CO MPASS SERIES mathematics textbook part -1 3 Name: Learn@Home Sec�on: Roll No.: School:
Preface ClassKlap partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. ClassKlap presents the Traveller series, designed specifically to meet the requirements of the new curriculum released in November 2016 by the Council for the Indian School Certificate Examinations (CISCE). Guiding principles: The 2016 CISCE curriculum states the following as a few of its guiding principles for Mathematics teaching: D evelop mathematical thinking and problem-solving skills and apply these skills to formulate and solve problems. A cquire the necessary mathematical concepts and skills for everyday life and for continuous learning in Mathematics and related disciplines. R ecognise and use connections among mathematical ideas and between Mathematics and other disciplines. R eason logically, communicate mathematically and learn cooperatively and independently. Each of these principles resonates with the spirit in which the ClassKlap textbooks, workbooks and teacher companion books have been designed. The ClassKlap team of pedagogy experts has carried out an intensive mapping exercise to create a framework based on the CISCE curriculum document. Key features of ClassKlap Traveller series: Theme-based content that holistically addresses all the learning outcomes specified by the CISCE curriculum. T he textbooks and workbooks are structured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved. Student engagement through simple, age-appropriate content with detailed explanation of steps. Learning is supported through visually appealing images, especially for Grades 1 and 2. Increasing difficulty level in sub-questions for every question. Multiplication tables provided as per CISCE requirement. All in all, the Traveller Mathematics books aim to develop problem-solving and reasoning skills in the learners’ everyday lives while becoming adept at mathematical skills as appropriate to the primary level. – The Authors
Textbook Features I Will Learn About I Think Contains the list of concepts to be covered Arouses the student’s in the chapter along with the learning curiosity before objectives introducing the concept I Recall I RUenmdeermsbtearndand Pin-Up-Note Recapitulates the Elucidates the basic Highlights the key points or prerequisite knowledge for elements that form the definitions the concept learnt previously basis of the concept ? Train My Brain I Apply I Explore(H.O.T.S.) C hecks for learning to gauge Connects the concept E ncourages the student to the understanding level of the to real-life situations by extend the concept learnt student providing an opportunity to more complex scenarios to apply what the student has learnt Maths Munchies Connect the Dots Drill Time Aims at improving speed of Aims at integrating Revises the concepts with calculation and problem Mathematical concepts practice questions at the solving with interesting facts, with other subjects end of the chapter tips or tricks A Note to Parent E ngages the parent in the out-of- classroom learning of their child
Contents 1 Shapes 1.1 Geometrical Features of Shapes��������������������������������������������������������������������� 1 2 Patterns 2.1 Patterns in Shapes and Numbers������������������������������������������������������������������ 12 3 Numbers 3.1 Count by Thousands�������������������������������������������������������������������������������������� 24 3.2 Compare 4-digit Numbers����������������������������������������������������������������������������� 30 4 Addition 4.1 Add 3-digit and 4-digit Numbers������������������������������������������������������������������ 38 4.2 Estimate the Sum of Two Numbers���������������������������������������������������������������� 42 4.3 Mental Maths Techniques: Addition�������������������������������������������������������������� 47 5 Subtraction 5.1 Subtract 3-digit and 4-digit Numbers����������������������������������������������������������� 50 5.2 Estimate the Difference between Two Numbers������������������������������������������ 55 5.3 Mental Maths Techniques: Subtraction��������������������������������������������������������� 58
Shapes1Chapter I Will Learn About • recognising 2D shapes with straight and curved lines. • counting the sides, corners and diagonals of 2D shapes. 1.1 Geometrical Features of Shapes I Think There is a paper folding activity in Neena’s class. Her teacher asks the students to make two triangles out of a square. How will Neena fold the paper to make the triangles? I Recall We have learnt the different types of lines. Let us recall them. Straight Line Curved Line 1
