MATHEMATICS TEXTBOOK – PART 1 2 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________
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 Program presents the latest version of this series – updated and revised after considering the perceptive feedback and comments shared by our experienced reviewers and users. This series endeavours to be faithful to the spirit of the prescribed board curriculum. 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 larger aim of the curriculum 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 Mathematics textbooks and workbooks offer the following features: Structured 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 W ord 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 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
Textbook Features Let Us Learn About Think Contains the list of learning objectives Introduces the concept and to be covered in the chapter arouses curiosity among students Recall Discusses the prerequisite knowledge for the concept from the previous academic year/chapter/ concept/term Remembering and Understanding Explains the elements in detail that form the Application basis of the concept Ensures that students are engaged in learning throughout Connects the concept to real-life situations by enabling students to apply what has been learnt through the practice questions Higher Order Thinking Skills (H.O.T.S.) Encourages students to extend the concept learnt to advanced scenarios Drill Time Additional practice questions at the end of every chapter
1 Shapes 1.1 Identify the Geometrical Features of Objects ........................................... 1 2 Patterns 2.1 Patterns Using Shapes................................................................................. 11 73 Numbers 0 +3.1 Count by Hundreds..................................................................................... 18 1 -3.2 Ordinal Numbers......................................................................................... 26 3 46 x3.3 Compare 3-digit Numbers......................................................................... 31 954 Addition 8 24.1 Add 2-digit and 3-digit Numbers............................................................... 38 5 Subtraction 5.1 Subtract 2-digit and 3-digit Numbers........................................................ 44 5.2 S ubtract Two 1-digit Numbers Mentally.................................................... 49
Chapter Shapes 1 Let Us Learn About • lines, open figures and closed figures. • drawing figures using lines. • basic flat and solid figures. • flat figures as outlines of the surfaces of solid figures. Concept 1.1: Identify the Geometrical Features of Objects Think David drew shapes using objects like a can, a matchbox, a bangle and a cup. Do you know what these shapes are? 1
Recall We know about the following plane shapes: Now, let us recall and learn more about them in detail. If we observe our surroundings, we will find objects of different shapes. square rectangle circle In your classroom, you find many objects of different shapes. For example, a book, paper or a blackboard looks like a rectangle. Sometimes, we see different objects having the same shape. For example, a wall clock, a photo frame or a biscuit looks like a square. 2
& Remembering and Understanding We can draw shapes using straight lines or curved lines. Let us learn about straight lines. Point: A point is a dot. It has no shape or thickness and no dimensions. A point is denoted by a capital letter of the English alphabet. For example, A, X, Y, P and M shown below are points. X Y A PM Line: Many points placed close to each other form a line. It has no thickness or breadth. A line only has length. So, it is called a one-dimensional figure. A straight line has no ends. It extends on both the sides. AB We name two points A and B on a line and write it as AB . We read it as line AB. Line segment: A line segment is a part of a line. It has two points, a starting point and an end point. A line segment has an exact length. AB We write line segment AB as AB . We read it as segment AB. Ray: A ray is a part of a straight line, which has a starting point but no end point. It extends only on one side. A We write ray AB as AB . We read it as ray AB. B Straight lines are of three types. They are horizontal lines, vertical lines and slant lines. Shapes 3
