by classklap MATHEMATICS TEXTBOOK - PART 1 Class 2 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________ NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 1 12/19/2018 10:52:46 AM
Preface IMAX partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. IMAX presents the latest version of the Passport series – updated and revised after considering the perceptive feedback and comments shared by our experienced reviewers and users. Designed specifically for CBSE schools, the Passport series endeavours to be faithful to the spirit of the National Curriculum Framework (NCF) 2005. Therefore, our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. The books are split into two parts to manage the bag weight. The aim of the NCF 2005 regarding Mathematics teaching is to develop the abilities of a student to think and reason mathematically, pursue assumptions to their logical conclusion and handle abstraction. The Passport Mathematics textbooks and workbooks for CBSE schools offer the following features: Structured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved S tudent engagement through simple, age-appropriate language S upported learning through visually appealing images, especially for grades 1 and 2 Increasing rigour in sub-questions for every question in order to scaffold learning for students Word problems based on real-life scenarios, which help students to relate Mathematics to their everyday experiences Mental Maths to inculcate level-appropriate mental calculation skills Stepwise breakdown of solutions to provide an easier premise for learning of problem-solving skills Overall, the IMAX Passport Mathematics textbooks, workbooks and teacher companion books aim to enhance logical reasoning and critical thinking skills that are at the heart of Mathematics teaching and learning. – The Authors NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 2 12/19/2018 10:52:47 AM
I Will Learn About I Recall Contains the list of learning objectives to be covered in the Discusses the prerequisite chapter knowledge for the concept from the previous academic I Think year/chapter/concept/term Introduces the concept and arouses curiosity among students I Remember and Understand Train My Brain Explains the elements in detail that Checks for learning to gauge the form the basis of the concept Ensures understanding level of students, that students are engaged in learning testing both skill and knowledge throughout Pin-up Note Contains key retention points concerning the concept I Apply I Explore (H.O.T.S.) Connects the concept to Encourages students to extend real-life situations by enabling the concept learnt to advanced students to apply what has been scenarios learnt through the practice questions Connect the Dots Maths Munchies A multidisciplinary section that Aims at improving speed of connects a particular topic to calculation and problem solving other subjects in order to enable with interesting facts, tips or tricks students to relate better to it Drill Time A Note to Parent Additional practice questions at Engages a parent in the the end of every chapter out-of-classroom learning of their child and conducting activities to reinforce the learnt concepts NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 3 12/19/2018 10:52:47 AM
Contents Class 2 1 Shapes 1.1 Identify the Geometrical Features of Objects ........................................... 1 2 Patterns 2.1 Patterns Using Shapes................................................................................. 13 73 Numbers 03.1 Count by Hundreds..................................................................................... 21 +3.2 Ordinal Numbers......................................................................................... 29 1 -3.3 Compare 3-digit Numbers......................................................................... 34 3 46 x4 Addition 9 54.1 Add 2-digit and 3-digit Numbers............................................................... 42 8 25 Subtraction 5.1 Subtract 2-digit and 3-digit Numbers........................................................ 49 5.2 S ubtract Two 1-digit Numbers Mentally.................................................... 54 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 4 12/19/2018 10:52:47 AM
Chapter Shapes 1 I Will Learn About • lines, open figures and closed figures. • drawing figures using lines. • basic flat and solid figures. • flat figures as outlines of the surfaces of solid figures. Concept 1.1: Identify the Geometrical Features of Objects I Think David drew shapes using objects like a can, a matchbox, a bangle and a cup. Do you know what these shapes are? 1 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 5 12/19/2018 10:52:47 AM
