2110011-Passport-G2-FoundationMax-Maths-FY

Class 2 MATHEMATICS TEXTBOOK Name : __________________________ Section : __________ Roll No: _______ School : ___________________________ Maths_TB_Nameslip_Book Explainer.indd 1 21/01/2017 6:38:25 PM

How do we hone crucial learning? R REMEMBERING U UNDERSTANDING A APPLICATION H H.O.T.S. The first step of the learning process As we progress with recollecting information, We begin relating what we learn to Having applied the concepts learnt, we involves remembering new things and we parallelly start understanding it by breaking real life situations around us, thereby extend the field of application to more recollecting all crucial information it down and exploring its length and breadth applying what we have learnt advanced and challenging scenarios such as meanings and concepts Connects the concept to real-life situations by giving Contains the list of concepts I Apply an opportunity to apply to be covered in the Chapter what the child has learnt chapter along with learning 1 Shapes through practice questions objectives number of sides of a 2D shape. I Explore (H.O.T.S.) Encourages the child to extend the concept learnt I will Learn to advanced application Introduces the Concepts of the box is a square. scenarios concept/subtopic in such a 1.1: Vertices and Diagonals of Two-Dimensional Shapes Maths Munchies manner as to arouse curiosity among the students We can use tangrams to make many shapes such as: Ideas to increase speed 1 2 3 of calculation and I Think 1 3 2 problem solving There is a paper folding activity in Neena’s class. Her teacher asked the students to fold the paper across the vertices of the diagonals. Discusses the prerequisite knowledge for the sub-topic from previous academic I Recall Connect the Dots year/chapter/concept/term Multidisciplinary section We have learnt various shapes formed by straight lines or curved lines. Let us recall Social Studies fun connects all other subjects them. We can see 2D shapes such as rectangles, to a particular topic to squares, circles and 3D shapes such as cubes enable a student to and cuboids in the buildings in our Explains the elements in I Remember and Understand neighbourhood. relate better to it. detail that forms the basis As we have already learnt various shapes, let us now learn of the concept. It ensures that how to name their parts. Consider a rectangle ABCD as students are engaged in shown. In the given rectangle, named AC and BD are Vertex: The point where at called diagonals. least two sides of a learning throughout. figure meet is called A Note to Parent vertex. Pin-Up Note: Contains key Train my brain Take your child to public places like hospitals, markets, religious places like temples, To engage a parent in retention points from the mosques and churches and so on. out-of-classroom learning concept diagonals. Drill time of their child and conduct activities given in the a) b) c) Concept 1.1 Vertices and Diagonals of Two-Dimensional Shapes section to reinforce the Find the number of vertices and diagonals of the following shapes: learnt concepts Checks for learning to gauge the understanding level of Additional practice the child, testing both skill questions given at the end and knowledge of every chapter Maths_TB_Nameslip_Book Explainer.indd 2 21/01/2017 6:38:26 PM

