Passport-G3-FoundationMax-Maths-FY_opt

Class 3 MATHEMATICS TEXTBOOK Name : __________________________ Section : __________ Roll No: _______ School : ___________________________ Maths_TB_Nameslip_Book Explainer.indd 1 1/13/2017 5:12:29 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 lesson Chapter what the child has learnt 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 2 1 3 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 1/13/2017 5:12:30 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 lesson Chapter what the child has learnt 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 2 1 3 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 1/13/2017 5:12:30 PM

Contents Shapes .................................................1 1.1 Vertices and Diagonals of Two-dimensional Shapes 2 Patterns ................................................13 2.1 Patterns in Shapes and Numbers 14 Numbers ..............................................25 3.1 Count by Thousands 26 3.2 Compare 4-digit Numbers 33 Addition ...............................................42 4.1 Add 3-digit and 4-digit Numbers 43 4.2 Estimate the Sum of Two Numbers 48 4.3 Add 2-digit Numbers Mentally 53 Subtraction ..........................................60 5.1 Subtract 3-digit and 4-digit Numbers 61 5.2 Estimate the Difference between Two Numbers 68 5.3 Subtract 2-digit Numbers Mentally 71 Multiplication ......................................78 6.1 Multiply 2-digit Numbers 79 6.2 Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 84 6.3 Double 2-digit and 3-digit Numbers Mentally 91 TOC.indd 1 1/13/2017 11:49:16 AM

Time......................................................97 7.1 Read a Calendar 98 7.2 Read Time Correct to the Hour 104 Division ..............................................113 8.1 Division as Equal Grouping and Relate Division to Multiplication 114 8.2 Divide 2-digit and 3-digit Numbers by 1-digit Numbers 120 Fractions ............................................132 9.1 Fraction as a Part of a Whole 133 9.2 Fraction of a Collection 142 Money................................................152 10.1 Convert Rupee into Paise 153 10.2 Add and Subtract Money with Conversion 157 10.3 Multiply and Divide Money 162 10.4 Make Rate Charts and Bills 166 Measurement ....................................176 11.1 Conversion of Standard Units of Length 177 11.2 Conversion of Standard Units of Weight 185 11.3 Conversion of Standard Units of Volume 191 Data Handling ...................................200 12.1 Record Data Using Tally Marks 201 TOC.indd 2 1/13/2017 11:49:17 AM

TOC.indd 3 1/13/2017 11:49:17 AM

Sha Shapespes I Will Learn Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes L1_V2_PPS_Math_G3_TB_05112016_V0.indd 1 1/12/2017 9:55:10 PM

Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes I Think There is a paper folding activity in Neena’s class. Her teacher asked the students to fold the paper across the vertices or the diagonals. How will Neena fold the paper? To answer this question, we must learn about vertices and diagonals of two -dimensional shapes. 1.1 I Recall We have learnt various shapes formed by straight lines or curved lines. Let us recall them. A B A B A B Line Line segment Ray (a) (b) (c) Horizontal lines Vertical lines Slant lines Curved lines (d) (e) (f) (g) The straight and the curved lines help us make closed and open figures. Figures which end at the point where they start are called closed figures. Figures which do not end at the point where they start are called open figures. 2 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 2 1/12/2017 9:55:14 PM

Closed figures Open figures Try this: Write open figure or closed figure in the given blanks: ____________ ______________ ____________ ____________ Shapes such as rectangle, triangle, square and circle that can be laid (or drawn) flat on a piece of paper are called two-dimensional shapes. Their outlines are called two dimensional figures. In short, they are called 2D figures. Identify the following shapes and separate them as 1D or 2D shapes. One has been done for you. Object Shape Name of the shape 1D or 2D Triangle 2D Shapes 3 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 3 1/12/2017 9:55:15 PM

Object Shape Name of the shape 1D or 2D 1.1 I Remember and Understand As we have already learnt various shapes, let us now D C learn how to name their parts. Consider a rectangle ABCD as shown. In the given rectangle, AB, BC, CD and DA are called A B its sides. There are lines joining A to C and B to D. These lines named AC and BD are called diagonals. Points A, B, C and D where two sides of the rectangle Vertex: The point where at least meet are called vertices. two sides of a figure meet is called a vertex. The plural of vertex is A square too has all these parts. vertices. Diagonal: A straight line inside Note: A triangle and a circle do not a shape that joins the opposite have any diagonal. vertices is called a diagonal. Try this: Fill the given table with vertices, sides and diagonals of the different shapes. One has been done for you. Shape Vertices Sides Diagonals D C A, B, C, D AB, BC, CD, DA AC, BD A B S R ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ P Q 4 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 4 1/12/2017 9:55:17 PM