Straight lines and curved lines help us draw closed and open figures. Closed Figures: Figures in which the lines end at the point where they start. Open figures : Figures in which the lines do not end at the point where they start. Closed figures Open figures Try this! Write open or closed in the blanks for the given figures: ____________ ______________ ____________ ____________ 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. Draw the given shapes using straight or curved lines on the dot grid. Identify them as 1D or 2D shapes. One has been done for you. Name of the shape Shape 1D or 2D Triangle 2D Square 2
Name of the shape Shape 1D or 2D Circle Line Rectangle I Remember and Understand We have already learnt various shapes. Let us now learn how to name their parts. Consider a rectangle ABCD as shown. D C 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 lines named as AC and BD are called its diagonals. Points A, B, C and AB Vertex: The point where at least D where two sides of the rectangle two sides of a figure meet is called meet are called vertices. a vertex. The plural of vertex is A square too has all these parts. vertices. Note: A triangle and a circle do not Diagonal: A straight line inside have any diagonals. a shape that joins the opposite vertices is called a diagonal. Try this! Name the vertices, sides and diagonals of the given shapes in the table below. One has been done for you. Shapes 3
Shape Vertices Sides Diagonals DC A, B, C, D AB, BC, CD, DA AC, BD AB Y Z X ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ W ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ SR PQ ? Train My Brain Name the given figures and find the number of their vertices and diagonals. a) b) c) I Apply A C B 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 4
triangle show that the lengths of all the 3 sides are different. The same number of small lines on the sides of the triangle show that the lengths of all the 3 sides are the same. Let us now learn to find the number of sides of a few 2D shapes and name them. Shape Name of the shape Number of sides Names of sides SR Square 4 PQ, QR, RS, SP (All sides are equal) PQ DC 4 Rectangle (Opposite sides AB, BC, CD, DA AB are equal) A Triangle 3 AB, BC, CA BC (All sides are equal in this case) We find many shapes in the objects around us. Fill in the following table by writing the basic shapes of the given objects. Also write the number of their vertices and diagonals. Object Basic shape Number of vertices Number of diagonals Shapes 5
Object Basic shape Number of vertices Number of diagonals Tangram A tangram is a Chinese geometrical puzzle. It consists of a 1 4 square cut into pieces as shown in the given figure. 5 2 To create different shapes, we arrange these tangram 6 3 pieces with their sides or vertices touching one another. 7 Let us make our own tangram. 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
Steps Figure B Step 4: Fold the other big triangle as shown. Step 5: Unfold this piece and cut it across 3 the 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 5 paper as shown. We get a square on cutting at the fold. Step 8: Fold the remaining paper again. 6 We now get one more triangle on cutting 7 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
I Explore (H.O.T.S.) Observe the object in the given figure. It looks like a box. Each side of the box is a square. EF In the figure, AB is the length and BF is the breadth of the box. A B 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 H G shapes or solid shapes. D C In the figure, Cube 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 DC Step 1: Draw a square ABCD. A B Step 2: Draw another square EFGH H G over square ABCD as shown. D C Step 3: Join DH, AE, BF and CG. E F B A H G D C E F A B 8
A few other such three-dimensional shapes are cuboids and cones. Solid shapes with flat rectangular faces are called cuboids. Solid shapes with a circular base and a curved surface Cuboid Cone are called cones. Try this! Draw and colour a cuboid and a cone. Show the formation of the shape in steps. Shape Step 1 Step 2 Step 3 Cuboid Cone Maths Munchies We can use tangrams to make many shapes such as: Boat Candle Rocket Can you make a house with the following tangrams? (You can use the same shape twice.) Shapes 9
Connect the Dots English Fun Try drawing a square while reciting the rhyme. From the bottom to the top, straight across right and then you stop. Straight down to the bottom again, across left and stop where you began. If the lines are the same size, then a square is formed for you a surprise. Social Studies Fun n We can see 2D shapes such as rectangles, squares, circles and 3D shapes such as cubes and cuboids in the buildings in our neighbourhood. Identify some 2D and 3D shapes in this picture! Drill Time 1.1 Geometrical Features of Shapes Find the number of vertices and diagonals of the following shapes: Shape Vertices Diagonals 10
