The Leading Maths - 4

Allied Publication Pvt. Ltd. Sitapaila, Kathmandu Ph. No.: 01-5388827 The Leading MATHS 4 Author Ashok Dangol M.Ed., Maths (TU) ALLIED Prepared on New Curriculum Issued by CDC, Sanothimi, Bhaktapur, Nepal

Allied The Leading MATHS 4 Publisher Allied Publication Pvt. Ltd. Sitapaila, Kathmandu Phone : 01-5378629, 5388827 Written by Ashok Dangol M.Ed., Maths (TU) Special Thanks Nabaraj Pathak Lalbabu Prasad Yadav Jit Bahadur Khanal Rupa Maharjan Copyright All rights reserved with the copyright holder. Edition First - 2080 (5000 pcs.) Computer Icon Design House #9849098999 Printed in Nepal

iv Creative Maths -VI Approved by CDC, Nepal PREFACE This Allied The Leading Mathematics - 4 is basically meant for making the teachers and taught active while teaching and learning mathematics. The contents and extent of the series are strictly contained and arranged in accordance with the new vision and mission of the latest New Curriculum 4-5 of Basic Level of CDC, Nepal. This series is basically an outcome of my untiring effort and patience. The long and dedicated service in teaching and popularization of mathematics has been a great asset in preparing this series. It has been designed as a textbook for English medium private and government school students with a new approach. This book provides maximum benefit to both teachers and students because of the following unique features: Unique Features of this Book Ö Arranged especially focusing on child psychology of teaching and learning mathematics which are based on the Areas of Basic Level Crriculum 6-8. Ö Prepared with the firm belief that “Mathematics begins at Home, grows in the Surroundings and takes shape in School (HSS Way)”, and sincere attempts have been made to make the learner, the teacher and reader feel “Mathematics is Fun, Mathematics is Easy and Mathematics is Everywhere (FEE Concept)”. Ö Written the focus of students’ activities and easily perform teaching-learning activities for teachers. Ö Well arranged the four colours of the whole book supports to find easily Units, Chapters, Lessons, Examples, Practices, and other topics from Content. Ö Every Theme begins with its estimated teaching hours (Theory + Practical), competency, learning outcomes, Warm-Up for pre-knowledge. Ö Highlighted the important terms, notes and key points. Ö Included sufficiently all types of Classwork Examples and Home Assessments from simple to complex with suitable figures and reasons. Ö Included Project Works as self-practice to the students at home for some days' activities to memories long time about the entire chapters. Ö Included Mixed Practice and Confidence Level Tests as self-evaluations for Success and Competent by themselves. Ö Available Individual Practical Evaluation Sheet at the end. PREFACE It is very much hoped that with all the above features, this book will be found really fruitful by teachers and students alike. Thank Allied Publication Pvt. Ltd., Kathmandu, Nepal for taking responsibility for publishing this book, Nariswor Gautam for language editing, Dev Krishna Maharjan for an attractive art of pictures, and Binod Bhandari for an attractive design. I would like to extend my sincere gratitude to the persons whose ideas or creations are directly or indirectly incorporated into the text. I would like to extend my thanks to the teachers and the students who helped me to verify the answers and to check the manuscript of this book. Also, many thanks to the schools that applied this book and suggested it to me. Finally, I heartily welcome criticisms, feedbacks and suggestions from readers so that it may appear with revise from in the coming edition and will be gratefully and thankfully acknowledged and honored.

iv Creative Maths -VI Approved by CDC, Nepal PREFACE This Allied The Leading Mathematics - 4 is basically meant for making the teachers and taught active while teaching and learning mathematics. The contents and extent of the series are strictly contained and arranged in accordance with the new vision and mission of the latest New Curriculum 4-5 of Basic Level of CDC, Nepal. This series is basically an outcome of my untiring effort and patience. The long and dedicated service in teaching and popularization of mathematics has been a great asset in preparing this series. It has been designed as a textbook for English medium private and government school students with a new approach. This book provides maximum benefit to both teachers and students because of the following unique features: Unique Features of this Book Ö Arranged especially focusing on child psychology of teaching and learning mathematics which are based on the Areas of Basic Level Crriculum 6-8. Ö Prepared with the firm belief that “Mathematics begins at Home, grows in the Surroundings and takes shape in School (HSS Way)”, and sincere attempts have been made to make the learner, the teacher and reader feel “Mathematics is Fun, Mathematics is Easy and Mathematics is Everywhere (FEE Concept)”. Ö Written the focus of students’ activities and easily perform teaching-learning activities for teachers. Ö Well arranged the four colours of the whole book supports to find easily Units, Chapters, Lessons, Examples, Practices, and other topics from Content. Ö Every Theme begins with its estimated teaching hours (Theory + Practical), competency, learning outcomes, Warm-Up for pre-knowledge. Ö Highlighted the important terms, notes and key points. Ö Included sufficiently all types of Classwork Examples and Home Assessments from simple to complex with suitable figures and reasons. Ö Included Project Works as self-practice to the students at home for some days' activities to memories long time about the entire chapters. Ö Included Mixed Practice and Confidence Level Tests as self-evaluations for Success and Competent by themselves. Ö Available Individual Practical Evaluation Sheet at the end. PREFACE It is very much hoped that with all the above features, this book will be found really fruitful by teachers and students alike. Thank Allied Publication Pvt. Ltd., Kathmandu, Nepal for taking responsibility for publishing this book, Nariswor Gautam for language editing, Dev Krishna Maharjan for an attractive art of pictures, and Binod Bhandari for an attractive design. I would like to extend my sincere gratitude to the persons whose ideas or creations are directly or indirectly incorporated into the text. I would like to extend my thanks to the teachers and the students who helped me to verify the answers and to check the manuscript of this book. Also, many thanks to the schools that applied this book and suggested it to me. Finally, I heartily welcome criticisms, feedbacks and suggestions from readers so that it may appear with revise from in the coming edition and will be gratefully and thankfully acknowledged and honored.

