MATHEMATICS 2 TEXTBOOK – 2 Name: ___________________________________ Section: ________________ 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 6 Subtraction 6.1 Subtract 2-digit Numbers and 3-digit Numbers������������������������������������������� 1 6.2 M ental Maths Techniques: Subtraction��������������������������������������������������������� 6 7 Money 7.1 Add and Subtract Money without Conversion��������������������������������������������10 8 Multiplication 8.1 Repeated Addition and Skip Counting��������������������������������������������������������17 9 Division 9.1 R epeated Subtraction�����������������������������������������������������������������������������������30 10 M easurement 10.1 Measure Lengths Using Non-standard Units����������������������������������������������40 10.2 Comparing Mass and Volume by Estimation �������������������������������������������47 11 Data Handling 11.1 Pictographs��������������������������������������������������������������������������������������������������62
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) What is the difference when a number is subtracted from itself? I Apply We use the concept of subtraction to solve some real-life situations. Let us see a few examples. Example 3: There are 390 students in a school. Among them,150 students are girls. How many boys are there in the school? Solution: Number of students in the school = 390 HTO Number of girls = 150 Number of boys = 390 – 150 39 0 So, there are 240 boys in the school. −15 0 24 0 Example 4: There are 52 candies in a jar. Children ate up 37 candies. How many candies are left in the jar? S olution: Number of candies in a jar = 52 TO Number of candies eaten by children = 37 4 12 Number of candies left in the jar = 52 – 37 52 So, there are 15 candies left in the jar. −3 7 15 I Explore (H.O.T.S.) Let us now learn to frame a story sum based on subtraction. Subtraction 5
Example 5: Given 163 −120 = 43, frame a story sum. Solution: Two numbers and their difference are given. We can use some situation to frame the story sum. Step 1: Think of a situation. For example- Shyam takes some chocolates to school on his birthday. Since it is subtraction, these chocolates should be given away. Step 2: Write the story in your words. Shyam takes 163 chocolates to school on his birthday. He shares 120 chocolates among his classmates. How many chocolates are left with him? 6.2 Mental Maths Techniques: Subtraction Mental Maths Let us now learn to subtract 2-digit numbers mentally. Subtract 52 from 76 mentally. Steps Solved Solve this 76 – 52 69 – 35 Step 1: Subtract the ones mentally. 6–2=4 ______ – ______ = ______ Step 2: Subtract the tens mentally. The digits in the tens The digits in the tens place are 7 and 5. place are ___ and ____. So, imagine that 7 So, imagine that ____ fingers are open. fingers are open. Then imagine closing Then imagine closing 5 of them. Count the of them. Count the remaining number of remaining number of fingers that are open. fingers that are open. 7–5=2 ____ – ____ = ____ 6
Steps Solved Solve this 76 – 52 69 – 35 Step 3: Write the So, 69 – 35 = ____. differences obtained in the steps 1 and 2 as the So, 76 – 52 = 24. difference of the given numbers. ? Train My Brain Solve the following mentally: a) 53 – 31 b) 65 – 23 c) 65 – 14 d) 29 – 19 e) 81 – 11 Maths Munchies 1 0 0 − 8 6 from 9 = 1 4 from 10 Subtraction of 2-digit numbers from 100: Consider the example 100 – 86. In this example, we have subtracted 8 from 9 and then 6 from 10 which results in 14. This trick helps in faster calculations. Connect the Dots EVS Fun You have invited 15 people. Six of them are your friends. Also, there is one uncle, one aunt and three cousins. Your parents and grandparents are also there. If we separate all the extended family members, how many guests will remain? Subtraction 7
English Fun Let us read a poem about subtraction. Here we go subtracting numbers, Away a part, away a part, Subtracting numbers, subtracting Next you take away a part, numbers To find the difference Here we go subtracting numbers, You have found the other part, To find the difference The other part, the other part, First you start with the whole, You have found the other part, With the whole, with the whole, That is the difference. First you start with the whole, To find the difference Next you take away a part, Drill Time 6.1 Subtract 2-digit Numbers and 3-digit Numbers 1) Subtract the following with regrouping. a) 25 – 18 b) 37 – 29 c) 48 – 19 d) 56 – 27 e) 90 – 25 2) Subtract the following without regrouping. a) 356 – 256 b) 197 – 106 c) 786 – 122 d) 476 – 111 e) 854 – 221 3) Word problems a) V ishu has 33 cups in a box. He used 17 of them for a birthday party. How many cups are left in the box? b) N isha has 41 handkerchiefs with her. She gave 24 handkerchiefs for washing. How many handkerchiefs are left with her? 8
