : Sthir Babu Subedi

Bishnu Prasad Poudel

Layout Design : Zeeta Computer Service Pvt. Ltd.

Ghantaghar, Kathmandu

Phone : 01-4263459, 9841418545

Copyright © : Publisher

Edition : First: 2075 B.S.

Second Revised : 2077 B.S.

© : Publisher

No part of this book may be reproduced or transmitted by means(electronic,
photocopying, recording or otherwise) without prior written permission from the
publisher. Any breach of this condition will entail legal action and prosecution.

Printed in Nepal

Preface

Maths Zone with Maths for Fun and Practice Zone is developed
according to the National Curriculum of Nepal Government. It is the
textbook with new design and layout. The lessons are designed as per
an innovations. A colourful presentation is made so that this description
should look as interesting. This may lead to an interactive approach. Our
efforts are to make textbooks teachable with quality, i.e. maintaining of
standards. We have made specific endeavours to publish the text and
illustrations in much effective form.

The textbook is student-friendly and easy to practise and understand.
It doesn’t contain only the exercises, as in traditional textbooks. It is all
mixed together with the explanation, exploration, examples, exercises,
etc. It is designed for students to learn in a small collaborative group
setting, where students practise together, helping each other to learn
the material. Ideally, the instructor would not necessarily lecture, but
would act more as a facilitator, and be available to clarify ideas.

This series is the complete program to help children practice the essential
Math skills they learn. Matches the Math curriculum so the children will
reach their full potential and on important standardized tests. It applies
interesting and successful way to improve the child’s Math. It comprises
explanation in simple language, examples with clear instruction,
worksheets to increase the child’s confidence, enjoyment, and success.

We are hopping for positive and constructive suggestions from our
respected teachers, guardians and well wishes for the improvement of
this series. Any comments or suggestions for the improvement of the
book will be always welcome.

Authors

Contents

Unit 1 Geometry 5

32

Unit 2 Concept of Numbers

70

Unit 3 Basic Operation of Mathematics

88

Unit 4 Time and Money



Unit 5 Measurement 109



Unit 6 Mensuration 127

147

Unit 7 Fraction, Decimal and Percentage

204

Unit 8 Unitary Method & Simple Interest

216

Unit 9 Bill and Budget



Unit 10 Statistics 224

Unit 11 Set 235

Unit 12 Algebra 245

Specification Grid 268
Model Questions 270

UNIT

1 GEOMETRY

Specific Objective Prescribed by CDC

‰‰ To draw the angles from 0° to 180° (in difference of 10° ) by using protractor.
‰‰ To measure the sides and angles of the given triangles and the quadrilaterals.
‰‰ To recognize and distinguish the triangles on the basis of sides and angles.

Maths Zone - Grade 5 5

Warm-up Questions

1. Name the solid objects and identify the number of edges, vertices
and faces.

a. b.

Vertices________ Vertices________

Edges __________ Edges __________

Faces__________ Faces__________

........................... ...........................

c. d. Vertices________
Vertices________ Edges __________
Edges __________ Faces__________
Faces__________

........................... ...........................

e. f.

Vertices________ Vertices________

Edges __________ Edges __________

Faces__________ Faces__________

........................... ...........................

2. Identify the types of angles by inspection method:

(a) P (b) A (c) X

QR BC YZ

........................................ ........................................ .........................................

6 Maths Zone - Grade 5

1 AnglesLesson

An angle is defined as a figure formed by two lines that meet at a common

point. A
� The common point of two lines is called vertex. Arm
� The two lines are called arms of the angle.
O Angle
In the given figure, 'O' is vertex and AO & OB are arms Vertex B
of the angle AOB.
Arm

Angles can be measured by the protector in degree.

Measurement of Angles

Outer scale
70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚
50˚ 90˚ 130˚

40˚ Inner scale 140˚
30˚ 150˚

20˚ 160˚

10˚ 170˚

0˚ 180˚ 0˚ 180˚
Base line Base line
(Left side) (Right side)

� In general, Inner scale is in ascending

This is protractor. order from right to left and 0° to

It is used to measure 180°.
the angles.
� Outer scale is also in ascending

order from left to right 0° to 180°.

� Always use the scale with 0° on one of the base arms of the angle.
� Always count round the edge from 0°

Maths Zone - Grade 5 7

Let's measure an angle PQR using protractor.

� Place the centre point of the protractor on the Q P
vertex 'Q' of the angle PQR. R

� Adjust the protractor so that one arm 'QR' of
the angle PQR is along the baseline.

� 'QR' arm is along the right side base of the
protractor line, so use inner scale.

� Count round the measure of the angle PQR
where the other arm QP crosses the scale.

Here, ∠PQR = 50°.

P

QR

Let's measure an angle ABC using protractor.

� Place the centre point of the protractor on the A
vertex 'B' of the angle ABC.

� Adjust the protractor so that one arm 'BC' of

the angle ABC is along the baseline.

� 'BC' arm is along the left side base of the C B

protractor so use outer scale.

� Count round the measure of the angle ABC where the other arm 'BA'

crosses the scale.

Here, ∠ABC = 40°

A

C B
8 Maths Zone - Grade 5

Exercise 1.1

1. Read the measure of the angle and write in the box.

a. b.
A R 70˚ 80˚ 90˚ 100˚ 110˚
70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚ 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70° 50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚ 120° 60° 130˚
130° 50° 130° 50°
40˚ 140˚ 40˚ 140˚

30˚ 140° 40° 150˚ 30˚ 140° 40° 150˚

20˚ 150° 30° 160˚ 20˚ 150° 30° 160˚
160° 20° 160° 20°

10˚ 170° B 10° 170˚ C 10˚ 170° Q 10° 170˚
0˚ 180˚ 0˚ 180˚ 0˚ 180˚
P 0˚ 180˚

∠ABC = ∠PQR =

Z Y

c. d.

