Preface IMAX partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. IMAX presents the latest version of the Passport series – updated and revised after considering the perceptive feedback and comments shared by our experienced reviewers and users. Designed specifically for CBSE schools, the Passport series endeavours to be faithful to the spirit of the National Curriculum Framework (NCF) 2005. Therefore, our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. The books are split into two parts to manage the bag weight. The aim of the NCF 2005 regarding Mathematics teaching is to develop the abilities of a student to think and reason mathematically, pursue assumptions to their logical conclusion and handle abstraction. The Passport Mathematics textbooks and workbooks for CBSE schools offer the following features: S tructured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved Student engagement through simple, age-appropriate language S upported learning through visually appealing images, especially for grades 1 and 2 Increasing rigour in sub-questions for every question in order to scaffold learning for students Word problems based on real-life scenarios, which help students to relate Mathematics to their everyday experiences Mental Maths to inculcate level-appropriate mental calculation skills S tepwise breakdown of solutions to provide an easier premise for learning of problem-solving skills Overall, the IMAX Passport Mathematics textbooks, workbooks and teacher companion books aim to enhance logical reasoning and critical thinking skills that are at the heart of Mathematics teaching and learning. – The Authors NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 2 12/17/2018 4:06:35 PM
I Will Learn About I Recall Contains the list of learning objectives to be covered in the Discusses the prerequisite chapter knowledge for the concept from the previous academic I Think year/chapter/concept/term Introduces the concept and arouses curiosity among students I Remember and Understand Train My Brain Explains the elements in detail that Checks for learning to gauge the form the basis of the concept Ensures understanding level of students, that students are engaged in learning testing both skill and knowledge throughout Pin-up Note Contains key retention points concerning the concept I Apply I Explore (H.O.T.S.) Connects the concept to Encourages students to extend real-life situations by enabling the concept learnt to advanced students to apply what has been scenarios learnt through the practice questions Connect the Dots Maths Munchies A multidisciplinary section that Aims at improving speed of connects a particular topic to calculation and problem solving other subjects in order to enable with interesting facts, tips or tricks students to relate better to it Drill Time A Note to Parent Additional practice questions at Engages a parent in the the end of every chapter out-of-classroom learning of their child and conducting activities to reinforce the learnt concepts NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 3 12/17/2018 4:06:35 PM
Contents Class 1 Shapes 3 1.1 Vertices and Diagonals of Two-dimensional Shapes 1 2 Patterns 12 2.1 Patterns in Shapes and Numbers 22 28 73 Numbers 03.1 Count by Thousands 37 1 +3.2 Compare 4-digit Numbers 41 3 46 -x4 Addition 46 4.1 Estimate the Sum of Two Numbers 53 56 9 54.2 Add 3-digit and 4-digit Numbers 62 8 24.3 Add 2-digit Numbers Mentally 69 5 Subtraction 73 79 5.1 Estimate the Difference between Two Numbers 5.2 Subtract 3-digit and 4-digit Numbers 5.3 Subtract 2-digit Numbers Mentally 6 Multiplication 6.1 Multiply 2-digit Numbers 6.2 Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 6.3 Double 2-digit and 3-digit Numbers Mentally NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 4 12/17/2018 4:06:35 PM
Chapter Shapes 1 I Will Learn About • identifying 2D shapes with straight and curved lines. • identifying sides, corners and diagonals. • making a tangram. • recognising 3D shapes and their faces and edges. Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes I Think There is a paper folding activity in Farida’s class. Her teacher asked the students to fold the paper across the vertices or the diagonals. How will Farida fold the paper? 1.1 I Recall We have learnt various shapes formed by straight lines or curved lines. Let us recall them. AB A BA B line line segment ray NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 5 1 12/17/2018 4:06:35 PM
horizontal lines vertical lines slant lines curved lines The straight and curved lines help us make closed and open figures. Figures which end at the point from where they start are called closed figures. Figures which do not end at the point from where they start are called open figures. 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 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. 2 12/17/2018 4:06:35 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 6