Shape Vertices Sides Diagonals Y Z X ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ W Train My Brain Name the given figures and find the number of their vertices and diagonals. a) b) c) 1.1 I Apply We know that a 2D shape has length and breadth. Let us now learn to find the number of sides of a 2D shape. Consider a triangle as shown. The given triangle has 3 sides named as AB, BC and CA. We can also name them as BA, CB and AC. The different number of small lines on the sides of the triangle show that the lengths of all the 3 sides are different. A The same number of small lines on the sides of the triangle show that the lengths of all the 3 sides are the same. Let us now learn to find the number of sides of a few 2D shapes and name them. B C Shapes 5 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 5 1/12/2017 9:55:19 PM

Shape Name of the shape Number of sides Names of sides S R 4 Square (All sides are PQ, QR, RS, SP equal) P Q D C 4 Rectangle (Opposite sides AB, BC, CD, DA are equal) A B A 3 Triangle (All sides equal in AB, BC, CA this case) B C We find many shapes in the objects around us. Fill in the following table by writing the basic shapes of these given objects, number of their vertices and diagonals. Object Basic shape Number of vertices Number of diagonals 6 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 6 1/12/2017 9:55:24 PM

A tangram is a Chinese geometrical puzzle consisting of a square cut into seven pieces. These pieces can be arranged in different ways to make various shapes. To create different shapes, we arrange these tangram pieces with their sides touching one beside another. We may also arrange these shapes with their vertices touching each other. Make your own tangram Materials needed: 1) A square sheet of paper 2) A pair of scissors 3) A ruler (Optional) Procedure: Steps Figure Step 1: Fold the square sheet of paper as shown. Step 2: Cut the square into two triangles, across the fold. A B Step 3: Cut one of the triangles A obtained in step 2, into two equal parts. 2 We get two smaller triangles as shown. 1 Step 4: Fold the other big triangle as shown. B Shapes 7 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 7 1/12/2017 9:55:25 PM

Steps Figure Step 5: Unfold this piece and cut it across the fold. We get one more triangle. 3 Step 6: Fold the boat-shaped piece from one end as shown. We get a triangle again on cutting at the fold. 4 Step 7: Fold the remaining part of the paper again as shown. We get a square on cutting at the fold. 5 Step 8: Fold the remaining paper again. We now get one more triangle on cutting at the fold. From all these cuts, we get seven pieces 6 of the tangram. 7 Step 9: Colour these shapes using different colours. You can use these tangram pieces to make different shapes. 1.1 I Explore (H.O.T.S.) Observe the object in the given figure. It looks like a box. Each E F side of the box is a square. A B In the figure, AB is the length and BF is the breadth of the box. AD is called the height of the box. So, this shape has three dimensions - length, breadth and height. H G D C 8 Cube L1_V2_PPS_Math_G3_TB_05112016_V0.indd 8 1/12/2017 9:55:28 PM

Such shapes are called three-dimensional shapes or 3D shapes or solid shapes. In the figure, • The points A, B, C, D, E, F, G and H are called vertices. • The lines AB, BC, CD, DA, BF, FE, EA, CG, GH, HD, HE and GF are called edges. • The squares ABCD, ABFE, BFGC, GCDH, EFGH and AEHD are called faces. Solid shapes with all flat square faces are called cubes. Let us learn how to draw a cube in a few simple steps. Steps Figure Step 1: Draw a square ABCD. D C A B Step 2: Draw another square EFGH H G cutting square ABCD as shown. D D C C E F A A B B Step 3: Join DH, AE, BF and CG. H G D C E F A B A few other such three-dimensional shapes are cuboids and cones. Solid shapes with flat rectangular faces are called cuboids. Cuboid A solid shape with a circular base and a curved surface is called a cone. Cone Shapes 9 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 9 1/12/2017 9:55:28 PM

Try this: Draw a cuboid and a cone showing the formation of the figure in steps. Shape Step 1 Step 2 Step 3 Cuboid Cone Maths Munchies We can use tangrams to make many shapes such as: 2 3 1 Train My Brain Boat Candle Rocket Can you make a house with the following tangrams? You can use the same shape twice. 10 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 10 1/12/2017 9:55:30 PM

Connect the Dots Social Studies Fun We can see 2D shapes such as rectangles, squares, circles and 3D shapes such as cubes and cuboids in the buildings in our neighbourhood. English Fun Try drawing a square while reciting the rhyme. From the bottom to the top, straight across right and then you stop. Straight down to the bottom again, across left and stop where you began. If the lines are the same size, then a square is formed for you a surprise. A Note to Parent Take your child to public places like hospitals, markets, religious places like temples, mosques and churches and so on. Help them name the 3D shapes that are commonly seen on these structures. Shapes 11 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 11 1/12/2017 9:55:43 PM

Drill Time Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes Find the number of vertices and diagonals of the following shapes: Shape Vertices Diagonals 12 L1_V2_PPS_Math_G3_TB_05112016_V0.indd 12 1/12/2017 9:55:44 PM

P Patternsatterns I Will Learn Concept 2.1: Patterns in Shapes and Numbers Ch_2_Patterns.indd 13 1/12/2017 9:57:42 PM