Horizontal lines: Sleeping lines drawn from left to right or from right to left are called horizontal lines. Vertical lines: Standing lines drawn from top to bottom are called vertical lines. Slant lines: Sloping lines are called slanting lines. Note: We name a straight line by any two points on it. Curved lines: Lines that are not straight are called curved lines. A straight line or a curved line is a one-dimensional (1D) figure. Using straight lines, we can draw geometrical shapes such as a square, a rectangle or a triangle. Example 1: Draw the following figures. a) Circle using a curved line b) Square using straight lines Solution: a) b) 4
We can draw figures using straight lines or curved lines. Open figures: Figures which do not end at the point where they begin from are called open figures. Closed figures: Figures which end at the point where they begin from are called closed figures. Square, rectangle, triangle and circle are closed figures. Application We can draw closed figures on a sheet of paper. These figures have both height and width. So, they are called two-dimensional figures or 2D figures or 2D shapes. Let us learn about them in detail. Square 1) It has four straight lines as sides. In the given figure, AB, BC, CD and DA are the sides. 2) All its sides are equal in length. D C 3) It has four corners. In the given figure, A, B, C and D are its corners. 4) W e name a square using its corners. We name the given square as square ABCD. A B Shapes 5
Rectangle 1) It has four straight lines as sides. In the given figure, AB, BC, CD and DA are the sides. 2) T wo pairs of opposite sides are equal in D C length. 3) It has four corners. In the given figure, A, B, C and D are its corners. 4) We name a rectangle using its corners. We A B name the given rectangle as rectangle ABCD. Triangle A 1) It has three straight lines as sides. In the given figure, AB, BC and CA are the sides. 2) It has three corners. In the given figure, A, B, and C are the corners. 3) W e name a triangle using its corners. We name the B C triangle as triangle ABC. Circle .O 1) It is a curved line. 2) It has no sides or corners. 3) We name a circle by its centre ‘O’. Example 2: Join the dots in order and name the shapes formed. Q RQ G F R PS PE H a) b) c) 6
Solution: QR Q F G E H P P RS a) Triangle PQR b) Square PQRS c) Rectangle EFGH Example 3: Observe the following pictures. Tick the type of lines used to form each object. One is done for you. Object Straight lines Curved lines Higher Order Thinking Skills (H.O.T.S.) Some shapes have length, breadth and thickness. Such figures are called three-dimensional figures or 3D figures or solid shapes. The geometrical shapes of some solid objects are as follows: Shapes 7
Solid objects Geometrical shapes Cube Cuboid Cylinder Sphere Cone Let us now see the geometrical features of these objects. Object Geometrical figures Geometrical features Vertex Face • It has 6 square faces, Edge 12 edges and 8 vertices. • All the edges of a cube are equal in length. Cube • It has 6 rectangular faces, 12 edges and 8 vertices. Edge Face • The opposite faces of a Vertex cuboid are of the same Cuboid size. • The opposite edges of a cuboid are equal in length. 8
Object Geometrical figures Geometrical features Edge • It has 2 circular flat faces Flat Face and 1 curved face. Curved face • It has 2 circular edges but Cylinder no corners. • The 2 flat faces are of the same size. Curved face • It has a curved face. Sphere • It has no edges and no Corner corners. Curved face • It has 1 flat circular face, 1 curved face and 1 corner. Flat Face Edge • It has a circular edge. Cone Let us find the geometrical shapes of a few solid objects. Example 4: Draw the geometrical shapes that form the base of these objects. Name the shapes that are formed. Shapes 9
Solution: The shapes formed are: Object Shape of the base Circle Rectangle Triangle Circle Square Drill Time Concept 1.1: Identify the Geometrical Features of Objects 1) Draw the following: a) Line b) Line segment c) Ray d) Horizontal lines e) Vertical lines 2) Identify whether the following figures are open or closed. a) b) c) d) e) 3) Name the sides of the following: a) Square PQRS b) Triangle XYZ c) Rectangle EFGH SR Z HG P QX E F Y 10
Chapter Patterns 2 Let Us Learn About • identifying basic shape(s) in a pattern. • creating patterns using objects, shapes and numbers. Concept 2.1: Patterns Using Shapes Think David made shapes using modelling clay and moulds. He arranged them as shown. Do you make such arrangements? Do you know what they are called? Recall We have already learnt about flat shapes and solid shapes. Let us revise them. 11