CONTENTS UNIT-1: GEOMETRY 7 Chapter 1 : Lines and Angles 8 Chapter 2 : PLANE FIGURES 24 Chapter 3 : SOLID OBJECTS 33 UNIT-2: NUMBERS SENSE 45 Chapter 4 : Numeral System 46 Chapter 5 : ROUNDING OFF NUMBER 73 UNIT-3: BASIC OPERATIONS 79 Chapter 6 : Addition 80 Chapter 7 : Subtraction 86 Chapter 8 : Multiplication 96 Chapter 9 : Division 108 Chapter 10 : Simplification 124 UNIT-4: FRACTION, DECIMAL AND PRECENTAGE 129 Chapter 11 : Fraction 130 Chapter 12 : Decimal 150 Chapter 13 : Percentage 161 UNIT-5: MEASUREMENT 175 Chapter 14 : Time 176 Chapter 15 : Money 193 Chapter 16 : Distance 205 Chapter 17 : Capacity 218 Chapter 18 : Weight 226 Chapter 19 : Perimeter, Area and Volume 238 UNIT-6: STATISTICS 258 Chapter 20 : Bill and Budget 259 Chapter 21 : Bar Graph 267 UNIT-7: ALGEBRA 277 Chapter 22 : Algebraic Expression 278

GEOMETRY UNIT I Estimated Working Hours : 25 COMPETENCY  Measurement and construction of lines and angles, and identification of different parts of solid objects CHAPTERS 1. Lines and Angles 2. Plane Figures 3. Solid Objects LEARNING OUTCOMES After completion of this content area, the learner is expected to be able to:  measure and draw the angles from 0° to 180° by using protractor.  measure the interior angles of the given triangle and quadrilateral.  classify the right angle, acute angle and obtuse angle.  draw perpendicular line and parallel line in square grid paper.  count the number of vertices, edges and surfaces of the cube and cuboid.

8 The Leading Mathematics - 4 CHAPTER 1 Lines and Angles ” What do you see on the railing of ladder? ” What are the steps of ladder in your home? ” What you see on the crossing roads? ” What are lines ? Discuss. ” When two lines intersect, what do you see at common part of them? ” How are the edges and corners of the board, book and duster ? ” What are parallel, intersecting and perpendicular lines ? ” What is an angle ? ” Can you measure the angles ? ” Can you draw the given angle ? ” How can you identify the greater and smaller angles ? WARM-UP Lesson Topics Pages 1.1 Revision on Line and Angle 9 1.2 Angle and Its Parts 13 1.3 Measuring Angle 17 1.4 Drawing Angle 22

GEOMETRY 9 Point and Lines Point, Dot ( ) P A B Line AB A point is that from which we begin. We use a dot (.) to denote it. It is named by a letter like as A, B, ... . A line is an unending extension of a point either side of it. It is denoted by two sided arrow-head ( ). A B Ray AB A B Line Segment It is a half line. It starts from a point and goes on and on one side only. It is represented by one -sided arrowhead ( ). A line segment AB is the join of two points A and B. It has a fixed measure called length of the line. Drawing and Measure Line segments A B CM 1 2 3 4 5 6 7 8 9 6 5 4 3 P Q 1.1 Revision on Line and Angle When two points A and B (or P and Q) are joined by straight edge or ruler, we get a line segment. It has fixed length which is easily measurable.

10 The Leading Mathematics - 4 1. Identify the name of the following : (a) (b) (c) (d) Measure the line PQ. P P Q P Q Q Indicate the points P and Q. Remove the scale. \ PQ = 3 cm Fix a scale at P overlapping with 0 and read the number in scale against Q. Q is at 3 cm on scale. EXERCISE 1.1 Your mastery depends on practice. Practice like you play. Draw AB = 4cm. Table point A. Fix scale at A overlapping with 0 and take another point B at 4. A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 5 4 3 2 1 4 cm A B

GEOMETRY 11 2. Fill in the blanks : (a) A line has ....................... on both sides. (b) A ray has ........................... on one side. (c) ................................... is dimensionless. (d) A line segment has ..................... length. (e) A line represents ........................ length. (f) A point has ................................. . 3. Match the following: Group ‘A’ Group ‘B’ Point has a length Line has position. Ray extends on both sides. Line segment has on one side. Line extends one end point. 2. Draw the line segments of the following lengths. (a) 3 cm (b) 4 cm (c) 7 cm (d) 6 cm (e) 4.5 cm P Q 3. Measure the following line segments using a cm scale. (a) (b) (c) A B \ AB = ................... \ PQ = ................... \ MN = ................... M N