Object Shape Name of the shape 1D or 2D Triangle 2D 1.1 I Remember and Understand D C As we have already learnt various shapes, let us now name their parts. Consider a rectangle ABCD as shown. In the given rectangle, AB, BC, CD and DA are called its sides. There are lines joining A to C and B to D. These A B lines named AC and BD are called the diagonals of the rectangle. Vertex: The point where at least two sides of a figure meet is Points A, B, C and D where two sides of the called a vertex. The plural of rectangle meet are called the vertices. A square also has sides, diagonals and vertices. vertex is vertices. Note: A triangle and a circle do not have any Diagonal: A straight line inside a shape that joins the opposite diagonals. vertices is called a diagonal. Shapes 3 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 7 12/17/2018 4:06:35 PM
Try this! Complete the table with vertices, sides and diagonals of the given different shapes. One has been done for you. Shape Vertices Sides Diagonals DC A, B, C, D AB, BC, CD, DA AC, BD A B S R ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ PQ 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 A 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. B C 4 12/17/2018 4:06:36 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 8
The different number of markings on the sides of the triangle show that the lengths of all the 3 sides are different. If all the sides have the same number of markings, we can say that the lengths of all the 3 sides are the same. Let us now find the number of sides of a few 2D shapes and name them. Shape Name of the shape Number of sides Names of sides SR Square 4 PQ, QR, RS, SP PQ (All sides are equal.) D C Rectangle 4 AB, BC, CD, DA B Triangle (Opposite sides are A A equal.) 3 AB, BC, CA (All sides are equal in this case.) BC We find objects of various shapes around us. Complete in the following table by writing the basic shapes, number of the vertices and diagonals of the given objects. Object Basic shape Number of vertices Number of diagonals Shapes 5 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 9 12/17/2018 4:06:36 PM
Object Basic shape Number of vertices Number of diagonals Tangram A tangram is a Chinese geometrical puzzle. It consists of a 36 square that is cut into pieces as shown in the given figure. To create different shapes, we arrange these tangram pieces 4 1 with their sides or vertices touching one another. 7 5 Let us make our own tangram. 2 Materials needed: a square sheet of paper a pair of scissors a ruler (optional) Procedure: Figure Steps Step 1: Fold the square sheet of paper as shown. Step 2: Cut the square into two triangles, A across the fold. B Step 3: Cut one of the triangles obtained A1 in step 2, into two equal parts. We get two 2 smaller triangles as shown. 6 12/17/2018 4:06:36 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 10
Steps Figure Step 4: Fold the bigger triangle as shown. B Step 5: Unfold this piece and cut it across the 3 fold. We get one more triangle. 4 Step 6: Fold the boat-shaped piece from one end as shown. We get a triangle again on cutting at the fold. Step 7: Fold the remaining part of the paper 5 as shown. We get a square on cutting at the fold. Step 8: Fold the remaining paper again as 6 shown. We now get one more triangle on 7 cutting at the fold. We, thus, get the seven pieces of the tangram. Step 9: Colour these shapes using different colours. You can use these tangram pieces to make different shapes. Shapes 7 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 11 12/17/2018 4:06:36 PM
1.1 I Explore (H.O.T.S.) Observe the given figure. It looks like a box. Each side of the box is a E F square. A B In the figure, AB is the length and BF is the breadth of the box. AD is HG called the height of the box. So, this shape has three dimensions - DC length, breadth and height. cube 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. DC Step 2: Draw another square EFGH A B cutting square ABCD as shown. H G Step 3: Join DH, AE, BF and CG. D C 8 E F A B NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 12 H G D C E F B A 12/17/2018 4:06:36 PM
A few other such three-dimensional shapes are cuboids and cones. Solid shapes with flat rectangular faces are called cuboids. A solid shape with a circular base, a vertex and a curved Cuboid Cone surface is called a cone. 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: 213 Train My Brain Boat Candle Rocket Can you make a house with the following tangrams? You can use the same shape twice. Shapes 9 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 13 12/17/2018 4:06:36 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 12/17/2018 4:06:36 PM 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. 10 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 14
Drill Time Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes 1) Find the number of vertices and diagonals of the following shapes: a) b) c) d) e) A Note to Parent Take your child to public places such as hospitals, markets and religious places. Help them name the 3D shapes that are commonly seen on these structures. Shapes 11 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 15 12/17/2018 4:06:36 PM