Concept 2.1: Patterns in Shapes and Numbers I Think Neena went to her father’s office on a Sunday. She saw that the floor of each hall in the office is of different designs. She found that the designs are made up of triangles, squares, circles and rectangles. She wanted to know if such repetition of a design has any special name. Do you also want to know? To know that, we need to learn about patterns in shapes. 2.1 I Recall There are many patterns around us. Patterns are similar to drawings. Let us see some of the patterns around us. Saree borders Carpets Window grills Nature 14 Ch_2_Patterns.indd 14 1/12/2017 9:57:44 PM

2.1 I Remember and Understand A pattern is an arrangement of shapes or numbers that follow a particular rule. Consider these examples: a) b) c) 150, 152, 154, 156 We see that each example has a repetition of some shapes to form a pattern. Each shape or group of shapes that repeats is called a basic shape. In example a), one and one make a pattern. In this pattern, the basic shape is . In example b), two and one make a pattern. In this pattern, the basic shape is . In example c), the first number is 150. The next numbers are got by adding 2 to the previous number. Patterns in lines and shapes Observe the following patterns. These are made up of lines and shapes. a) b) Patterns 15 Ch_2_Patterns.indd 15 1/12/2017 9:57:45 PM

c) d) Let us see a few examples of making patterns. Example 1: Complete the following pattern: a) b) Solution: a) b) In the same way, we can use numbers to make different patterns. Patterns in numbers We have seen that patterns are formed by repeating shapes in a particular way. Similarly, we can repeat numbers and create patterns. Each number pattern follows a rule. Patterns in odd and even numbers are the easiest patterns that we usually come across. Let us learn to form these patterns of odd and even numbers. Pattern with even numbers: An even number always ends with 2, 4, 6, 8 or 0. You can make a pattern with even numbers by adding 2 to the given even number. 16 Ch_2_Patterns.indd 16 1/12/2017 9:57:46 PM

For example, 2 + 2 = 4 4 + 2 = 6 6 + 2 = 8 and so on Therefore, the pattern is 2, 4, 6, 8, …. In this pattern, 2 is the first term, 4 is the second term, 6 is the third term, 8 is the fourth term and so on. Similarly, 18, 20, 22, 24, 26,… and 246, 248, 250, 252,…. are some more patterns of even numbers. Pattern with odd numbers: An odd number always ends with 1, 3, 5, 7 or 9. You can make a pattern with odd numbers by adding 2 to the given odd number. For example, 1 + 2 = 3 The numbers ending in 2, 3 + 2 = 5 4, 6, 8 or 0 are called even numbers. 5 + 2 = 7 and so on. The numbers end with 1, Therefore, the pattern is 1, 3, 5, 7, …. In this pattern, 3, 5, 7 or 9 are called odd 1 is the first term, 3 is the second term, 5 is the third numbers. term, 7 is the fourth term and so on. Similarly, 27, 29, 31, 33,… and 137, 139, 141, 143, … are some more patterns of odd numbers. Growing patterns Growing patterns can be found in shapes. Let us see some examples. Example 2: Complete the following patterns: a)     _________ __________ _________ b) ____________ ___________ __________ c) ___________ ___________ ___________ Patterns 17 Ch_2_Patterns.indd 17 1/12/2017 9:57:46 PM

Solution: a)        b) c) In these patterns, we observe that each term has one more basic shape than in the previous term. Some patterns have terms increasing by a certain number. We can find this number by subtracting two consecutive terms. Consider the following patterns. a) 20, 30, 40, 50, _____ b) 100, 200, 300, _____ c) 11, 21, 31, 41, _____ d) 145, 155, 165, _____ e) 246, 346, 446, _____ In pattern a), 40 – 30 = 10 and 30 – 20 = 10. So, the terms increase by 10. Similarly, the terms in c) and d) also increase by 10. In pattern b), 300 – 200 = 100 and 200 – 100 = 100. So, the terms increase by 100. Similarly, the terms in e) also increase by 100. Therefore, we can define the rule of the patterns in a), c) and d) as: increase by 10. The rule of the patterns in b) and e) as: increase by 100. Some patterns can be formed by decreasing the terms by a certain number. Consider the following patterns. a) 820, 720, 620, 520, … b) 100, 90, 80, 70, … c) 61, 56, 51, 46, … d) 165, 155, 145, … e) 846, 646, 446, … 18 Ch_2_Patterns.indd 18 1/12/2017 9:57:46 PM