70˚ 80˚ 90˚ 100˚ 110˚ 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚ 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70° 50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚ 120° 60° 130˚
130° 50° 130° 50°
40˚ 140˚ 40˚ 140˚

30˚ 140° 40° 150˚ 30˚ 140° 40° 150˚

20˚ 150° 30° 160˚ 20˚ 150° 30° 160˚
160° 20° 160° 20°

10˚ 170° Y 10° 170˚ X R 10˚ 170° 10° 170˚
0˚ 180˚ 0˚ 180˚ 0˚ 180˚
A 0˚ 180˚

∠XYZ = ∠RAY =

e. f. A

G 70˚ 80˚ 90˚ 100˚ 110˚ 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚ 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70° 50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚ 120° 60° 130˚
130° 50° 130° 50°
40˚ 140˚ 40˚ 140˚

30˚ 140° 40° 150˚ 30˚ 140° 40° 150˚

20˚ 150° 30° 160˚ 20˚ 150° 30° 160˚
160° 20° 160° 20°

10˚ 170° 10° 170˚ 10˚ 170° R 10° 170˚
0˚ 180˚
0˚ 180˚ B 0˚ 180˚ S P 0˚ 180˚

∠GBS = ∠PRA =

g. h.

10˚ 20˚ 30˚ 40˚ 50˚ 60˚ 70˚ 80˚ 90˚ 100˚ 110˚ 120˚ 130˚ 140˚ 301°502˚0°16100˚°
180˚ 170° 160° 150° 140° 130° 120° 110° 100° 90˚ 90˚ 80° 70° 60° 50° 40°
0˚ R90˚ 170˚
100˚ 0˚ 180˚
80° 110˚ 80˚
70° 506˚0˚70˚13102°01°10°100°
60° 120˚
130˚
50°
S 40° 140˚
10°203°01°701˚6105˚0˚ A 40˚ 140°
180˚ 302˚0˚10˚115600°1°701°80˚
A

0˚

0˚

U D

∠USA = ∠DRA =
Maths Zone - Grade 5
9

2. Measure the following angles by using protractor and fill in the

boxes.

a. A b. P

B CQ R
X ∠ABC =
c. D d. ∠PQR =

Y Z E ∠DEF = F
∠XYZ =

3. Measure the following angles by using protractor and fill in the

boxes. B
a. b.

K

Y LS D
L
∠KLY = X ∠BDS =

c. d.

Z Y N M
∠XYZ = ∠LMN =

10 Maths Zone - Grade 5

Construction of Angles

Let's draw an angle of 65° using the protractor. OB

� Draw a line segment 'OB'. 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚
� Place the protractor such that its centre is 50˚ 110° 100° 90˚ 80° 70°
at 'O' and its baseline is on OB. 120° 60° 130˚
130° 50°
� Count round the edge 0° to 65° (using 40˚ 140˚
inner scale) and mark 'A'.
30˚ 140° 40° 150˚
� Remove the protractor. Join the points O
and A by using scale. 20˚ 150° 30° 160˚
160° 20°
∴ ∠AOB = 65°
10˚ 170° O 10° 170˚ B
0˚ 180˚ 0˚ 180˚ B

70˚ 80˚ 90˚ 100˚ 110˚ A
60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚
130° 50°
40˚ 140˚

30˚ 140° 40° 150˚

20˚ 150° 30° 160˚
160° 20°

10˚ 170° O 10° 170˚
0˚ 180˚ 0˚ 180˚

A

OB

Let's draw an angle of 125° using protractor. XY

� Draw a line segment XY. 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚
� Place the protractor such that its centre is 50˚ 110° 100° 90˚ 80° 70°
at 'Y' and its baseline is on XY. 120° 60° 130˚
130° 50°
� Count round the edge 0° to 125° (using 40˚ 140˚
outer scale) and mark 'Z'
30˚ 140° 40° 150˚
� Remove the protractor. Joint the points Y
and Z by using scale. 20˚ 150° 30° 160˚
160° 20°
∠XYZ = 125°
X 10˚ 170° O 10° 170˚
0˚ 180˚ 0˚ 180˚

Y

70˚ 80˚ 90˚ 100˚ 110˚ Z
60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚
130° 50°
40˚ 140˚

30˚ 140° 40° 150˚

20˚ 150° 30° 160˚
160° 20°

X 10˚ 170° O 10° 170˚
0˚ 180˚ 0˚ 180˚

Y

Z

XY

Maths Zone - Grade 5 11

Exercise 1.2

1. Draw the following angles using protractor.
a. 15° b. 35° c. 47° d. 83°
e. 95° f. 145° g. 170°

2. Draw the following angles using protractor.
a. 27° b. 57° c. 83° d. 99°
e. 125° f. 145° g. 165°

3. Draw the following angles using protractor.
a. 25° b. 35° c. 65° d. 105°
e. 155° f. 185°

Types of Angles

On the basis of their sizes angles are categorized into 6 different types.
They are as follows:

Types of Angles Details Examples

(a) Acute Angles An angle whose

A measurement is

between 0° and 90° is 20°, 45°, 47°, 80°,

called acute angle. 89° etc.

B C

(b) Right Angle An angle whose
measurement is exactly
P 90° is called Right angle.

90°

QR

12 Maths Zone - Grade 5

(c) An obtuse Angle An angle whose

X measurement is

between 90° and 180° is 95°, 110°, 150°,
called obtuse angle.
176° etc.

YZ

(d) A straight angle An angle whose 180°
measurement is exactly
YQ R 180° is called straight
angle.
(e) A Reflex angle
An angle whose
Q
R measurement is

between 180° and 360° 181°, 190°, 250°,
is called reflex angle. 300°, 359°, etc.

P 360°

(f) Angle of a Complete An angle whose
turn measurement is exactly
C 360° is called complete
A B turn.