Chapter Patterns 2 I Will Learn About • tiling of the given shape. • identifying and creating patterns in shapes and numbers. Concept 2.1: Patterns in Shapes and Numbers I Think Farida 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? 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 12 12/17/2018 4:06:36 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 16
Carpets Window grills Nature 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 in each example some shapes or numbers are repeated to form a pattern. Each shape or a 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. We get the next numbers are got by adding 2 to the previous number. Patterns 13 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 17 12/17/2018 4:06:36 PM
Patterns in lines and shapes Observe the following patterns. These are made up of lines and shapes. a) b) c) d) Let us see a few examples of patterns. Example 1: Complete the following patterns. 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 the 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 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. For example, 2 + 2 = 4; 4 + 2 = 6; 6 + 2 = 8 and so on 14 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 18 12/17/2018 4:06:36 PM
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, The numbers ending with 2, 4, 6, 8 or 0 are 1 + 2 = 3; 3 + 2 = 5; 5 + 2 = 7 and so on. called even numbers. The numbers ending Therefore, the pattern is 1, 3, 5, 7… In this pattern, 1 is the with 1, 3, 5, 7 or 9 are first term, 3 is the second term, 5 is the third term, 7 is the called odd numbers. 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 a few examples. Example 2: Complete the following patterns. a) b) c) Solution: a) b) c) Patterns 15 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 19 12/17/2018 4:06:36 PM
In these patterns, we observe that each term has one more basic shape than the previous term. Some patterns have terms increasing by a certain number. We can find this number by subtracting any 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… 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 patterns 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) 9, 29, 49, 69, _____, _____, _____ b) 13, 23, 33, 43, _____, _____, _____ c) 5, 10, 15, 20, _____, _____, _____ 16 12/17/2018 4:06:36 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 20
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. Tiling can also be done using different shaped tiles as shown here. Example 3: Draw the basic shape in the given tiling patterns. a) b) Solution: a) b) 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. Patterns 17 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 21 12/17/2018 4:06:36 PM
1) Rule: Turn the shape upside down. B asic shape: Pattern: 2) Rule: Turn the shape horizontally to the right and then back vertically. Basic shape: Pattern: 3) Rule: Rotate the shape quarter 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 4: 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 write the next terms. a) 12, 24, 36, _____, _____, _____. b) 1+ 2 = 3, 2 + 3 = 5, 3 + 4 = 7, ____________, ____________, ____________. 18 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 22 12/17/2018 4:06:36 PM
Example 5: Form a pattern using the rule, '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... Maths Munchies Pascal’s triangle 1 213 In the given triangle, each number is the 11 sum of the two numbers above it. This is 12 1 known as Pascal’s triangle. 13 31 14641 Pascal’s triangle is a triangular number 1 5 10 10 5 1 pattern named after Blaise Pascal, a French mathematician. 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. Here are a few pictures in which we can observe patterns that are found in nature. English Fun Little Frog A In poems, we see a B certain pattern or I saw a little frog, A a rhyming scheme. He was cuter than can be, B In this poem, we He was sitting on a log, see the pattern of And I'm sure he croaked at me! rhyming in alternate lines. Patterns 19 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 23 12/17/2018 4:06:36 PM
Drill Time Concept 2.1: Patterns in Shapes and Numbers 1) Complete the following patterns. a) ___________ ___________ ___________ ☺☺☻☺☺☻ b) ___________ ___________ c) _____________ ____________ d) ____________ ____________ e) ________________ ______________ 2) Fill the blanks with the next two terms of the given patterns. a) 122, 133, 144, ______, ______ b) 303, 304, 305, ______, ______ c) 40, 42, 44, _______, ________ d) 8, 24, 40, ________, ________ e) 35, 30, 25, ________, ________ f) 82, 72, 62, _______, ________ 20 12/17/2018 4:06:36 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 24
