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MATHEMATICS 2 TEXTBOOK Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________ NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 1 11/30/2017 4:56:17 PM

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. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. IMAX presents the Traveller series, designed specifically to meet the requirements of the new curriculum released in November 2016 by the Council for the Indian School Certificate Examinations (CISCE). Guiding principles: The 2016 CISCE curriculum states the following as a few of its guiding principles for Mathematics teaching:  Develop mathematical thinking and problem-solving skills and apply these skills to formulate and solve problems.  Acquire the necessary mathematical concepts and skills for everyday life and for continuous learning in Mathematics and related disciplines.  Recognise and use connections among mathematical ideas and between Mathematics and other disciplines.  Reason logically, communicate mathematically and learn cooperatively and independently. Each of these principles resonates with the spirit in which the IMAX textbooks, workbooks and teacher companion books have been designed. The IMAX team of pedagogy experts has carried out an intensive mapping exercise to create a framework based on the CISCE curriculum document. Key features of IMAX Traveller series:  Theme-based content that holistically addresses all the learning outcomes specified by the CISCE curriculum.  The textbooks and workbooks are 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 content with detailed explanation of steps.  L earning is supported through visually appealing images, especially for Grades 1 and 2.  Increasing difficulty level in sub-questions for every question.  Multiplication tables provided as per CISCE requirement. All in all, the Traveller Mathematics books aim to develop problem-solving and reasoning skills in the learners’ everyday lives while becoming adept at mathematical skills as appropriate to the primary level. – The Authors NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 2 11/30/2017 4:56:17 PM

Textbook Features I Will Learn I Think Contains the list of concepts to be covered Arouses the student’s in the chapter along with the learning curiosity before objectives introducing the concept I Recall I RUenmdeermsbtearndand Pin-Up-Note Recapitulates the Elucidates the basic Highlights the key points or prerequisite knowledge for elements that form the definitions the concept learnt previously basis of the concept ? Train My Brain I Apply I Explore(H.O.T.S.) C hecks for learning to gauge Connects the concept Encourages the student to the understanding level of the to real-life situations by extend the concept learnt student providing an opportunity to more complex scenarios to apply what the student has learnt Maths Munchies Connect the Dots Drill Time Aims at improving speed of Aims at integrating Revises the concepts with calculation and problem Mathematical concepts practice questions at the solving with interesting facts, with other subjects end of the chapter tips or tricks A Note to Parent E ngages the parent in the out-of- classroom learning of their child NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 3 11/30/2017 4:56:18 PM

Contents 1 Shapes 7 Money 1.1 Lines and Shapes������������ 1 7.1 Add and Subtract Money without 2 Patterns Conversion����������������������70 2.1 R epeating Patterns���������12 8 Multiplication 3 Numbers 8.1 Repeated Addition and Skip Counting�����������������76 3.1 Count by Hundreds��������20 3.2 C ompare 3-digit 9 Division Numbers�������������������������28 9.1 R epeated Subtraction����88 3.3 O rdinal Numbers������������34 10 M easurement 4 Addition 10.1 M easure Lengths 4.1 Add 2-digit Numbers and Using Non-standard 3-digit Numbers��������������42 Units�������������������������������98 4.2 M ental Maths Techniques: 10.2 C omparing Mass and Addition��������������������������47 Volume by Estimation �������������������105 5 Time 11 Data Handling 5.1 Read the Clock and Calendar�������������������������51 11.1 Pictographs�����������������119 6 Subtraction 6.1 Subtract 2-digit Numbers and 3-digit Numbers�������������������������61 6.2 Mental Maths Techniques: Subtraction���������������������66 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 4 11/30/2017 4:56:19 PM

1Chapter Shapes I Will Learn About • corners and sides. • basic flat and solid figures. • flat figures as outlines of the surfaces of solid figures. 1.1 Lines and Shapes I Think Raj’s teacher asked him to draw an animal. Raj has drawn a cat using straight and curved lines. Which animal do you think you can draw in the same way? I Recall We have learnt about flat and solid shapes. Let us recall them. Flat shapes NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 5 1 11/30/2017 4:56:19 PM