How do we hone crucial learning? R REMEMBERING U UNDERSTANDING A APPLICATION H H.O.T.S. The first step of the learning process As we progress with recollecting information, We begin relating what we learn to Having applied the concepts learnt, we involves remembering new things and we parallelly start understanding it by breaking real life situations around us, thereby extend the field of application to more recollecting all crucial information it down and exploring its length and breadth applying what we have learnt advanced and challenging scenarios such as meanings and concepts Connects the concept to real-life situations by giving Contains the list of concepts I Apply an opportunity to apply to be covered in the Chapter what the child has learnt chapter along with learning 1 Shapes through practice questions objectives number of sides of a 2D shape. I Explore (H.O.T.S.) Encourages the child to extend the concept learnt I will Learn to advanced application Introduces the Concepts of the box is a square. scenarios concept/subtopic in such a 1.1: Vertices and Diagonals of Two-Dimensional Shapes Maths Munchies manner as to arouse curiosity among the students We can use tangrams to make many shapes such as: Ideas to increase speed 1 2 3 of calculation and I Think 1 3 2 problem solving There is a paper folding activity in Neena’s class. Her teacher asked the students to fold the paper across the vertices of the diagonals. Discusses the prerequisite knowledge for the sub-topic from previous academic I Recall Connect the Dots year/chapter/concept/term Multidisciplinary section We have learnt various shapes formed by straight lines or curved lines. Let us recall Social Studies fun connects all other subjects them. We can see 2D shapes such as rectangles, to a particular topic to squares, circles and 3D shapes such as cubes enable a student to and cuboids in the buildings in our Explains the elements in I Remember and Understand neighbourhood. relate better to it. detail that forms the basis As we have already learnt various shapes, let us now learn of the concept. It ensures that how to name their parts. Consider a rectangle ABCD as students are engaged in shown. In the given rectangle, named AC and BD are Vertex: The point where at called diagonals. least two sides of a learning throughout. figure meet is called A Note to Parent vertex. Pin-Up Note: Contains key Train my brain Take your child to public places like hospitals, markets, religious places like temples, To engage a parent in retention points from the mosques and churches and so on. out-of-classroom learning concept diagonals. Drill time of their child and conduct activities given in the a) b) c) Concept 1.1 Vertices and Diagonals of Two-Dimensional Shapes section to reinforce the Find the number of vertices and diagonals of the following shapes: learnt concepts Checks for learning to gauge the understanding level of Additional practice the child, testing both skill questions given at the end and knowledge of every chapter Maths_TB_Nameslip_Book Explainer.indd 3 21/01/2017 6:38:26 PM

Contents Contents 1 Shapes..........................................1 1.1 Identify the Geometrical Features of Objects 2 2 Patterns..............................14 2.1 Patterns Using Shapes 15 3 Numbers....................................23 3.1 Count by Hundreds 24 3.2 Ordinal Numbers 31 3.3 Compare 3-digit Numbers 36 4 Addition..............................43 4.1 Add 2-digit Numbers and 3-digit Numbers 44 5 Subtraction..............................50 5.1 Subtract 2-digit Numbers and 3-digit Numbers 51 5.2 Subtract Two 1-digit Numbers Mentally 55 ToC TOC TB.indd 1 1/28/2017 11:05:35 AM

6 Time................................................62 6.1 Days of a Week and Months of a year 63 6.2 Sequence the Events Over Longer Period 68 7 Money...................................77 7.1 Add and Subtract Money without Conversion 78 8 Multiplication..............................84 8.1 Concept of Repeated 9 Addition 85 Measurement .....................100 9.1 Measure Lengths Using 8.2 Skip Counting 88 Standard Units 101 9.2 Compare Objects Using a Simple Balance 108 9.3 Compare Containers for Capacities 114 10 Data Handling.......................123 10.1 Pictograph 124 TOC TB.indd 2 1/28/2017 11:05:37 AM

Merged file_G2_Maths_TB_13012017.indb 6 23/01/2017 4:15:07 PM

Sha Shapespes I Will Learn Concept 1.1: Identify the Geometrical Features of Objects Merged file_G2_Maths_TB_13012017.indb 1 23/01/2017 4:15:07 PM

Concept 1.1: Identify the Geometrical Features of Objects I Think Raj drew shapes using objects like a can, matchbox, bangle, and so on as shown. Do you know what these shapes are? To answer this, we must learn about the geometrical shapes of objects. 1.1 I Recall We know about the following plane shapes: Now, let us recall them.We will also learn more about them in detail. If we observe our surroundings, we will find objects of different shapes. Square Rectangle Circle 2 Merged file_G2_Maths_TB_13012017.indb 2 23/01/2017 4:15:12 PM

In your classroom, you find many objects in the shapes you have learnt. For example, a book or a blackboard looks like a rectangle. Sometimes, we see different objects having the same shape. For example, a handkerchief, photo frame or a biscuit looks like a square. 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 is denoted by a capital letter of the English A point has alphabet. For example, A, X, Y, P and M shown no dimension. below are points. X Y A M P Line: Many points when placed close to each other, forms a straight line. It has no thickness and breadth. A line only has length. So, it is called a one-dimensional figure. Shapes 3 Merged file_G2_Maths_TB_13012017.indb 3 23/01/2017 4:15:13 PM