Drill Time 3) Draw the basic shapes in the given tiling patterns. a) b) c) d) 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 wall hanging which can be used to brighten upTyroauirn My Brain room! 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 a bed sheet. Patterns 21 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 25 12/17/2018 4:06:36 PM
Chapter Numbers 3 I Will Learn About • writing 4-digit numbers with place value chart. • identifying and forming the greatest and the smallest number. • writing the standard and the expanded forms of the number. • comparing and ordering numbers. Concept 3.1: Count by Thousands I Think Farida went to buy one of the toy cars shown. She ` 1937.00 could not read the price on one of the cars. Can you read the price on both the cars and understand what they mean? ` 657.00 3.1 I Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. Let us now count by tens and hundreds as: 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 When we multiply a digit by the value of its place, we get its place value. Using place values, we can write a number in its expanded form. 22 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 26 12/17/2018 4:06:36 PM
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 of 255 is _______________________________________. 3.1 I Remember and Understand To know about 4-digit numbers, we count by thousands using boxes. Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred Numbers 23 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 27 12/17/2018 4:06:37 PM
= 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. Using a spike abacus and beads of different colours, we represent 999 as shown. 9 blue, 9 green and 9 pink beads on the abacus represent 999. H TO Remove all the beads and Th H T O represent 999 put an orange bead on the represent 1000 next spike. This represents one thousand. We write it as 1000. 1000 is the smallest 4-digit number. Now, we know four places: ones, tens, hundreds and thousands. Let us represent 4732 in the place value chart. 24 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 28
Thousands (Th) Hundreds (H) Tens (T) Ones (O) The greatest 4-digit 4 7 32 number is 9999. We count by 1000s as 1000 (one thousand), 2000 (two thousand)... till 9000 (nine thousand). Expanded form of 4-digit numbers 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 TO a) 3746 = 3000 + 700 + 40 + 6 a) 3 7 46 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 TO Place values 80 15 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. 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 in the place value chart. Numbers 25 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 29 12/17/2018 4:06:37 PM
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 (Number names): 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 its 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 3 46 5 digits 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 Write the number names of: a) 2884 b) 4563 c) 9385 3.1 I Apply We can solve a few real-life examples using the knowledge of 4-digit numbers. Example 4: Ram has some money with him as shown. Calculate the amount that Ram has and write it in figures and words. 26 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 30
Solution: 1 note of ` 2000 = ` 2000 1 note of ` 100 = ` 100 3 notes of ` 10 = ` 30 1 coin of ` 5 = ` 5 So, the amount 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 schools is given in the table. Read the table and answer the questions that follow. Name of schools Number of students Unique High School 2352 Modern High School 4782 Ideal High School 7245 Talent High School 9423 Concept High School 1281 a) W hat is the number of students in Ideal High School? Write the number in words. b) H ow 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. A place value chart helps us to form numbers using given digits. Here is an example. 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 according to Th H T O their places as shown. So, the required number is 6514. 6 5 1 4 3.1 I Explore (H.O.T.S.) We have learnt the concepts of expanded form and place value chart. Now, we will solve a few examples to identify numbers from the abacus. Numbers 27 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 31 12/17/2018 4:06:37 PM
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 each Th H T O Number Step 2: place in the place value chart. a) 1 3 3 2 1332 Put a 0 in the places where there are b) 5 0 3 0 5030 no beads. c) 4 0 3 4 4034 Example 8: Draw beads on the abacus to show the given numbers. a) 3178 b) 6005 c) 4130 Th H T O Solution: Step 1: Follow these steps to show the given numbers. a) 3 1 7 8 Write the digits of the given numbers in the place b) 6 0 0 5 value chart. c) 4 1 3 0 Step 2: Draw the number of beads on each spike of the abacus to show the digit in each place of the number. Th H T O Th H T O Th H T O a) 3178 b) 6005 c) 4130 Concept 3.2: Compare 4-digit Numbers I Think Farida has 3506 paper clips and her brother has 3605 paper clips. Farida wants to know who has more paper clips. But the numbers appear to be the same, and she is confused. Can you tell who has more number of paper clips? 28 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 32