A Note to Parent Give your child a few toffees. Now play a game according to the following rules: a) Ask for 0 toffees. Then tell your child to count the number of toffees that remain. b) A sk your child to give you one toffee. Tell him or her child to count the number of toffees that remain. c) Ask your child to give you different numbers of toffees and then ask how many are left. Subtraction 9
7Chapter Money I Will Learn About • addition and subtraction of an amount up to ` 100 without conversion. • estimation of money. 7.1 Add and Subtract Money without Conversion I Think Raj and his mother bought a few items from a shop. When Raj’s mother paid the bill, the shopkeeper gave her some change. Raj wondered why the shopkeeper gave his mother some money. Do you know why? I Recall We add or subtract numbers by writing them one below the other. This method of addition or subtraction is called the column method. 10
Solve the following to recall the addition and subtraction of numbers. T O T O T O T O 2 6 3 4 3 4 8 0 +1 1 +2 2 –1 3 –1 0 Let us revise the concept of addition of notes and coins. Complete the table with the number of notes and coins that will add up to the given value. One is done for you. ` 20 note ` 10 note ` 5 coin ` 2 coin ` 1 coin ` 47 2 11 ` 23 ` 35 ` 78 ` 99 I Remember and Understand Money is written in rupees and paise, In the column method, we write rupees under separated by a dot. rupees. Then we write paise under paise, exactly one below the other. When paise is not given, For example, ` 3.50 is we put 00 in the paise column. Then we add or read as three rupees subtract as usual. and fifty paise. Addition of money Let us understand the addition of money through an example. Example 1: Add: ` 45.50 and ` 32.20 Solution: Arrange rupees and paise in two columns. Steps Solved Solve these Step 1: Add the paise. Write the sum in the `p `p paise column. 45 . 50 11 . 11 +32 . 20 +22 . 22 70 Money 11
Steps Solved Solve these Step 2: Add the rupees. Write the sum in the `p `p rupees column. 45 . 50 20 . 19 +32 . 20 +32 . 20 77 . 70 Subtraction of money Let us understand the subtraction of money through an example. Example 2: Subtract: ` 25.40 from ` 75.60 Solution: Arrange rupees and paise in two columns as shown. Write the larger amount above the smaller amount. Steps Solved Solve these Step 1: Subtract the paise. `p Write the difference in the `p paise column. 75 . 60 45 . 45 –25 . 40 –12 . 12 Step 2: Subtract the rupees. Write the 20 `p difference in the rupees 98 . 43 column. `p –46 . 22 75 . 60 –25 . 40 50 . 20 ? Train My Brain c) ` 76.24 – ` 12.10 Solve the following: a) ` 34.33 – ` 24.22 b) ` 21.25 + ` 42.23 I Apply Let us see some real-life examples of addition and subtraction of money. Example 3: Five pens cost ` 20 and two pencils cost ` 12.50. What is their total cost? Write in words. 12
Solution: Cost of five pens = ` 20 ` p 00 Cost of two pencils = ` 12.50 20 . 50 50 Their sum = ` 20 + ` 12.50 +12 . So, the total cost of pens and pencils is 32 . ` 32.50. In words, it is thirty-two rupees and fifty paise. Example 4: Veer bought a ball for ` 12.50 and gave the shopkeeper ` 15.50. How much change did the shopkeeper give Veer? Solution: The amount Veer paid the shopkeeper = ` 15.50 `p Cost of the ball = ` 12.50 Difference in the amounts = ` 15.50 – ` 12.50 1 5 . 5 0 So, the shopkeeper gave Veer ` 3. – 12 . 50 I Explore (H.O.T.S.) 3 . 00 Let us see a few more examples of addition and subtraction of money. Example 5: Vani has ` 500. How many of the given items can she buy? Write any four combinations. Bucket Bag of rice Fruit basket Toy robot Clock ` 100 ` 250 ` 150 ` 350 ` 200 Solution: The total cost of the items that Vani can buy must be less than or equal to ` 500. a) Combination 1 b) Combination 2 ` 100 ` 250 ` 150 ` 100 ` 350 Money 13