Identify the following shapes. Write their names in the space given below. Flat shapes Names Solid shapes Names & Remembering and Understanding Repeating a shape or a group of shapes in a particular order gives rise to a pattern. For example, a) b) c) Same shapes of different colours can also be arranged to get a pattern. For example, a) b) 12
c) To continue a given pattern, follow these steps. Step 1: Observe the first few shapes in the pattern to find a repetition. Step 2: Identify the order in which the shapes or group of shapes are repeated. Step 3: Repeat the same shape or group of shapes the required number of times. Observe the given patterns. A part of the pattern is repeated. The repeated parts of a pattern is called its basic shape(s). It is highlighted as shown. a) b) c) The basic shapes in the above patterns are: a) b) c) Let us now see a few examples. Example 1: Find the basic shapes in the given patterns. a) b) c) Solution: The groups of basic shapes in the patterns are: Patterns 13
a) b) c) Example 2: Draw and colour the missing shapes to complete the given patterns. One is done for you. a) b) c) Application Let us now look at some patterns that we see around us. Example 3: Identify the basic shape in each of the following patterns. a) b) c) Solution: The basic shapes in the given patterns are: 14
a) b) c) Example 4: Complete the given patterns by colouring. One is done for you. a) b) c) Example 5: Complete the following patterns. One is done for you. a) b) c) d) e) Patterns 15
Higher Order Thinking Skills (H.O.T.S.) We can form patterns using numbers and letters too. Example 6: Fill in the missing letters or numbers in these patterns. One is done for you. a) 1A 3B 5C 7D 9E 11F 13G b) 2 4 6 8 c) A C E G d) 1 4 7 10 e) 22 20 18 16 f) M9 L8 K7 J6 Drill Time Concept 2.1: Patterns Using Shapes 1) Complete the patterns given below. a) b) c) d) 16
e) 2) Identify the basic shapes or group of basic shapes in each of the following patterns. a) b) c) d) e) Patterns 17
Chapter Numbers 3 Let Us Learn About • reading and writing numerals and number names up to 999. • p lace values, face values and expanded forms of numbers. • ordinal and cardinal numbers. • comparing two numbers. • forming the greatest and the smallest 3-digit numbers. Concept 3.1: Count by Hundreds Think David went to a toy store. He saw that ` 990 was `990 written on a toy. He could not read the number. Can you read it? Recall We know that 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are 1-digit numbers. Numbers from 10 to 99 are 2-digit numbers. 10 is the smallest 2-digit number. 99 is the largest 2-digit number. We can count 2-digit numbers by ones and tens. 18
Look at the following picture. Start from 1 and connect all the dots in order. You will find a friend smiling back at you. & Remembering and Understanding Suppose shows 1. Ten such boxes show a 10. So, = 10 ones Numbers 19
= 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred = 1 hundred = 100 = 2 hundreds = 200 = 3 hundreds = 300 = 4 hundreds = 400 20
In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. The smallest 3-digit number is 100. The largest 3-digit number is 999. Let us understand this concept using a spike abacus. We have learnt how to show the number 99 on an abacus. To show the number 100, we remove all the green beads from the tens place. We also remove all the blue beads from the ones place. We then put 1 pink bead in the third spike (hundreds place). 1 = 1 unit in the ones spike TO H TO 1 = 1 unit in the tens spike 99 100 1 = 1 unit in the hundreds spike Thus, to show 999, we put 9 pink beads in the hundreds spike, 9 green beads in the tens spike and 9 blue beads in the ones spike. H TO 999 In the same way, we can show the numbers 298 and 459 on the abacus. H TO H TO H TO 124 298 459 Numbers 21
We can write the number names of these numbers as: 124 = One hundred and twenty-four 298 = Two hundred and ninety-eight 459 = Four hundred and fifty-nine Place value and face value Place Value: Every digit in a number has a place in the place value chart. Each digit gets its value from the place it occupies. This value is called its place value. Face Value: The value of a digit that remains the same at any place in a number is called its face value. Let us understand the place values of the digits in 3-digit numbers. Consider the 3-digit number 110. Its number name is one hundred and ten. 110 has 1 hundred, 1 ten and 0 ones. It is written in the place value chart as shown. Places Hundreds (H) Tens (T) Ones (O) Values 1 10 Example 1: Find the place values and the face values of the digits in 842. Solution: 842 2 ones 4 tens 8 hundreds Place Value Face Value 22 40 4 800 8 22