Shape Vertices Diagonals A Note to Parent When you go with your child to public places such as hospitals, markets or religious places, help him or her to identify the 3D shapes that are commonly seen on these structures. Shapes 11
Patterns2Chapter I Will Learn About • tiling of a given shape. • forming shapes using tangram pieces. • identifying basic shapes in patterns. • extending and creating patterns. 2.1 Patterns in Shapes and Numbers I Think Neena went to her father’s office one day. She saw that the floor of each hall had different designs. It had triangles, squares, circles and rectangles. She wanted to make a similar design. Can you make some designs using these shapes? I Recall There are many patterns around us. Patterns are similar to drawings. Let us see some of the patterns around us. 12
Saree borders Carpets Grills Nature I Remember and Understand A pattern is an arrangement of shapes or numbers that follow a particular rule. Consider these examples: a) Patterns 13
b) c) 150, 152, 154, 156 We see that examples a) and b) have a repetition of some shapes 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), one , one and one make a pattern. In this pattern, the basic shape is . In example c), the first number is 150. We get the next number by adding 2 to the previous number. Let us learn more about different kind of patterns in detail. Patterns in lines and shapes Observe the following patterns. These are made up of lines and shapes. a) b) c) d) e) 14
Let us see a few examples of forming patterns. Example 1: Complete the following patterns: a) b) c) Solution: a) b) c) 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 to be formed. They are also the most common number patterns that we 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. We can make a pattern with even numbers by adding 2 to the given even number. For example, The numbers ending in 2, 4, 6, 8 or 2+2=4 0 are called even numbers. 4+2=6 The numbers ending in 1, 3, 5, 7 or 6 + 2 = 8 and so on. 9 are called odd numbers. Patterns 15
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. We 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 formed using shapes. Let us see some examples. Example 2: Complete the following patterns: a) ____________ ____________ b) ______________ ______________ c) ______________ ______________ Solution: a) b) c) 16
In these patterns, we observe that each term has the same basic shape. The number of basic shapes increases in number than in the previous term. Some patterns can be formed by increasing the terms 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, … f) 571, 671, 771, … 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) and f) 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), e) and f) as: increase by 100. Reducing pattern in numbers 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, … f) 792, 692, 592, … In pattern a), 820 – 720 = 100 and 720 – 620 = 100. So, the terms decrease by 100. Similarly, the terms in f) decrease by 100. 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) and f) as decrease by 100; in patterns b) and d) as decrease by 10; in pattern c) as decrease by 5 and in pattern e) as decrease by 200. Patterns 17
? Train My Brain Complete these patterns by writing their next three terms. a) 7, 14, 21, 28, _______, _______, _______ b) 11, 15, 19, 23, _______, _______, _______ c) 5, 10, 15, 20, _______, _______, _______ 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. 18
Example 3: Draw the basic shape in the given tiling patterns. a) b) Solution: a) b) I Explore (H.O.T.S.) Tiling patterns have shapes that cover a surface without any gaps or overlaps. Shapes that leave gaps or overlap with each other do not tile. Example 4: Which of the given designs do not tile? a) b) c) Solution: As a) and c) have gaps left in their design, they do not tile. Patterns with Rules We have also seen that patterns in shapes and numbers follow certain rules. Using the rule, we can form a pattern with the given basic shapes. Consider the following examples. 1) Rule: Turn the shape upside down. Basic shape: Pattern: Patterns 19
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 5: Complete the given pattern: 9, 17, 25, ____,____ ,_____, ____ Solution: In the given pattern, the first term is 9, the second term is 17 and the third term is 25. This pattern has numbers increasing by 8. So, the rule of this pattern is adding 8. So, the next terms of the pattern are: 25 + 8 = 33; 33 + 8 = 41; 41 + 8 = 49; 49 + 8 = 57. Therefore, the pattern is 9, 17, 25, 33, 41, 49, 57 Try this! Find the rule in each of the following patterns and continue them. a) 12, 24, 36, ________, ________, ________ b) 1+ 2 = 3, 2 + 3 = 5, 3 + 4 = 7, ________ , ________ , ________ 20