In pattern a), 820 – 720 = 100 and 720 – 620 = 100. So, the terms decrease by 100. Similarly, the terms in e) decrease by 200. In pattern b), 100 – 90 = 10 and 90 – 80 = 10. So, the terms decrease by 10. Similarly, the terms in d) also decrease by 10. In pattern c), 61 – 56 = 5 and 56 – 51 = 5. So, the terms decrease by 5. Therefore, we can define the rule of the pattern in a) as decrease by 100; in pattern e) as decrease by 200; in pattern b) and d) as decrease by 10; in pattern c) as decrease by 5. Train My Brain Complete these patterns by writing their next 3 terms. a) 7, 14, 21, 28, _____, _____, _____ b) 8, 16, 24, 32, _____, _____, _____ c) 5, 10, 15, 25, _____, _____, _____ 2.1 I Apply We see and use patterns in real life every day. We use ceramic tiles, marble, granite and other such stones for the floors of our houses. Covering a surface with flat shapes like tiles without any gaps or overlaps is called tiling. We see tiling of floors and roofs of buildings and houses. Parking areas have parking tiles laid. Some tiling patterns are as follows. Patterns 19 Ch_2_Patterns.indd 19 1/12/2017 9:57:47 PM

Tiling can also be done using different shaped tiles as shown here. 2.1 I Explore (H.O.T.S.) We have seen that patterns in shapes and numbers follow certain rules. Using the rule, we can form the pattern with the given basic shapes. Consider the following examples. 1) Rule: Repeat each shape twice. Basic shape: Pattern: 2) Rule: Turn the shape horizontally and then back vertically. Basic shape: Pattern: 20 Ch_2_Patterns.indd 20 1/12/2017 9:57:47 PM

3) Rule: Rotate the shape half way to the right. Basic shape: Pattern: Number patterns also follow certain rules. Once the rule is identified, we can continue the given pattern. For example, the rule for a pattern is “Begin with 1, add 3 and subtract 1 alternately”. The pattern is: 1, 4, 3, 6, 5, 8, 7, ...... Example 3: Complete the given pattern: 8, 16, 24, ____,____ ,_____, ____ Solution: In the given pattern, the first term is 8, the second term is 16 and the third term is 24. This pattern has numbers increasing by 8. So, the next terms of the pattern are: 24 + 8 = 32; 32 + 8 = 40; 40 + 8 = 48; 48 + 8 = 56. So, the rule of this pattern is adding 8. Therefore, the pattern is 8, 16, 24, 32, 40, 48, 56 Try these: Find the rule of the following patterns and continue them. a) 12, 24, 36, _____, _____, _____ b) 1+ 2 = 3, 2 + 3 = 5, 3 + 4 = 7, _____, _____, _____, Example 4: Form a pattern given that the rule is 'Begin with 5 and multiply by 2'. Solution: If the rule is 'Begin with 5 and multiply by 2', the terms in the pattern are: 5, 10, 20, 40, ..... Patterns 21 Ch_2_Patterns.indd 21 1/12/2017 9:57:47 PM

Maths Munchies Pascal’s triangle 1 2 3 1 Pascal’s triangle is a triangular number 1 1 pattern named after Blaise Pascal, a French 1 2 1 mathematician. In the triangle, each number 1 3 3 1 is the sum of the two numbers above it. 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 Connect the Dots Science Fun We see patterns all around us. Flowers, leaves, stripes on animals and so on have patterns in them. Here are a few pictures in which we can observe patterns in nature. Train My Brain English Fun In poems, we see a Roses are Red certain pattern or a Roses are red, A rhyming scheme. In this violets are blue. B poem, we see the Sugar is sweet, A pattern of rhyming and so are you! B alternate lines. 22 Ch_2_Patterns.indd 22 1/12/2017 9:57:53 PM

A Note to Parent We observe different patterns every day. Here is an activity you can do with your child with some inspiration from these patterns. Make a quilt which can be put up to brighten up your walls! This can be done by cutting square sheets of different coloured paper and pasting it on a base sheet. If you have waste piece of cloth, it can also be woven into the bed sheet. Drill Time Concept 2.1: Patterns in Shapes and Numbers 1) Complete the following patterns: a) ___________ ___________ ___________, b) ☺☺☻ ☺☺☻ _______________ _______________ c) ___________ ___________ d) ____________ ____________, e) __________________ __________________ Patterns 23 Ch_2_Patterns.indd 23 1/12/2017 9:57:53 PM

Drill Time 2) Fill the blanks with the next two terms of the given pattern. a) 122, 133, 144, _______, _______ b) 303, 304, 305, _______, _______ c) 40, 42, 44, ________, _________ d) 8, 24,40, _________, _________ e) 10, 20, 30, ________, ________ 3) Draw the basic shape in the given tiling patterns. a) b) c) d) 24 Ch_2_Patterns.indd 24 1/12/2017 9:57:54 PM

Numb Numbersers I Will Learn Concepts 3.1: Count by Thousands 3.2: Compare 4-digit Numbers L3_V2_PPS_Math_G3_TB_Numbers.indd 25 1/12/2017 10:00:09 PM