12 The Leading Mathematics - 4 AB = ..................... BC = ..................... AC = ..................... A B C P S Q R PQ = ..........., RS = ........... PS = ..........., QR = ........... AB = ..........., BC = ........... CD = ..........., EF = ........... (d) (e) (f) (b) A D B C LM = ..................... MN = ..................... LN = ..................... L N M

GEOMETRY 13 When two objects meet at fixed point, there forms an angle show by drawing the line segment. In the above figures, the angles are formed in different positions as shown in the marked by red colour. The fixed point is called a vertex and the two line segment are called arms. In the adjoining figure, O is the vertex, OA and OB are arms. The coloured red corner is the angle. Let us choose any two points say A and B. Draw a ray AB. Now, choose another point C not on AB. Then draw AC. Your figure looks like one of the following figures: A is the common point of AB and AC. The other points are not common points. The angle is formed when two rays meet at a common point. The common point is called a vertex and the rays are called arms. The name of the angle formed by AB and AC with the common point A is ∠ABC or ∠CAB or simply ∠A. C A B C A B C A B C A B C A B Introduction to Angle Parts of Angle 1.2 Angle and Its Parts Geometry 11 When two objects meet at fixed point, there forms an angle show by drawing the line segment. In the above figures, the angles are formed in different positions as shown in the marked by red colour. The fixed point is called a vertex and the two line segment are called arms. In the adjoining figure, O is the vertex, OA and OB are arms. The coloured red corner is the angle. Let us choose any two points say A and B. Draw a ray AB. Now, choose another point C not on AB. Then draw AC. Your figure looks like one of the following figures: A is the common point of AB and AC. The other points are not common points. The angle is formed when two rays meet at a common point. The common point is called a vertex and the rays are called arms. The name of the angle formed by AB and AC with the common point A is ABC or CAB or simply A. C A B C A B C A B C A B C A B Introduction to Angle Parts of Angle 1.1 (A) Angle and Its Parts

14 The Leading Mathematics - 4 (d) (e) (f) 1. Colour the angles in the following objects: 12 Allied Mathematicss-4 d. e. f. 1. Colour the angles in the following objects: (a) (b) (c) (d) (e) (f) (g) (h) 2. Draw the angles by joining the following sets of the points and name them. C A B R P Q P O M Z X Y K M L F E G 3. Copy the following angles and write the name of vertex, arms and angle. a. b. c. a. b. c. R O P C A B P S D EXERCISE 1.1 (A) Your mastery depends on practice. Practice like you play. 1. Colour the angles in the following objects: 2. Draw the angles by joining the following sets of the points and name them. C A B R P Q P O M Z X Y K M L F E G (a) (b) (c) EXERCISE 1.2 Your mastery depends on practice. Practice like you play.

GEOMETRY 15 3. Observe the following figures and answer the following questions. (i) Copy the following angles. (ii) Write the name of vertex, arms and angle. (a) (b) (c) R O P C A B P S D (d) (e) (f) R O P C A B P S D 4. Name each of the following angles in two ways. (a) (b) (c) (d) (e) (f) A O B 1 P Q R 2 X Y Z 3 M N O a b T U S H I G x

16 The Leading Mathematics - 4 6. Study the following figures and name all different angles. If you find 8 angles, you are clever. A B C D E A B C D Y W Z X R O W A (a) (b) (c) (d) (e) (f) F E G D H J C I T A R S L 5. Observe the given figure and answer the following questions. (a) How many angles are formed in the figure ? (b) Name the all angles. (c) Which angles have the same arms ? Name them. A B C O

GEOMETRY 17 Which angle is greater or smaller among ABC and PQR ? To identify which angle is greater or less, we measure the amount of turning of angle in standard form. To do so, at first, the circle is equally divided into 360 parts. This is called angle gauge and used to measure the amount of angle. In the angle gauge, each small division is 1 360 of a complete rotation or circle. We call that each division is one degree (1°). A protractor is a device or tool to measure and construct angles. It has line segments marked 0 and 180 (inner one from right to left and outer one from left to right). This is the straight base. Its mid point is called the centre of the protractor. In the figure, 10th, 20th, ..., 180th rays are labeled 10, 20, 30, ..., 180. To measure the angle, we use semi-circler geometric instrument called protractor. It has 180° on both directions (clockwise or anti- clock wise). The measurement of an angle is denoted by m or . 360 Equal Parts Circle Read, Think and Learn C B A R Q P Protractor 0 180 170 10 160 20 30 150 140 40 130 50 110 100 80 100 110 70 60 50 40 30 20 10 0 180 170 160 150 140 130 120 90 80 70 120 60 1.3 Measuring Angle

18 The Leading Mathematics - 4 Steps to measure an angle Consider the angle to be measured and select a clear and good sized protractor. 60° Vertex O Base arm A C Center or middle point base line 0 180 170 10 160 20 30 150 140 40 130 50 110 100 80 100 110 70 60 50 40 30 20 10 0 180 170 160 150 140 130 120 90 80 70 120 60 Steps -1 : Coincide the centre of the protractor with the vertex O of the angle. Step - 2 : Overlap the base arm (any one of the two arms) with the base line of the protractor. Step - 3 : The ray OC passes through 60° in the inner scale. Therefore, AOC = 60° or AOC = 60°. 0 180 170 10 160 20 30 150 140 40 130 50 110 100 80 100 110 70 60 50 40 30 20 10 0 180 170 160 150 140 130 120 90 80 70 120 60 A O B C Similarly, the ray OC passes through 120° in outer scale. Therefore, AOC =120° or AOC = 120°.