Exercise 1.3

1. Categorize the following angles as acute angle, obtuse angle, Right
angle, straight angle, Reflex angle and the angle of a complete turn.
5°, 10°, 38°, 92°, 180°, 47°, 275°,
25°, 30°, 60°, 220°, 360°, 127°, 155°

Maths Zone - Grade 5 13

2. Measure the following angles and state whether they are Acute
angle, Obtuse angle, Right angle, Straight angle or Reflex angle.

a. b.

P Size : _______ O Size : _______

Types : _____ Types : _____

QR

PQ

c. B Size : _______ d. X Size : _______
S Types : _____ Types : _____
A Y
C Z
e. D
f. Size : _______
R Size : _______ C Types : _____
Types : _____ G
E
T I
g.
h.

W Y Size : _______ H Size : _______
Types : _____ Types : _____

X

3. Answer the following questions.
a. What do you call an angle which is exactly 180°?

b. How many degrees are there in a right angle?

c. What do you call an angle which is smaller than 180° and greater
than 90°?

d. Is 225° a reflex angle? Why?

e. Give any five examples of acute angle.

14 Maths Zone - Grade 5

Lesson

2 Triangles

Classification of Triangles

A closed plane figure having three sides, three angles and three vertices is

known as triangle. P

In Triangle PQR,

Vertices : P, Q and R are vertices

Angles: ∠P, ∠Q, and ∠R are angles Q R

Sides : PQ, QR and RP are sides

Class Activities

Ask students to do this activities in the class.

Required Materials : Standard Pencils or Paper roll.

First option : Take all three equal stands.

Second option : Take two equal and one non-equal stands.

Third option : Take all three non-equal stands.

Ask students to make the triangles of all options.

1st option 2nd option 3rd option

Q. Can you find the fourth option?

Now, Name the triangles so formed as Equilateral Triangle, Isosceles
Triangle and Scalene Triangle.

On the basis of the sides of a triangle, we classify them as,

(a) Equilateral triangle: Having all sides equal in length.

(b) Isosceles triangle: Having two sides equal in length.

Maths Zone - Grade 5 15

(c) Scalene Triangle : Having none of the sides equal in length.

AP X

Y

BC Q R
Equilateral Triangle Isosceles Triangle Z

Scalene Triangle

Exercise 1.4

1. Classify the following triangles into Equilateral Triangle, Isosceles
Triangle and Scale Triangle.

a. b. c.

_____________ _____________ _____________

d. e. f.

_____________ ______________ _____________

16 Maths Zone - Grade 5

2. Measure the length of each sides of the triangles and classify them
as Equilateral Triangle, Isosceles Triangle and Scalene Triangle.

a. b.

P PQ = ___ cm A AB = ___ cm

QR = ____ cm BC = ___ cm

Q R PR = ____ cm B CA = ___ cm

C

∴DPQR is ............. Triangle. ∴DABC is ............. Triangle.

c. d.

X XY = ___ cm L LM = ___ cm

YZ = ____ cm MN = ___ cm

XZ = ____ cm LN = ___ cm

YZ MN

∴DXYZ is ............. Triangle. ∴DLMN is ............. Triangle.

e. f. W WX = ___ cm
XY = ___ cm
S ST = ___ cm
TU = ____ cm X WY=___ cm
SU = ____ cm
Y
TU
∴DWXY is ............. Triangle.
∴DSTU is ............. Triangle.

Maths Zone - Grade 5 17

Class Activities

Show this activities by the teacher and ask students to do the same

Required Material :

Geoboard or graph board or a sheet of graph paper.

First option : Make all angle acute and show the triangle in board
or graphpaper.

Second option : Make one angle right and show the triangle
geoboard, graph board or graphpaper

Third option : Make one angle obtuse and show the triangle in
geoboard, graph board or graphpaper.

Ask students to make the triangle of all options.

Q.1 Can you find the fourth option?
Q.2. By taking a straight angle, reflex angle can we make a triangle.
Name the angles so formed as,

Acute angled triangle, Right angled Triangles and Obtuse angled
triangle?

On the basis of angles of a triangle we classify them as,
(a) Acute angled Triangle: All angles are acute (less than 90°)

(b) Right angled Triangle: One angle is right angle (exactly 90°)

(c) Obtuse angled Triangle: One angle is obtuse (more than 90° and
less than 180°)

AP X

BC QR YZ
Acute angled Triangle Right angled Triangle Obtuse angled Triangle

18 Maths Zone - Grade 5

Exercise 1.5

1. Classify the following triangles into Acute angled Triangle, Right
angled Triangle and Obtuse angled Triangles.

a. b. c.

_____________ _____________ _____________

d. e. f.

_____________ ______________ _____________

2. Measure the angles of the following triangles with the help of a
protractor and classify them into Acute, Right and Obtuse angled
triangle.

a. b. ∠P = _____
∠A = _____ P ∠Q = _____
A
∠B = _____

∠C = _____ ∠R = _____

BC QR

∴DABC is ............. Triangle. ∴DPQR is ............. Triangle.

Maths Zone - Grade 5 19

c. d. A ∠A = _____
P ∠P = _____
Q ∠B = _____
∠Q = _____
∠C = _____
∠R = _____ C
B
R

........................................................................................... ...........................................................................................

e. f.

X ∠X = _____ L ∠L = _____

Z ∠Y = _____ ∠M = _____

Y ∠Z = _____ M N∠N = _____

........................................................................................... ...........................................................................................

3. Write (T) for true and (F) for false for the following statements.
a. A right angled triangle has two Acute angles. ................................
b. An Equilateral Triangle is also Isosceles Triangle. ....................
c. An Isosceles Triangle can be Obtuse angled Triangle also ...........
d. An Isosceles Triangle can be Right angled Triangle also. ..................
e. A Triangle cannot have two right angles. .........................................
f. An Equilateral Triangle can have an obtuse angle. ..........................
g. A Scalene Triangle can be Isosceles Triangle also. ..........................

