1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text_Reduced

3 MATHEMATICS TEXTBOOK Name : __________________________________ Section: ________________ Roll No:__________ School : __________________________________ JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___1 / 184

How do we hone crucial learning? R REMEMBERING U UNDERSTANDING The first step of the learning process As we progress with recollecting information, involves remembering new things and we parallelly start understanding it by breaking recollecting all crucial information it down and exploring its length and breadth such as meanings and concepts Contains the list of concepts Chapter to be covered in the chapter along with learning 1 Shapes objectives Concept List (I Will Learn) Introduces the concept/subtopic in such a Think manner as to arouse curiosity among the students 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 Recall from previous academic year/chapter/concept/term We have learnt various shapes formed by straight lines or curved lines. Let us recall them. Explains the elements in Remembering & Understanding detail that forms the basis of the concept. It ensures that As we have already learnt various shapes, let us now learn how to name students are engaged in their parts. Consider a rectangle ABCD as shown. In the given rectan- learning throughout. gle, named AC and BD are called diagonals. JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___2 / 184

A APPLICATION H H.O.T.S. We begin relating what we learn to Having applied the concepts learnt, we real life situations around us, thereby extend the field of application to more applying what we have learnt advanced and challenging scenarios Application Connects the concept to real-life situations by giving number of sides of a 2D shape. an opportunity to apply Higher Order Thinking Skills (H.O.T.S.) what the child has learnt through practice questions of the box is a square. Encourages the child to Drill time extend the concept learnt Concept 1.1 Vertices and Diagonals of Two-Dimensional Shapes to advanced application Find the number of vertices and diagonals of the following shapes: scenarios Additional practice questions given at the end of every chapter JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___3 / 184

Contents 1. Shapes..................................................1 1.1 V ertices and Diagonals of Two-dimensional Shapes 2 2. Patterns ................................................11 2.1 P atterns in Shapes and Numbers 12 3. Numbers ..............................................21 3.1 C ount by Thousands 22 3.2 Compare 4-digit Numbers 29 4. Addition ...............................................36 4.1 A dd 3-digit and 4-digit 37 Numbers 4.2 Estimate the Sum of Two Numbers 41 4.3 A dd 2-digit Numbers Mentally 46 5. Subtraction ..........................................51 5.1 Subtract 3-digit and 4-digit 52 Numbers 5.2 E stimate the Difference between Two Numbers 58 5.3 Subtract 2-digit Numbers Mentally 61 6. Multiplication ......................................66 6.1 Multiply 2-digit Numbers 67 6.2 Multiply 3-digit Numbers by 72 1-digit and 2-digit Numbers 6.3 D ouble 2-digit and 3-digit Numbers Mentally 78 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___4 / 184

7. Time......................................................82 7.1 R ead a Calendar 83 7.2 Read Time Correct to the Hour 87 8. Division ...............................................95 8.1 D ivision as Equal Grouping and Relate Division to Multiplication 96 8.2 Divide 2-digit and 3-digit Numbers by 1-digit Numbers 101 9. Fractions .............................................111 9.1 Fraction as a Part of a Whole 112 9.2 Fraction of a Collection 120 10. Money................................................127 10.1 Convert Rupee into Paise 128 10.2 Add and Subtract Money with Conversion 132 10.3 M ultiply and Divide Money 136 10.4 M ake Rate Charts and Bills 138 11. Measurement....................................146 11.1 Conversion of Standard Units of Length 147 11.2 C onversion of Standard Units of Weight 154 11.3 Conversion of Standard Units of Volume 159 12. Data Handling...................................167 12.1 Record Data Using Tally Marks 168 Multiplication Tables ............................173 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___5 / 184

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Shapes1CHAPTER I Will Learn Concept s 1.1: Ve1rt.1ic:eVs earntidceDsiaagnodnDailas goof nTwalos-odfimTweon-sDioimnaelnSshioanpaelsShapes JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___7 / 184

Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes 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. 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 (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. Closed figures Open figures 2 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___8 / 184

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 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___9 / 184