Expanded form of a 3-digit number Consider the number 425. We write 425 in the place value chart as shown. H TO Place values 425 5 ones = 5 2 tens = 20 4 hundreds = 400 We can write the place values of the digits of a given number with a ‘+’ sign between them. This gives the expanded form of the number. So, the expanded form of 425 is 400 + 20 + 5. The number name of 425 is four hundred and twenty-five. 425 is the standard form of the number. Consider the following examples to understand the concept better. Example 2: Write the standard forms of the following numbers. a) 9 hundreds + 4 tens + 6 ones b) 4 hundreds + 2 tens + 3 ones c) 3 hundreds + 0 tens + 8 ones Solution: To write the standard forms, write the numbers in the place value chart, as shown: HTO a) 9 4 6 b) 4 2 3 c) 3 0 8 So, the standard forms of the given numbers are: a) 946 b) 423 c) 308 Numbers 23
Example 3: Count and write the following numbers in their expanded forms. Then, write their number names. a) b) c) Solution: To write the expanded forms, write the numbers in the place value chart as shown below. Number Place Value Expanded Forms Number Names Chart H TO a) 523 523 523 = Five hundred and 500 + 20 + 3 twenty-three b) 432 432 432 = Four hundred and 400 + 30 + 2 thirty-two c) 634 634 634 = Six hundred and thirty-four 600 + 30 + 4 24
Application Let us see a few examples where we use 3-digit numbers. Example 4: Pooja collected two hundred and twenty-nine stamps. Reema collected six hundred and thirty-three stamps. Write the numerals for the number of stamps each of them collected. Solution: Stamps with Pooja = two hundred and twenty-nine = 229 Stamps with Reema = six hundred and thirty-three = 633 Example 5: Vinod has some amount with him: 1 note of ` 100, 1 note of ` 20 and 1 coin of ` 1. How much money does he have in all? Solution: 1 note of ` 100 = ` 100 1 note of ` 20 = ` 20 1 coin of ` 1 = ` 1 Total money = ` 100 + ` 20 + ` 1 = ` 121 So, Vinod has ` 121 (One hundred and twenty-one rupees). Higher Order Thinking Skills (H.O.T.S.) Let us learn to show 3-digit numbers on a spike abacus. Consider these examples. Example 6: Show the following numbers on the abacus: a) 434 b) 623 c) 476 Solution: To show 434, draw: 4 pink beads on the hundreds spike, 3 green beads on the tens spike and 4 blue beads on the ones spike. Similarly, we can show the other numbers as follows: Numbers 25
a) b) c) H TO H TO H TO 434 623 476 Concept 3.2: Ordinal Numbers Think David was confused when his teacher said, ‘All those sitting on the first, third and fifth benches, please stand up!’ He did not understand the words first, third and fifth. Have you ever heard these words? Do you know what they are? Recall Observe the given picture. It shows cars of different colours. The red car is before the The blue car is between the The black car is after blue car. red and the black cars. the blue car. 26
The words before, after and between give the positions of the cars. Let us recall the concept by filling the blanks. a) The ______________ is before the camel. b) The camel is between the frog and the _____________________. c) The crocodile is ______________ the camel. Camel Crocodile Frog & Remembering and Understanding Look at the chicks walking in a line. We can give each chick a position. First Second Third Fourth Fifth There are five chicks in a row. We start counting from the left. We number the chicks as first, second, third, fourth and fifth. These numbers which tell about the positions of objects are called ordinal numbers. The numbers one, two, three and so on are called cardinal numbers. The following table gives the ordinal numbers from 1 to 10 and their short forms. Number 1 2 345 Ordinal number First Second Third Fourth Fifth 1st 2nd 3rd 4th 5th Short form Number 6 7 8 9 10 Ordinal number Sixth Seventh Eighth Ninth Tenth 10th Short form 6th 7th 8th 9th Numbers 27
Example 7: Observe the toys on the shelves. Begin counting from the left and answer the questions given. a) On which shelf is the rings toy? b) Which toy is on the fourth shelf? c) On which shelf is the ball? d) Which toy is on the second shelf? e) What is the position of the toy truck on the shelf? Rings toy Toy Car Ball Toy Duck Toy Truck Solution: a) The rings toy is on the first shelf. b) The toy duck is on the fourth shelf. c) The ball is on the third shelf. d) The toy car is on the second shelf. e) The toy truck is on the fifth shelf. Application We use ordinal numbers to denote the position of things. Usually, the position is counted from the left to the right. For example, • to tell the winning positions in a competition. • to tell the periods in our timetable. Example 8: Look at the weekly activities of the students of Class 2. Answer the questions that follow. 28