Concept 3.1: Count by Thousands I Think Neena went to buy one of the toy cars shown. She could not read the price on one of them. Can you read the price on both the cars? To read 4-digit numbers, we must learn numbers ` 1500.00 ` 700.00 greater than hundreds. 3.1 I Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. We can count by tens and hundreds. Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80 and 90 Counting by 100s: 100, 200, 300, 400, 500, 600, 700, 800 and 900 A digit multiplied by the value of its place gives its place value. Using place values, we can write the numbers in the expanded form. Let us answer these to revise the concept. a) The number for two hundred and thirty-four is _____________. b) In 857, there are _______ hundreds, _______ tens and _______ ones. c) The expanded form of 444 is _______________________. d) The place value of 9 in 493 is _____________. e) The number name for 255 is _______________________________________. 26 L3_V2_PPS_Math_G3_TB_Numbers.indd 26 1/12/2017 10:00:12 PM

3.1 I Remember and Understand To know about 4-digit numbers, we count by thousands using boxes. Let be 1 ones. is the same as 10 ones 1 tens 10 tens = = One hundred hundred H T O 1 0 0 H T O = 100 = 1 0 0 = One hundred H T O = 200 = 2 0 0 = Two hundreds H T O = 300 = 3 0 0 = Three hundreds H T O = 400 = 4 0 0 = Four hundreds Numbers 27 L3_V2_PPS_Math_G3_TB_Numbers.indd 27 1/12/2017 10:00:14 PM

H T O = 500 = 5 0 0 = Five hundreds H T O = 600 = 6 0 0 = Six hundreds H T O = 700 = 7 0 0 = Seven hundreds H T O = 800 = 8 0 0 = Eight hundreds H T O = 900 = 9 0 0 = Nine hundreds = 1000 = Th H T O 1 0 0 0 = Ten hundreds = One thousand Using a spike abacus and beads of different colours, we represent 999 as shown. 9 blue, 9 green and 9 red beads on the abacus represent 999. H T O Represent 999 Remove all beads and put a yellow bead on the next spike. This represents a thousand. It is written as 1000. Th H T O It is the smallest 4-digit number. Represent 1000 28 L3_V2_PPS_Math_G3_TB_Numbers.indd 28 1/12/2017 10:00:17 PM

Now, we know four places – ones, tens, hundreds and thousands. Places Thousands (Th) Hundreds (H) Tens (T) Ones (O) Values 1000 100 10 1 This chart is called the place value chart. We count by 1000s as 1000 (one thousand), 2000 (two thousand), ... till 9000 (nine thousand). The greatest 4-digit number Expanded form of 4-digit numbers is 9999. The form in which a number is written as the sum of the place values of its digits is called its expanded form. Let us now learn to write the expanded form of 4-digit numbers. Example 1: Expand the following numbers: a) 3746 b) 6307 Solution: Write the digits of the given numbers in the place value chart, as shown. Expanded forms: Th H T O a) 3746 = 3000 + 700 + 40 + 6 a) 3 7 4 6 b) 6307 = 6000 + 300 + 0 + 7 b) 6 3 0 7 Writing number names of 4-digit numbers Observe the expanded form and place value chart for a 4-digit number, 8015. Th H T O 8 0 1 5 Place values 5 ones = 5 1 tens = 10 0 hundreds = 0 8 thousands = 8000 We can call 8015 as the standard form of the number. Let us look at an example. Numbers 29 L3_V2_PPS_Math_G3_TB_Numbers.indd 29 1/12/2017 10:00:18 PM

Example 2: Write the expanded forms and number names of these numbers. a) 1623 b) 3590 Solution: To expand the given numbers, write them in the correct places of the place value chart: Expanded forms: Th H T O a) 1623 = 1000 + 600 + 20 + 3 a) 1 6 2 3 b) 3590 = 3000 + 500 + 90 + 0 b) 3 5 9 0 Writing in words: a) 1623 = One thousand six hundred and twenty-three b) 3590 = Three thousand five hundred and ninety We can write the standard form of a number from the given expanded form. Let us see an example. Example 3: Write the standard form of 3000 + 400 + 60 + 5. Solution: Write the numbers in the place value Th H T O chart in the correct places. Write the digits 3 4 6 5 one beside the other starting from the thousands place. 3000 + 400 + 60 + 5 = 3465 So, the standard form of 3000 + 400 + 60 + 5 is written as 3465. Train My Brain Say the number names of the following numbers: a) 2884 b) 4563 c) 9385 3.1 I Apply We can solve some real-life examples using the knowledge of 4-digit numbers. 30 L3_V2_PPS_Math_G3_TB_Numbers.indd 30 1/12/2017 10:00:18 PM