3.2 I Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise the concept. A 2-digit number is always greater than a 1-digit number. A 3-digit number is always greater than a 2-digit number and a 1-digit number. So, a number with more number of digits is always greater than a number with lesser digits. 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 If two numbers have 3-digit numbers. an equal number of digits, start comparing Let us understand the steps to compare through an example. from the leftmost digit. Example 9: Compare: 5382 and 5380 Solution: Follow these steps to compare the given numbers. Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 1: Compare the number of digits Both 5382 and Count the number of digits in the given numbers. 5380 have 4 The number having more number of digits is digits. greater. Step 2: Compare thousands 5=5 ____ = ____ If two numbers have the same number of digits, compare the thousands digits. The number with the greater digit in the thousands place is greater. Step 3: Compare hundreds 3=3 ____ = ____ If the digits in the thousands place are the same, compare the digits in the hundreds place. The number with the greater digit in the hundreds place is greater. Numbers 29 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 33 12/17/2018 4:06:37 PM
Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 4: Compare tens 8=8 ____ > ____ If the digits in the hundreds place are also same, So, compare the digits in the tens place. The number with the greater digit in the tens place is greater. ____ > ____ Step 5: Compare ones 2>0 - If the digits in the tens place are also the same, So, compare the digits in the ones place. The 5382 > 5380 number with the greater digit in the ones place is greater. When the ones place are the same, the numbers are equal. Note: Once we can decide a greater/smaller number, the steps that follow need not be carried out. Train My Brain Find the greater number in each of the following pairs. a) 7364, 7611 b) 8130, 8124 c) 4371, 4378 3.2 I Apply Train My Brain 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. 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 the ascending and descending orders. Solution: Follow these steps to arrange the given numbers in the ascending and descending orders. 30 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 34 12/17/2018 4:06:37 PM
Ascending 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 – 0 hundreds, 4126 –1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds So, 4005 < 4126 < 4305 < 4906 Step 3: Arranging the numbers in 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 – 0 hundreds, 4126 – 1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds So, 4906 > 4305 > 4126 > 4005 Step 3: Arranging the numbers in descending order: 4906, 4305, 4126, 4005 Simpler way! The descending order of numbers is just the reverse of their ascending order. 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 and the smallest 4-digit number using 4, 3, 7 and 5 (without repeating the digits). Solution: T he given digits are 4, 3, 7 and 5. The steps to find the greatest 4-digit number are given below. Step 1: Arrange the digits in descending order as 7 > 5 > 4 > 3. Step 2: Place the digits in the place value chart from left to right. So, the greatest 4-digit number formed is 7543. Th H T O 7543 Numbers 31 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 35 12/17/2018 4:06:37 PM
The steps to find the smallest 4-digit number are given below. Step 1: Arrange the digits in ascending order as Th H T O 3 < 4 < 5 < 7. 34 5 7 Step 2: Place the digits in the place value chart from left to right. So, the smallest 4-digit number formed is 3457. Example 12: Form the smallest 4-digit number using 4, 1, 0 and 6 (without repeating the digits). Solution: The given digits are 4, 1, 0 and 6. Step 1: Arrange the digits in ascending order as 0 < 1 < 4 < 6. Step 2: Place the digits in the place value chart from left to Th H T O right. But the number formed is 0146 or 146. 01 4 6 It is a 3-digit number. In such cases, we interchange the first two digits in Th H T O the place value chart. 10 4 6 So, the smallest 4-digit number formed is 1046. Example 13: Form the smallest and the largest 4-digit numbers using 4, 0, 8 and 6 (with repeating the digits). Solution: The given digits are 4, 0, 8 and 6. Follow the steps to form the smallest 4-digit number. Step 1: Find the smallest digit. 0 is the smallest of the given digits. (But a number cannot begin with 0.) Step 2: If the smallest digit is ‘0’, find the next smallest digit, which is 4. Write ‘4’ in the thousands place. Write ‘0’ in the rest of the places. Therefore, the smallest 4-digit number is 4000. Note: If the smallest of the given digits is not ‘0’, repeat the smallest digit four times to form the smallest number. Now, let us form the largest 4-digit number from the given digits. Step 1: The largest of the given digits is 8. Step 2: Repeat the digit four times to form the largest 4-digit number. Therefore, the largest 4-digit number that can be formed is 8888. 32 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 36