A straight line has no end. It extends on both the sides. A B We name two points A and B on a line and write it as AB . We read it as line AB. Line segment: The line segment is a part of a line. It has two end points, a starting point and an end point. A line segment has an exact length. A B We write line segment AB as AB. We read it as segment AB. Ray: A ray is a straight line, which has a starting point but A no end point. It extends only on one side. B We write ray AB as AB. We read it as ray AB. Straight lines are of three types. They are horizontal lines, vertical lines and slant lines. 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 two points on it. 4 Merged file_G2_Maths_TB_13012017.indb 4 23/01/2017 4:15:13 PM

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) We can draw the figures given below using straight lines or curved lines. Open figures: Figures which do not end at the point where they begin are called open figures. a) b) c) d) e) Closed figures: Figures which end at the point where they begin are called closed figures. Square, rectangle, triangle and circle are closed figures. a) b) c) d) e) Shapes 5 Merged file_G2_Maths_TB_13012017.indb 5 23/01/2017 4:15:13 PM

Train My Brain Identify ray, line and segment from the following: X Y A B a) b) R Q c) 1.1 I Apply We can draw closed figures on a sheet of paper. They have length and breadth. So, they are called two–dimensional figures or 2D figures or 2D shapes. Let us learn about them in detail. Square: 1) It has four straight lines as sides. In the given figure, AB, BC, CD and DA are the sides. D C 2) All its sides are equal in length. 3) It has four corners. In the given figure, A B A, B, C and D are its corners. 4) We name a square using its corners. We name the square above as, square ABCD. Rectangle: 1) It has four straight lines as sides. In the given figure, AB, BC, CD and DA are the sides. D C 2) Two pairs of opposite sides are equal in length. 3) It has four corners. In the A B given figure, A, B, C and D are its corners. 6 Merged file_G2_Maths_TB_13012017.indb 6 23/01/2017 4:15:14 PM

4) We name a rectangle using its corners. We name the rectangle above 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) We name a triangle using its corners. We name B C the triangle as triangle ABC. Circle: 1) It is a curved line. 2) It has no sides or corners. .O 3) We name a circle by its centre ‘O’. Example 2: Join the dots in order and name the shapes formed. R S R H G E F P Q P Q a) b) c) Solution: R S R H n G E F P Q P Q a) Triangle PQR b) Square PQRS c) Rectangle EFGH Shapes 7 Merged file_G2_Maths_TB_13012017.indb 7 23/01/2017 4:15:14 PM

Example 3: Observe the following shapes and tick the type of lines used to form them: Straight Curved Straight Curved Straight Curved Straight Curved lines lines lines lines lines lines lines lines Solution: Straight Curved Straight Curved Straight Curved Straight Curved lines lines lines lines lines lines lines lines 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. Some objects having solid shapes are given here: a) b) c) d) e) 8 Merged file_G2_Maths_TB_13012017.indb 8 23/01/2017 4:15:15 PM

The geometrical shapes of these objects are as follows: a) b) c) d) e) Cube Cuboid Cylinder Sphere Cone Let us now see the geometrical features of these objects. Object Geometrical figures Geometrical features • It has 6 square faces, 12 Corner H G edges and 8 corners D C • All the edges of a cube are Face equal in length E F Edge A B Cube H G Edge • It has 6 rectangular faces, 12 D C Face edges and 8 corners E F • The opposite faces of a cuboid are of the same size A B Corner Cuboid • It has 2 flat circular faces and Flat Face 1 curved face • It has 2 edges and no Curved face corners • The 2 flat faces are of the Cylinder same size Shapes 9 Merged file_G2_Maths_TB_13012017.indb 9 23/01/2017 4:15:15 PM

Object Geometrical figure Geometrical features • It has a curved face. • It has no edge and no corner Curved face Sphere Corner • It has 1 flat circular face, 1 curved face and 1 corner Curved face Flat Face Cone Example 4: Draw geometrical shapes using the base of these objects and name them. 10 Merged file_G2_Maths_TB_13012017.indb 10 23/01/2017 4:15:16 PM