20 Maths Zone - Grade 5

Sum of Interior Angles of a Triangle

Class Activities

First Option
Take a wooden model of a triangle as shown in the figure and fold all the
angles at a point of a side.

⇒

At this point all angles forms a

Wooden Model straight line.



So, sum of interior angles of a triangles is 180°.

Second Option

Ask the students to make a paper triangle and request them to fold the
angles at a point of a side and prepare that the sum of the interior angles
of a triangle.

⇒

Paper Triangle At this point all angles
forms and straight line.

Third option

Take three congruent triangles. and mark the interior angles by A, B, C
respectively in all triangles. Then, join all three angles at a point taking A
of first B of second & C of third triangles.

B CA B⇒ B
CA B AC
CA

Maths Zone - Grade 5 21

Using any one option, make the students clear about the sum of interior
angles of a triangle is 180°.

Class Activities

Ask the students to draw a triangle of their choice and ask them to name
the vertices and measure all angles. Again ask them to add all the angles.

Now, what is the sum of the interior angles of a triangle? A
∠A = _____

∠B = _____

∴ 180° ∠C = _____ B C
Sum = 180°
⇔

Example 1

Find the unknown angles of the given triangle without measurement.
A
Solution:

∠A + ∠B + ∠C = 180° 80°

or, 80° + 60° + x° = 180° 60° x°
or, 140° + x° = 180° B C
or, x° = 180° – 140°
or, x° = 40° Alternate process

First add the known angles,
i.e., 80° + 60° = 140°.
Then, Subtract the sum from 180°
i.e. 180° – 140° = 40°
Hence unknown angle x° = 40°

22 Maths Zone - Grade 5

Exercise 1.6

1. Find the unknown angles of the following triangles.

a. b. c.

AP M
25°
x° 60°

60° x° x° 135°
BC Q 70° N O

R

d. e. f.
AX P

x° a° x°

50° 50° a° a° 80° 50°
B C Y Z Q R

g. h. i.

A P X

2x x° 3x

x 60° x° Yx 2x Z

B CQ R

Maths Zone - Grade 5 23

Lesson

3 Quadrilaterals

A closed plane figure having four sides, four angles and four vertices is

known as quadrilateral. P

In Quadrilateral OPQR O Q
‰‰ OP, PQ, QR and OR are sides.
‰‰ ∠O, ∠P, ∠Q and ∠R are angles.
‰‰ O, P, Q and R are vertices.

Class Activities 1 R

Ask the students to draw a quadrilateral of their choice and measure all the
interior angles add all the angles of the quadrilateral.

Now, ask them, what is the sum of interior angles of a quadrilateral?

∠P = _____ P

∠Q = _____

∠R = _____ S Q
∠S = _____ R
∴ 360° ⇔ Sum = 360°



Class Activities 2

First Option
Ask the students to make a quadrilateral of the paper and ask them to cut
into two triangles.
And, clarify them, the sum of angles of 1st triangle is 180°.
The sum of angles 2nd triangle is 180°.
∴ In total 180° + 180° = 360°
The sum of interior angles of a quadrilateral is 360°.

24 Maths Zone - Grade 5

⇒⇒ 180°

+ 180°

360°

Second option
Take four congruent quadrilaterals of different colors. Mark the interior
angles by 1, 2, 3 and 4 and arrange the four angles 1,2,3, 4 of all quadrilaterals
at a point. It makes a complete turn at that point. Therefore, the sum of
interior angles of a quadrilaterals is 360°.

In figure,

1

42

1 111 ⇒ 11
4 2 4 24 24 2 3

3 333 4 24 2

1 3
3

42

3

Example 1 P
110°
Find the unknown angle of a quadrilateral.

S x°

Solution: 80° Q

∠P + ∠Q + ∠R + ∠S = 360° 120°

or, 110° + 80° + 120° + x° = 360° R

or, 310° + x° = 360° Alternate process

or, x° = 360° – 310° First add the known angles,
\ x° = 50°. i.e., 110° + 80° + 120° = 310°.
Now, subtract the sum from 360°

i.e. 360° – 310° = 50°

∴The unknown angle x° = 50°

Maths Zone - Grade 5 25

Exercise 1.7

1. Find the measurement of the length of all sides of the given
quadrilaterals.

a. b. c. M

A S R

B O

D P N
C PQ

AB = _____ cm PQ = _____ cm MN = _____ cm
BC = _____ cm QR = _____ cm NO = _____ cm
CD = _____ cm RS = _____ cm OP = _____ cm
DA= _____ cm SP= _____ cm PM = _____ cm

d. e. f.

S T RS EF

VU U T HG

ST = _____ cm RS = _____ cm EF = _____ cm

TU = _____ cm ST = _____ cm FG = _____ cm

UV = _____ cm TU = _____ cm GH = _____ cm

VS = _____ cm UR = _____ cm HE = _____ cm

2. Measure the angles of the following quadrilaterals and find the sum

of each of them.

a. b. c.

A PQ E

B

S RG
DC HF

26 Maths Zone - Grade 5

∠A = ∠P = ∠E =
∠B = ∠Q = ∠F =
∠C = ∠R = ∠G =
∠D = ∠S = ∠H =
Sum = Sum = Sum =

d. e. f. TQ

I J MN

LK P OS R

∠I = ∠M = ∠Q =
∠J = ∠N = ∠R =
∠K = ∠O = ∠S =
∠L = ∠P = ∠T =
Sum = Sum = Sum =

3. Find the unknown angles of the following quadrilaterals.

a. b. c.

A B PQ MN
79° x°
x° 90° z° 45°

70° 85° C 90° 90° 45° 135°
D
S R P O

d. e. f.

X Z LM C D

15° Y 15° 120° y° 90° x°

x° 60° 70° N 90° 45°
30°
O F E

W

g. h. i.

P Q A EF
2x° 4x° x°
3x° x°

D x° x° B x° 150°

S 2x° x° R x° H G

C Maths Zone - Grade 5 27

Maths Fun

Remove six line segments to leave four triangles

Move two line segments to make the pig moving towards opposite
direction.