1.1 I Recall We know about the following plane shapes: Now, let us recall and learn more about them in detail. If we observe our surroundings, we will find objects of different shapes. square rectangle circle In your classroom, you find many objects of different shapes. For example, a book, paper or a blackboard looks like a rectangle. Sometimes, we see different objects having the same shape. For example, a wall clock, a photo frame or a biscuit looks like a square. 2 12/19/2018 10:52:47 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 6
1.1 I Remember and Understand We can draw shapes using straight lines or curved lines. Let us learn about straight lines. Point: A point is a dot. It has no shape or thickness. A point has no dimensions. A point is denoted by a capital letter of the English alphabet. For example, A, X, Y, P and M shown below are points. X Y A PM Line: Many points placed close to each other form a line. It has no thickness or breadth. A line only has length. So, it is called a one-dimensional figure. A straight line has no ends. It extends on both the sides. AB W e name two points A and B on a line and write it as AB . We read it as line AB. Line segment: A line segment is a part of a line. It has two points, a starting point and an end point. A line segment has an exact length. AB We write line segment AB as AB . We read it as segment AB. Ray: A ray is a part of a straight line, which has a starting point but no end point. It extends only on one side. A We write ray AB as AB . We read it as ray AB. B Straight lines are of three types. They are horizontal lines, vertical lines and slant lines. Shapes 3 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 7 12/19/2018 10:52:48 AM
Horizontal lines: Sleeping lines drawn from left to right or from right to left are called horizontal lines. Vertical lines: Standing lines drawn from top to bottom are called vertical lines. Slant lines: Sloping lines are called slanting lines. Note: We name a straight line by any two points on it. Curved lines: Lines that are not straight are called curved lines. A straight line or a curved line is a one-dimensional (1D) figure. Using straight lines, we can draw geometrical shapes such as a square, a rectangle or a triangle. Example 1: Draw the following figures. a) Circle using a curved line b) Square using straight lines Solution: a) b) 4 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 8
We can draw figures using straight lines or curved lines. Open figures: Figures which do not end at the point where they begin from are called open figures. Closed figures: Figures which end at the point where they begin from are called closed figures. Square, rectangle, triangle and circle are closed figures. Train My Brain Identify the ray, line and segment from the following: a) X b) A B Y c) R Q 1.1 I Apply We can draw closed figures on a sheet of paper. These figures have both height and width. So, they are called two-dimensional figures or 2D figures or 2D shapes. Let us learn about them in detail. Shapes 5 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 9 12/19/2018 10:52:48 AM
Square 1) It has four straight lines as sides. In the given figure, AB, BC, CD and DA are the sides. 2) All its sides are equal in length. DC 3) It has four corners. In the given figure, A, B, C and D are its A B corners. 4) W e name a square using its corners. We name the given square as square ABCD. Rectangle D C 1) It has four straight lines as sides. In the given figure, AB, BC, CD and DA are the sides. 2) Two pairs of opposite sides are equal in length. A B 3) It has four corners. In the given figure, A, B, C and D are its corners. 4) W e name a rectangle using its corners. We name the given rectangle as rectangle ABCD. Triangle 1) It has three straight lines as sides. In the given figure, AB, BC and CA are the sides. A 2) It has three corners. In the given figure, A, B, and C are the corners. 3) W e name a triangle using its corners. We name the triangle as B C triangle ABC. Circle 1) It is a curved line. .O 2) It has no sides or corners. 3) We name a circle by its centre ‘O’. 6 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 10
Example 2: Join the dots in order and name the shapes formed. G H QRQ F G RP S PE c) a) b) Solution: QR Q F E H P P RS a) Triangle PQR b) Square PQRS c) Rectangle EFGH Example 3: Observe the following pictures. Tick the type of lines used to form each object. One is done for you. Object Straight lines Curved lines Shapes 7 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 11 12/19/2018 10:52:48 AM