Example 4: Ram has some money with him as shown. Write the money Ram has in figures and words. Solution: 1 note of ` 2000 = ` 2000 1 note of ` 100 = ` 100 3 notes of ` 10 = ` 30 1 note of ` 5 = ` 5 So, the money that Ram has = ` 2000 + ` 100 + ` 30 + ` 5 = ` 2135 In words, ` 2135 is two thousand one hundred and thirty-five rupees. Example 5: The number of students in different high schools are as follows: Name of the school Name of the students Unique High School 2352 Modern High School 4782 Ideal High School 7245 Talent High School 9423 Concept High School 1281 a) What is the number of students in Ideal High School? Write the number in words. b) How many students are there in Concept High School? Write the number in words. Solution: a) The number of students in Ideal High School is 7245. In words, it is seven thousand two hundred and forty-five. b) The number of students in Concept High School is 1281. In words, it is one thousand two hundred and eighty-one. Numbers 31 L3_V2_PPS_Math_G3_TB_Numbers.indd 31 1/12/2017 10:00:19 PM

A place value chart helps us to form numbers using the given digits. Here are a few examples. Example 6: A number has 6 in the thousands place and 5 in the hundreds place. It has 1 in the tens place and 4 in the ones place. What is the number? Solution: Write the digits in the place value chart Th H T O according to their places as shown. So, the 6 5 1 4 required number is 6514. 3.1 I Explore (H.O.T.S.) We have learnt the concepts of expanded form and place value chart. Now, we shall solve some examples to identify numbers from the abacus. Example 7: Write the numbers represented by these abacuses: a) b) c) Th H T O Th H T O Th H T O Solution: Follow these steps to write the numbers: Step 1: Write the number of beads in Th H T O Number each place in the place value a) 1 3 3 2 1332 chart. b) 5 0 3 0 5030 Step 2: Put a 0 in the places where c) 4 0 3 4 4034 there are no beads. Example 8: Draw circles on abacus to show the given numbers: a) 3178 b) 6005 c) 4130 Solution: Follow these steps to show the given numbers. Step 1: Write the digits of the given numbers in Th H T O the place value chart. a) 3 1 7 8 Step 2: Draw the number of circles on the abacus b) 6 0 0 5 as per the digit in each place. c) 4 1 3 0 32 L3_V2_PPS_Math_G3_TB_Numbers.indd 32 1/12/2017 10:00:19 PM

Th H T O Th H T O Th H T O a) 3178 b) 6005 c) 4130 Maths Munchies I am a 4-digit number. The digit in my thousands place is the same as that 1 2 3 in the ones place. The digit in the ones place is 5. The digit in my tens place and hundreds place is the same. The digit in hundreds place is 3 less than the digit in my thousands place. Who am I? Concept 3.2: Compare 4-digit Numbers I Think Neena has 3506 paper clips and her brother has 3605 paper clips. Neena wants to know who has more paper clips. But the numbers look the same and she is confused. Can you tell who has more paper clips? To answer this question, we must learn to compare 4-digit numbers. 3.2 I Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise. Numbers 33 L3_V2_PPS_Math_G3_TB_Numbers.indd 33 1/12/2017 10:00:20 PM

A 2-digit number is always greater than a 1-digit number. A 3-digit number is always greater than a 2-digit number. So, a number with more number of digits is always greater. We use the symbols >, < or = to compare two numbers. 3.2 I Remember and Understand Comparing two 4-digit numbers is similar to comparing two 3-digit numbers. Let us understand the steps through an example. If two numbers have equal number of digits, Example 9: Compare: 5690 and 5380 start comparing from Solution: Follow these steps to compare the given the left most digit. numbers: Solved Solve this Steps 5690 and 7469 and 5380 7478 Step 1: Compare number of digits Both 5690 Count the number of digits in the given numbers. and 5380 The number with more digits is greater. have 4-digits. Step 2: Compare thousands Train My Brain If two numbers have the same number of digits, 5 = 5 compare the thousands digits. The number with ____ = ____ the greater digit in the thousands place is greater. Step 3: Compare hundreds If the digits in the thousands place are the same, 6 > 3 compare the digits in the hundreds place. The So, ____ = ____ number with the greater digit in the hundreds place 5690 > 5380 is greater. Step 4: Compare tens ____ > ____ If the digits in hundreds place are also same, - compare the digits in the tens place. The number So, with the greater digit in the tens place is greater. ____ > ____ 34 L3_V2_PPS_Math_G3_TB_Numbers.indd 34 1/12/2017 10:00:20 PM

Solved Solve this Steps 5690 and 7469 and 5380 7478 Step 5: Compare ones If the digits in the tens place are also the same, - - compare the digits in the ones place. The number with the greater digit in the ones place is greater. Note: Once we could decide a greater/smaller number, the next steps need not be carried out. Train My Brain Find the greater number from each of the following pairs: a) 7364, 7611 b) 8130, 8124 c) 4371, 4378 3.2 I Apply We can apply the knowledge of comparing numbers and place value to: 1) arrange numbers in the ascending and descending orders. 2) form the greatest and the smallest numbers using the given digits. 1) Ascending and descending orders Ascending Order: The arrangement of numbers from the smallest to the greatest Descending Order: The arrangement of numbers from the greatest to the smallest Example 10: Arrange 4305, 4906, 4005 and 4126 in ascending and descending orders. Solution: Follow these steps to arrange the given numbers in ascending and descending orders: Ascending Order Step 1: Compare the digits in the thousands place: Numbers 35 L3_V2_PPS_Math_G3_TB_Numbers.indd 35 1/12/2017 10:00:20 PM