Solution: The shapes formed and their names are: Object a) b) c) d) e) Shape drawn Rectangle Circle Rectangle Circle Circle Object f) g) h) i) j) Shape drawn Circle Square Circle Circle Rectangle Maths Munchies We cannot draw a line and a ray on paper. But we can draw a line 1 2 3 segment on paper. Shapes 11 Merged file_G2_Maths_TB_13012017.indb 11 23/01/2017 4:15:16 PM

Connect the Dots EVS Fun What different shapes will you use while drawing a human body? English Fun Read the poem aloud. Can you see the square that’s there? The square that’s wearing black bear’s hair... square in bear’s hair Can you see the square that’s there? The square that’s sitting in a chair... square on chair Can you see the square that’s here? Coloured square Four straight sides that make two pairs! A Note to Parent Play a game ‘I-Spy with my eyes’ with your child, while 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 Merged file_G2_Maths_TB_13012017.indb 12 23/01/2017 4:15:17 PM

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) 3) Name the sides of the following: S R Z H G E F P Q X Y a) Square PQRS b) Triangle XYZ c) Rectangle EFGH Shapes 13 Merged file_G2_Maths_TB_13012017.indb 13 23/01/2017 4:15:17 PM

P Patternsatterns I Will Learn Concept 2.1: Patterns Using Shapes Merged file_G2_Maths_TB_13012017.indb 14 23/01/2017 4:15:18 PM

Concept 2.1: Patterns Using Shapes I Think I Think Raj made shapes using modelling clay and moulds. He arranged them as shown below. Did you ever make such arrangements? Do you know what are they called? To answer these questions, we must learn about patterns using shapes. 2.1 I Recall We have already learnt about plane shapes and solid shapes. Let us revise them. Write the names of the following shapes in the space given below them. Plane shapes Names Solid shapes Names Patterns 15 Merged file_G2_Maths_TB_13012017.indb 15 23/01/2017 4:15:19 PM

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) ......................................... c) ................................. To continue the given pattern, follow the steps given below: Step 1: Observe the first 3 or more shapes in the given pattern until you 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. 16 Merged file_G2_Maths_TB_13012017.indb 16 23/01/2017 4:15:20 PM

In the following patterns, we observe that some part of the design is repeated. The repeating design is coloured as shown. The repeated parts of these patterns are called basic shapes. The basic shapes in the above patterns are: a) b) Repetition of a basic shape to get a definite c) d) arrangement is called a Pattern. Let us now see few examples. Example 1: Complete the following patterns by finding the missing shapes. a) ______, ______, ______, ______, b) _____, _____, _____, c) _____, _____, _____, _____, Solution: The missing shapes are – a) , , and b) and Patterns 17 Merged file_G2_Maths_TB_13012017.indb 17 23/01/2017 4:15:21 PM

c) and The completed patterns are - a) b) c) Example 2: Complete the following pattern. _______, _______, _______, ________ Solution: The missing shapes are: and The completed pattern is: Train My Brain Complete the following patterns: a) _______ _______ _______ b) _______ _______ _______ 18 Merged file_G2_Maths_TB_13012017.indb 18 23/01/2017 4:15:21 PM

2.1 I Apply Look at the following patterns carefully. Try to find the basic shapes in them. 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: Find the group of basic shapes in the patterns given: a) b) c) Solution: The group of basic shapes in the given patterns are: a) b) Patterns 19 Merged file_G2_Maths_TB_13012017.indb 19 23/01/2017 4:15:22 PM

c) 2.1 I Explore (H.O.T.S.) Let us now complete the patterns given below. Example 5: Complete the following patterns. a) b) c) Solution: a) b) c) Example 6: Fill in the missing shapes, letters or numbers in these patterns. a) A C E G b) 1A 3B 5C c) 20 Merged file_G2_Maths_TB_13012017.indb 20 23/01/2017 4:15:22 PM