1.1 I Explore (H.O.T.S.) Some shapes have length, breadth and thickness. Such figures are called three-dimensional figures or 3D figures or solid shapes. The geometrical shapes of some solid objects are as follows: Solid objects Geometrical shapes Cube Cuboid Cylinder Sphere Cone Let us now see the geometrical features of these objects. Object Geometrical figures Geometrical features Vertex Face • It has 6 square faces, 12 edges and 8 vertices. Edge Cube • All the edges of a cube are equal in length. Edge Face • It has 6 rectangular faces, 12 edges and 8 vertices. Vertex Cuboid • The opposite faces of a cuboid are of the same size. • The opposite edges of a cuboid are equal in length. 8 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 12
Object Geometrical figures Geometrical features Edge • It has 2 circular flat faces Flat Face and 1 curved face. Curved face • It has 2 circular edges but Cylinder no corners. • The 2 flat faces are of the same size. Curved face • It has a curved face. Sphere • It has no edges and no Corner corners. Curved face • It has 1 flat circular face, 1 curved face and 1 corner. Flat Face Edge • It has a circular edge. Cone Let us find the geometrical shapes of a few solid objects. Example 4: Draw the geometrical shapes that form the base of these objects. Name the shapes that are formed. Shapes 9 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 13 12/19/2018 10:52:48 AM
Solution: The shapes formed are: Object Shape of the base Circle Rectangle Triangle Circle Square Maths Munchies 213 We cannot draw a complete line and a ray on paper. But we can draw a line segment on paper. Connect the Dots EVS Fun What different shapes will you use while drawing a human body? 10 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 14
English Fun Read the poem aloud. Solid shapes are fat not flat, A cone is like a party hat, A sphere is a bouncy ball, A cuboid is a building tall, A cylinder is like a soda pop, A cube is like a die you drop. Solid shapes are here and there, solid shapes are everywhere. Drill Time Concept 1.1: Identify the Geometrical Features of Objects 1) Draw the following: a) Line b) Line segment c) Ray d) Horizontal lines e) Vertical lines 2) Identify whether the following figures are open or closed. a) b) c) d) e) Shapes 11 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 15 12/19/2018 10:52:48 AM
Drill Time 3) Name the sides of the following: a) Square PQRS R b) Triangle XYZ S Z P Q X Y c) Rectangle EFGH G H EF A Note to Parent Play a game ‘I-Spy with my eyes’ with your child, in which you spy common objects around the house and the child identifies the shape. For example, television, tiffin box, plate, flask, loaf of bread and so on. 12 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 16
Chapter Patterns 2 I Will Learn About • identifying basic shape(s) in a pattern. • creating patterns using objects, shapes and numbers. Concept 2.1: Patterns Using Shapes I Think David made shapes using modelling clay and moulds. He arranged them as shown. Do you make such arrangements? Do you know what they are called? 2.1 I Recall We have already learnt about flat shapes and solid shapes. Let us revise them. NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 17 13 12/19/2018 10:52:48 AM
Identify the following shapes. Write their names in the space given below. Flat shapes Names Solid shapes Names 2.1 I Remember and Understand Repeating a shape or a group of shapes in a particular order gives rise to a pattern. For example, a) b) c) Same shapes of different colours can also be arranged to get a pattern. For example, a) b) 14 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 18
c) To continue a given pattern, follow these steps. Step 1: O bserve the first few shapes in the pattern to find a repetition. Step 2: Identify the order in which the shapes or group of shapes are repeated. Step 3: Repeat the same shape or group of shapes the required number of times. Observe the given patterns. A part of the pattern is repeated. It is highlighted as shown. a) b) c) The basic shapes in the above patterns are: The repeated a) b) c) parts of a pattern is called its basic Let us now see a few examples. shape(s). Example 1: Find the basic shapes in the given patterns. a) b) c) Solution: The groups of basic shapes in the patterns are: Patterns 15 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 19 12/19/2018 10:52:48 AM