All the numbers have 4 in their thousands place. Step 2: Compare the digits in the hundreds place: 4005 – No hundreds, 4126 –1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds So, 4005 < 4126 < 4305 < 4906. Step 3: Arrange in the ascending order: 4005, 4126, 4305, 4906 Descending Order Step 1: Compare the digits in the thousands place: All the numbers have 4 in their thousands place. Step 2: Compare the digits in the hundreds place: 4005 – No hundreds, 4126 – 1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds. So, 4906 > 4305 > 4126 > 4005. Step 3: Arrange in descending order: 4906, 4305, 4126, 4005 Simpler way! Descending order of numbers is just the reverse of their ascending order. 2) Forming the greatest and the smallest 4-digits numbers Let us learn to form the greatest and the smallest 4-digit numbers. Look at the following examples: Example 11: Form the greatest number using 3, 5, 4 and 7. Solution: The given digits are 3, 5, 4 and 7. To form the greatest 4-digit number, follow these steps: Step 1: Draw the place value chart with four places. Th H T O Step 2: Choose the largest digit and place it under the thousands place. The largest of the digits 3, 5, 4 and Th H T O 7 7 is 7. So, place 7 under the thousands place. 36 L3_V2_PPS_Math_G3_TB_Numbers.indd 36 1/12/2017 10:00:21 PM

Step 3: Choose the largest of the remaining digits and place it under the hundreds place. The largest of the remaining digits 3, 5 and 4 is 5. Th H T O Place 5 under the hundreds place. 7 5 Step 4: Choose the larger of the remaining digits. Place it Th H T O under the tens place. The larger of the digits 3 and 7 5 4 4 is 4. So, place 4 under the tens place. Step 5: Write the remaining digit under the ones place. Th H T O The remaining digit is 3. So, place 3 under the ones 7 5 4 3 place. Therefore, the greatest number that can be formed using the given digits is 7543. Example 12: Form the smallest 4-digit number using 4, 0, 8 and 6. Solution: The given digits are 4, 0, 8 and 6. To form the smallest 4-digit number, follow these steps: Step 1: Write the place value chart with the four places. Th H T O Step 2: The smallest of 4, 0, 8 and 6 is 0. But a 4-digit number cannot begin with 0. So, we choose the next Th H T O 4 0 smallest number, which is 4. So, write 4 in the thousands place and 0 in the hundreds place. Step 3: Choose the smaller of the remaining two digits. Place it under the tens place. The smaller of the Th H T O digits 6 and 8 is 6. So, place 6 under the tens place. 4 0 6 Step 4: Write the remaining digit in the ones place. The remaining digit is 8. So, place 8 under the ones Th H T O place. 4 0 6 8 Therefore, the smallest number that can be formed using the given digits is 4068. Numbers 37 L3_V2_PPS_Math_G3_TB_Numbers.indd 37 1/12/2017 10:00:21 PM

3.2 I Explore (H.O.T.S.) Let us see a few real-life examples of comparison of 4-digit numbers. Example 13: 4538 people visited an exhibition on Saturday and 3980 people visited it on Sunday. On which day did fewer people visit the exhibition? Solution: Number of people who visited the exhibition on Saturday = 4538 Number of people who visited the exhibition on Sunday = 3980 Comparing both the numbers using the place value chart, Th H T O Th H T O 4 5 3 8 3 9 8 0 4 > 3 or in other words, 3 < 4 So, 3980 < 4538. Therefore, fewer people visited the exhibition on Sunday. Example 14 : Raju arranged the numbers 7123, 2789, 2876 and 4200 in ascending order as 2876, 2789, 4200, 7123. Reena arranged them as 2789, 2876, 4200, 7123. Who arranged them correctly? Why? Solution: Reena’s arrangement is correct. Reason: Comparing the hundreds place of the smaller of the given numbers, 7 hundreds < 8 hundreds. So, 2789 is the smallest number. Maths Munchies Atul, Sanjay, Reema and Swati received roll numbers for their exam as 1 2 3 8762, 9174, 1834 and 8936 respectively. Their teacher asked them to sit in the ascending order of their roll numbers. Who should sit on the first bench and the last bench? 38 L3_V2_PPS_Math_G3_TB_Numbers.indd 38 1/12/2017 10:00:21 PM

Connect the Dots Social Studies Fun Without the concept of thousands, we would have never been able to estimate the height of the tallest mountain peaks in the world! Take a look at the tallest peaks across each continent. English Fun There are two kinds of letters – vowels and consonants. Underline all the vowels in the given words. a) HUNDRED b) THOUSAND c) DIGITS A Note to Parent Play a new dice game with your child. Each player rolls the dice four times in a row and writes the numbers from left to right. The winner is the one who gets the smallest number in one round. Play multiple rounds until your child understands the concept of place value and comparison of 4-digit numbers. Numbers 39 L3_V2_PPS_Math_G3_TB_Numbers.indd 39 1/12/2017 10:00:24 PM