Example 6: 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, ..... Maths Munchies 1 Pascal’s triangle 11 12 1 In Pascal’s triangle, each number is the sum 13 31 of the two numbers above it. It is a triangular 14641 number pattern named after Blaise Pascal, a 1 5 10 10 5 1 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 in them. Here are a few pictures in which we can observe patterns in nature. Train My Brain English Fun Little Frog A B In poems, we see a I saw a little frog, A certain pattern or He was cuter than can be, B a rhyming scheme. He was sitting on a log, In this poem, we And I'm sure he croaked at me! see the pattern of rhyming in alternate lines. Patterns 21
Drill Time 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, _______, _________ 3) Draw the basic shapes in the given tiling patterns. a) b) 22
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 up your 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 23
Numbers3Chapter I Will Learn About • reading and writing 4-digit numbers with place value chart. • identifying greater and smaller number, ascending and descending orders. • forming numbers. 3.1 Count by Thousands I Think Neena went to buy one of the toy cars shown. She could ` 1937.00 not read the price on one of them. Can you read the ` 657.00 price on both the cars? I Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. We can count by tens and hundreds. Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80 and 90 Counting by 100s: 100, 200, 300, 400, 500, 600, 700, 800 and 900 A digit multiplied by the value of its place gives its place value. Using place values, we can write the numbers in the expanded form. 24
Let us answer these to revise the concept. a) The number for two hundred and thirty-four is _____________. b) The expanded form of 444 is _______________________. c) The place value of 9 in 493 is _____________. d) The number name of 255 is _______________________________________. I Remember and Understand To know about 4-digit numbers, we count by thousands using boxes. 10 hundreds = 1 thousand 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 a orange bead on the Represent 1000 next spike. This represents a thousand. It is written as 1000. It 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. The greatest Thousands (Th) Hundreds (H) Tens (T) Ones (O) 4-digit 4 7 32 number is 9999. Numbers 25
We count by 1000s as 1000 (one thousand), 2000 (two thousand), ... till 9000 (nine thousand). Expanded form of 4-digit numbers We can write a number as the sum of the place values of its digits. This form of the number is called its expanded form. Let us now learn to write the expanded forms of 4-digit numbers. Example 1: Expand the given numbers: a) 3746 b) 6307 Solution: Write the digits of the given numbers in the place value chart, as shown. ExpTahndeHd formT s: O a) 3 7 4 6 a) 3746 = 3000 + 700 + 40 + 6 b) 6 3 0 7 b) 6307 = 6000 + 300 + 0 + 7 Writing number names of 4-digit numbers We can write the number name of a number by writing its expanded form. Observe the place value chart and the place values of a 4-digit number, 8015. Th H TO Place values 80 15 5 ones = 5 1 tens = 10 0 hundreds = 0 8 thousands = 8000 So, the expanded form of 8015 is 8000 + 0 + 10 + 5. The number name of 8015 is Eight thousand fifteen. Note: 8015 is called the standard form of the number. Example 2: Write the number, its expanded form and the number name from the following figure: 26
Solution: T here are 1 thousand, 6 hundreds, 9 tens and 3 Th H T O ones in the given figure. 1 693 So, the number it represents is 1693. To expand the given number, write its digits in the correct places of the place value chart as shown: Expanded form: 1693 = 1000 + 600 + 90 + 3 Writing in words:1693 = One thousand six hundred ninety-three 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 digits in the correct places in the place value chart as shown. From the thousands place to ones Th H T O place, write the digits one beside the 3 46 5 other. Therefore, the standard form of 3000 + 400 + 60 + 5 is 3465. ? Train My Brain Say the number names of the following numbers: a) 2884 b) 4563 c) 9385 I Apply We can solve some real-life examples using the knowledge of 4-digit numbers. Example 4: The number of students in different high schools is as follows: Name of the school Number of students Modern High School 4782 7245 Ideal High School 9423 Talent High School 1281 Concept High School Numbers 27