a) b) c) Example 2: Draw and colour the missing shapes to complete the given patterns. One is done for you. a) b) c) Train My Brain _________ _________ __________ Complete the following patterns. a) __________ _________ __________ ____________ ___________ ____________ b) c) 2.1 I Apply Let us now look at some patterns that we see around us. 16 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 20
Example 3: Identify the basic shape in each of the following patterns. a) b) c) Solution: The basic shapes in the given patterns are: a) b) c) Example 4: Complete the given patterns by colouring. One is done for you. a) b) c) Example 5: Complete the following patterns. One is done for you. a) b) Patterns 17 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 21 12/19/2018 10:52:48 AM
c) d) e) 2.1 I Explore (H.O.T.S.) We can form patterns using numbers and letters too. Example 6: Fill in the missing letters or numbers in these patterns. One is done for you. a) 1A 3B 5C 7D 9E 11F 13G b) 2 4 6 8 c) A C E G d) 1 4 7 10 e) 22 20 18 16 f) M9 L8 K7 J6 Maths Munchies 213 The patterns on our fingers and thumbs are called our fingerprints. No two people in this world have the same fingerprint pattern – not even identical twin children. 18 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 22
Connect the Dots EVS Fun Living things such as flowers, birds and animals also have different patterns. For example, orchids, peacock feathers and so on. English Fun Complete the following patterns using the letters. a) P, R, _______, _______, ________ b) Z, Y, X, _______, V, ___________ Drill Time Concept 2.1: Patterns Using Shapes 1) Identify the basic shapes or group of basic shapes in each of the following patterns. a) b) c) d) e) Patterns 19 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 23 12/19/2018 10:52:48 AM
Drill Time 2) Complete the patterns given below. a) b) c) d) e) A Note to Parent Give your child patterns of missing shapes, numbers or letters to complete. Let them complete and come up with different patterns from those patterns. 20 12/19/2018 10:52:48 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 24
Chapter Numbers 3 I Will Learn About • reading and writing numerals and number names up to 999. • place values, face values and expanded forms of numbers. • ordinal and cardinal numbers. • comparing two numbers. • forming the greatest and the smallest 3-digit numbers. Concept 3.1: Count by Hundreds I Think David went to a toy store. He saw that ` 990 was written on a toy. He could not read the number. Can you read it? `990 3.1 I Recall We know that 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are 1-digit numbers. Numbers from 10 to 99 are 2-digit numbers. 10 is the smallest 2-digit number. 99 is the largest 2-digit number. We can count 2-digit numbers by ones and tens. NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 25 21 12/19/2018 10:52:49 AM
Look at the following picture. Start from 1 and connect all the dots in order. You will find a friend smiling back at you. 3.1 I Remember and Understand 9. shows 1. Ten such boxes show a 10. Suppose So, = 10 ones 22 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 26
= 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred = 1 hundred = 100 = 2 hundreds = 200 = 3 hundreds = 300 = 4 hundreds = 400 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 27 Numbers 23 12/19/2018 10:52:49 AM
In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. Let us understand this concept using a spike abacus. 1 = 1 unit in the ones We have learnt how to show the number 99 on spike an abacus. To show the number 100, we remove all the 1 = 1 unit in the green beads from the tens place. We also tens spike remove all the blue beads from the ones place. TO We then put 1 pink bead in the third spike 99 (hundreds place). 1 = 1 unit in the hundreds spike The smallest 3-digit Thus, to show 999, we put 9 pink number is 100. beads in the hundreds spike, The largest 3-digit 9 green beads in the tens spike and number is 999. 9 blue beads in the ones spike. Let us show the number 124 using a spike abacus. We put 1 pink bead in the hundreds spike. We then put TO H TO 2 green beads in the tens spike and 99 100 4 blue beads in the ones spike. In the same way, we can show the numbers 298 and 459 on the abacus. H TO 999 H TO H TO HT O 124 298 459 We can write the number names of these numbers as: 124 = One hundred and twenty-four 298 = Two hundred and ninety-eight 459 = Four hundred and fifty-nine 24 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 28 12/19/2018 10:52:49 AM