c) Combination 3 d) Combination 4 ` 150 ` 350 ` 250 ` 200 Maths Munchies Presently we have 2000, 500, 100, 50, 10 and 5 rupee notes. The new ` 2000 and ` 500 notes were introduced in November 2016. They look like the images given here. The old ` 500 notes and ` 1000 notes looked like the images given here. These notes are no longer used. 14
Connect the Dots EVS Fun Have you seen ATMs in your city or town? ATM stands for ‘Automated Teller Machine’. Every bank has its own ATM. Most ATMs work for 24 hours. We can go and get money from there anytime! English Fun Think of at least three rhyming words for ‘money’. Drill Time 7.1 Add and Subtract Money without Conversion 1) Add: a ) ` 27.17 + ` 12.12 b) ` 35.88 + ` 12.11 c) ` 46.37 + ` 10.10 d) ` 87.22 + ` 12.77 e) ` 11.11 + ` 22.22 2) Subtract: b) ` 45.23 – ` 11.13 c) ` 76.43 – ` 15.20 a) ` 99.99 – ` 11.11 e) ` 65.65 – ` 35.35 d) ` 39.28 – ` 27.10 Money 15
3) Word problems a) Ram has ` 52.50. He gave ` 40.00 to Shama. How much money does Ram have left? b) Soham bought some chocolates for ` 41.00. Rehan bought some chocolates for ` 24.50. How much amount did they spend in all? A Note to Parent Take your child for grocery shopping on a weekend. Ask him or her to count the coins and notes before paying the shopkeeper. Such hands-on experiences will strengthen your child’s understanding of the uses of money. 16
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) I Apply Let us now learn to construct the multiplication tables of numbers from 2 to 5. Multiplication 21
Observe the following figure. It is a group of 2 stars. So, we see that 1 group of 2 is 2. We write it as ‘2 × 1 = 2’ which means ‘2 times 1 is 2’. The symbol ‘×’ is used for multiplication. It is read as ‘times’. We read it as ‘2 ones are 2’. There are 2 groups with 2 stars in each. We write it as 2 + 2 = 4 and read it as 2 groups of 2 is 4. We can also write it as ‘2 × 2 = 4’ which means ‘2 times 2 is 4’. We read it as ‘2 twos are 4’. These are 3 groups with 2 stars in each. We write it as 2 + 2 + 2 = 6 and read it as 3 groups of 2 is 6. This can be written as ‘2 × 3 = 6’ which means ‘2 times 3 is 6’. We read it as ‘2 threes are 6’. In this way, we can form the multiplication table of 2. Forming the multiplication table of 2 2×1=2 1 + 1 2 times 1 is 2. 2×2=4 2 + 2 2 times 2 is 4. 22
2 × 3 = 6 3 + 3 2 times 3 is 6. 2 × 4 = 8 4 + 4 2 times 4 is 8. 2 × 5 = 10 5 + 5 2 times 5 is 10. 2 × 6 = 12 6 + 6 2 times 6 is 12. 2 × 7 = 14 7 + 7 2 times 7 is 14. 2 × 8 = 16 8 + 8 2 times 8 is 16. 2 × 9 = 18 9 + 9 2 times 9 is 18. 2 × 10 = 20 10 + 10 2 times 10 is 20. Multiplication 23
The following are the multiplication tables of 2, 3, 4 and 5. Read them aloud. 2 3 4 5 2×1=2 3×1=3 4×1=4 5×1=5 2×2=4 3×2=6 4×2=8 5 × 2 = 10 2×3=6 3×3=9 4 × 3 = 12 5 × 3 = 15 2×4=8 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 2 × 5 = 10 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 2 × 6 = 12 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 2 × 7 = 14 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 2 × 8 = 16 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 2 × 10 = 20 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 Let us now apply the concept of repeated addition and multiplication. Example 4: Suresh has three pet dogs. How many legs do these dogs have altogether? Solution: Suresh has three pet dogs. So, the number of groups is 3. Each dog has 4 legs. So, the number of equal objects in each group is 4. 4 + 4 + 4 = 12 So, 3 groups of 4 is12. We can also use the multiplication table to find the number of legs. As there are 3 dogs with 4 legs each, we write 3 × 4 = 12. So, the three pet dogs have 12 legs altogether. 24
I Explore (H.O.T.S.) Let us see another example of skip counting. Example 5: C omplete the wheel using the method of skip counting by 3 and 5. Solution: We can complete the wheel using skip counting by 3 and 5 as shown. Maths Munchies Interesting facts about multiplication of a number by 0 and 1. Multiplying a number by 0, gives a 0. For example, 3 × 0 = 0; 58 × 0 = 0 and so on. Multiplying a number by 1 gives the same number. For example, 24 × 1 = 24; 18 × 1 = 18 and so on. Multiplication 25
Connect the Dots EVS Fun Each tree has one big trunk that leads to different branches. These branches multiply to form many other branches. Thus, you can see a big tree growing with many branches. English Fun Read and make interesting poems as given here. One and two climb a tree. They find the number three. Three and eight got on the floor. Three times eight is twenty-four. Drill Time 8.1 Repeated Addition and Skip Counting 1) Count, add and write the total number. a) 26