PIG

28 Maths Zone - Grade 5

Practice Zone

Group 'A'

A. Circle the correct answer of the following questions.

1. What instrument is used to measure the angles?

a. Compass b. Divider c. Ruler d. Protractor

2. Which of the following is obtuse angle?

a. 800 b. 2800 c. 1080 d. 1800

3. The angle which lies between 181° to 359° is called __________ angle.

a. Acute b. Obtuse c. Reflex d. Straight

4. What is the sum of the angles of a triangle?

a. 170° b. 190° c. 270° d. none

5. The sum of four angles of a quadrilateral is

a. 180° b. 90° c. 360° d. 60°

6. What is the triangle of all sides equal called?

a. Isosceles Triangle b. Equilateral Triangle

c. Right Triangle d. Scalene Triangle

B. Fill in the blanks

1. 2250 is called………….angle.

2. A triangle in which two of its sides are equal is called a…........

triangle.

3. The instrument used to measure an angle is………………….

4. How many vertices & sides are there in a A

quadrilateral? ….and .....

5. Name the angle in two ways……… and ….........

B C

Maths Zone - Grade 5 29

Group 'B'
A. Solve the following questions

1. Categorize the following angles. :..............
15°, 115°, 215°, 315°, 36 12°, 90°, 91°, 179°
a. Obtuse angles :.............. b. Reflex angles

c. Acute angles : ………. d. Right angle : …….....

2. Measure the following angles.

AP
C

Q T P
A
B R
.............................
............................. ............................

3. Identify the following triangles.

a. 4 cm b.
4 cm
20°

120°
40°

4 cm


30 Maths Zone - Grade 5

4. Classify the triangles according to sides that is Equilateral Triangle,
Isosceles Triangle and Scalene Triangle.

A 5 cm A A

6 cm 6 cm B 7 cm 7 cm 8 cm

B 6 cm C 5 cm B 6 cm C
C


5. If, in a triangle ABC, ∠A = 80°, ∠B = 75°, find the value of∠C.

6. Find the value of x in the given quadrilateral P

PQRS. x
85° Q

S 90°

104°

R

Exercise 1.1 Answers of Unit 1
Exercise 1.2
Exercise 1.3 : Show to your teacher
Exercise 1.4 : Show to your teacher
Exercise 1.5 : Show to your teacher
Exercise 1.6 : Show to your teacher
Exercise 1.7 : Show to your teacher
: Show to your teacher
: Show to your teacher

Maths Zone - Grade 5 31

UNIT

2 CONCEPT OF
NUMBERS

Specific Objective Prescribed by CDC

‰‰ T o count, read and write the numbers more than crore in Hindu Arabic
Numerals (number and number names) and their place value table.

‰‰ To read and write numbers up to 1 million.
‰‰ T o use comma(,) for the numbers both in Nepali and International system
‰‰ To distinguish the prime and composite numbers from 1 to 100.
‰‰ To round off the numbers as needed.
‰‰ To find the square numbers from 1 to 10 and cubic numbers from 1 to 5 and

their roots (square and cube).
‰‰ To find the prime factors up to three digits numbers.

32 Maths Zone - Grade 5

Lesson

1 Number System

National System of Numeration

Class Discussion

Periods Crores Lakhs Thousands Ones

Place Name Ten Crores Ten Lakhs Ten Thousands Hundred Tens Ones

Crores Lakhs Thousands

342576192 3 4 2 5 7 6 1 92

∴Thirty four Crore Twenty five lakh Seventy Six thousand one hundred
and Ninety two.

34 25 76 192}
Ones}
Thousands}
Lakhs}
Crores

Use of Commas:

To indicate periods in the National system of numeration we place the first
comma after three digits from the right and then after every two digits.
∴ 34, 25, 76, 192

Example 1

Rewrite the number using comma and in words in National System.
(a) 537621796 (b) 703214918
Solution:

(a) 537621796 =53,76,21,796
∴ Fifty three crore seventy six lakh twenty one thousand seven

hundred and ninety six.

Maths Zone - Grade 5 33

Solution:
(b) 703214918 = 70,32,14,918
∴ Seventy crore thirty two lakh fourteen thousand nine hundred
and eighteen.

Example 2

Write down the numerals using place value chart for forty seven
crores sixty five lakhs thirty two thousands nine hundred and
seventy two.

Solution:

Forty seven crore, sixty five lakh thirty two thousand nine hundred
and seventy two.

Ten Crores Ten Lakhs Ten Thousand Hundred Ten One

Crores Lakhs Thousands

4 765 3 2 9 72

∴ It is 47, 65, 32, 972

Example 3

Write down the numerals for fifty six crore forty nine lakhs seven

thousand three hundred and twenty four.

Solution: Fifty six crore forty nine lakh seven thousand three

hundred and twenty four.

First: {upto ten crore nine

then 5 6 , 4 9 , 0 7 , 3 2 4 digits are there}

∴ It is 56, 49, 07, 324. Alternative Process
∴ It is 56, 49, 07, 324.
56 Crores 56, 00, 00, 000

49 Lakhs 49, 00, 000

7 Thousands 7, 000

3 hundreds 300

2 tens 20

4 ones + 4

56,49,07,324

34 Maths Zone - Grade 5

National System of numeration in Devanagari

Class Discussion

lkl/o8 s/f]8 nfv xhf/ Ps

:yfg gfd bz s/f8] s/f8] bz nfv nfv bz xhf/ xhf/ ;o bz Ps

#%$^#@!&^ # % $ ^ # @ !&^

∴ kt} L; s/f]8 5ofnL; nfv aQL; xhf/ Ps ;o 5oxQ/

sdf ko| f]u ubf{ #%,$^,#@,!&^

Face value and place value

576219821 is a 9 digit number.
Each digits of this number has two types of values.
Face value: The actual value of digit is called its face value.
Place value: The value of a digit according to its position is called its

place value.
So, In above number the face value of 5 is 5 and place value of 5 is

500000000 or fifty crore.