Day 1 Day 2 Day 3 Swimming Horse riding Cycling Day 4 Day 5 Day 6 Rock climbing Archery Fishing a) On which day do the students learn horse riding? b) What do the students learn on the fourth day? c) On which day do the students enjoy fishing? Solution: a) Students learn horse riding on the second day. b) Students learn rock climbing on the fourth day. c) Students enjoy fishing on the sixth day. Example 9: Suppose you live in Mumbai. a) H ow many letters are there in the name of your city? What are they? Numbers 29
b) What is the first letter of the name? c) What is the last letter of the name? d) Is any letter being repeated in the name of your city? Which letter is it? Solution: e) In which places in the name is the repeated letter/letters? a) There are 6 letters in it. They are M, u, m, b, a and i. b) The first letter is M. c) The last letter is i. d) Yes, the letter ‘M’ is repeated. e) The repeated letter is in the first and third place. Higher Order Thinking Skills (H.O.T.S.) Consider the following example. Example 10: The given image shows the marks of six students in a class test. Look at the image and answer the following questions. a) Who came first in the class? b) What is Riya’s rank? Solution: To find the positions of the students, Piyush Vaishnavi Riya arrange their marks in descending 89 94 78 order. 94 > 91 > 89 > 83 > 78 > 72 Vaishnavi’s marks > Pooja’s marks > Piyush’s marks > Shubhro’s marks > Riya’s marks > Swati’s marks a) Vaishnavi came first in the class. Shubhro Swati Pooja b) Riya gets the fifth rank. 83 72 91 30
Concept 3.3: Compare 3-digit Numbers Think David has 504 colour pencils and his brother has 582 colour pencils. He wants to find out who has more colour pencils. How do you think David can find that out? Recall We have already learnt to compare numbers using the signs <, = or >. Let us recall the same. Count the number of objects in each image. Compare them using the proper sign <, > or = in the given boxes. a) Numbers 31
b) c) & Remembering and Understanding A 2-digit number is always smaller than a 3-digit number. Comparing two 3-digit numbers is similar to comparing two 2-digit numbers. We can compare two 3-digit numbers as shown in this example. Example 11: Compare: a) 723 and 456 b) 436 and 412 c) 623 and 628 Solution: Follow these steps to compare 3-digit numbers. 32
723 and 456 436 and 412 623 and 628 Step 1: Count the Step 1: Count the Step 1: Count the number number of digits number of digits of digits 723 456 436 412 623 628 Both have 3 digits. Both have 3 digits. Both have 3 digits. Step 2: Compare the Step 2: Compare the Step 2: Compare the hundreds hundreds hundreds 723 456 436 412 623 628 As 7 > 4, As 4 = 4, As 6 = 6, 723 > 456. compare the tens. compare the tens. Step 3: Compare the tens Step 3: Compare the tens 436 412 623 628 As 3 > 1, As 2 = 2, 436 > 412. compare the ones. Step 4: Compare the ones 623 628 As 3 < 8, 623 < 628. Numbers 33
Application We can use the place value chart to compare 3-digit numbers. It helps us in: 1) writing numbers in ascending and descending orders. 2) forming the greatest and the smallest numbers from a given set of digits. Ascending and descending orders Example 12: Write the numbers a) 777, 717, 771, 177 in the ascending order. b) 932, 384, 515, 869 in the descending order. Solution: Let us follow these steps to arrange the numbers in ascending and descending orders. a) For ascending order: Step 1: Compare the digits in the hundreds place of each number. 1<7 A number having the smallest number in the hundreds place is the least or the smallest. So, 177 is the least. Step 2: Compare the digits in the tens place of each number. 1<7 So, 717 < 771, 777. Step 3: Compare the digits in the ones place of each number. 1<7 So, 771 < 777. Step 4: Write the numbers from the smallest to the largest. Ascending order: 177, 717, 771, 777 b) F or descending order: Step 1: Compare the digits in the hundreds place of each number. 9>8>5>3 Step 2: Write the numbers from the greatest to the smallest. Descending order: 932, 869, 515, 384 34