GEOMETRY 19 A 60° 120° O B C Note : When we measure the amount of angle, the arm of the angle should not go out the protractor, we extend the arm by using a scale. B O A EXERCISE 1.3 Your mastery depends on practice. Practice like you play. 1. Fill in the blanks: (a) The shape of the protractor is ............. . (b) The straight line on the bottom of the protractor is called ............ . (c) A protractor is divide into ......... measuring parts. (d) A protractor has marked from 0 to .......... . 2. Measure the size of the following angles by using a protractor. ABC = ......... PQR = ......... (a) (b) P Q R C B A

20 The Leading Mathematics - 4 U V O G H O F E D L M N LMN = ......... IJK = ......... DFE = ......... GOH = ......... (c) (d) (e) (f) 3. Measure and write the angles formed by two arms of the clocks given below: (a) (b) (c) (d) (e) (f) 12 9 3 10 1 7 4 11 2 8 5 6 12 9 3 10 1 7 4 11 2 8 5 6 12 9 3 10 1 7 4 11 2 8 5 6 12 9 3 10 1 7 4 11 2 8 5 6 12 9 3 10 1 7 4 11 2 8 5 6 12 9 3 10 1 7 4 11 2 8 5 6

GEOMETRY 21 5. Observe the flag of Nepal. (a) How many angles are there in the our National Flag ? (b) Measure and write these angles. 4. Measure the each angles of the following shapes and write them with their names. A B C D E (a) (b) B C D A C B A 1. Collect the things found in your surroundings that represents the angle and draw on the A4 paper. Also, measure these angles by using protractor and present in your classroom. 2. Make the groups of 5/5 students and collect 5/5 thin straws and paste them on the A4 paper by making angles or any shape. Measure each angle on it and write these angles. 3. Cut down a paper in any shapes. Paste it on next A4 paper and name it. Measure and write the angles formed in it. PROJECT WORK

22 The Leading Mathematics - 4 We can draw angle by using protractor. Using a protractor draw an angle of 50°. Steps to draw an angle in inner scale Step -1 Draw a ray OA Step -2 Place the protractor along OA so that its center is at O. Step -3 Find 50 in the inner scale of the protractor and plot a point B on it. 0 180 170 10 160 20 30 150 140 40 130 50 110 100 80 100 110 70 60 50 40 30 20 10 0 180 170 160 150 140 130 120 90 80 70 120 60 B O A B O A 50° Step -4 Remove the protractor and join OB by using a scale and pencil. Therefore, the measure of the angle AOB is 50° i.e., AOB = 50° Steps to draw an angle in outer scale Repeat the steps 1 and 2. Step -3 Find 50° in the outer scale of the protractor and plot a point B on it. Step -4 Repeat the step 4 as above. Therefore, the measure of the angle AOB is 50°. i.e., AOB = 50° O A Read, Think and Learn 0 180 170 10 160 20 30 150 140 40 130 50 110 100 80 100 110 70 60 50 40 30 20 10 0 180 170 160 150 140 130 120 90 80 70 120 60 B B A O A O 50° 1.4 Drawing Angle

GEOMETRY 23 1. Using the inner scale, draw the following angles. (a) 10° (b) 20° (c) 40° (d) 60° (e) 80° (f) 90° (g) 100° (h) 170° (i) 105° (j) 115 (k) 135° (l) 160° 2. Using the outer scale, draw the following angles. (a) 15° (b) 25° (c) 45° (d) 75° (e) 80° (f) 90° (g) 105° (h) 115° (i) 125° (j) 140° (k) 165° (l) 175° 3. Complete the following steps. (a) Draw a line segment PQ of the length of 5.6 cm (b) Draw the angles of 60° and 45° at P and Q. (c) Are the arms that make the angles 60° and 45° at P and Q intersected? 4. Complete the following steps. (a) Draw a line segment MN of the length of 6.2 cm. (b) Draw the angles of 90° at M and N. (c) Are the arms that make the angles 90° and 90° at M and N intersected ? Draw the clocks of the time 3 o’clock, 6 o’clock, quarter to 10, half past 4 and quarter past 8. Now, measure and write the angles formed by the two hands in each clock below it. PROJECT WORK EXERCISE 1.4 Your mastery depends on practice. Practice like you play.

24 The Leading Mathematics - 4 CHAPTER 2 PLANE FIGURES ” What is the shape of the above paper note ? ” Do you measure its length and breadth of the above paper note? ” But, what is its thickness? ” How many dimensions are there with this paper note? ” What is the shape of the play-card of the traffic rule? ” What is the shape of the photo? ” What are the upper surface cheese, biscuit and clock ? WARM-UP Lesson Topics Pages 2.1 Review on Plane Figures 25 2.2 Parts of Plane Figure 26 2.3 Measuring Sides of Plane Figure 31

GEOMETRY 25 Introduction to Plane Surface What are the pointers of the needles and thorns ? What type of figure can we make from a point ? Do you imagine ? If two points are joined, what type of figure do you obtain ? What types of lines are formed ? If four points are joined on the same plane in closed shape, what types of figures do you obtain ? If any one point among the four points is not contained on the same plane, what happen ? So, we join more than three points on the same plane, we obtain a plane surface. If all the points do not contain on the same plane, what happens ? Does it make the plane figure ? Similarly, two pencils make an angle. But, which shape is obtained from three pencils when joined together in closed shape? If these pencils are not joined in closed shape, is a plane figure made? B C A D B C E A A A B B 2.1 Review on Plane Figures