Solid shapes We find objects of different shapes in our surroundings. Square Rectangle Circle Cube Sphere Cylinder Look at the picture and complete the table. Shape Number of shapes Square Circle Triangle Rectangle I Remember and Understand We can draw shapes using straight lines or curved lines. Let us learn about them. 2 11/30/2017 4:56:19 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 6

Straight lines: T hese lines are of three types. They are horizontal lines, vertical lines and slant lines. Horizontal lines Vertical lines Slant lines Sleeping lines drawn Standing lines drawn Sloping lines are from left to right or from top to bottom called slanting lines. from right to left are or bottom to top are called horizontal lines. called vertical lines. Curved lines: Lines that are not straight are Flat figures are called called curved lines. two-dimensional figures or 2D figures or 2D shapes. Try this! Hold a piece of rope as shown, with the help of your friend. When you pull the rope tight, it looks like a straight line. When you hold the rope loosely, it looks like a curved line. Shapes 3 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 7 11/30/2017 4:56:19 PM

Example 1: Look at the picture given and complete the table. One is done for you. Type of line Number of lines Horizontal line 3 Vertical line Slant line Curved line Open figures: Figures in which the lines do not end at the point where they begin are called open figures. a) b) c) d) e) Closed figures: Figures in which the lines end at the point where they begin are called closed figures. Square, rectangle, triangle and circle are closed figures. a) b) c) d) e) Example 2: Draw the following figures. a) Circle using a curved line b) Square using straight lines Solution: a) b) 4 11/30/2017 4:56:19 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 8

? Train My Brain Identify the type of line from the following: a) b) c) I Apply Two-dimensional shapes have some features. Let us learn more about them. Shape Features Corner • It has four straight lines as sides. Side • All its sides are equal in length. Square • It has four corners. Corner • It has four straight lines as sides. Side • Two pairs of opposite sides are equal in length. Rectangle • It has four corners. Corner Side • It has three straight lines as sides. • It has three corners. Triangle • It has a curved line. • It has no sides or corners. Circle Shapes 5 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 9 11/30/2017 4:56:19 PM

Example 3: Join the dots in order and name the shapes formed. 22 3 3 2 13 1 4 1 4 a) b) c) Solution: n a) Triangle b) Square c) Rectangle Example 4: Observe the following pictures. Tick the type of lines used to form each object. One is done for you. Straight Curved Straight Curved Straight Curved Straight Curved lines lines lines lines lines lines lines lines  6 11/30/2017 4:56:19 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 10

The geometrical shapes of some solid objects are as follows: Solid objects Geometrical shapes Cube Cuboid Cylinder Sphere Cone The flat side of a solid object is called its face. Two faces of a solid object meet to form an edge. A point where two or more edges of a solid meet is called its vertex. Plural of vertex is vertices. Let us now see the geometrical features of solid objects. Object Geometrical figures Geometrical features Vertex • It has 6 square faces, Face 12 edges and 8 vertices. Edge • All the edges of a cube Cube are equal in length. Edge • It has 6 rectangular faces, Face 12 edges and 8 vertices. Vertex Cuboid • The opposite faces of a cuboid are of the same size. • Opposite edges of a cuboid are equal in length. Shapes 7 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 11 11/30/2017 4:56:19 PM

Object Geometrical figures Geometrical features • It has 2 circular flat faces Edge 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. • It has no edges and no Sphere Corner corners. Curved face • It has 1 flat circular face, 1 curved face and 1 Flat Face corner. Edge • It has a circular edge. Cone I Explore (H.O.T.S.) Let us find the geometrical shapes of a few solid objects. Example 5: Draw the geometrical shapes that form the base of these objects. Name the shapes so formed. 8 11/30/2017 4:56:19 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 12

Solution: The shapes formed and their names are: Object Shape of the base Circle Rectangle Triangle Circle Square Maths Munchies Flat figures are called two-dimensional figures or 2D figures. A straight line or a curved line is a one-dimensional or 1D figure. Connect the Dots 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. Shapes 9 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 13 11/30/2017 4:56:19 PM

EVS Fun We can draw the outline of the human body using straight and curved lines. Drill Time 1.1 Lines and Shapes 1) Draw the following: a) Slant lines b) Horizontal lines c) Vertical lines d) Curved lines 2) Identify and write whether the following figures are open or closed. a) b) c) d) e) 3) Name the shape and write the number of sides in each case. Shape - a) Number of sides - Shape - b) Number of sides - 10 11/30/2017 4:56:19 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 14