Solution: a) A C E G I K M b) 1A 3B 5C 7D 9E 11F 13G c) Maths Munchies The patterns on our fingers and thumbs are called our fingerprints. 2 3 1 No one in this world have the same fingerprint pattern – not even twins. Connect the Dots EVS Fun Living things like flowers, birds and animals also have different patterns. For example, orchids, peacock feathers and so on. English Fun Complete the following patterns using alphabets: a) P R _______, _______, ________ b) Z Y X _______ V___________ Patterns 21 Merged file_G2_Maths_TB_13012017.indb 21 23/01/2017 4:15:25 PM

Drill Time Concept 2.1: Patterns using shapes 1) Identify the basic shape in each of the following patterns. a) b) c) d) e) 2) Complete the patterns given below. a) b) c) d) e) 22 Merged file_G2_Maths_TB_13012017.indb 22 23/01/2017 4:15:26 PM

Numb Numbersers I Will Learn Concepts 3.1: Count by Hundreds 3.2: Ordinal Numbers 3.3: Compare 3-digit Numbers Merged file_G2_Maths_TB_13012017.indb 23 23/01/2017 4:15:27 PM

Concept 3.1: Count by Hundreds I Think I Think Raj went to a toy store. He saw a toy for ` 990. He could not read the number. Can you read the number? To answer this, we should know to count by hundreds. 3.1 I Recall We know that the numbers 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 and 99 is the largest 2-digit number. We can count the numbers by ones and tens. Counting by 1s: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80, 90 Let us now learn about numbers greater than 99. 3.1 I Remember and Understand Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. 24 Merged file_G2_Maths_TB_13012017.indb 24 23/01/2017 4:15:28 PM

= 10 tens = 1 hundred = 1 hundred = 2 hundreds = 3 hundreds = 4 hundreds Similarly, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. Numbers 25 Merged file_G2_Maths_TB_13012017.indb 25 23/01/2017 4:15:29 PM

Let us understand this concept using a spike abacus. We have learnt how to show the number 99 on an abacus. 1 = 1 unit in the ones spike 1 = 1 unit in the tens spike 1 = 1 unit in the hundreds spike H T O Shows 99 To show the number 100, we remove the green beads from the tens place. We also have to remove all red beads from the ones place. We then put 1 blue bead in the third spike (hundreds place). H T O H T O Shows 99 Shows 100 100 = 1 blue bead 400 = 4 blue beads 700 = 7 blue beads 200 = 2 blue beads 500 = 5 blue beads 800 = 8 blue beads 300 = 3 blue beads 600 = 6 blue beads 900 = 9 blue beads Thus, 999 will be 9 blue beads in hundreds spike, 9 green beads in the tens spike and 9 red beads in the ones spike. 26 Merged file_G2_Maths_TB_13012017.indb 26 23/01/2017 4:15:29 PM

The smallest 3-digit number is 100. The largest 3-digit H T O number is 999. Shows 999 The abacus shows three places – hundreds, tens and ones. Let us now understand the place values of 3-digit numbers. Look at the place value chart given below. Places Hundreds (H) Tens (T) Ones (O) Values 100 10 1 So, the number 999 will be represented on the place value chart as: Places H T O Digits 9 9 9 1) Expanded form of a 3-digit number Consider the number 425. We write 425 in the place value chart as shown. 4 2 5 Place values 5 ones = 5 2 tens = 20 4 hundreds = 400 The form in which a number is expressed as a sum of the place values of its digits is called its expanded form. So, the expanded form of 425 is 400 + 20 + 5. Numbers 27 Merged file_G2_Maths_TB_13012017.indb 27 23/01/2017 4:15:29 PM