26 The Leading Mathematics - 4 2.2 Parts of Plane Figure How many sticks or lines are needed to form an angle ? Each stick or line is called an arm and pointed part is called vertex. How many angles are formed by the two arms ? But, in triangle, how many sticks or lines are needed to form it ? What is the name of stick or line that forms the triangle ? Oh! It is called a side, not arm. And the pointed parts of the triangle are called vertices (singular; Vertex). How many sides and vertices are there in a triangle ? How many joints of two sides are there in a triangle? What are they called ? How many angles are there in a triangle? Do you know, how is its name a triangle ? Oh! A triangle has three angles. So, its name becomes triangle. Therefore, ‘Tri’ means ‘three’. Its is also called trilateral, where ‘Tri’ means ‘three’ and ‘lateral’ means ‘side’. 22 Allied Mathematicss-4 1.2 (A) Parts of Plane Surface How many sticks or lines need to form an angle ? Each stick or line is called an arm and pointed part is called vertex. How many angles are formed by two arms ? But, in triangle, how many sticks or lines need to form it ? What is the name of stick or line that forms the triangle ? Oh! It is called a side, not arm. And the pointed part of the triangle are called vertices (singular; Vertex). How many sides and vertices are there in a triangle ? How many joint of two sides are there in a triangle? What are there called ? How many angles are there in a triangle? Do you know, how do its name be triangle ? Oh! A triangle has three angles. So, its name becomes triangle. Therefore, ‘Tri’ means ‘three’. Its is also called trilateral, where ‘Tri’ means ‘three’ and ‘lateral’ means ‘side’. The sides of the triangle is also called its edges. A flat surface made by three or more sides oe edges is called a plane surface. It is smooth surface. arm vertex angle arm Side Side Side Vertex Vertex Vertex Angles C A B Angles Side Vertex Vertex Vertex Vertex Side Side Side arm vertex angle arm Side Side Side Vertex Vertex Vertex Angles C A B Angles Side Vertex Vertex Vertex Vertex Side Side Side

GEOMETRY 27 The sides of the triangle are also called its edges. A flat surface made by three or more sides or edges is called a plane surface. It is smooth surface. Are the surfaces of a carrot and a book plane surface ? When the carrot is cut down, what type of surface do you obtain? If any one among three corners is not joined, does it form a plane surface ? What is the name of the plane surface made by four sides ? Similarly, in quadrilateral, how many sides, vertices and angles are there ? What are the name of plane surface made by five and six sides ? How many sides, vertices and angles are there in them ? But, how many sides, vertices and angles are there in a circle ? Observe the number of vertices, angles and sides in the following plane surfaces. SN Name of Plane Surface Figure Number of Vertices Number of Angles Number of Sides 1 Triangle 3 3 3 2 Quadrilateral 4 4 4 3 Pentagon 5 5 5

28 The Leading Mathematics - 4 SN Name of Plane Surface Figure Number of Vertices Number of Angles Number of Sides 4 Hexagon 6 6 6 5 Heptagon 7 7 7 6 Octagon 8 8 8 7 Nonagon 9 9 9 8 Decagon 10 10 10 9 Circle Undefined Undefined Undefined What can you say the conclusion from the above table ? CLASSWORK EXAMPLES Example 1 Write the name of the given plane surface with vertices, angles and sides. Solution : The given plane surface is a triangle in which its vertices are A, B and C, its sides are AB, BC and CA, and its angles are ∠ABC, ∠BCA and ∠ BAC. B C A

GEOMETRY 29 2. Which of the following figures are plane surfaces or not ? EXERCISE 2.2 Your mastery depends on practice. Practice like you play. 1. Observe the surfaces of the following objects. Tick () which have the plane surface and cross () which do not have plane surfaces.

30 The Leading Mathematics - 4 3. Write the name of the following plane surfaces with vertices, angles and sides. (a) (b) (c) (d) (e) (f) 4. Draw the plane surfaces of the following and name their parts. (a) Triangle (b) Pentagon (c) Octagon (d) Quadrilateral (e) Heptagon (f) Hexagon 5. Observe the given shape and answer the following questions. (a) How many sides are there in the given plane shape? (b) Measure all the angles of the shape. (c) Are all the angles equal? D C B A E Q R P D C E F G A H B K J I G H L J N M L K C D P Q X W V U T S Y

GEOMETRY 31 D A C B 2.3 Measuring Sides of Plane Figure What are the measure of the length and breadth of the given duster ? For easier, we trace out its outlines and obtain a rectangle named as ABCD. We can easily measure the length and breadth of the duster by using a ruler. Length AB = ....... cm Breadth CD = ....... cm Again, measure CD and AD. What do you find? Oh! AB = CD = ...... cm CD = AD = ..... cm EXERCISE 2.3 Your mastery depends on practice. Practice like you play. 1. Complete the following steps. (a) Draw three different plane shapes and name them. (b) By using a ruler, find the measures of their sides. 2. Observe the given figures and answer the following questions. (a) (b) (c) (i) Name the given figures. (ii) Find the lengths of the sides of all figures: (iii) Write the longest and the shortest sides in each figure.

