202110766-TRAVELLER_PREMIUM-STUDENT-TEXTBOOK-MATHEMATICS-G02-Combine

MATHEMATICS TEXTBOOK – Grade 2 Name: _________________________ Section: ________Roll No: _______ School: ________________________

Contents Part 1 3 Numbers 3.1 Count by Hundreds................................................................... 20 ���������������������������������������������������������� ������������������������������� 42

Numbers3Chapter I Will Learn About • reading and writing numerals for numbers up to 999. • place value and face value. • comparing 3-digit numbers. • forming the greatest and the smallest 3-digit numbers. • ordinal numbers. 3.1 Count by Hundreds I Think Raj went to a toy store. He saw that ` 990 was written on a toy. He could not read the number. Can you read it? `990 I 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 numbers by ones and tens. 20

Look at the following picture. Start from 1 and connect all the dots in order. You will find a friend smiling back at you. I Remember and Understand Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Numbers 21

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 In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. 22

Let us understand this concept using a spike abacus. We have learnt how to show the number 99 1 = 1 unit in on an abacus. the ones spike To show the number 100, we remove all the green beads from the tens place. We also 1 = 1 unit in remove all the blue beads from the ones place. We then put 1 pink bead in the third TO the tens spike (hundreds place). 99 spike 1 = 1 unit in the hundreds spike The smallest 3-digit Thus, to show 999, we put 9 number is 100. pink beads in the hundreds spike, 9 green beads in the The largest 3-digit number is 999. tens spike and 9 blue beads in the ones spike. Let us show the number 124 using TO H T O a spike abacus. We put 1 pink 99 100 bead in the hundreds spike. We then put 2 green beads in the tens spike and 4 blue beads in the ones spike. In the H TO 999 same way, we can show the numbers 298 and 459 on the abacus. H TO H TO H TO 124 298 459 Numbers 23

We can write the number names of these numbers as: 124 = One hundred twenty-four 298 = Two hundred ninety-eight 459 = Four hundred 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 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: 4 2 8 2 ones Place Value Face Value 4 tens 22 40 4 8 hundreds 800 8 24

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 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 25

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 Number Names Chart Forms Five hundred H TO 523 = twenty-three 500 + 20 + 3 Four hundred thirty-two a) 523 5 2 3 432 = Six hundred thirty-four b) 432 4 3 2 400 + 30 + 2 c) 634 6 3 4 634 = 600 + 30 + 4 26

? Train My Brain Write the number names of: a) 358 b) 409 c) 991 Numbers 27

3.2 Compare 3-digit Numbers I Think Raj 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 Raj can find that out? I Recall We have already learnt to compare numbers using the signs <, = or >. Let us recall the same. 28

Count and compare the number of objects in each image and write the proper sign <, > or = in the given boxes. a) b) c) I Remember and Understand A 2-digit number is always smaller than Comparing two 3-digit numbers is similar to a 3-digit number. comparing two 2-digit numbers. Use the steps to compare two 3-digit numbers as shown in this example. Numbers 29

Example 7: Compare: a) 723 and 456 b) 436 and 412 c) 623 and 628 Solution: Follow these steps to compare 3-digit numbers. 723 and 456 436 and 412 623 and 628 Step 1: Count the Step 1: Count the Step 1: Count the number of digits number of digits number 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 Step 3: Compare the tens 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. 30

? Train My Brain Find the greater number in each of the following pairs: a) 222 and 212 b) 555 and 545 c) 444 and 443 Numbers 31

4Chapter Addition I Will Learn About • adding 2-digit numbers and 3-digit numbers. • properties of addition. • solving word problems based on addition. • mental Maths techniques. 4.1 Add 2-digit Numbers and 3-digit Numbers I Think Raj 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. Raj wants to find the total number of stamps with each of them. How do you think Raj can find that? 42

I 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 43

I Remember and Understand 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 While adding two numbers. numbers, always begin from the In some cases, we need to regroup the 2-digit sum. ones place. We carry forward its tens digit to the next place. Consider these examples. Example 1: Add: 27 + 55 Solution: Arrange the numbers vertically. Steps Solved Solve these Step 1: Add the ones, 7 + 5 = 12. TO TO We can write only ones digit of 1 the sum in the ones place. 27 4 4 +5 5 +3 8 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. Add the carry forward (1) from TO TO the ones place to this sum. 1 27 3 6 7+1=8 +5 5 +4 9 82 Write this sum in the tens place. So, 27 + 55 = 82. 44

Add 3-digit numbers without regrouping Let us understand how to add 3-digit numbers through some examples. 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 show some properties. Let us learn a few of them. 1) Zero property: When we add 0 to a number, the sum is the same as 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 two numbers are added, 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 45