Example 13: T here were 879 students in Class A and 880 in Class B. Which class had more number of students? Solution: Number of students in Class A = 879 Number of students in Class B = 880 Compare both the numbers using the place value chart. H T O H TO 879 880 The hundreds digit in both the 3-digit numbers is the same. So, compare the digits in the tens place. As, 8 > 7, 880 > 879. So, Class B had more number of students. Forming the greatest and the smallest 3-digit numbers Let us learn to form the greatest and the smallest 3-digit numbers. Consider the following examples. Example 14: Form the greatest numbers using the given digits, without repeating any of the digits. a) 1, 5, 1 b) 6, 1, 9 Solution: We can form the greatest numbers by following these steps. Step 1: Arrange the given digits in descending order. a) 5, 1, 1 b) 9, 6, 1 Step 2: Write the digits in the place value chart from left to right. a) H T O b) H T O 511 961 Example 15: Form the smallest numbers using the given digits, without repeating any of the digits. a) 3, 5, 7 b) 7, 9, 5 Solution: We can form the smallest numbers by following these steps. Numbers 35
Step 1: Arrange the given digits in the ascending order. Step 2: a) 3, 5, 7 b) 5, 7, 9 Write the digits in the place value chart from left to right. a) H T O b) H T O 357 579 Higher Order Thinking Skills (H.O.T.S.) Consider the following example. Example 16: Compare the numbers in each pair and write <, = or > between them. a) 10 + 9 + 200 _____ 8 + 20 + 200 b) 300 + 5 + 40 _____ 60 + 7 + 200 Solution: a) 10 + 9 + 200 = 219 and 8 + 20 + 200 = 228. As 219 is less than 228, we put the < symbol in the blank. So, 219 < 228. b) 300 + 5 + 40 = 345 and 60 + 7 + 200 = 267. As 345 is greater than 267, we put the > symbol in the blank. So, 345 > 267. Drill Time Concept 3.1: Count by Hundreds 1) Write the given numbers in the place value chart. a) 346 b) 123 c) 987 d) 459 e) 784 2) Write the expanded form of each of the following numbers. a) 298 b) 158 c) 490 d) 231 e) 847 3) Write the number name of each of the following numbers. a) 124 b) 967 c) 281 d) 100 e) 210 36
4) Form numbers with: a) 3 in the hundreds place, 1 in the tens place and 0 in the ones place b) 7 in the hundreds place, 2 in the tens place and 9 in the ones place c) 4 in the hundreds place, 3 in the tens place and 1 in the ones place d) 8 in the hundreds place, 0 in the tens place and 4 in the ones place e) 2 in the hundreds place, 5 in the tens place and 7 in the ones place Concept 3.2: Ordinal Numbers 5) Write the ordinal numbers and short forms of the following: a) 9 b) 4 c) 8 d) 1 e) 6 Concept 3.3: Compare 3-digit Numbers 6) Compare the numbers in the given pairs: a) 234, 432 b) 234, 233 c) 222, 222 d) 243, 243 e) 100, 900 7) Arrange the numbers in ascending and descending orders. a) 333, 313, 331, 133 b) 879, 865, 890, 812 c) 980, 981, 982, 983 d) 562, 589, 521, 514 e) 100, 300, 400, 700 8) Form the greatest and the smallest 3-digit numbers (without repeating the digits). a) 4, 8, 1 b) 9, 1, 0 c) 1, 5, 2 d) 6, 3, 8 e) 9, 8, 7 Numbers 37
Chapter Addition 4 Let Us Learn About • a dding 2-digit and 3-digit numbers. • properties of addition. Concept 4.1: Add 2-digit and 3-digit Numbers Think David had 306 stamps in one bag and 462 stamps in another bag. Meena had 12 stamps in one bag and 18 stamps in the other. David wants to find the total number of stamps with each of them. How do you think David can find that? 38
Recall We know how to add 2-digit numbers without regrouping. Let us recall the same. Write and add the number of objects in the boxes. a) b) c) d) Addition 39
& Remembering and Understanding Let us learn to add 2-digit numbers with regrouping and 3-digit numbers without regrouping. Add 2-digit numbers with regrouping Adding 2-digit numbers is similar to adding 1-digit numbers. While adding two numbers, always begin from the ones place. In some cases, we need to regroup the 2-digit sum. We carry forward its tens digit to the next place. Consider an example. Example 1: Add: 27 + 55 Solution: Arrange the numbers vertically. Steps Solved Solve these Step 1: Add the ones, 7 + 5 = 12. TO T O We can write only the ones digit of 1 44 the sum in the ones place. 2 7 +38 +5 5 So, we regroup 12 as 10 + 2. 2 Write 2 in the ones place. Carry forward 1 to the tens place. Step 2: Add the tens, 2 + 5 = 7. T O TO Add the carry forward 1 from the 1 ones place to this sum. 2 7 36 7+1=8 +5 5 +49 Write this sum in the tens place. 2 So, 27 + 55 = 82. 8 40