Place value and face value Place Value: Every digit in a number has a place in the place value chart. Each digit gets its value from the place it occupies. This value is called its place value. Face Value: The value of a digit that remains the same at any place in a number is called its face value. Let us understand the place values of the digits in 3-digit numbers. Consider the 3-digit number 110. Its number name is one hundred and ten. 110 has 1 hundred, 1 ten and 0 ones. It is written in the place value chart as shown. Places Hundreds (H) Tens (T) Ones (O) Values 1 10 Example 1: Find the place values and the face values of the digits in 842. Solution: 2 84 2 ones Place Value Face Value 22 4 tens 40 4 8 hundreds 800 8 Expanded form of a 3-digit number Consider the number 425. We write 425 in the place value chart as shown. H TO Place values 425 5 ones = 5 2 tens = 20 4 hundreds = 400 Numbers 25 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 29 12/19/2018 10:52:49 AM
We can write the place values of the digits of a given number with a ‘+’ sign between them. This gives the expanded form of the number. So, the expanded form of 425 is 400 + 20 + 5. The number name of 425 is four hundred and twenty-five. 425 is the standard form of the number. Consider the following examples to understand the concept better. Example 2: Write the standard forms of the following numbers. a) 9 hundreds + 4 tens + 6 ones b) 4 hundreds + 2 tens + 3 ones c) 3 hundreds + 0 tens + 8 ones Solution: To write the standard forms, write the numbers in the place value chart, as shown: HTO a) 9 4 6 b) 4 2 3 c) 3 0 8 So, the standard forms of the given numbers are: a) 946 b) 423 c) 308 Example 3: Count and write the following numbers in their expanded forms. Then, write their number names. a) b) 26 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 30
c) Solution: To write the expanded forms, write the numbers in the place value chart as shown below. Number Place Value Expanded Forms Number Names Chart H TO a) 523 523 523 = Five hundred and 500 + 20 + 3 twenty-three b) 432 432 432 = Four hundred and 400 + 30 + 2 thirty-two c) 634 634 634 = Six hundred and thirty-four 600 + 30 + 4 Train My Brain c) 991 Say the number names for: a) 358 b) 409 3.1 I Apply Let us see a few examples where we use 3-digit numbers. Example 4: Pooja collected two hundred and twenty-nine stamps. Reema collected six hundred and thirty-three stamps. Write the numerals for the number of stamps each of them collected. Solution: Stamps with Pooja = two hundred and twenty-nine = 229 Stamps with Reema = six hundred and thirty-three = 633 Numbers 27 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 31 12/19/2018 10:52:49 AM
Example 5: Vinod has some amount with him: 1 note of ` 100, 1 note of ` 20 and 1 coin of ` 1. How much money does he have in all? Solution: 1 note of ` 100 = ` 100 1 note of ` 20 = ` 20 1 coin of ` 1 = ` 1 Total money = ` 100 + ` 20 + ` 1 = ` 121 So, Vinod has ` 121 (One hundred and twenty-one rupees). 3.1 I Explore (H.O.T.S.) Let us learn to show 3-digit numbers on a spike abacus. Consider these examples. Example 6: Show the following numbers on the abacus: a) 434 b) 623 c) 476 Solution: To show 434, draw: 4 pink beads on the hundreds spike, 3 green beads on the tens spike and 4 blue beads on the ones spike. Similarly, we can show the other numbers as follows: a) b) c) H TO H TO H TO 434 623 476 28 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 32
Concept 3.2: Ordinal Numbers I Think David was confused when his teacher said, ‘All those sitting on the first, third and fifth benches, please stand up!’ He did not understand the words first, third and fifth. Have you ever heard these words? Do you know what they are? 3.2 I Recall Observe the given picture. It shows cars of different colours. The red car is before the The blue car is between the The black car is after blue car. red and the black cars. the blue car. The words before, after and between give the positions of the cars. Let us recall the concept by filling the blanks. a) The ______________ is before the camel. b) T he camel is between the frog and the _____________________. c) The crocodile is ______________ the camel. Camel Crocodile Frog Numbers 29 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 33 12/19/2018 10:52:49 AM
3.2 I Remember and Understand Look at the chicks walking in a line. We can give each chick a position. First Second Third Fourth Fifth The numbers one, two, three and so on are called cardinal numbers. There are five chicks in a row. We start counting from the left. We number the chicks as first, second, third, fourth and fifth. These numbers which tell about the positions of objects are called ordinal numbers. The following table gives the ordinal numbers from 1 to 10 and their short forms. Number 1 2 345 Ordinal number First Second Third Fourth Fifth 1st 2nd 3rd 4th 5th Short form Number 6 7 8 9 10 Ordinal number Sixth Seventh Eighth Ninth Tenth 10th Short form 6th 7th 8th 9th Example 7: Observe the toys on the shelves. Begin counting from the left and answer the questions given. a) O n which shelf is the rings toy? b) Which toy is on the fourth shelf? c) On which shelf is the ball? d) Which toy is on the second shelf? e) What is the position of the toy truck on the shelf? 30 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 34