& Remembering & Understanding 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 meet are called vertices. A square too has all these parts. Note: A triangle and a circle do not have any 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 DC A, B, C, D AB, BC, CD, DA AC, BD AB SR ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ PQ Y Z X ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ W 4 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___10 / 184

Application 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 B C 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) DC 4 (Opposite sides Rectangle are equal) AB, BC, CD, DA AB A Triangle 3 AB, BC, CA BC (All sides equal in this case) 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. Shapes 5 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___11 / 184

Object Basic shape Number of vertices Number of diagonals 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. 6 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___12 / 184

Steps Figure Step 2: Cut the square into two A triangles, across the fold. B Step 3: Cut one of the triangles A obtained in step 2, into two equal parts. We get two smaller triangles as shown. 2 1 Step 4: Fold the other big triangle as B shown. 3 Step 5: Unfold this piece and cut it across the fold. We get one more 4 triangle. 5 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 again as shown. We get a square on cutting at the fold. Shapes 7 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___13 / 184

Steps Figure Step 8: Fold the remaining paper again. 67 We now get one more triangle on cutting at the fold. From all these cuts, we get seven pieces of the tangram. Step 9: Colour these shapes using different colours. You can use these tangram pieces to make different shapes. Higher Order Thinking Skills (H.O.T.S.) Observe the object in the given figure. It looks like a box. Each A E B F side of the box is a square. H G 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. Such shapes are called three-dimensional shapes or 3D shapes D C Cube 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 A B 8 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___14 / 184

Steps Figure HG Step 2: Draw another square EFGH DC cutting square ABCD as shown. Step 3: Join DH, AE, BF and CG. EF AB HG D C E F AB Cuboid 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 and a curved surface is called a cone. 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 Shapes 9 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___15 / 184

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 Train My Brain 10 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___16 / 184

Patterns2CHAPTER 1 11 1 21 1331 1 4 6 41 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 I Will Learn Concept s 2.1: Pa1t.t1e:rnVseinrtiScheas paensdaDniadgNounmalbs eorfsTwo-Dimensional Shapes JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___17 / 184

Concept 2.1: Patterns in Shapes and Numbers 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. 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 & Remembering & Understanding A pattern is an arrangement of shapes or numbers that follow a particular rule. Consider these examples: 12 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___18 / 184

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) c) d) Patterns 13 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___19 / 184

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. 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. 14 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___20 / 184

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 3+2=5 5 + 2 = 7 and so on. Therefore, the pattern is 1, 3, 5, 7, …. In this pattern, 1 is the first term, 3 is the second term, 5 is the third 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) ___________ ___________ ___________     Solution: a)    b) c) In these patterns, we observe that each term has one more basic shape than in the previous term. Patterns 15 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___21 / 184

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, … 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. 16 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___22 / 184

Application 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. Higher Order Thinking Skills (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. Patterns 17 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___23 / 184

Basic shape: Pattern: 2) Rule: Turn the shape horizontally and then back vertically. Basic shape: Pattern: 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. 18 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___24 / 184

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, ..... Drill Time Concept 2.1: Patterns in Shapes and Numbers 1) Complete the following patterns: a) ___________ ___________ ___________, ☺☺☻ ☺☺☻ b) _______________ _______________ c) ___________ ___________ d) ____________ ____________, e) __________________ __________________ Patterns 19 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___25 / 184

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) 20 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___26 / 184

Numbers3CHAPTER I Will Learn Concepts 3.1: Co1u.1n:t VbeyrtTihcoeus saannddDs iagonals of Two-Dimensional Shapes 3.2: Compare 4-digit Numbers JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___27 / 184

Concept 3.1: Count by Thousands Think ` 1500.00 ` 700.00 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 greater than hundreds. 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 _______________________________________. & Remembering & Understanding To know about 4-digit numbers, we count by thousands using boxes. Let be 1 ones. is the same as 10 ones 1 tens 22 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___28 / 184

10 tens = = One hund red hundred H TO 100 HT O = 100 = 1 0 0 = One hundred O HT 0 = 200 = 2 0 = Two hundreds H TO = 300 = 3 0 0 = Three hundreds = 400 = H T O 4 0 0 = Four hundreds O HT 0 = 500 = 5 0 = Five hundreds HT O = 600 = 6 0 0 = Six hundreds H TO = 700 = 7 0 0 = Seven hundreds Numbers 23 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___29 / 184