3.2 I Explore (H.O.T.S.) Let us see a few real-life examples where we use the comparison of 4-digit numbers. Example 14: 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 53 8 3 98 0 4 > 3 or in other words, 3 < 4 So, 3980 < 4538. Therefore, fewer people visited the exhibition on Sunday. Example 15: Razia arranged the numbers 7123, 2789, 2876 and 4200 in the 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 I am a 4-digit number. The digit in my thousands place is the same as that 213 in my ones place. The digit in my ones place is 5. The digits in my tens place and hundreds place are the same. The digit in my hundreds place is 3 less than the digit in my thousands place. Who am I? Numbers 33 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 37 12/17/2018 4:06:37 PM
Connect the Dots Social Studies Fun Without the concept of thousands, we would have never been able to estimate the heights 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 sounds – vowels and consonants. Underline all the vowels in the given words. a) Hundred b) Thousand c) DIGITS 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 e) 9819 2) Write the numbers in their expanded forms. a) 8712 b) 6867 c) 1905 d) 4000 34 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 38
Drill Time 3) Write the number names of the following numbers: 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 is 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. 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 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 Numbers 35 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 39 12/17/2018 4:06:37 PM
Drill Time 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) A shopkeeper sold 1105 milk chocolates and 2671 white chocolates. Which type of chocolates did he sell more? 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 concepts of place value and comparison of 4-digit numbers. 36 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 40
Chapter Addition 4 I Will Learn About • adding numbers with and without regrouping. • rounding off numbers to the nearest tens. • estimating the sum by adding mentally. Concept 4.1: Estimate the Sum of Two Numbers I Think Farida has ` 450 with her. She wants to buy a toy car for ` 285 and a toy train for ` 150. Do you think she has enough money to buy the toys? 4.1 I Recall We have learnt addition of 2-digit and 3-digit numbers. Here is a quick recap of the steps. Step 1: Place the numbers one below the other, according to their places. Step 2: Start adding from the ones place. Step 3: Regroup the sum and carry it forward to the next place, if necessary. Step 4: Write the answer. NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 41 37 12/17/2018 4:06:37 PM
4.1 I Remember and Understand Many a times, knowing the exact number may not be needed. When we say there are about 50 students in class, we mean If the digit in the ones that the number is close to 50. place is equal to or greater than 5, we Numbers which are close to the exact number can be round off the number rounded off. Rounding off numbers is also known as to the closest multiple estimation. of ten, greater than the given number. Let us now learn to round off or estimate the given numbers. Rounding to the nearest 10 Observe the number line given. The numbers on it are written in tens. 12 is between 10 and 20 and is closer to 10. (12) (28) (35) (49) So, we round off 12 down to 10. 35 is exactly in between 30 and 40. So, 0 10 20 30 40 50 we round it off up to 40. Let us now learn a step-wise procedure to round off numbers to the nearest 10. Example 1: Round off the following numbers to the nearest 10. a) 86 b) 42 Solution: Let us round off the given numbers using a step-wise procedure. Steps Solved Solve these 86 42 57 25 63 Step 1: Observe the digit in the ones place 86 42 57 25 63 of the number. Step 2: If the digit in 6>5 2 < 5 ____ > 5 ____ = 5 ____ < 5 the ones place is 4 or less, round the number 86 is 42 is ____ is ____ is ____ is down to the previous rounded rounded rounded rounded rounded ten. up to 90 down to 40 up to ____ up to ____ down to If it is 5 or more, round the number up, to the ____ next tens. 38 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 42 12/17/2018 4:06:37 PM