Shape - c) Number of sides - Shape - d) Number of sides - A Note to Parent Play a game ‘I-Spy with my eyes’ with your child. You spy common objects around the house and ask the child to identify their shapes. For example, a television, tiffin box, plate, flask, loaf of bread and so on. Shapes 11 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 15 11/30/2017 4:56:19 PM

Patterns2Chapter I Will Learn About • creating patterns using objects, shapes and numbers. 2.1 Repeating Patterns I Think Raj made shapes using modelling clay and moulds. He arranged them as shown. Do you ever make such arrangements? Do you know what they are called? I Recall We have already learnt about flat shapes and solid shapes. Let us revise them. 12 11/30/2017 4:56:19 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 16

Identify the following shapes. Write their names in the space given below. Flat shapes Names Solid shapes Names 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) c) Patterns 13 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 17 11/30/2017 4:56:19 PM

To continue a given pattern, follow these steps: Step 1: Observe 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: R epeat 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 or shapes. Example 1: Find the basic shapes in the given patterns. a) b) c) Solution: a) In this pattern, is the group of basic shapes. 14 11/30/2017 4:56:20 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 18

b) In this pattern, is the group of basic shapes. c) In this pattern, is the group of basic shapes. 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) ____________ ___________ ____________ Patterns 15 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 19 11/30/2017 4:56:20 PM

I Apply Let us now look at some patterns that we see around us. 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) 16 11/30/2017 4:56:20 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 20

Example 5: Complete the following patterns. One is done for you. a) b) c) d) e) 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 Patterns 17 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 21 11/30/2017 4:56:20 PM

Maths Munchies The patterns on our fingers are called our fingerprints. No two persons in this world have the same fingerprint pattern – not even twins. Connect the Dots EVS Fun Flowers, birds and animals also show different patterns. For example, orchids, peacock feathers and so on. English Fun Complete the following patterns using alphabets: a) P R T _______ _______ ________ b) Z Y X _______ V _______ ________ Drill Time 2.1 Repeating Patterns 1) Identify the basic shapes or group of basic shapes in each of the following patterns. a) b) c) d) 18 11/30/2017 4:56:20 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 22

e) 2) Complete the given patterns. a) b) c) d) e) 3) Complete the given pattern by colouring. a) b) A Note to Parent Give your child patterns of missing shapes, numbers or letters to complete. Patterns 19 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 23 11/30/2017 4:56:21 PM

Numbers3Chapter I Will Learn About • reading and writing numerals for numbers up to 999. • place value and face value. • comparing 3-digit numbers. • forming the greatest and the smallest 3-digit numbers. • ordinal numbers. 3.1 Count by Hundreds I Think Raj 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 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 numbers by ones and tens. 20 11/30/2017 4:56:21 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 24

Look at the following picture. Start from 1 and connect all the dots in order. You will find a friend smiling back at you. I Remember and Understand Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Numbers 21 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 25 11/30/2017 4:56:21 PM

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 In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. 22 11/30/2017 4:56:21 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 26

Let us understand this concept using a spike abacus. We have learnt how to show the number 99 1 = 1 unit in on an abacus. the ones spike To show the number 100, we remove all the green beads from the tens place. We also 1 = 1 unit in remove all the blue beads from the ones place. We then put 1 pink bead in the third TO the tens spike (hundreds place). 99 spike 1 = 1 unit in the hundreds spike The smallest 3-digit Thus, to show 999, we put 9 number is 100. pink beads in the hundreds spike, 9 green beads in the The largest 3-digit number is 999. tens spike and 9 blue beads in the ones spike. Let us show the number 124 using TO H T O a spike abacus. We put 1 pink 99 100 bead in the hundreds spike. We then put 2 green beads in the tens spike and 4 blue beads in the ones spike. In the H TO 999 same way, we can show the numbers 298 and 459 on the abacus. H TO H TO H TO 124 298 459 Numbers 23 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 27 11/30/2017 4:56:21 PM

We can write the number names of these numbers as: 124 = One hundred twenty-four 298 = Two hundred ninety-eight 459 = Four hundred fifty-nine 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 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: 4 2 8 2 ones Place Value Face Value 4 tens 22 40 4 8 hundreds 800 8 24 11/30/2017 4:56:21 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 28