Rings toy Toy Car Ball Toy Duck Toy Truck Solution: a) T he rings toy is on the first shelf. b) The toy duck is on the fourth shelf. c) The ball is on the third shelf. d) The toy car is on the second shelf. e) The toy truck is on the fifth shelf. Train My Brain This is a list of the top four students in a class. Write the ordinal numbers of their positions. a) Megha – Rank 2 – _______________________ b) Razia – Rank 3 – _______________________ c) Harsh – Rank 1 – _______________________ d) Shubhro – Rank 4 – _______________________ 3.2 I Apply We use ordinal numbers to denote the position of things. Usually, the position is counted from the left to the right. For example, • to tell the winning positions in a competition. • to tell the periods in our timetable. Numbers 31 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 35 12/19/2018 10:52:49 AM
Example 8: Look at the weekly activities of the students of Class 2. Answer the questions that follow. Day 1 Day 2 Day 3 Swimming Horse riding Cycling Day 4 Day 5 Day 6 Rock climbing Archery Fishing a) On which day do the students learn horse riding? b) What do the students learn on the fourth day? c) On which day do the students enjoy fishing? Solution: a) Students learn horse riding on the second day. b) Students learn rock climbing on the fourth day. c) Students enjoy fishing on the sixth day. 32 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 36
Example 9: Suppose you live in Mumbai. a) H ow many letters are there in the name of your city? What are they? b) What is the first letter of the name? c) What is the last letter of the name? d) Is any letter being repeated in the name of your city? Which letter is it? e) In which places in the name is the repeated letter/letters? Solution: a) There are 6 letters in it. They are M, u, m, b, a and i. b) The first letter is M. c) The last letter is i. d) Yes, the letter ‘M’ is repeated. e) The repeated letter is in the first and third place. 3.2 I Explore (H.O.T.S.) Consider the following example. Example 10: The given image shows the marks of six students in a class test. Look at the image and answer the following questions. a) Who came first in the class? b) What is Riya’s rank? Solution: To find the positions of the students, Piyush Vaishnavi Riya arrange their marks in descending 89 94 78 order. 94 > 91 > 89 > 83 > 78 > 72 Vaishnavi’s marks > Pooja’s marks > Piyush’s marks > Shubhro’s marks > Riya’s marks > Swati’s marks a) Vaishnavi came first in the class. b) Riya gets the fifth rank. Shubhro Swati Pooja 83 72 91 Numbers 33 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 37 12/19/2018 10:52:49 AM
Concept 3.3: Compare 3-digit Numbers I Think David has 504 colour pencils and his brother has 582 colour pencils. He wants to find out who has more colour pencils. How do you think David can find that out? 3.3 I Recall We have already learnt to compare numbers using the signs <, = or >. Let us recall the same. Count the number of objects in each image. Compare them using the proper sign <, > or = in the given boxes. a) 34 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 38
b) c) 3.3 I Remember and Understand Comparing two 3-digit numbers is similar to comparing two 2-digit numbers. We can compare two 3-digit numbers as shown in this A 2-digit number is example. always smaller than a 3-digit number. Example 11: Compare: a) 723 and 456 b) 436 and 412 c) 623 and 628 Solution: Follow these steps to compare 3-digit numbers. Numbers 35 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 39 12/19/2018 10:52:49 AM
723 and 456 436 and 412 623 and 628 Step 1: Count the Step 1: Count the Step 1: Count the number number of digits number of digits of digits 723 456 436 412 623 628 Both have 3 digits. Both have 3 digits. Both have 3 digits. Step 2: Compare the Step 2: Compare the Step 2: Compare the hundreds hundreds hundreds 723 456 436 412 623 628 As 7 > 4, As 4 = 4, As 6 = 6, 723 > 456. compare the tens. compare the tens. Step 3: Compare the tens Step 3: Compare the tens 436 412 623 628 As 3 > 1, As 2 = 2, 436 > 412. compare the ones. Step 4: Compare the ones 623 628 As 3 < 8, 623 < 628. 36 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 40