Rounding off numbers is used to estimate the sum of two 2-digit and 3-digit numbers. Let us understand this through an example. Example 2: Estimate the sum of: a) 64 and 15 b) 83 and 18 Solution: a) 64 + 15 Rounding off 64 to the nearest tens gives 60 (as 4 < 5). R ounding off 15 to the nearest tens gives 20 (as 5 = 5). So, the required sum is 60 + 20 = 80. b) 83 + 18 Rounding off 83 to the nearest tens gives 80 (as 3 < 5). Rounding off 18 to the nearest tens gives 20 (as 8 > 5). So, the required sum is 80 + 20 = 100. Example 3: Estimate the sum in the following: a) 245 and 337 b) 483 and 165 Solution: a) 245 + 337 R ounding off 245 to the nearest tens gives 250 (as 5 = 5). Rounding off 337 to the nearest tens gives 340 (as 7 > 5). So, the required sum is 250 + 340 = 590. b) 483 + 165 R ounding off 483 to the nearest tens gives 480 (as 3 < 5). Rounding off 165 to the nearest tens gives 170 (as 5 = 5). So, the required sum is 480 + 170 = 650. Train My Brain Estimate the sum of the following: a) 13 + 12 b) 824 + 295 c) 518 + 181 4.1 I Apply Here are a few examples where the estimation of the sum can be useful. Example 4: Arun wants to distribute sweets among students in the two sections of his class. In Section A, there are 43 students and in Section B, there are 36 students. Estimate the number of sweets that Arun should take to the class. Addition 39 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 43 12/17/2018 4:06:37 PM
Solution: Number of students in Section A = 43 Rounding off 43 to the nearest tens, we get 40. Number of students in Section B = 36 Rounding off 36 to the nearest tens, we get 40. Their sum is 40 + 40 = 80. Therefore, Arun should take about 80 sweets to the class. Example 5: Raj buys vegetables for ` 63 and fruits for ` 25. Estimate the amount he should pay to the shopkeeper. Solution: Amount spent on vegetables = ` 63 63 rounded to the nearest tens is 60. Amount spent on fruits = ` 25 25 rounded to the nearest tens is 30. Total amount to be paid = ` 60 + ` 30 = ` 90 So, Raj should pay about ` 90 to the shopkeeper. 4.1 I Explore (H.O.T.S.) Observe a few more situations where estimation of sum is used. Example 6: There are 416 walnut trees in a park. The park workers plant 574 more walnut trees. Estimate the number of walnut trees in the park after the workers finish planting. Solution: Number of trees in the park = 416 Rounding off 416 to the nearest tens, we get 420. Number of more trees the workers plant = 574 Rounding off 574 to the nearest tens, we get 570. Their sum is 420 + 570 = 990. Therefore, the park will have about 990 walnut trees after the workers finish planting. Example 7: Ramya has 26 cookies and 34 toffees. Renu has 42 cookies and 13 toffees. Estimate the total number of cookies and toffees. 40 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 44
Solution: Number of cookies with Ramya = 26 Number of toffees with her = 34 Rounding off 26 and 34 to the nearest tens, we get 30 and 30 respectively. Number of cookies with Renu = 42 Number of toffees with her = 13 Rounding off 42 and 13 to the nearest tens, we get 40 and 10 respectively. So, the sum of cookies = 30 + 40 = 70 Sum of toffees = 30 + 10 = 40 Therefore, they have 70 cookies and 40 toffees altogether. Concept 4.2: Add 3-digit and 4-digit Numbers I Think Farida’s father bought her a shirt for ` 335 and a skirt for ` 806. Farida wants to find how much her father had spent in all. How do you think she can find that? 4.2 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 and solve the following. a) 22 + 31 = _________ b) 42 + 52 = _________ c) 82 + 11 = _________ d) 101 + 111 = _________ e) 100 + 200 = _________ f) 122 + 132 = _________ Addition 41 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 45 12/17/2018 4:06:38 PM
4.2 I Remember and Understand Let us now understand the addition of two 3-digit numbers with While adding, regrouping. We will also learn to add two 4-digit numbers. regroup if the Add 3-digit numbers with regrouping sum of the digits is more than 9. Sometimes, the sum of the digits in a place is more than 9. In such cases, we need to regroup the sum. We then carry forward the digit to the next place. Example 8: Add 245 and 578. Solution: Arrange the numbers one below the other. Regroup if necessary. Step 1: Add the ones. Solved Step 3: Add the hundreds. H TO Step 2: Add the tens. H TO 1 11 245 H TO 245 11 +578 245 +578 3 +578 823 23 H TO Solve these H TO H TO 823 171 +197 390 +219 +121 Add 4-digit numbers without regrouping Adding two 4-digit numbers is similar to adding two 3-digit numbers. Let us understand this through an example. Example 9: Add 1352 and 3603. Solution: Arrange the numbers one below the other. 42 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 46 12/17/2018 4:06:38 PM
Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 135 2 135 2 +3 6 0 3 +3 6 0 3 5 55 Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 135 2 13 5 2 +3 6 0 3 +3 6 0 3 955 49 5 5 Th H T O Solve these Th H T O 41 9 0 11 1 1 +2 0 0 0 Th H T O +2 2 2 2 200 2 +3 0 0 3 Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 10: Add 1456 and 1546. Solution: Arrange the numbers one below the other. Add and regroup, if necessary. Solved Step 1: Add the ones. Step 2: Add the tens place. Th H T O Th H T O 1 11 1456 1456 +1 5 4 6 +1 5 4 6 2 02 Addition 43 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 47 12/17/2018 4:06:38 PM