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 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 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 Numbers 25 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 29 11/30/2017 4:56:21 PM

Example 3: Count and write the following numbers in their expanded forms. Then, write their number names. a) b) c) Solution: To write the expanded forms, write the numbers in the place value chart as shown below. Number Place Value Expanded Number Names Chart Forms Five hundred H TO 523 = twenty-three 500 + 20 + 3 Four hundred thirty-two a) 523 523 432 = Six hundred thirty-four b) 432 432 400 + 30 + 2 c) 634 634 634 = 600 + 30 + 4 26 11/30/2017 4:56:21 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 30

? Train My Brain Write the number names of: a) 358 b) 409 c) 991 I Apply Let us see a few examples where we use 3-digit numbers. Example 4: 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 twenty-one rupees). Example 5: Pooja collected two hundred twenty-nine stamps. Reema collected six hundred thirty-three stamps. Write the numerals for the number of stamps each of them collected. Solution: Stamps with Pooja = two hundred twenty-nine = 229 Stamps with Reema = six hundred thirty-three = 633 I Explore (H.O.T.S.) Let us learn to show 3-digit numbers on a spike abacus. Consider these examples. Numbers 27 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 31 11/30/2017 4:56:21 PM

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 3.2 Compare 3-digit Numbers I Think Raj 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 Raj can find that out? I Recall We have already learnt to compare numbers using the signs <, = or >. Let us recall the same. 28 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 32

Count and compare the number of objects in each image and write the proper sign <, > or = in the given boxes. a) b) c) I Remember and Understand A 2-digit number is always smaller than Comparing two 3-digit numbers is similar to a 3-digit number. comparing two 2-digit numbers. Use the steps to compare two 3-digit numbers as shown in this example. Numbers 29 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 33 11/30/2017 4:56:22 PM

Example 7: Compare: a) 723 and 456 b) 436 and 412 c) 623 and 628 Solution: Follow these steps to compare 3-digit numbers. 723 and 456 436 and 412 623 and 628 Step 1: Count the Step 1: Count the Step 1: Count the number of digits number of digits number 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 Step 3: Compare the tens 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. 30 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 34

? 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 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 8: 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 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 starting with 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. Numbers 31 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 35 11/30/2017 4:56:22 PM

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 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 9: 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 smallest 3-digit numbers Let us learn to form the greatest and the smallest 3-digit numbers. Consider the following examples. Example 10: Form the greatest numbers using the given digits, without repeating any of the digits. 32 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 36

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 Example 11: 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 I Explore (H.O.T.S.) Consider the following example. Example 12: 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) 1 0 + 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. Numbers 33 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 37 11/30/2017 4:56:22 PM

3.3 Ordinal Numbers I Think Raj 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? I Recall Observe the given picture. It shows cars of different colours. The red car is before The blue car is in between The black car is after the blue car. the red and the black cars. the blue car. The words before, after and between give the positions of the car. Let us learn about the numbers that tell us about such positions. 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 as cardinal numbers. 34 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 38

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 and their short forms from 1-10. Number 1 2 345 Ordinal number First Second Third Fourth Fifth Short form 1st 2nd 3rd 4th 5th Number 6 7 8 9 10 Ordinal number Sixth Seventh Eighth Ninth Tenth Short form 10th 6th 7th 8th 9th Example 13: 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? 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. Numbers 35 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 39 11/30/2017 4:56:22 PM

? Train My Brain T his 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 – _______________________ 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, • T o tell the winning positions in a competition. • To tell the periods in our timetable. Example 14: Look at the weekly activities of the students of Class 2. Answer the questions that follow using ordinal numbers. Day 1 Day 2 Day 3 Swimming Horse riding Cycling 36 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 40