We can call 425 as the standard form of the number. Consider the following examples to understand the concept better. Example 1: 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: H T O a) 9 4 6 b) 4 2 3 c) 3 0 8 Therefore, the standard forms of the given numbers are: a) 946 b) 423 c) 308 Example 2: Write the following numbers in their expanded forms: a) 526 b) 653 c) 281 d) 987 Solution: To write the expanded forms, write the numbers in the place value chart as shown below. Number H T O a) 526 5 2 6 b) 653 6 5 3 c) 281 2 8 1 d) 987 9 8 7 Therefore, the expanded forms are: a) 526 = 500 + 20 + 6 b) 653 = 600 + 50 + 3 c) 281 = 200 + 80 + 1 d) 987 = 900 + 80 + 7 28 Merged file_G2_Maths_TB_13012017.indb 28 23/01/2017 4:15:29 PM

2) Writing number names of 3-digit numbers Using expanded forms and place value chart, we can write the number names of the given numbers. Let us see an example. Example 3: Write the following numbers in their expanded forms. a) 403 b) 721 c) 589 Solution: a) 403 = 4 hundreds + 0 tens + 3 ones 400 + 0 + 3 Four hundred and three b) 721 = 7 hundreds + 2 tens + 1 ones 700 + 20 + 1 Seven hundred and twenty-one c) 589 = 5 hundreds + 8 tens + 9 ones 500 + 80 + 9 Five hundred and eighty-nine Train My Brain Say the number names for: a) 358 b) 409 c) 991 3.1 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 Numbers 29 Merged file_G2_Maths_TB_13012017.indb 29 23/01/2017 4:15:29 PM

1 note of ` 20 = ` 20 1 coin of ` 1 = ` 1 So, ` 100 + ` 20 + ` 1 = ` 121. So, Vinod has ` 121 (One hundred and twenty-one rupees). Example 5: There are 249 students in Class A and 336 students in Class B. Class C has 387 students and Class D has 161 students. a) What is the number of students in Class A? Write its number name. b) What is the number of students in Class D? Write its number name. Solution: a) There are 249 students in Class A. The number name of 249 is two hundred and forty-nine. b) There are 161 students in Class D. The number name of 161 is one hundred and sixty-one. We can use place value chart to form numbers. Consider a few examples. Example 6: If 9 is in the hundreds place, 2 in the tens place and 1 in the ones place, form the number. Solution: To form the number, write the given H T O digits correctly in the place value chart. So, the required number is 9 2 1 921. 3.1 I Explore (H.O.T.S.) We will now show numbers on a spike abacus. Consider the examples given below. Example 7: Show the following numbers on the abacus: a) 434 b) 623 c) 476 Solution: To show 434, we draw 4 blue beads for 4 hundreds. We draw 3 green beads for 3 tens and 4 red beads for 4 ones, as shown. 30 Merged file_G2_Maths_TB_13012017.indb 30 23/01/2017 4:15:30 PM

a) b) c) H T O H T O H T O 434 623 476 Example 8: Add 4 tens and 3 tens and show the answer on an abacus. Which spikes will be empty? Solution: Adding 4 tens and 3 tens, we get 7 tens. So, put 7 green beads on the abacus. The hundreds and the ones spikes on the abacus will be empty. H T O Concept 3.2: 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? To know these words, let us learn about ordinal numbers. Numbers 31 Merged file_G2_Maths_TB_13012017.indb 31 23/01/2017 4:15:31 PM

3.2 I Recall Observe the given pictures. It shows cars of different colours. We observe that the red car is before the green car. The green car is after the red car. The red car is between the blue car and the green car. The words before, after and between give the positions of a car with respect to the other cars. Let us learn what such positions of numbers are called. 3.2 I Remember and Understand Observe the ice cream scoops on the cone in the picture. They are placed one above the other. 7 Seventh scoop 7 th 6 Sixth scoop 6 th 5 Fifth scoop 5 th 4 Fourth scoop 4 th 3 Third scoop 3 rd The numbers 2 Second scoop 2 nd which tell about the position are 1 First scoop 1 st called ordinal numbers. 32 Merged file_G2_Maths_TB_13012017.indb 32 23/01/2017 4:15:31 PM