Solved Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 111 111 1456 1456 +1 5 4 6 +1 5 4 6 002 3002 Th H T O Solve these O Th H T O Th H T 175 8 459 2 +5 6 6 2 267 8 +1 4 5 6 +1 3 3 2 Train My Brain c) 8837 + 1040 Solve: a) 321 + 579 b) 725 + 215 4.2 I Apply Look at a few examples where we use addition of 3-digit and 4-digit numbers. Example 11: Vinod had some stamps out of which he gave 278 stamps to his brother. Vinod now has 536 stamps left with him. How many stamps did he have in the beginning? H TO Solution: Number of stamps Vinod has now = 536 11 Number of stamps he gave his brother = 278 5 36 Number of stamps Vinod had in the +2 78 beginning = 536 + 278 = 814 8 14 Therefore, Vinod had 814 stamps in the beginning. 44 12/17/2018 4:06:38 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 48
Example 12: Ajit collected ` 2683 and Radhika collected ` 3790 for donating to a nursing home. What is the total money Th H T O collected? Solution: Amount collected by Ajit = ` 2683 11 Amount collected by Radhika = ` 3790 2 6 83 Total amount collected for the donation +3 7 9 0 =` 2683 + ` 3790 = ` 6473 6 4 73 Example 13: The number of Class 3 students in Heena’s school is 236. The number of Class 3 students in Veena’s school is 289. How many total number of Solution: students were present in Class 3 of both the school? H TO Number of students in Heena’s school = 236 11 Number of students present in Veena’s school = 289 2 36 Total number of students present in Class 3 of both + 2 8 9 the schools = 236 + 289 = 525 5 25 4.2 I Explore (H.O.T.S.) Let us see a few more examples on the addition of 4-digit numbers. Example 14: Three pieces of ribbon of lengths 2134 cm, 1185 cm and 3207 cm are cut from a long ribbon. What was the total length of the ribbon before the pieces were cut? Solution: The pieces of ribbon are 2134 cm, 1185 cm Th H T O and 3207 cm long. 11 Length of the ribbon before the pieces were 2134 cut = 2134 cm + 1185 cm + 3207 cm +1 1 8 5 Therefore, the ribbon was 6526 cm long before + 3 2 0 7 the pieces were cut. 6 5 2 6 Example 15: Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. Frame an addition problem. Solution: An addition problem contains words such as - in all, total, altogether and so on. So, the question can be ‘‘Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. How many stamps do they have altogether?” Addition 45 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 49 12/17/2018 4:06:38 PM
Concept 4.3: Add 2-digit Numbers Mentally I Think Farida had 18 colour pencils. Her sister gave her 71 more. Farida wanted to calculate the total number of pencils mentally. Do you know how Farida could do? 4.3 I Recall We have already learnt to add two 1-digit numbers mentally. To do so, we keep the larger number in mind and add the smaller one to it. Let us answer the questions to revise the concept. a) 5 + 4 = ________ [ ] (A) 5 (B) 4 (C) 1 (D) 9 b) 3 + 3 = ________ [ ] (A) 3 (B) 6 (C) 0 (D) 5 c) 1 + 4 = ________ [ ] (A) 3 (B) 4 (C) 6 (D) 5 d) 5 + 0 = ________ Train My Brain [ ] (A) 4 (B) 5 (C) 0 (D) 6 e) 6 + 3 = ________ [ ] (A) 4 (B) 6 (C) 3 (D) 9 4.3 I Remember and Understand Let us now learn to add two 2-digit numbers mentally, through these examples. Add 2-digit numbers mentally without regrouping Example 16: Add mentally: 53 and 65 Solution: To add the given numbers mentally, follow these steps: 46 12/17/2018 4:06:38 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 50
Steps Solved Solve this 53 and 65 38 and 41 Step 1: Add the digits in the ones place of the two 3+5=8 _____ + _____ = _____ numbers mentally. Step 2: Add the digits in The digits in the tens The digits in the tens place the tens place of the two place of the two of the two numbers are ___ numbers mentally. numbers are 5 and 6. and ____. Keep ____ in your Keep 6 in your mind, mind, count ___ forward as Step 3: Write sum of count 5 forward as 7, 8, ____, ____and ____. the digits obtained in 9, 10 and 11. ____ + ____ = ___ step 1 and sum of the 5 + 6 = 11 digits obtained in step 2 So, 53 + 65 = 118. So, 38 + 41 = ___. together. This is the sum of the given numbers. Add 2-digit numbers mentally with regrouping To mentally add two 1-digit numbers, keep the larger Example 17: Add mentally: 29 and 56 number in mind and the smaller on the fingers. Solution: To add the given numbers mentally follow these steps. Steps Solved 29 and 56 Solve this 83 and 47 Step 1: Regroup the two 29 = 20 + 9 83 = ___ + ____ given numbers as tens and 56 = 50 + 6 47 = ___ + ____ ones mentally. ____ + ____ = ____ Step 2: Add the ones of the 9 + 6 = 15 ____ + ____ = ____ two numbers mentally. ____ + ___ = ____ Step 3: Add the tens of the 20 + 50 = 70 two numbers mentally. So, 83 + 47 = ___. Step 4: Add the sums from 70 + 15 steps 2 and 3 mentally = 70 + 10 + 5 (regroup if needed). = 85 So, 29 + 56 = 85. Step 5: Write the sum of the given numbers. Addition 47 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 51 12/17/2018 4:06:38 PM
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