The smallest and the greater number

Number formed with Smallest number Greatest number
1 digit 1 9
2 digits 10 99
3 digits 100 999

9 digits 100000000 999999999

The smallest and the greatest numbers formed by the given digits.
Let's take the digits 4, 2, 7, 9, 8, 1, 6
First arrange them in increasing order : 1246789 (Smallest number)
And arrange them in decreasing order: 9876421 (Greatest number)

Maths Zone - Grade 5 35

Now numbers including zero
Greatest number and smallest number formed by 4, 0, 7, 3, 5, 9, 8
Smallest number : 3045789
Greatest number : 9875430
Do not write '0' at first because 30 is two digits number but 03 is one
digit number.

Exercise 2.1

1. Rewrite the given numerals and write the face value and place value
of colored digit.

(a) 35879234 (b) 428729881

(c) 819237845 (d) 456791820

2. Rewrite the given number using commas and in words (number
name).

(a) 437291885 (b) 579812320

(c) 373742198 (d) 502040333

3. Write down the numerals (number) using place value charts
(periods) for.

(a) Forty six crore, sixty five lakh thirty three thousand two hundred
and forty one.

(b) Thirty seven crore twenty three lakh forty five thousand nine
hundred and seventy three.

(c) Fifty crore forty lakh thirty six thousand two hundred and eighty.

(d) Sixty seven crore ninety two thousand forty eight.

4. Write down the numerals for the following number names.
(a) Thirty six crore twenty five lakh twenty three thousand four
hundred and fifteen.

(b) Eighty crore seventy three lakh forty six thousand two hundred
and thirty seven.

36 Maths Zone - Grade 5

(c) Sixty three crore forty six thousand nine hundred ten.
(d) Forty four crore eighty lakh three hundred and two.
5. Write the number in Devnagari numerals.

(a) krkGg s/f]8 k}tL; nfv ;f7L xhf/ bO' {;o rf}lt;

(b) aL; s/f]8 rf}jfnL; nfv ;t;¶L xhf/ cf7 ;o gAa]
(c) krxQ/ s/f]8 ;f7L nfv 5ofnL; xhf/ gf} ;o ;tf;L

6. Write the numerals in Nepali words.

(a) #$,#&,%$,^!& (b) #%,$$,%%,#(@ (c) @),**,#(,$))

7. (a) Write the greatest numbers of 8 digits and smallest numbers of
9 digits and find their sum.

(b) Find the difference of greatest and smallest number formed by
the digits 3, 5, 2, 4, 7, 9, 6, 1

(c) Find the greatest and smallest number formed by the digits 2, 3,
0, 4, 9, 7, 8

International System of Numeration

Class Discussion

Periods Millions Thousands Ones
Place name HTO
423851967 H.M T.M. M H. Th T.Th. Th. 967

4 238 5 1

∴ Four hundred twenty three millions, eight hundred fifty one thousand
nine hundred and sixty seven.

423 851 967
Ones
Thousands

Millions
}
}
}

Note: H.M = Hundred Million, T.M = Thousand Million, M = Million,

H. Th = Hundred Thousand, T.Th = Ten Thousand, Th = Thousand,
H = Hundred, T = Tens, O = Ones

Maths Zone - Grade 5 37

Use of Commas

To indicate periods in international system, we place commas after
every three digits from the right.
∴ 423, 851, 967

Example 1

Rewrite the number in international system using comma and in
words (number names) for

427813225
Solution:
427813225 = 427,813,225

∴ Four hundred twenty seven millions, eight hundred thirteen
thousand two hundreds and twenty five.

Example 2

Write down the number using place value chart (periods) for five
hundred twenty three millions, two hundred forty six thousand,
seven hundred and sixty three.

Solution:
Five hundred twenty three millions, two hundred forty six thousand
seven hundred and sixty three.
H.M T.M. M H. Th T.Th. Th. H T O
523246763

∴ It is 523, 246, 763

Example 3

Write down the numerals for three hundred forty millions, five
hundred twenty thousand six hundred eleven.

Solution: Three hundred forty millions, five hundred twenty thousand six
hundred and eleven.

∴ It is 340, 520, 611

38 Maths Zone - Grade 5

Comparison between National and International System

National System

Crores Lakhs Thousands Ones
Ten One Hundreds Tens
Ten One Ten One Ones
crores crore lakhs lakh Thousands Thousand 100 10
Hundred Ten 1
100000000 10000000 1000000 100000 10000 1000 One
Ones
Hundred Ten Millions Hundred Ten One
Millions Millions
Thousand Thousand Thousand
Millions
Thousands

International System

National System : International System
1 Lakhs : 100 Thousands
10 Lakhs : 1 Million
1 Crore : 10 Millions
10 Crores : 100 Millions

Exercise 2.2

1. Rewrite the given numbers in international system using commas
and in words (number names).

(a) 213517347 (b) 425618205

(c) 800700444 (d) 918763258

2. Write down the number using place value chart (periods) for :

(a) Four hundred sixty three million, two hundred ninety seven
thousand five hundred and twenty four.

(b) Eight hundred forty six million, four hundred fifty six thousand
nine hundred and seventy three.

(c) Seven hundred and million, four hundred forty thousand six
hundred eighty six.

Maths Zone - Grade 5 39

3. Write down the numerals for
(a) Two hundred eighteen million, five hundred three thousand six

hundred and eighty two.
(b) Four hundred and seventy six million, three hundred thousands

two hundred ninety.
(c) Five hundred two million, three hundred ninety eight thousand

and five.
4. Write the place name and place value of the coloured digits of the

numerals in both National and International system using commas.
(a) 637250654 (b) 276432119
5. Write the corresponding values
(a) 1 lakh = ............ thousands
(b) 10 lakhs = ............ millions
(c) ............ lakhs = 5 millions
(d) ............ Crore = 10 millions
(e) 50 crores = ............ millions





40 Maths Zone - Grade 5

Lesson

2 Rounding of Numbers

Class Discussion

Rounding means making a number simpler but keeping its value close to

what it was. The result is less accurate but easier to us.