? Train My Brain Answer the following: a) What is the sum of 22 and 1? b) What is the sum of 90 and 0? c) Given 17 + 18 = 35 and 18 + 17 = 35. Which property of addition do the numbers 17 and 18 show? 46

Contents Part 2 6 Subtraction 6.1 Subtract 2-digit Numbers and 3-digit Numbers ....................... 1 ������������������������������� 9 Division 9.1 Repeated Subtraction ................................................................ 30

6Chapter Subtraction I Will Learn About • subtraction of 2-digit and 3-digit numbers. • solving daily-life problems with subtraction. • mental Maths techniques. 6.1 Subtract 2-digit Numbers and 3-digit Numbers I Think Raj has got 83 candies from his parents for his birthday. He gives 27 candies to his friend Neha. How can Raj find the number of candies left with him without counting? I Recall In class 1 we have learnt to subtract using a number line and also by counting. We have also done subtraction using the place value chart. Let us solve the following to recall the concept of subtraction. 1

Count, write and subtract the numbers in the boxes. a) b) c) d) 2

I Remember and Understand Subtraction of 2-digit numbers with regrouping The place values of digits in 2-digit numbers are tens While subtracting, and ones. Sometimes, subtracting 2-digit numbers always begin from needs regrouping. Let us see some examples. the ones place. Example 1: Subtract 48 from 56. Solution: Write the numbers according to their places. Write the bigger number on the top. Steps Solved Solve these Step 1: Subtract the ones. TO TO As 8 > 6, we cannot subtract 8 from 6. So, regroup the tens. 56 44 −4 8 −3 8 5 tens = 4 tens + 1 ten (1 ten = 10 ones) Step 2: Add 1 ten to the ones. So, it becomes 16 ones. Also, subtract 1 ten from the tens place (that is, 5 – 1 = 4). Now, subtract 8 from 16; 16 – 8 TO T O 9 8 = 8. Write the difference in the ones place. 4 16 −3 9 (Note: You cannot subtract from zero. You 5 6 T O 8 8 6 must borrow from the next place instead. For − 4 8 −2 7 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 tens. TO That is, 4 – 4 = 0. Write the difference in the tens 4 16 place. 56 So, 56 – 48 = 8. −4 8 08 Subtraction 3

Subtraction of 3-digit numbers without regrouping Let us understand how to subtract 3-digit numbers through some examples. Example 2: Subtract 141 from 943. Solution: Arrange the numbers according to their place values. Steps Solved Solve these Step 1: Subtract the ones. Write H T O H T O the difference in the ones 9 4 3 4 9 6 place. That is, 3 – 1 = 2. −1 4 1 −2 6 2 2 Step 2: Subtract the tens. Write HT O H T O the difference in the tens 94 3 6 3 6 place. That is, 4 – 4 = 0. −1 4 1 −1 3 0 02 Step 3: Subtract the hundreds. HT O H T O Write the difference in the 94 3 8 4 6 hundreds place. −1 4 1 −4 2 0 That is, 9 − 1= 8. 80 2 So, 943 – 141 = 802. Properties of subtraction 1) Zero property: When we subtract 0 from a number, the difference is the number itself. F or example, 12 – 0 = 12; 28 – 0 = 28 and so on. 2) B efore numbers property: When we subtract 1 from a number, we get the number just before it. For example, 35 – 1 = 34; 59 – 1 = 58 and so on. 3) Subtracting a number from itself: When we subtract a number from itself, the difference is 0. For example, 35 – 35 = 0; 62 – 62 = 0 and so on. 4

? Train My Brain a) Subtract 0 from 12. b) Find the difference between 50 and 1. c) W hat is the difference when a number is subtracted from itself? Subtraction 5

8Chapter Multiplication I Will Learn About • repeated addition. • skip counting. • multiplication tables of 2, 3, 4 and 5. 8.1 Repeated Addition and Skip Counting I Think Raj wants to buy toffees for his birthday. His mother asks him to get 3 toffees for each of his friends. He has 7 friends. How can Raj find out quickly how many toffees he has to buy? I Recall We already know how to add objects by counting. Let us recall the same through the following exercise. Multiplication 17

Count, add and write the number of objects. a) Number of honey bees = _____________ b) Number of trees = ___________ c) Number of birds = ___________ d) Number of windows = ___________ I Remember and Understand Let us learn about repeated addition and skip counting. 18

Repeated addition In repeated addition, we put Repeated addition is adding the same number the objects into again and again. equal groups to find their total. Let us see a few examples. Example 1: Use repeated addition to find the total number of houses. Number of groups = 4 Solution: The number of objects in each group = 2 Total number of objects = 2 + 2 + 2 + 2 = 8 So, there are 8 houses in all. We read it as 4 groups of 2 becomes 8. Skip counting ‘Skip Counting’ is counting by a number other than 1. It helps you to: a) count many things quickly. b) learn multiplication tables. Multiplication 19