32 The Leading Mathematics - 4 2. Study the given figures and answer the following questions. (a) (b) (c) (i) Name the following figures. (ii) Find the lengths of the sides of all figures: (iii) Write the longest and the shortest sides in each figure. 3. Observe the given figures and answer the following questions. (a) (b) (i) Name the following figures. (ii) Find the lengths of the sides of all figures:. (iii) Are all the sides equal ? Draw the outlines of five solids that have plane surfaces and name them. Measure and write their length and breadth. PROJECT WORK J K L M N K J L G H I

GEOMETRY 33 CHAPTER 3 SOLID OBJECTS ” What are the above pictures ? Name them. ” What are the differences between thread and paper sheet or board? ” What are the differences between paper sheet and duster? ” What is a solid ? Why is solid different from a plane shape ? ” What is the meaning of 3-dimensional figure? ” What are the shapes of your book, Rubik, box, eraser, dice and pencil ? ” What is the difference between the shapes of duster and dice ? ” What are the faces, edges and vertices of the board and duster ? ” How many faces, edges and vertices have duster and dice ? ” How many faces, edges and vertices are there in duster ? ” What are the faces of duster and dice? WARM-UP Lesson Topics Pages 3.1 Review on Solid Objects 34 3.2 Different Surfaces of Solid Objects 37 3.3 Geometric Shapes of Cube and Cuboid 39 3.4 Face, Edge and Vertex of Cube and Cuboid 40

34 The Leading Mathematics - 4 How is the solid object? How is the solid object different from plane shape? How many faces or surfaces are on the rectangular paper sheet and duster ? The plane surface has only one surface but the duster has 6 surfaces. How many surfaces does the given triangular pyramid have? A shape that has more than three surfaces, is called a solid. Also, the plane surface has only length and breadth, but the solid has length, breadth and height. What are the differences in the given two solids ? What are their name? The red solid has 6 identical plane surfaces, but the blue solid has only opposite identical surfaces. So, the red typed solid is called cube and the blue typed solid is called cuboid. For example, dice and geometric box are cube and cuboid shaped solids respectively. Cube and Cuboid are the geometric names of solid. Geometry 27 How is solid object? Hoe does the solid different from plane shape? How many faces or surfaces on the rectangular paper sheet and duster ? The plane surface has only one surface but the duster has 6 surfaces. How many surfaces does the given triangular pyramid have? A shape that has more than three surfaces, is called a solid. Also, the plane surface has only length and breadth, but the solid has length, breadth and height. What are different in the given two solids ? What are their name? The red solid has 5 identical plane surfaces, but the blue solid has only opposite identical surfaces. So, the red typed solid is called cube and the blue typed solid is called cuboid. For example, dice and geometric box are in cube and cuboid shaped solids respectively. Cube and Cuboid are the geometric names of solid. EVISION CHAPTER 3.1 1.3Review on Solid Objects SHAPES OF SOLID OBJECTS

GEOMETRY 35 But what are the name of the following solids ? Discuss. (a) (b) (c) (d) (e) (f) (i) This is ................................... geometric shape. (ii) This is ................................... geometric shape. (iii) This is ................................... geometric shape. (iv) This is ................................... geometric shape. (v) This is ................................... geometric shape. (vi) This is ................................... geometric shape. EXERCISE 3.1 Your mastery depends on practice. Practice like you play. 1. Write the geometric name of the following solid objects:

36 The Leading Mathematics - 4

GEOMETRY 37 Which one has flat surface (s) ? Which one has round curved surface ? How many surfaces are there in each of them ? EXERCISE 3.2 Your mastery depends on practice. Practice like you play. 3.2 Different Surfaces of Solid Objects 30 Allied Mathematicss-4 Which one has flat surface (s)? Which one has round curved surface? How many surfaces are there in each of them? 1. Tick the correct answers. a. Which solids have flat surface ? b. Which solid has a perfectly round surface ? c. Which solid has both flat and curved surfaces ? 1.3 (A) Different Surfaces of Solid Objects Read, Think and Speak (i) (i) (i) (ii) (ii) (ii) (iii) (iii) (iii) (iv) (iv) (iv) EXERCISE 1.3 (A) Your mastery depends on practice. Practice like you play. Read, Think and Learn 1. Tick the correct answers. (a) Which solids have flat surface ? (b) Which solid has a perfectly round surface ? (c) Which solid has both flat and curved surfaces ?

38 The Leading Mathematics - 4 (d) Which solid has both flat and curved surfaces ? 2. Write down the number of surfaces in the following solids : Solids No. of flat surface No. of curved surface Total No. of surfaces

GEOMETRY 39 3.3 Geometric Shapes of Cube and Cuboid Read, Think and Learn Discuss the shapes of surfaces, geometric name and shape and complete the table Solid Objects Geometric Name Surface Name No. of Surface Geometric Shape 32 Allied Mathematicss-4 Discuss the shapes of surfaces, geometric name and shape and complete the table Solid Objects Geometric Name Surface Name No. of Surface Geometric Shape Cube ................ ................ Cuboid ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ 1.3 (B) Geometric Shapes of Cube and Cuboid Read, Think and Speak Cube ................ ................ Cuboid ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ ................