Round off the given numbers nearest to 10, 100 and 1000

14 is nearer to 10 17 is nearer to 20 We can write 14 as 10
and 17 as 20 rounded
10 11 12 14 15 16 17 18 19 20 off nearest to 10.

15 is in the middle but always look forward We can write 15 as 20
Round off to nearest 100. rounded off nearest
10.

100 110 120 130 140 150 160 170 180 190 200 We can write 130 as 100
and 160 as 200 rounded
off nearest 100.

150 is in the middle but always look forward We can write 150
Round off to nearest 1000. as 200 rounded off
nearest 100.
3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000
We can write 3200 as 3000
and 3800 as 4000 rounded
off nearest 1000.

3500 is in the middle but always look forward We can write 3500
as 4000 rounded off
Rules for Round off Numbers nearest 1000.

Let's take a number 35279

• Find the place to which you wish to round and underline it

35279 35279 35279
Tens Hundred Thousand and so on.

• If the digit to the right of underline digit is 5 or greater, add 1 to the
underlined digit.

• If the digit to the right is less than 5, leave the underlined digit unchanged.

Maths Zone - Grade 5 41

• Replace each digit to the right of the underline place with zero.

35279 35279 35279

9>5 7>5 2< 5
∴ 35280 ∴ 35300 ∴ 35000

Similarly, we can Round off to the nearest lakhs, ten lakhs, crore and
millions, Ten millions etc.

Exercise 2.3

1. Round off the number to the nearest 10.

(a) 23 (b) 35 (c) 214 (d) 567

2. Round off the number to the nearest 100.

(a) 454 (b) 666 (c) 4567 (d) 4827

3. Round off the number to the nearest 1000.

(a) 4879 (b) 2329 (c) 27435 (d) 25512

4. Round off the number 587673421 to the nearest,

(a) Ten thousands (b) Lakhs (c) Crores

(d) Million (e) Ten million

5. (a) Total number of tourists visiting Rara Lake during last year was
56,232. Express this number into nearest ten thousands.

(b) House of Representatives Result of Nepal of the election 2074 is
given below. Round off these numbers into nearest lakh.

Party CPN- Nepali Maoist SSF RJP Others
Votes UML Congress Centre 472254 470201 996685
3128389 1303721
3173494

42 Maths Zone - Grade 5

Various Types of Numbers

Natural Numbers/Counting Numbers:

The counting numbers such as 1, 2, 3, 4 ..... 5 etc are called
Natural numbers. Smallest natural number is 1 greatest number
is undefined.

Whole Numbers:

The counting numbers including 0(zero) are called whole numbers.

E.g.: 0, 1, 2, 3 .......... smallest whole number is 0 and greatest whole

number is undefined.

Even Numbers: Factors

The natural numbers which are The numbers which can divide a
exactly divisible by 2 are called number without leaving remainder
are called factors of the number.

even numbers. E.g.: 2, 4, 6, 8, ...... Factors of 6 are 1, 2, 3, and 6.

Odd Numbers:

The natural numbers which are not exactly divisible by 2 are called

odd numbers. E.g.: 1, 3, 5, 7, 9 , ...... Multiples

Prime numbers The numbers which can be divided

The numbers that have 1 and the by a number are called multiples of
number itself as a factors are prime the number.

numbers. E.g.: 2, 3, 5, 7, ........ Multiples of 5 are 5, 10, 15, 20, ....

Composite numbers

The numbers that have more than two factors are composite numbers.

E.g.: 4, 6, 9, 12, ........



Now, let's investigate the ideas for prime and composite numbers.

Numbers Arrangements Factors/Products
1
1

2 1×2

3 1×3

Maths Zone - Grade 5 43

4 1 × 4, 2 × 2
5 1×5
6 1 × 6, 2 × 3, 3 × 2
7 1×7

8 1 × 8, 2 × 4, 4 × 2

9 1 × 9, 3 × 3

From the table we can see that the numbers 2, 3, 5 and 7 have only one
arrangement. So, these numbers are prime numbers.

Class Activities

Perform the following activities 9 10
19 20
Step 1 : Write down the numbers from 1 to 100 as shown. 29 30
39 40
Table - 1 49 50
59 60
12345678 69 70
11 12 13 14 15 16 17 18 79 80
21 22 23 24 25 26 27 28 89 90
31 32 33 34 35 36 37 38 99 100
41 42 43 44 45 46 47 48
51 52 53 54 55 56 57 58
61 62 63 64 65 66 67 68
71 72 73 74 75 76 77 78
81 82 83 84 85 86 87 88
91 92 93 94 95 96 97 98

44 Maths Zone - Grade 5

Step 2:

(i) Cross 1 because it is not prime.
(ii) Encircle 2 and 5 then cross all the numbers of the column 2 and 5.
(iii) Encirlce 3 and 7.
(iv) Cross all the numbers of the column 4, 6, 8 and 10 because all
these numbers are even.

Step 3: Rewrite the remaining numbers in table 2.

Table - 2

23 5 7 9

11 13 17 19

21 23 27 29

31 33 37 39

41 43 47 49

51 53 57 59

61 63 67 69

71 73 77 79

81 83 87 89

91 93 97 99

Step 4 : Cross the multiples of 3 and 7 respectively and rewrite the remaining

numbers in table 3.

Table - 3

23 5 7

11 13 17 19

23 29

31 37

41 43 47

53 59

61 67

71 73 79

83 89

97
Step 5: Write all the prime numbers from 1 to 100.

∴ The prime numbers from 1 to 100 are ..........

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,

43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Note: Teachers can use Sieve of Eratosthenes method to find prime number.