H TO = 800 = 8 0 0 = Eight hundreds = 900 = H T O 9 0 0 = Nine hundreds = 1000 = Th H T O 1 000 = 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 TO Represent 999 Remove all beads and put a yellow bead on the next spike. Th H T O This represents a thousand. It is written as 1000. Represent 1000 It is the smallest 4-digit number. Now, we know four places – ones, tens, hundreds and thousands. Places Thousands (Th) Hundreds (H) Tens (T) Ones (O) 100 10 1 Values 1000 This chart is called the place value chart. We count by 1000s as 1000 (one thousand), 2000 (two thousand), ... till 9000 (nine thousand). 24 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___30 / 184

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 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 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 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 Numbers 25 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___31 / 184

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. Application We can solve some real-life examples using the knowledge of 4-digit numbers. 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 26 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___32 / 184

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. 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. Higher Order Thinking Skills (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. Numbers 27 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___33 / 184

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 Step 2: each place in the place value a) 1 3 3 2 1332 chart. b) 5 0 3 0 5030 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 Step 2: the place value chart. a) 3 1 7 8 Draw the number of circles on the abacus b) 6 0 0 5 c) 4 1 3 0 as per the digit in each place. Th H T O Th H T O Th H T O a) 3178 b) 6005 c) 4130 28 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___34 / 184

Concept 3.2: Compare 4-digit Numbers 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. Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise. 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. & Remembering & Understanding Comparing two 4-digit numbers is similar to comparing two 3-digit numbers. Let us understand the steps through an example. Example 9: Compare: 5690 and 5380 Solution: Follow these steps to compare the given numbers: Steps Solved Solve this 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 have 4-digits. The number with more digits is greater. Numbers 29 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___35 / 184

Steps Solved Solve this 5690 and 7469 and 5380 7478 Step 2: Compare thousands ____ = ____ 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 ____ > ____ So, is greater. ____ > ____ Step 4: Compare tens If the digits in hundreds place are also same, - compare the digits in the tens place. The number with the greater digit in the tens place is greater. 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. Train My Brain Note: Once we could decide a greater/smaller number, the next steps need not be carried out. Application 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. 30 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___36 / 184

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: 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. Numbers 31 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___37 / 184

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 Th H T O thousands place. The largest of the digits 3, 5, 4 and 7 7 is 7. So, place 7 under the thousands place. 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 75 Place 5 under the hundreds place. 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 Th H T O 40 cannot begin with 0. So, we choose the next smallest number, which is 4. 32 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___38 / 184

So, write 4 in the thousands place and 0 in the hundreds place. Step 3: Choose the smaller of the remaining two digits. T O 6 Step 4: Place it under the tens place. The smaller of the Th H O digits 6 and 8 is 6. So, place 6 under the tens place. 4 0 8 Write the remaining digit in the ones place. The remaining digit is 8. So, place 8 under the ones Th H T place. 0 6 4 Therefore, the smallest number that can be formed using the given digits is 4068. Higher Order Thinking Skills (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 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 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. Numbers 33 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___39 / 184

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. 34 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___40 / 184

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 35 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___41 / 184

Addition4CHAPTER II WWiillll LLeeaarrnn CCoonncceeppttss 4.1 : Add 3-digit and 4-digit Numbers 4.2: Estimate the Sum of Two Numbers 4.3: Add Two-digit Numbers Mentally JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___42 / 184

Concept 4.1: Add 3-digit and 4-digit Numbers 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. 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 = _________ & Remembering & Understanding Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit numbers. 1) Add 3-digit numbers with regrouping 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 the digit to the next place. Addition 37 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___43 / 184

Example 1: 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 H TO Step 2: Add the tens. 1 H TO 11 245 245 +578 11 +578 245 823 3 +578 23 H TO Solve these H TO HTO 823 171 +197 39 0 +219 +12 1 2) 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 2: Add 1352 and 3603. Solution: Arrange the numbers one below the other. Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O 13 5 2 Th H T O 135 2 + 36 0 3 +3 6 0 3 5 55 38 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___44 / 184

Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 13 5 2 135 2 +3 6 0 3 + 36 0 3 955 49 5 5 Th H T O Solve these Th H T O 419 0 111 1 +2 0 0 0 Th H T O +2 2 2 2 200 2 +3 0 0 3 3) Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 3: 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 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 Addition 39 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___45 / 184

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 Application Look at some examples where we use the addition of 3-digit and 4-digit numbers. Example 4: 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? Solution: Number of stamps Vinod has now = 536 HT O Example 5: Number of stamps he gave his brother = 278 11 Solution: Number of stamps Vinod had in the 536 beginning = 536 + 278 = 814 +2 7 8 814 Ajit collected ` 2683 and Radhika collected ` 3790 for donating to an old age home. What is the total money collected? Th H TO Amount collected by Ajit = ` 2683 Amount collected by Radhika = ` 3790 1 1 83 Total amount collected for the donation 2 6 90 = ` 2683 + ` 3790 = ` 6473 +3 7 73 6 4 Example 6: The number of students in Class 3 of Heena’s school is 236. The number of students in Class 3 of Veena’s school is 289. How many total number of students of Grade 3 were present in both the school. 40 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___46 / 184

Solution: Number of students present in Heena’s school = H TO 236 + 1 1 Number of students present in Veena’s school = 2 36 289 2 89 5 25 Total number of students present in class 3 of both the schools = 236 + 289 = 525 Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples on the addition of 4-digit numbers. Example 7: Three pieces of ribbon of lengths 2134 cm, 1185 cm and 3207 cm are cut from a long ribbon. What was the length of the ribbon before the Solution: pieces were cut? Th H T O 11 The pieces of ribbon are 2134 cm, 1185 cm and 3207 cm long. Length of the ribbon before the pieces were 2134 cut = 2134 cm + 1185 cm + 3207 cm +1 1 8 5 Therefore, the length of the ribbon before the + 3 2 0 7 pieces were cut = 6526 cm 6526 Example 8: 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?” Concept 4.2: Estimate the Sum of Two Numbers Think Neena 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 them? To answer this question, we must learn to estimate the sum of two numbers. Addition 41 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___47 / 184

Recall We have learnt addition of 2-digit and 3-digit numbers. Here is a quick recap of the steps. Step 1: We place the numbers one below the other, according to their places. Step 2: Start adding from the ones place. Step 3: Regroup the necessary sum and carry it forward to the next place. Step 4: Write the answer. & Remembering & Understanding Many a times, knowing the exact number may not be needed. When we say there are about 50 students in class, we mean that the number is close to 50. Numbers which are close to the exact number can be rounded off. Rounding off numbers is also known as estimation. 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. So, we round off 12 down to 10. 35 is exactly in between 30 and 40. So, we round it off up to 40. Let us now learn a step-wise procedure to round off numbers to the nearest 10. 42 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___48 / 184

Example 9: 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 86 42 57 25 63 ones place of the number. 6>5 2<5 ____ > 5 ____ = 5 ____ < 5 Step 2: If the digit 86 is 42 is ____ is ____ is ____ is in the ones place is rounded rounded rounded 4 or less, round the up to 90 down to rounded rounded down to number down to the previous ten. 40 up to ____ up to ____ ____ If it is 5 or more, round the number up, to the next tens. 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 10: Estimate the sum: a) 64 and 15 b) 83 and 18 Solution: a) 64 + 15 Rounding off 64 to the nearest tens gives 60 (as 4 < 5). Rounding 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 11: Estimate the sum in the following: a) 245 and 337 b) 483 and 165 Solution: a) 245 + 337 Addition 43 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___49 / 184

Rounding 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 Rounding 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. Application Here are some examples where the estimation of the sum can be used. Example 12: Arun wants to distribute sweets among 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. 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 13: Raj buys vegetables for ` 63 and fruits for ` 25. Estimate the amount of money he should give 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 Raj should give about ` 90 to the shopkeeper. 44 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___50 / 184