40 The Leading Mathematics - 4 A face is the flat surface of solid. An edge is formed when two faces meet. A vertex (or corner) is a point where the edges meet. Does a cone have a face? Does a sphere have an edge and face? Does a cylinder have any vertex? 1. Write the name and number of faces, edges and vertices in the given solids: EXERCISE 3.4 Your mastery depends on practice. Practice like you play. 3.4 Face, Edge and Vertex of Cube and Cuboid Vertices Faces Edges E H F D C B A G Read, Think and Learn Solid Name Geometric Shape No. of Faces Number of Edges Number of Vertices

GEOMETRY 41 Solid Geometric Name Geometric Shape with naming Name of Vertices Name of Edges Name of Faces 2. Write the naming of the following geometric shapes and name of faces, edges and vertices in the following solids: Collect any five cubes and cuboids that are found at your home, your surrounding and at the school and then name them. Identify their surfaces, edges and vertices. PROJECT WORK

42 The Leading Mathematics - 4 1. A triangle ABC with ∠ABC = 30o and ∠BAC = 60o is shown in the figure. (a) Measure the angle of ∠ACB by using a protractor. (b) Measure the length of BC and AC. (c) Is AC shorter than AB? Justify. 2. A line AB with 6 cm is given below. A 6 cm B (a) Draw a line AB = 6 cm by using a ruler. (b) Draw the angle of 600 from A and B naming the point of intersection C. (c) Are the length of AC and BC equal? 3. A triangle ABC is shown with BC = 4 cm. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 5 4 3 2 1 B C A (a) Measure the length of sides AC by using a ruler. (b) How long is the length of AC than length of AB? (c) Measure the angle of ABC by using a protractor. A Y X C B 60° 30° MIXED PRACTICE–I Read, Understand, Think and Do

GEOMETRY 43 4. A quadrilateral ABCD is shown in the figure. (a) How many angles are there in this quadrilateral? (b) Measure the length of sides AB and BC. (c) How much greater is the length of BC than length of AB? 5. Observe the given plane shape and answer the following question. (a) What is the name of the given shape? (b) Measure all the sides of the given shape by using ruler. (c) Which sides are equal to each other? (d) Measure all the angles of the shape by using a protractor. (e) Are all the angles of the shape equal? Which angles are equal? 6. A cuboid is shown in the figure. (a) Write any two vertices from the figure. (b) Write any two edges from the figure. (c) Write the name of largest faces. (d) Are the length of DC and EF equal? Justify. 7. A shape of cube is given alongside in figure. (a) Write any two differences between cube and cuboid. (b) Write any two pair of faces. (c) If S be the vertex of cuboid, what is the name of SX. (d) Are the length of SX, QR and PQ equal? Justify. A B C D C B D A A E F H G B D C A E F H G B D C

44 The Leading Mathematics - 4 1. Follow the following steps and answer the following questions. (a) Draw a line segment AB = 5 cm. [1] (b) Draw a angles of 30° and 60° at A and B by using a protractor. [2] (c) Are the arms that made the given angles intersected? If yes, name the intersecting point C. [2] 2. Observe the given figure and answer the following questions. (a) What is the name of the given figure? [1] (b) Measure the length of its sides using a ruler. [2] (c) Measure its angles by using a protractor. [2] 3. Observe the given solid. (a) Write the name of its geometric shape. [1] (b) Draw its geometric shape. [2] (c) Write the number of faces, edges and vertices of the solid. [2] 4. A shape of cube is given alongside in figure. (a) Write any one difference between cube and cuboid. [1] (b) Write any two pairs of faces. [1] (c) What is the name of CG? [1] (d) Are the length of AB, BF and CD equal? Justify. [2] S R Q P A E H B B G F D Attempt all the questions. FM : 20 Time : 40 Min. CONFIDENCE LEVEL TEST I GEOMETRY

ARITHMETIC 45 ARITHMETIC: NUMBER SENSE UNIT II Estimated Working Hours : 16 COMPETENCY  Counting and use of numbers up to crore in Hindu-Arabic and Devanagari numeral systems CHAPTERS 4 Numeral System 5 Rounding off Numbers LEARNING OUTCOMES After completion of this content area, the learner is expected to be able to:  read, write and present in the place value table to the numbers up to 7 digits according to national system by using Hindu-Arabic and Devanagari digits.  rounding off the numbers of 4-digit nearest tens and hundreds.

46 The Leading Mathematics - 4 CHAPTER 4 Numeral System ” Why do we use numbers in our daily life? ” Which is the starting number of counting? ” Which is the starting number of whole numbers? ” Count the scales of the ruler in cm and inches. ” What is the area of Nepal now ? ” What is the sum and difference of numbers 12 and 6? Find it by using fingers. WARM-UP Lesson Topics Pages 4.1 Revision on Numeral System 47 4..2 Counting Ten Lakhs 52 4.3 Place Value (National System) 56 4.4 Expanded Form of Numbers 60 4.5 Numbers from 1,00,000 to 9,99,999 62 4.6 Numbers from 10,00,000 to 19,99,999 64 4.7 Numbers from 20,00,000 to 39,99,999 66 4.8 Numbers from 40,00,000 to 59,99,999 68 4.9 Numbers from 60,00,000 to 79,99,999 69 4.10 Numbers from 80,00,000 to 99,99,999 70 4.11 Numbers up to One Crore 71