Maths Zone - Grade 5 45

Exercise 2.4

A. Circle the correct option.
1. The smallest natural number is

(a) 1 (b) 0 (c) Undefined (d) 2

2. The greatest whole number is

(a) 1 (b) 0 (c) 2 (d) Undefined

3. The natural numbers which are exactly divisible by 2 are called

(a) Natural number (b) Whole number

(c) Odd number (d) Even number

4. 1, 3, 5, 7 ........... are the example of
(a) Natural number (b) Whole number

(c) Odd number (d) Even number

5. The first three multiples of 4 are ..........

(a) 2, 4, 6 (b) 4, 6, 8 (c) 4, 8, 12 (d) 8, 12, 20

6. The possible factors of 6 are ............

(a) 2 and 3 (b) 1, 2, 3 and 6

(c) 1 and 6 (d) 1, 2, 3

7. The numbers that have only two factors are called

(a) Natural numbers (b) Whole numbers

(c) Odd numbers (d) Prime numbers

8. Composite numbers have .......... factors

(a) one (b) two (c) no factors (d) more than two

9. The prime numbers between 10 to 20 are

(a) 11, 13, 15, 17, 19 (b) 11, 13, 17, 19

(c) 13, 15, 17, 19 (d) 11, 15, 17, 19

10. How many prime numbers are there between 1 to 100.

(a) 15 (b) 25 (c) 35 (d) 45

11. The even prime number is

(a) 2 (b) 4 (c) 6 (d) 10

12. Write first five composite numbers.

(a) 2, 3, 5, 7, 11 (b) 2, 4, 6, 8, 10

(c) 4, 6, 8, 9, 10 (d) 1, 3, 5, 7, 9

B. Write the prime numbers between 1 to 100. Also identify the even
prime numbers.

46 Maths Zone - Grade 5

}Lesson

}3 Prime Factorization

Class Discussion

A prime number has exactly two factors 1 and itself.
1×7= 7

Factors Product

The first four prime numbers are 2, 3, 5 and 7

Divisibility test of first four prime numbers

By 2 : All even numbers end with a digit of 0, ,2, 4, 6 and 8.
eg: 10, 14, 44, 88 etc
By 3 : If the sum of the digits of a number is divisible by 3, then the

number is also divisible by 3.
eg: 54 ⇒ 5 + 4 = 9, 9 is divisible by 3
So 54 is divisible by 3.
By 5 : If the last digit of a number is 5 or 0, then the number is also

divisible by 5.
eg: 50, 65, 105 etc.
By 7 : Double the last digit and subtract it from the remaining number.

If the result is divisible by 7, then the number is also divisible by
7.
e.g: 315 ⇒ 31 - ( 2 × 5) = 21
and 21 ÷ 7 = 3
So, 315 is divisible by 7.

The word composite means made up of various part.
Each composite number is made up of a single set of prime factors.

Maths Zone - Grade 5 47

Lets investigate the number up to 15. 4 5
123 =2×2
10
6 7 8 9 =2×5
=2×3 =2×2×2 =3×3
12 15
11 =2×2×3 13 14 =3×5
=2×7

The process of resolving a number into factors such that all of its factors
are prime is known as prime factorization

Factors Tree Method Successive Division method

Example 1

Find the prime factors of 24 by factor tree method.

Solution:

24

2 12 Composite

26 Composite
No Composite
Start with the 23
smallest prime
factor of the 24 = 2 × 2 × 2 × 3
given number. Factor Tree Method

Restate the prime factors: 24 = 2 × 2 × 2 × 3
Using Index/exponential notation 24 = 23 × 3

48 Maths Zone - Grade 5

It doesn't matter how you can split your composite numbers you always
get same prime factors.

24 24

38 42 × 162 Note: It is better to
3 ×2 ×4 write prime numbers
2×2×2 × 3 in ascending order.
3 ×2×2 × 2 24 = 2 × 2 × 2 × 3
∴ 24 = 2 × 2 × 2 × 3

Example 2

Find the prime factors of 18 by successive division method.

Solution:

2 18 18 is even so it is divisible by smallest prime number 2.
39
33 2 × 9 = 18, write the quotient below the dividend and repeat the
same process until not getting 1 in the quotient.
1

\ 18 = 2 × 3 × 3

Exercise 2.5

1. Express the following numbers as the product of their prime factors
by the 'factor - tree' method.

(a) 16 (b) 27 (c) 40 (d) 90 (e) 210

2. Find the prime factors of the following by successive division
method.

(a) 42 (b) 72 (c) 96 (d) 144 (e) 216

(f) 215 (g) 315 (h) 420

Maths Zone - Grade 5 49

Lesson

4 HCF and LCM

Highest Common Factor (HCF)

Highest Common Factors (HCF) of two or more numbers is the greatest
number which divides the given numbers without any remainder. Greatest
Common Divisor (GCD) or Greatest Common Factor (GCF).

Let us consider two numbers 12 and 16.

Possible factors of 12 are 1, 2, 3, 4, 6, 12 1 × 12, 2 × 6, 3 × 4

Possible factors of 16 are 1, 2, 4, 8, 16 1 × 16, 2 × 8, 4 × 4

Common factors are 1, 2, 4

Highest Common Factor = 4

∴ HCF = 4

Finding HCF: Possible Factors:
1. Possible factors method
2. Prime factorization method Number that multiply together to
3. Division method give you the original number.

Example 1 E.g. : 6 × 2 = 12

2 and 6 are factors of 12

Similarly 3 and 4 are also the
possible factors of 12

Find the HCF of 6 and 8 by possible factors method.

Solution:

Possible factors of 6 = 1 , 2 , 3, 6 1 × 6, 2 × 3

Possible factors of 8 = 1 , 2 , 4, 8 1 × 8, 2 × 4

Common factors = 1, 2

Highest Common Factors = 2

∴ HCF = 2

50 Maths Zone - Grade 5