Train My Brain Find the greater number in each of the following pairs. a) 222 and 212 b) 555 and 545 c) 444 and 443 3.3 I Apply We can use the place value chart to compare 3-digit numbers. It helps us in: 1) writing numbers in ascending and descending orders. 2) forming the greatest and the smallest numbers from a given set of digits. Ascending and descending orders Example 12: Write the numbers a) 777, 717, 771, 177 in the ascending order. b) 932, 384, 515, 869 in the descending order. Solution: Let us follow these steps to arrange the numbers in ascending and descending orders. a) F or ascending order: Step 1: Compare the digits in the hundreds place of each number. 1<7 A number having the smallest number in the hundreds place is the least or the smallest. So, 177 is the least. Step 2: Compare the digits in the tens place of each number. 1<7 So, 717 < 771, 777. Step 3: Compare the digits in the ones place of each number. 1<7 So, 771 < 777. Step 4: Write the numbers from the smallest to the largest. Ascending order: 177, 717, 771, 777 Numbers 37 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 41 12/19/2018 10:52:49 AM
b) F or descending order: Step 1: Compare the digits in the hundreds place of each number. 9>8>5>3 Step 2: Write the numbers from the greatest to the smallest. Descending order: 932, 869, 515, 384 Example 13: T here were 879 students in Class A and 880 in Class B. Which class had more number of students? Solution: Number of students in Class A = 879 Number of students in Class B = 880 Compare both the numbers using the place value chart. H T O H TO 879 880 The hundreds digit in both the 3-digit numbers is the same. So, compare the digits in the tens place. As, 8 > 7, 880 > 879. So, Class B had more number of students. Forming the greatest and the smallest 3-digit numbers Let us learn to form the greatest and the smallest 3-digit numbers. Consider the following examples. Example 14: Form the greatest numbers using the given digits, without repeating any of the digits. a) 1, 5, 1 b) 6, 1, 9 Solution: We can form the greatest numbers by following these steps. Step 1: Arrange the given digits in descending order. a) 5, 1, 1 b) 9, 6, 1 Step 2: Write the digits in the place value chart from left to right. a) H T O b) H T O 511 961 38 12/19/2018 10:52:49 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 42
Example 15: Form the smallest numbers using the given digits, without repeating any of the digits. a) 3, 5, 7 b) 7, 9, 5 Solution: We can form the smallest numbers by following these steps. Step 1: Arrange the given digits in the ascending order. a) 3, 5, 7 b) 5, 7, 9 Step 2: Write the digits in the place value chart from left to right. a) H T O b) H T O 357 579 3.3 I Explore (H.O.T.S.) Consider the following example. Example 16: Compare the numbers in each pair and write <, = or > between them. a) 10 + 9 + 200 _____ 8 + 20 + 200 b) 300 + 5 + 40 _____ 60 + 7 + 200 Solution: a) 10 + 9 + 200 = 219 and 8 + 20 + 200 = 228. As 219 is less than 228, we put the < symbol in the blank. So, 219 < 228. b) 3 00 + 5 + 40 = 345 and 60 + 7 + 200 = 267. As 345 is greater than 267, we put the > symbol in the blank. So, 345 > 267. Maths Munchies We can write the ordinal numbers for the numbers 11 to 20 as: 213 11th – Eleventh 12th – Twelfth 13th – Thirteenth 14th – Fourteenth 15th – Fifteenth 16th – Sixteenth 17th – Seventeenth 18th – Eighteenth 19th – Nineteenth 20th – Twentieth Numbers 39 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 43 12/19/2018 10:52:49 AM
Connect the Dots EVS Fun There are 206 bones in an adult human body. Write the place value of each digit of the number. English Fun Let us read a poem about numbers. Ones, tens, hundreds too, I face place value, What to do? Put all digits, In their places, Ones, tens, hundreds, In their spaces! Drill Time Concept 3.1: Count by Hundreds 1) Write the given numbers in the place value chart. a) 346 b) 123 c) 987 d) 459 e) 784 2) Write the expanded form of each of the following numbers. a) 298 b) 158 c) 490 d) 231 e) 847 3) Write the number name of each of the following numbers. a) 124 b) 967 c) 281 d) 100 e) 210 40 12/19/2018 10:52:50 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 44