Count by 2s In counting by 2s, we begin with a number and count every alternate number. Example 2: Help the frog to find its way to the snail. You can do so using skip counting by 2. Write the numbers on which it jumps. One is done for you. a) b) c) Count by 3s In counting by 3s, we count every third number from the given number. Let us see an example. Example 3: Begin with the given number and count by 3s. Write the numbers in the boxes given. One is done for you. a) 20

b) c) ? Train My Brain Identify the number of groups. Write the number of items present in each group. a) b) c) Multiplication 21

Division9Chapter I Will Learn About • equal sharing and equal grouping. • repeated subtraction. • division using a number line. 9.1 Repeated Subtraction I Think Raj wants to distribute 20 craft papers equally among 4 of his friends to make paper figures. How many craft papers do you think each of them would get? I Recall In the previous chapter, we have learnt about multiplication. Multiplication is finding the total number of objects that have been grouped equally. Let us use this to distribute objects equally in groups. 30

Consider 12 bars of chocolate. The different ways in which they can be distributed are as follows. Distributing in 1 group: 1 × 12 = 12 Distributing in 2 groups: 2 × 6 = 12 Distributing in 3 groups: 3 × 4 = 12 Distributing in 4 groups: 4 × 3 = 12 Distributing in 6 groups: 6 × 2 = 12 Distributing in 12 groups: 12 × 1 = 12 I Remember and Understand Distributing a given number of objects into equal groups is called division. We can understand division better by using equal sharing and equal grouping. Division 31

Equal sharing means having an equal number of objects in a group. We use division to find the number of things in a group. We can also find the number of groups by using division. Suppose 9 balloons are to be 1st round: 1 balloon is taken by shared equally among 3 friends. each friend. Let us use repeated subtraction to distribute the balloons. 9 – 3 = 6. So, 6 balloons remain. 2nd round: From the remaining 6 3rd round: From the remaining 3 balloons, 1 more balloon is taken balloons, 1 more balloon is taken by each friend. by each friend. Now, each friend has 2 balloons. Now, each of them has 3 balloons. 6 – 3 = 3. So, 3 balloons remain. 3 – 3 = 0. So, 0 balloons remain. Each friend gets 3 balloons. Here we subtracted the same number again and again. This is known as repeated subtraction. When 9 balloons are divided among 3 friends, each friend gets 3 balloons. 32

We can write it as 9 divided by 3 equals 3. Using the symbol of division, we write it as follows: ↓ ↓ ↓ The symbol for ‘is divided Number of by’ is ÷. groups Total Number of number of objects in each objects group Let us understand this through an example. Example 1: 20 pencils are to be equally distributed in a few pencil stands. Each stand can hold 5 pencils. How many stands will be needed? Solution: We use repeated subtraction to distribute 20 pencils equally. Given that each stand has 5 pencils, let us first put 5 pencils in one stand. 20 pencils – 5 pencils = 15 pencils remain From the remaining 15 pencils, put 5 pencils in another stand. Division 33

15 pencils – 5 pencils = 20 – 5 – 5 pencils = 10 pencils remain From the remaining 10 pencils, put 5 pencils in another stand. 10 pencils – 5 pencils = 20 – 5 – 5 – 5 pencils = 5 pencils remain 5 pencils – 5 pencils = 20 – 5 – 5 – 5 – 5 pencils = 0 pencils remain As no more pencils are left, we need 4 stands. So, we can distribute 20 pencils equally in 4 stands with 5 pencils in each. We can write it as 20 ÷ 5 = 4. (Total number of pencils) ÷ (Number of pencils in each stand) = (Number of stands needed) 34

Division using a number line We can use the number line to show repeated subtraction. Count backwards and make equal jumps to reach 0. Let us see an example. Example 2: Divide using a number line: a) 10 ÷ 2 b) 18 ÷ 3 Solution: a) 10 ÷ 2 (5) (4) (3) (2) (1) Starting from 10, jump backward in steps of 2. We reach 0 after 5 jumps as shown by the arrows. So, 10 – 2 – 2 – 2 – 2 – 2 = 0. We can write it as 10 ÷ 2 = 5. b) 18 ÷ 3 (6) (5) (4) (3) (2) (1) Starting from 18, jump backwards in steps of 3. We reach 0 after 6 jumps as shown by the arrows. So, 18 – 3 – 3 – 3 – 3 – 3 – 3 = 0. We can write it as 18 ÷ 3 = 6. ? Train My Brain Write the following using the division symbol. a) 21 divided by 3 gives 7 b) 42 divided by 7 gives 6 c) 32 divided by 8 gives 4 Division 35