a) What 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 forty-five. b) The number of students in Concept High School is 1281. In words, it is one thousand two hundred eighty-one. Example 5: The money with Ram is as shown. Write the amount in figures and words. Solution: 1 note of ` 2000 = ` 2000 1 note of ` 100 = ` 100 3 notes of ` 10 = ` 30 1 coin of ` 5 = ` 5 So, the money that Ram has = ` 2000 + ` 100 + ` 30 + ` 5 = ` 2135 In words, ` 2135 is two thousand one hundred thirty-five rupees. A place value chart helps us to form numbers using the given digits. Let us see 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 Th H T O according to their places as shown. 6514 Therefore, the required number is 6514. 28
I Explore (H.O.T.S.) We have learnt the concepts of expanded form and place value chart. We can now identify a number represented by an abacus. Let us see a few examples. 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: To write the numbers, follow these steps: Step 1: Write the number of beads in Th H T O Number Step 2: each spike in the correct places a) 1 3 3 2 1332 of the place value chart. b) 5 0 3 0 5030 c) 4 0 3 4 4034 Put a 0 in the places where there are no beads. Step 3: Write the digits from left to right, one beside the other. Example 8: Draw circles on the abacus to show the given numbers: a) 3178 b) 6005 c) 4130 Solution: To show the given numbers, follow these steps. Step 1: Write the digits of the given numbers in Th H T O the correct places of the place value a) 3 1 7 8 chart. b) 6 0 0 5 c) 4 1 3 0 Step 2: Draw as many circles on the correct spikes as the digits in each place. Step 3: Th H T O Th H T O Th H T O c) 4130 a) 3178 b) 6005 Note: Do not draw any circle if there is a 0 in any place. Numbers 29
3.2 Compare 4-digit Numbers I Think Neena has 3506 paper clips and her brother has 3605 paper clips. Neena wants to know who has more paper clips. But she is confused as the numbers look the same. Can you tell who has more paper clips? I Recall In class 2, we learnt to compare 3-digit numbers and 2-digit numbers. Let us now revise the same. 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 having more digits is always greater than the other. We use the symbols >, < or = to compare two numbers. I Remember and Understand Comparing two 4-digit numbers is similar to If two numbers comparing two 3-digit numbers. have equal number of digits, start Let us understand the steps through an example. comparing from their leftmost digit. Example 9: Compare: 5382 and 5380 Solution: To compare the given numbers, follow these steps. Steps Solved Solve this Step 1: Compare the number of digits 5382 and 5380 7469 and 7478 Count the number of digits in the given numbers. The number having more digits is Both 5382 and greater. 5380 have 4 digits. 30
Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 2: Compare thousands 5=5 ____ = ____ If two numbers have the same number of digits, compare the thousands digits. 3=3 ____ = ____ 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, compare the digits in the hundreds place. The number with the greater digit in the hundreds place is greater. Step 4: Compare tens 8=8 ____ > ____ If the digits in the hundreds place are also So, same, 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 So, same, compare the digits in the ones place. 5382 > 5380 The number with the greater digit in the ones place is greater. Note: Once we find the greater/smaller number, we need not carry out the next steps. Train My Brain ? Train My Brain Find the greater number from each of the following pairs: a) 7364, 7611 b) 8130, 8124 c) 4371, 4378 I Apply We can apply the knowledge of comparing numbers and place value to: 1) arrange numbers in the ascending and descending orders. 2) form the greatest and the smallest numbers using the given digits. Numbers 31
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: To arrange the given numbers in ascending and descending orders, follow these steps: 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: Write the numbers from the smallest to the largest. 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: Write the numbers from the largest to the smallest. Descending order: 4906, 4305, 4126, 4005 Simpler way! Descending order of numbers is just the reverse of their ascending order. 32
Forming the greatest and the smallest 4-digit numbers Let us learn to form the greatest and the smallest 4-digit numbers. Consider the following examples: Example 11: Form the greatest and smallest 4-digit number using 4, 3, 7 and 5 (without repeating the digits). Solution: The 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; 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 T he steps to find the smallest 4-digit number are 7 5 4 3 given below. Step 1: Arrange the digits in ascending order; 3 < 4 < 5 Th H T O < 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; 0 < 1 < 4 < 6. Step 2: Place the digits in the place value chart from Th H T O left to right. But number formed is 0146 or 146. It 0 1 4 6 is a 3-digit number. In such cases, we interchange the first two Th H T O digits in 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. Numbers 33