ARITHMETIC 47 The concept of number began together with the human civilization and people have been using numbers in different forms in different times since primitive age. Ancient people used the concept of one to one correspondence and represented number of objects by matching equal number of pebbles or sticks. 30 Allied Mathematicss-4 The concept of number began together with the human civilization and people have been using numbers in different forms in different times since primitive age. Ancient people used the concept of one to one correspondence and represented number of objects by matching equal number of pebbles or sticks. They represented three sheep by putting 3 pebbles matching one sheep to one pebble. Later on people started counting numbers in fingers, one finger one object, two fingers two objects and so on. 1 2 3 4 5 They were able to count up to 20 by using the fingers of hands and the feet. People in different civilizations have developed different numeration systems. For example, the Romans used the following symbols to represent numbers. CHAPTER - 2.1 : HINDU-ARABIC NUMBERS 2.1 Review of Numbers Read, Think and Speak They represented three sheep by putting 3 pebbles matching one sheep to one pebble. Later on people started counting numbers in fingers, one finger one object, two fingers two objects and so on. 1 2 3 4 5 They were able to count up to 20 by using the fingers of hands and the feet. People in different civilizations have developed different numeration systems. 4.1 Revision on Numeral System Read, Think and Learn

48 The Leading Mathematics - 4 For example, the Romans used the following symbols to represent numbers. I V X L C D M One Five Ten Fifty Hundred Five Hundred Thousand They also made some rules to write other numbers. The first 20 numbers in the Roman System are written as in the following : I II III IV V VI VII VIII IX X 1 2 3 4 5 6 7 8 9 10 XI XII XIII XIV XV XVI XVI XVII XIX XX 11 12 13 14 15 16 17 18 19 20 E So far, as we see here, the Romans used only three symbols I, V and X. E The symbols I and X are repeated but not V. E When I comes before the symbols V and X one is subtracted (e.g. IV = 5 - 1) E When I comes after V and X, one is added (e.g. VI = 5 + 1 = 6). E I is repeated up to three times. How many numbers can we write by using only these three symbols I, V and X in Roman system ? The Hindus in about 100 AD used the numerals : 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 and developed a system based on place value called the Hindu - Numeration system. Later on the Arabs adopted it and spread over the world and now the system is known as Hindu - Arabic Numeration System and we have been using till these days. Hindu- Arabic numbers 1 One 2 Two 3 Three 4 Four 5 Five Devanagari Numbers ! Ps @ b'O{ # tLg $ rf/ % kfFr

ARITHMETIC 49 Numerals in Place value Table and Abacus 10000 1000 100 10 1 Ten Thousand Thousand Hundred Ten One Thousand Family Unit Family T-Th Th H T O 2 3 7 4 5 Place Value Table In number system, comma (,) is used for separating the number family such as unit family, thousand family, etc. By using comma (,), 23745 is written as 23,745. 23745 in Place value table and Abacus, Abacus T-Th HTh T O 32 Allied Mathematicss-4 Numerals in Place value Table and Abacus EXERCISE 2.1 Your mastery depends on practice. Practice like you play. 1. Write the figure of digit in the following number systems. (a) Hindu - Arabic Systems (b) Devanagari System (c) Roman System 2. Write the number name of the following numbers by using comma (,): (a) 24 (b) 138 (c) 1250 (d) 2478 (e) 24823 (f) 34789 (g) 74728 (h) 342501 (i) 457821 (j) 878957 3. Write the number name of the following numbers : (a) * (b) #& (c) @$% (d) #$%! (e) %^($^ (f) *($%* (g) ($%)^ (h) !@$%^@ (i) %)^$)( (j) *($%&$ 10000 1000 100 10 1 Ten Thousand Thousand Hundred Ten One Thousand Family Unit Family T-Th Th H T O 2 3 7 4 5 Place Value Table In number system, comma (,) is used for separating the number family such as unit family, thousand family, etc. By using comma (,), 23745 is written as 23,745. 23745 in Place value table and Abacus, Abacus T-Th HTh T O Hindu- Arabic numbers 6 Six 7 Seven 8 Eight 9 Nine 10 Ten Devanagari Numbers ^ 5 & ;ft * cf7 ( gf} !) bz The most important features of the Hindu Arabic Numeration System are : E Use of ten digits, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. E Place value, the same digit has different value according to its place. E The introduction of 0 for the absence of the object in the set.

50 The Leading Mathematics - 4 EXERCISE 4.1 Your mastery depends on practice. Practice like you play. 1. Write the figure of digit in the following number systems. (a) Hindu - Arabic Systems (b) Devanagari System (c) Roman System 2. Write the numeral in words of the following numbers after using comma (,): (a) 24 (b) 138 (c) 1250 (d) 2478 (e) 24823 (f) 34789 (g) 74728 (h) 342501 (i) 457821 (j) 878957 3. Write the mineral in words of the following numbers in Devnagari system. (a) * (b) #& (c) @$% (d) #$%! (e) %^($^ (f) *($%* (g) ($%)^ (h) !@$%^@ (i) %)^$)( (j) *($%&$ 4. Write the Hindu - Arabic numbers into Devanagari numbers and Devanagari numbers into Hindu - Arabic numbers : (a) 278 (b) 7872 (c) 6249 (d) 72925 (e) 547577 (f) $)% (g) ^&*( (h) $%^&! (i) !#%@* (j) $%^&*$ 5. Write the following in Hindu-Arabic system by using a comm (,): (a) Sixty nine (b) Two hundred and seventy one (c) One thousand four hundred and five (d) Twenty five thousand and sixty seven (e) Five lakh two hundred and seven