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. Example 15: Suppose you live in Mumbai. a) How 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. Numbers 37 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 41 11/30/2017 4:56:22 PM

c) The last letter is i. d) Yes. The letter that is repeated is M. e) The repeated letter is in the first and third place. I Explore (H.O.T.S.) Consider the following example. Example 16: In a class test, Piyush scored 89 marks, Piyush Vaishnavi Riya Vaishnavi scored 94 marks, Riya 89 94 78 scored 78 marks, Shubhro scored 83 marks, Swati scored 72 marks and Pooja scored 91 marks. a) Who comes first in class? b) What is Riya’s rank? Shubhro Swati Pooja 83 72 91 Solution: To find the positions of the students, arrange their marks in descending order. 94 > 91 > 89 > 83 > 78 > 72 Vaishnavi > Pooja > Piyush > Shubhro > Riya > Swati a) Vaishnavi comes first in the class. b) Riya gets fifth rank. Maths Munchies We can write the ordinal numbers for the numbers 11 to 20 as: 11th – Eleventh 12th – Twelfth 13th – Thirteenth 14th – Fourteenth 15th – Fifteenth 16th – Sixteenth 17th – Seventeenth 18th – Eighteenth 19th – Nineteenth 20th – Twentieth 38 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 42

Connect the Dots EVS Fun There are 206 bones in an adult human body. 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 3.1 Count by Hundreds 1) Write the place value and face value of each digit in the following numbers. a) 346 b) 12 c) 98 d) 459 e) 784 Numbers 39 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 43 11/30/2017 4:56:22 PM

2) Write the expanded form of each of these numbers. a) 298 b) 158 c) 490 d) 231 e) 847 3) Write the number name of each of these numbers. a) 124 b) 967 c) 281 d) 100 e) 210 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. 3.2 Compare 3-digit Numbers 5) Compare the numbers in the given pairs: a) 234, 432 b) 334, 233 c) 222, 222 d) 243, 243 e) 100, 900 6) Arrange the numbers in ascending and descending order: 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 7) 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 40 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 44

3.3 Ordinal Numbers 8) T here are five houses in a row. Look at the picture and answer the following. Count the positions of the houses from left to right. a) What is the position of the green house? b) W hich house is at the fifth position? c) What is the position of the pink house? d) W hat is the position of the blue house? e) W hich house is at the first position? A Note to Parent After shopping, give your child the remaining notes of 100s and 10s and coins of 5s, 2s and 1s. Ask your child to count and tell you the amount of money you have left. Numbers 41 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 45 11/30/2017 4:56:22 PM

4Chapter Addition I Will Learn About • a dding 2-digit numbers and 3-digit numbers. • properties of addition. • s olving word problems based on addition. • mental Maths techniques. 4.1 Add 2-digit Numbers and 3-digit Numbers I Think Raj 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. Raj wants to find the total number of stamps with each of them. How do you think Raj can find that? 42 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 46

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_Traveller-G2-Textbook-Maths-FY_Txt.pdf 47 11/30/2017 4:56:22 PM

I Remember and Understand 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 While adding two numbers. numbers, always begin from the In some cases, we need to regroup the 2-digit sum. ones place. We carry forward its tens digit to the next place. Consider these examples. 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 ones digit of 1 the sum in the ones place. 27 4 4 +5 5 +3 8 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. Add the carry forward (1) from TO TO the ones place to this sum. 1 27 3 6 7+1=8 +5 5 +4 9 82 Write this sum in the tens place. So, 27 + 55 = 82. 44 11/30/2017 4:56:22 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 48

Add 3-digit numbers without regrouping Let us understand how to add 3-digit numbers through some examples. Example 2: Add 343 and 125. Solution: Arrange the numbers vertically. Step 1: Step 2: Step 3: Add the ones Add the tens Add the hundreds H T O H T O HT O 34 3 34 3 34 3 +1 2 5 +1 2 5 +1 2 5 46 8 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 show some properties. Let us learn a few of them. 1) Zero property: When we add 0 to a number, the sum is the same as 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 two numbers are added, 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_Traveller-G2-Textbook-Maths-FY_Txt.pdf 49 11/30/2017 4:56:23 PM

? 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? 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 balls are there in all? Solution: Write the numbers one below the other. Regroup TO the ones. 1 Number of balls in the first box 24 Number of balls in the second box +1 8 Total number of balls = 24 + 18 42 So, there are 42 balls in all. Example 4: Mohan has 142 pencils and Sohan has 126 pencils. How many pencils do they have altogether? Solution: Write the numbers one below the other. HT O Number of pencils with Mohan 14 2 Number of pencils with Sohan Total number of pencils = 142 + 126 +1 2 6 26 8 So, Mohan and Sohan together have 268 pencils. 46 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 50

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