Drill Time 4) Form numbers with: a) 3 in the hundreds place, 1 in the tens place and 0 in the ones place b) 7 in the hundreds place, 2 in the tens place and 9 in the ones place c) 4 in the hundreds place, 3 in the tens place and 1 in the ones place d) 8 in the hundreds place, 0 in the tens place and 4 in the ones place e) 2 in the hundreds place, 5 in the tens place and 7 in the ones place Concept 3.2: Ordinal Numbers 5) Write the ordinal numbers and short forms of the following: a) 9 b) 4 c) 8 d) 1 e) 6 Concept 3.3: Compare 3-digit Numbers 6) Compare the numbers in the given pairs: a) 234, 432 b) 234, 233 c) 222, 222 d) 243, 243 e) 100, 900 7) Arrange the numbers in ascending and descending orders. a) 333, 313, 331, 133 b) 879, 865, 890, 812 c) 980, 981, 982, 983 d) 562, 589, 521, 514 e) 100, 300, 400, 700 8) Form the greatest and the smallest 3-digit numbers (without repeating the digits). a) 4, 8, 1 b) 9, 1, 0 c) 1, 5, 2 d) 6, 3, 8 e) 9, 8, 7 A Note to Parent After shopping, give your child the remaining notes of 100s and 10s and coins of 5s, 2s and 1s. Ask them to count the notes and tell you the amount of money that you have. Numbers 41 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 45 12/19/2018 10:52:50 AM
Chapter Addition 4 I Will Learn About • a dding 2-digit and 3-digit numbers. • properties of addition. Concept 4.1: Add 2-digit and 3-digit Numbers I Think David had 306 stamps in one bag and 462 stamps in another bag. Meena had 12 stamps in one bag and 18 stamps in the other. David wants to find the total number of stamps with each of them. How do you think David can find that? 42 12/19/2018 10:52:50 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 46
4.1 I Recall We know how to add 2-digit numbers without regrouping. Let us recall the same. Write and add the number of objects in the boxes. a) b) c) d) Addition 43 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 47 12/19/2018 10:52:50 AM
4.1 I Remember and Understand 9. Let us learn to add 2-digit numbers with regrouping and 3-digit numbers without regrouping. Add 2-digit numbers with regrouping Adding 2-digit numbers is similar to adding 1-digit numbers. In some cases, we need to regroup the 2-digit sum. We While adding two carry forward its tens digit to the next place. Consider an numbers, always example. begin from the ones place. Example 1: Add: 27 + 55 Solution: Arrange the numbers vertically. Steps Solved Solve these Step 1: Add the ones, 7 + 5 = 12. TO T O We can write only the ones digit of 1 44 the sum in the ones place. 2 7 +38 +5 5 So, we regroup 12 as 10 + 2. 2 Write 2 in the ones place. Carry forward 1 to the tens place. Step 2: Add the tens, 2 + 5 = 7. T O TO Add the carry forward 1 from the 1 ones place to this sum. 2 7 36 7+1=8 +5 5 +49 Write this sum in the tens place. 2 So, 27 + 55 = 82. 8 Add 3-digit numbers without regrouping Let us understand how to add 3-digit numbers through an example. 44 12/19/2018 10:52:50 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 48
Example 2: Add 343 and 125. Solution: Arrange the numbers vertically. Step 1: Step 2: Step 3: Add the hundreds Add the ones Add the tens HT O H T O H T O 34 3 +1 2 5 34 3 34 3 46 8 +1 2 5 +1 2 5 8 68 Solve these H TO H TO H TO H TO 634 144 122 108 +1 5 2 +3 3 4 +4 0 1 +2 0 1 Properties of addition Addition of numbers have some properties. Let us learn a few of them. 1) Zero property: When we add 0 to a number, the sum is the number itself. For example, 89 + 0 = 89; 12 + 0 = 12 and so on. 2) After numbers property: When we add 1 to a number, we get the number just after it. For example, 35 + 1 = 36; 77 + 1 = 78 and so on. 3) Commutative property: Changing the order in which we add two numbers does not change their sum. For example, 2 + 3 = 5 and 3 + 2 = 5; 15 + 14 = 29 and 14 + 15 = 29 and so on. Addition 45 NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 49 12/19/2018 10:52:50 AM
Train My Brain Answer the following: a) What is the sum of 22 and 1? b) What is the sum of 90 and 0? c) Given 17 + 18 = 35 and 18 + 17 = 35. Which property of addition do the numbers 17 and 18 show? 4.1 I Apply We apply the concept of addition in solving some real-life situations. Let us see a few examples. Example 3: There are 24 balls in a box and 18 balls in another box. How many Solution: balls are there in all? TO Number of balls in the first box = 24 1 Number of balls in the second box =18 24 Total number of balls = 24 + 18 = 42 +1 8 So, there are 42 balls in all. 42 Example 4: Mohan has 142 pencils and Sohan has 126 pencils. How many pencils do they have altogether? HTO Solution: Number of pencils with Mohan =142 142 Number of pencils with Sohan = 126 +1 2 6 Total number of pencils = 142 + 126 = 268 2 6 8 So, Mohan and Sohan together have 268 pencils. 4.1 I Explore (H.O.T.S.) Framing story sums for some given numbers would be interesting. Example 5: Given 32 + 22 = 54, frame a story sum. 46 12/19/2018 10:52:50 AM NR_BGM_9789388700948 PASSPORT G02 MATHS TEXTBOOK PART 1_Text.pdf 50
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