The first scoop is placed on the cone. So, counting from the first scoop, there are seven scoops. These are counted as first, second, third, fourth, fifth, sixth and seventh. If one more scoop is placed on the seventh, it is named as the eighth scoop. Similarly, another scoop on the eighth is named as the ninth. Another scoop on the ninth is named as the tenth. Number 1 2 3 4 5 6 7 8 9 10 Ordinal number First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth Short 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th form Train My Brain This is the list of top three students in a class. Write their positions as ordinal numbers. a) Megha – Rank 2 – _______________________ b) Razia – Rank 3 – _______________________ c) Harsh – Rank 1 – _______________________ 3.2 I Apply Ordinal numbers are used to denote the position of things. Usually, the position is counted from the left to the right. The position can also be counted from the bottom to the top. For example, • To tell the winning positions in a competition. • To tell the periods in our timetable. Numbers 33 Merged file_G2_Maths_TB_13012017.indb 33 23/01/2017 4:15:32 PM

Example 9: Look at Ram’s class timetable and answer the questions that follow. Second First period Third period Fourth period Fifth period period Swimming Maths Play Time English Colouring a) When is the Maths period? b) Which is the fourth period? c) In which period can the students enjoy colouring? Solution: a) Maths is the second period. b) English is the fourth period. c) Students can enjoy colouring in the fifth period. Example 10: Look at the bags arranged in the shelf and answer the given questions. a) Raj’s bag is blue in colour. On which shelf is his bag? b) Shyam’s bag is on the fourth shelf. What is the colour of Shyam’s bag? c) Reena’s bag is on the topmost shelf. What is its ordinal number? Solution: a) Raj’s bag is on the second shelf. b) Shyam’s bag is yellow in colour. c) Reena’s bag is on the sixth shelf. 34 Merged file_G2_Maths_TB_13012017.indb 34 23/01/2017 4:15:32 PM

3.2 I Explore (H.O.T.S.) Consider the following example: Example 11: Consider your city’s name to be Mumbai. a) How many letters are there in it? What are they? b) What is the first letter of the name? c) What is the last letter? 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 that is repeated is M. e) The repeated letter is in the first and the third place. Example 12: Write the ordinal numbers of the following numbers: a) 11 b) 12 c) 13 d) 14 e) 15 Solution: The ordinal numbers are – a) 11 – Eleventh b) 12 – Twelfth c) 13 – Thirteenth d) 14 – Fourteenth e) 15 - Fifteenth Numbers 35 Merged file_G2_Maths_TB_13012017.indb 35 23/01/2017 4:15:32 PM

Concept 3.3: Compare 3-digit Numbers I Think Raj has 504 colour pencils and his brother has 582 colour pencils. Who has more number of colour pencils? To answer this, we must learn how to compare 3-digit numbers. 3.3 I Recall We can compare two or more 2-digit numbers using the following rules: 1) A 2-digit number is always greater than a 1-digit number. A 3-digit number is always greater than a 2-digit number. A 3-digit number is also greater than a 1-digit number. So, a number with more number of digits is greater. 2) We use the symbols >, < or = to compare two numbers. 3) If two numbers have the same number of digits, first compare the left most digits (having the highest place value). If they are the same, compare the digits to their right. If they are also the same, continue to compare the next digits on their right. Continue till you compare the ones digits. The number with a greater digit in any of these places is greater. 3.3 I Remember and Understand Comparing two 3-digit numbers is similar to comparing two 2-digit numbers. A 2-digit number Use the steps to compare two 3-digit numbers. is always smaller Example 13: Compare: 469 and 468. than a 3-digit number. 36 Merged file_G2_Maths_TB_13012017.indb 36 23/01/2017 4:15:33 PM

Solution: Follow these steps to compare 3-digits numbers. Solved Solve this Steps 469 and 468 367 and 245 Step 1: Compare the number of digits Both 469 and Count the number of digits in the given numbers. 468 have 3 The number with more digits is greater. digits. Step 2: Compare the hundreds 4 = 4 If two numbers have the same number of digits, compare their hundreds digits. The number with the greater digit in the hundreds place is greater. Step 3: Compare the tens 6 = 6 If the numbers have the same digit in their hundreds place, compare the tens digits of the two numbers. The number with the greater digit in the tens place is greater. Step 4: Compare the ones 9 > 8 If the numbers have the same digit in their tens So, 469 > 468. place, compare the ones digits of the two numbers. The number with the greater digit in the ones place is greater. 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 Comparing numbers and place value chart help us in: 1) arranging numbers in ascending and descending orders. 2) forming the greatest and the smallest numbers from a given set of digits. Numbers 37 Merged file_G2_Maths_TB_13012017.indb 37 23/01/2017 4:15:33 PM