Drill Time Concept 3.1: Count by Thousands 1) Write the numbers in the place value chart. a) 1451 b) 8311 c) 9810 d) 1000 e) 7613 2) Write the numbers in their expanded forms. a) 8712 b) 6867 c) 1905 d) 4000 e) 9819 3) Write the number names of the following: a) 9125 b) 5321 c) 3100 d) 1900 e) 7619 4) Form 4-digit numbers from the following: a) 4 in the thousands place, 3 in the hundreds place, 0 in the tens place and 2 in the ones place b) 9 in the thousands place, 1 in the hundreds place, 4 in the tens place and 0 in the ones place c) 5 in the thousands place, 4 in the hundreds place, 9 in the tens place and 7 in the ones place d) 8 in the thousands place, 2 in the hundreds place, 6 in the tens place and 5 in the ones place e) 1 in the thousands place, 2 in the hundreds place, 3 in the tens place and 4 in the ones place 5) Word problems a) The number of people in different rows in a football stadium are as given: Row 1: 2345 Row 2: 6298 Row 3: 7918 Row 4: 8917 Row 5: 1118 (A) What is the number of people in Row 1? Write the number in words. (B) How many people are there in Row 4? Write the number in words. b) Ram has a note of ` 2000, a note of ` 500, a note of ` 20 and a coin of ` 2. How much money does he have? Write the amount in figures and words. 40 L3_V2_PPS_Math_G3_TB_Numbers.indd 40 1/12/2017 10:00:25 PM

Drill Time Concept 3.2: Compare 4-digit Numbers 6) Compare the following numbers using <, > or =. a) 8710, 9821 b) 1689, 1000 c) 4100, 4100 d) 2221, 2222 e) 6137, 6237 7) Arrange the numbers in the ascending and descending orders. a) 4109, 5103, 1205, 5420 b) 7611, 7610, 7609, 7605 c) 9996, 8996, 1996, 4996 d) 5234, 6213, 1344, 5161 e) 4234, 6135, 4243, 6524 8) Form the greatest and the smallest numbers using: a) 3, 5, 9, 2 b) 1, 5, 9, 4 c) 7, 4, 1, 8 d) 9, 1, 3, 5 e) 8, 2, 3, 4 9) Word problems a) 5426 people visited a museum on a Friday and 3825 people visited it on the following Sunday. On which day did fewer people visit the museum? b) Bunny’s father gave him 1105 Eclairs chocolates and 2671 Melody chocolates. Which type of chocolate did he have more? Numbers 41 L3_V2_PPS_Math_G3_TB_Numbers.indd 41 1/12/2017 10:00:25 PM

Addi Additiontion I Will Learn Concepts 4.1: Add 3-digit and 4-digit Numbers 4.2: Estimate the Sum of Two Numbers 4.3: Add 2-digit Numbers Mentally L04_V2_PPS_Maths_G1_TB_Addition.indd 42 1/12/2017 10:04:16 PM

Concept 4.1: Add 3-digit and 4-digit Numbers I Think Neena’s father bought her a shirt for ` 335 and a skirt for ` 806. Neena wants to find how much her father had spent in all. How do you think she can find that? To answer this question, we must learn to find the sum of two numbers. 4.1 I Recall We can add 2-digit or 3-digit numbers by writing them one below the other. This method of addition is called vertical addition. Let us revise the earlier concept by solving the following. a) 22 + 31 = _________ b) 42 + 52 = _________ c) 82 + 11 = _________ d) 101 + 111 = _________ e) 100 + 200 = _________ f) 122 + 132 = _________ Addition 43 L04_V2_PPS_Maths_G1_TB_Addition.indd 43 1/12/2017 10:04:19 PM

4.1 I Remember and Understand Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit While adding, numbers. regroup if the sum 1) Add 3-digit numbers with regrouping of the digits is more Sometimes, the sum of the digits in a place is more than 9. than 9. In such cases, we need to regroup the sum. We then carry the digit to the next place. Example 1: Add 245 and 578. Solution: Arrange the numbers one below the other. Regroup if necessary. Solved Step 1: Add the ones. Step 2: Add the tens. Step 3: Add the hundreds. H T O H T O H T O 1 1 1 1 1 2 4 5 2 4 5 2 4 5 + 5 7 8 + 5 7 8 + 5 7 8 3 2 3 8 2 3 Solve these H T O H T O H T O 8 2 3 3 9 0 1 7 1 + 1 9 7 + 1 2 1 + 2 1 9 44 L04_V2_PPS_Maths_G1_TB_Addition.indd 44 1/12/2017 10:04:21 PM