Step 1: Find the smallest digit. 0 is the smallest of the given digits. (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. I Explore (H.O.T.S.) Let us see a few real-life examples of comparison of 4-digit numbers. Example 14: 4538 people visited an exhibition on a 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 a 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 3 < 4 So, 3980 < 4538. Therefore, fewer people visited the exhibition on Sunday. 34
Example 15 : R aju arranged the numbers 7123, 2789, 2876 and 4200 in ascending order as 2876, 2789, 4200, 7123. Reena arranged them as 2789, 2876, 4200, 7123. Who arranged them correctly? Why? Solution: Reena’s arrangement is correct. Reason: Comparing the hundreds place of the smaller of the given numbers, 7 hundreds < 8 hundreds. So, 2789 is the smallest number. Maths Munchies I am a 4-digit number. The digit in my thousands place is the same as that in my ones place. The digit in my ones place is 5. The digit 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? Connect the Dots Social Studies Fun Without the concept of thousands, we would have never been able to measure 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 letters – vowels and consonants. Underline all the vowels in the given words. a) Hundred b) Thousand c) Digits Numbers 35
Drill Time 3.1 Count by Thousands 1) Write the numbers in the place value chart. Using their expanded forms, write the number names. a) 1451 b) 8311 c) 9810 d) 1000 e) 7613 2) 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 3) Word problems a) T he 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. 3.2 Compare 4-digit Numbers 4) Compare the following numbers using <, > or =. a) 8710, 9821 b) 1689, 1000 c) 4100, 4100 d) 2221, 2222 e) 6137, 6237 36
5) 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 6) Form the greatest and the smallest 4-digit numbers without repeating the digits. 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 7) Word problems a) 5426 people visited a zoo on a Friday and 3825 people visited it on the following Sunday. On which day did fewer people visit the zoo? b) Kate’s father gave him 1105 butter chocolates and 2671 coconut chocolates. Which type of chocolate did he have more? A Note to Parent Play a new game of dice with your child. Each player rolls the die four times in a row and writes the numbers from left to right. The winner is the one who gets the smallest number in one round. Play multiple rounds until your child understands the concept of place value and comparison of 4-digit numbers. Numbers 37
Addition4Chapter I Will Learn About • using addition of 3-digit numbers in real-life. • adding numbers with and without regrouping. 4.1 Add 3-digit and 4-digit Numbers I Think Neena’s father bought her a shirt ` 335 ` 806 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? 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 concept by solving the following. a) 22 + 31 = _________ b) 42 + 52 = _________ 38
c) 82 + 11 = _________ d) 101 + 111 = _________ e) 101 + 201 = _________ f) 122 + 132 = _________ I Remember and Understand Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit numbers. Add two 3-digit numbers with regrouping Sometimes, the sum of the digits in a place is more than While adding, 9. In such cases, we carry the tens digit of the sum to the regroup if the next place. sum of the digits is more than 9. Example 1: Add 245 and 578. Solution: Arrange the numbers one below the other. Add the digits under a place. Regroup if needed and write the sum. Step 1: Add the ones. Step 2: Add the tens. Step 3: Add the hundreds. H TO H TO H TO 1 11 11 245 245 245 +578 +578 +578 823 23 3 H TO Solve these H TO HTO 823 39 0 171 +197 +12 1 +219 Addition 39
Add two 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. Add the digits under a place. Write the sum. Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 13 5 2 135 2 + 36 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 + 36 0 3 49 5 5 955 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 ? Train My Brain c) 8837 + 1040 Solve the following: a) 321 + 579 b) 725 + 215 40