1) Ascending and descending orders Example 14: 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 order. a) For ascending order, follow the steps given below. Step 1: Compare the digits in the hundreds place of each number. 7 = 7 = 7 > 1 A number starting with 1 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. 7 = 7 > 1 So, 717 < 777 and 771. Step 3: Compare the digits in the ones place of each number. 7 > 1 So, 771 < 777. Step 4: Write the numbers from the smallest to the largest. Ascending order: 177, 717, 771, 777 b) For descending order, follow these steps. 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 38 Merged file_G2_Maths_TB_13012017.indb 38 23/01/2017 4:15:33 PM

Example 15: There 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 Comparing both the numbers using the place value chart, H T O H T O 8 7 9 8 8 0 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. 2) 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 16: 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: Draw the place value chart. H T O Step 2: Write the largest of the given digits in the hundreds place. Step 3: Place the larger of the remaining digits in the H T O tens place. 5 1 1 9 6 1 Step 4: Place the smallest digit in the ones place. Numbers 39 Merged file_G2_Maths_TB_13012017.indb 39 23/01/2017 4:15:33 PM

Example 17: 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: Draw the place value chart. H T O Step 2: Write the smallest of the given digits in the hundreds place. H T O Step 3: Place the smaller of the remaining digits in the 3 5 7 tens place. 5 7 9 Step 4: Place the largest digit in the ones place. 3.3 I Explore (H.O.T.S.) Consider the following examples. Example 18: Fill in the blanks using the proper symbols (<, > or =). 10 + 9 + 200 _________ 8 + 20 + 200 Solution: 10 + 9 + 200 = 219 and 8 + 20 + 200 = 228. As 219 is less than 228, we must put the < symbol in the blank. So, 219 < 228. Maths Munchies If two different numbers have the same digits in 2 3 1 all their places, then you have to pick only one place of both the numbers and compare. For example, 333 and 888 Instead of comparing 333 with 888, take only one of its places and compare 3 with 8. The answer would be 3 < 8. Since all the other digits are the same, we can decide that 333 < 888. 40 Merged file_G2_Maths_TB_13012017.indb 40 23/01/2017 4:15:33 PM

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! A Note to Parent After shopping, give your child the remaining notes of 100s and 10s and coins of 5s, 2s and 1s. Ask her or him to count them and tell you the amount of money you have. Numbers 41 Merged file_G2_Maths_TB_13012017.indb 41 23/01/2017 4:15:35 PM

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 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 their short forms of the following: a) 9 b) 4 c) 8 d) 1 e) 4 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 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 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 42 Merged file_G2_Maths_TB_13012017.indb 42 23/01/2017 4:15:35 PM

Addition Addition I Will Learn Concept 4.1: Add 2-digit Numbers and 3-digit Numbers Merged file_G2_Maths_TB_13012017.indb 43 23/01/2017 4:15:36 PM

Concept 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 number of stamps with each of them. How do you think Raj can find that? To answer that, let us learn addition of 2-digit numbers and 3-digit numbers. 4.1 I Recall We know how to add 2-digit numbers without regrouping. Solve the following to recall the concept of addition. a) 22 + 11 = ________ b) 32 + 21 = ________ c) 34 + 43 = ________ d) 45 + 13 = ________ e) 84 + 11 = ________ f) 27 + 52 = ________ 4.1 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 numbers. In some cases, we need to regroup the sum. We carry forward the tens digit to the next place. Consider these examples: 44 Merged file_G2_Maths_TB_13012017.indb 44 23/01/2017 4:15:37 PM