Add 3-digit numbers without regrouping Let us understand how to add 3-digit numbers through an example. Example 2: Add 343 and 125. Solution: Arrange the numbers vertically. Step 1: Step 2: Step 3: Add the ones Add the tens Add the hundreds H T O H T O HT O 34 3 34 3 34 3 +1 2 5 +1 2 5 +1 2 5 8 68 46 8 Solve these H TO H TO H TO H TO 634 144 122 108 +1 5 2 +3 3 4 +4 0 1 +2 0 1 Properties of addition Addition of numbers have some properties. Let us learn a few of them. 1) Zero property: When we add 0 to a number, the sum is the number itself. For example, 89 + 0 = 89; 12 + 0 = 12 and so on. 2) After numbers property: When we add 1 to a number, we get the number just after it. For example, 35 + 1 = 36; 77 + 1 = 78 and so on. 3) Commutative property: Changing the order in which we add two numbers does not change their sum. For example, 2 + 3 = 5 and 3 + 2 = 5; 15 + 14 = 29 and 14 + 15 = 29 and so on. Addition 41
Application We apply the concept of addition in solving some real-life situations. Let us see a few examples. Example 3: There are 24 balls in a box and 18 balls in another box. How many Solution: balls are there in all? TO Number of balls in the first box = 24 1 Number of balls in the second box =18 24 Total number of balls = 24 + 18 = 42 +1 8 So, there are 42 balls in all. 42 Example 4: Mohan has 142 pencils and Sohan has 126 pencils. How many pencils do they have altogether? HTO Solution: Number of pencils with Mohan =142 142 Number of pencils with Sohan = 126 +1 2 6 Total number of pencils = 142 + 126 = 268 2 6 8 So, Mohan and Sohan together have 268 pencils. Higher Order Thinking Skills (H.O.T.S.) Framing story sums for some given numbers would be interesting. Example 5: Given 32 + 22 = 54, frame a story sum. Solution: Two numbers and their sum are given. We can use some situation to frame the story sum. Step 1: Think of a situation. Here, let us take the number of different fruits such as oranges and apples in a basket. Step 2: Write the story in your words. There were 32 oranges and 22 apples in a fruit basket. How many fruits were there in all? 42
Drill Time Concept 4.1: Add 2-digit and 3-digit Numbers 1) Add 2-digit numbers with regrouping. a) 77 + 13 b) 26 + 35 c) 19 + 35 d) 49 + 12 e) 55 + 25 2) Add 3-digit numbers without regrouping. a) 166 + 111 b) 612 + 352 c) 181 + 315 d) 490 + 100 e) 812 + 121 3) Word problems a) F arah has 11 balloons and her friend has 29 balloons. How many balloons do they have in all? b) A khil had 120 pens in one box and 121 pens in another box. How many pens did he have in all? Addition 43
Chapter Subtraction 5 Let Us Learn About • s ubtracting 2-digit and 3-digit numbers. • p roperties of subtraction. • mental Maths techniques for subtraction. Concept 5.1: Subtract 2-digit and 3-digit Numbers Think David got 83 candies from his parents for his birthday. He gives 27 candies to his friend Neha. How can David find the number of candies left with him without counting? Recall In class 1, we have learnt to subtract using a number line and also by counting. We have also learnt subtraction using the place value chart. Let us solve the following to recall the concept of subtraction. 44
Count, write and subtract the numbers in the boxes. a) b) c) d) Subtraction 45
& Remembering and Understanding Subtraction of 2-digit numbers with regrouping Place values of digits in 2-digit numbers are tens and ones. While subtracting, always start from the ones place. Sometimes, subtracting 2-digit numbers needs regrouping. Let us see some examples. Example 1: Subtract 48 from 56. Solution: To subtract, follow these steps: Steps Solved Solve these TO TO Step 1: Write the numbers according 56 44 to their places. Subtract the digits in the ones place. But, we cannot –4 8 –3 8 subtract 8 from 6. So, we have to regroup the tens. TO TO 4 16 98 5 tens = 4 tens + 1 ten. 56 –3 9 –4 8 We know that 1 ten = 10 ones. 8 Step 2: Add 1 ten to the ones place. So, it becomes 16 ones. Also, subtract 1 ten from the tens place (that is, 5 – 1 = 4). Now, subtract 8 from 16. That is, 16 – 8 = 8. Write the difference in the ones place. (Note: You cannot subtract from zero. You must borrow from the next place instead. For example, for subtracting 27 from 40, you cannot subtract 7 from 0. Hence, you borrow 1 from 4 (the tens place of 40) to give 10 for 0 and 3 for 4.) Step 3: Subtract the digits in the tens TO TO place. That is, 4 – 4 = 0. Write the 4 16 difference in the tens place. 56 86 –4 8 –2 7 So, 56 – 48 = 8. 08 46
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