I Apply Let us see a few examples involving the addition of 3-digit and 4-digit numbers. Example 3: Vinod had some stamps out of which he gave 278 stamps to his brother. Vinod now has 536 stamps left with H TO him. How many stamps did he have in the beginning? 11 Solution: Number of stamps Vinod has now = 536 5 36 Number of stamps he gave his brother = 278 +2 78 Number of stamps Vinod had in the 8 14 beginning = 536 + 278 = 814 Example 4: Ajit collected ` 2613 and Radhika collected ` 3110 for donating to a nursing home. What is the total money collected by them? Solution: Amount collected by Ajit = ` 2613 Th H TO Amount collected by Radhika = ` 3110 Total amount collected for the donation 2 6 13 =` 2613 + ` 3110 = ` 5723 +3 1 10 7 23 5 Example 5: 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 students of Class 3 were present in both the schools? Solution: Number of Class 3 students in Heena’s school H TO = 236 1 1 2 36 Number of Class 3 students in Veena’s school = 2 89 289 + 5 25 Total number of students present in Class 3 of both the schools = 236 + 289 = 525 I Explore (H.O.T.S.) Let us see a few more examples on the addition of 4-digit numbers. Addition 41
Example 6: One college is divided into three groups: 2130 students, 1125 students and 3202 students. How many students are there in the full college? Solution: The three groups are 2130 students, 1125 Th H T O students and 3202 students. 2130 Full college before students were divided = + 1 1 2 5 2130 students + 1125 students + 3202 students + 3 2 0 2 6457 Therefore, the full college before students were divided is 6457 students. Example 7: Payal, Eesha and Suma have 1214, 7523 and 1111 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 1214, 7523 and 1111 stamps respectively. How many stamps do they have altogether?” 4.2 Estimate the Sum of Two Numbers I 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? I Recall We have learnt addition of 2-digit and 3-digit numbers. Here is a quick recap of the steps. Step 1: Write the numbers one below the other, according to their places. Step 2: Start adding the digits from the ones place. Step 3: Regroup the sum if needed and carry it forward to the next place. Step 4: Write the answer. 42
I Remember and Understand Many a times, knowing the exact number may If the digit in the ones not be needed. When we say there are about 50 place is equal to or students in a class, we mean that the number is greater than 5, we close to 50. round off the number to the closest multiple Numbers which are close to the exact number can of ten greater than the be rounded off. Rounding off numbers is also known given number. 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) (28) (35) (49) 0 10 20 30 40 50 12 is between 10 and 20 but is closer to 10. So, we round 12 down to 10. 35 is exactly in between 30 and 40. So, we round it up to 40. 28 is between 20 and 30 and is closer to 30. So, we round it up to 30. Let us now learn a step-wise procedure to round off numbers to the nearest 10. Example 8: 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. Addition 43
Steps Solved Solve these 86 42 57 25 63 Step 2: If the digit in the ones place is 6>5 2<5 ____ > 5 ____ = 5 ____ < 5 4 or less, round the number down to the So, 86 is So, 42 is So, ____ is ____ is ____ is previous ten. rounded rounded rounded rounded rounded up to 90. down to If it is 5 or more, off to off to off to round the number 40. ____. ____. ____. up, to the next ten. 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 9: 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 estimated 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 estimated sum is 80 + 20 = 100. Example 10: Estimate the sum: a) 245 and 337 b) 483 and 165 Solution: a) 245 + 337 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 estimated 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 estimated sum is 480 + 170 = 650. 44
? Train My Brain a) Estimate the sum of 13 and 12. b) Estimate the sum of 824 and 295. c) Estimate the sum of 25 and 21. I Apply Here are some examples where the estimation of sums can be used. Example 11: Arun wants to distribute sweets among the students of 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 12: 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 Therefore, Raj should give about ` 90 to the shopkeeper. Addition 45
I Explore (H.O.T.S.) Let us see some more examples where estimation of sums is used. Example 13: 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 park workers plant = 574 Rounding off 574 to the nearest tens, we get 570. The estimated sum of the number of trees planted is 420 + 570 = 990. Therefore, the park will have 990 trees after the workers finish planting. Example 14: Ramya has 26 cookies and 34 toffees. Renu has 42 cookies and 13 toffees. Estimate the total number of cookies and toffees they have. 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 total number of cookies rounded off to the nearest ten = 30 + 40 = 70 The total number of toffees rounded off to the nearest ten = 30 + 10 = 40 Therefore, altogether they have 70 cookies and 40 toffees. 46
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