b) c) d) 2) Skip count and fill in the blanks. a) Skip count by 2 8 2 Multiplication 27
b) Skip count by 3 15 3 c) Skip count by 4 4 24 d) Skip count by 5 5 45 3) Word problems a) Seeta observed that there were 4 cars parked in a row. How many wheels could she count on the cars? 28
b) H ari counts some pens using skip counting by 3. How many pens does he count altogether? A Note to Parent Make your child practise multiplication tables regularly. Knowing tables by heart is important, as it makes it easier for your child to calculate faster. Multiplication 29
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
I Apply We can use repeated subtraction in some real-life situations. Here are a few examples. Example 3: Sunil has 18 beads. He wants to make a necklace with 6 beads each. How many necklaces can he make? Solution: Total number of beads = 18 Number of beads in each necklace = 6 Number of necklaces = 18 ÷ 6 = 3 So, Sunil can make 3 necklaces. Example 4: Renu wants to divide 30 feathers in 6 groups. How many feathers will be there in each group? Solution: Total number of feathers = 30 Number of groups = 6 Number of feathers in each group = 30 ÷ 6 = 5 36
So, there will be 5 feathers in each group. I Explore (H.O.T.S.) Division and multiplication are reverse operations. Let us understand this. Suppose there are 12 toys. We want to arrange them on 4 shelves. Number of toys on each shelf = 12 ÷ 4 = 3 So, there will be 3 toys on each shelf. If there are 3 toys on 4 shelves, we can find the total number of toys as 4 × 3 = 12. Division 37
So, we can say that division and multiplication are reverse operations. If 12 ÷ 4 = 3, then 4 × 3 = 12. Similarly, 3 × 4 = 12 Maths Munchies Interesting facts about division: Dividing a number by 1, gives the number itself. For example, 21 ÷ 1 = 21; 46 ÷ 1 = 46 and so on. Dividing a number by itself gives 1. For example, 39 ÷ 39 = 1; 18 ÷ 18 = 1 and so on. Connect the Dots English Fun Find these words in the word search puzzle. DIVISION EQUAL SHARING GROUPING RGAD I V I S I ON B S H R T E D B D B H UGH T F K T AA I EQUA L UGH T N O L A S PGD R N LWU Y E WWG R O U P I N G A G B W Q R P I E R H N MW I U C D T O L K AA YGA R T Q S L H T A E C N V L D J E J MW OE YDHDDX E YDV I V 38
EVS Fun Division mean equal sharing. It exists in our neighbourhood and families too. The members of a family share the work or tasks of the family. What kind of division of work do you see in your neighbourhood? Drill Time 9.1 Repeated Subtraction 1) Find using repeated subtraction. a) 16 ÷ 4 b) 18 ÷ 9 c) 20 ÷ 5 d) 32 ÷ 8 e) 10 ÷ 2 2) Find using a number line. a) 18 ÷ 2 b) 21 ÷ 3 c) 10 ÷ 5 d) 12 ÷ 2 e) 16 ÷ 2 3) Word problems a) 2 6 students are to be grouped equally in 2 groups. How many students will be there in each group? b) 14 pens must be distributed equally among 7 children. How many pens will each child get? A Note to Parent Engage your child in the activities that involve division in day-to-day life at home. For example, dividing chapatis amongst all on a dinner table, splitting pocket money or some chocolates with his or her siblings, putting flowers in vases and so on. Division 39
10Chapter Measurement I Will Learn About • measurement of length and distance using uniform units. • comparison of two or more objects by their weights. • use of the simple balance to compare weights. • the order of containers based on their capacities. 10.1 Measure Lengths Using Non-standard Units I Think Raj and his mother decided to measure the length of a table. They measured using their cubits. Do you think that they will get the same number of cubits? I Recall We have learnt to compare the lengths of objects. Let us recall the same. 40
Tick the tallest tree and cross the shortest. Tick the longest insect and cross the shortest. We have also learnt to measure the lengths of objects using hand span. Measurement 41
Complete the given table. Measuring the length of Number of hand Object the objects spans I Remember and Understand We can also use our palm, foot and Hand span and cubit are used to pace to measure lengths. measure small lengths. Foot and pace are used to measure longer lengths. 42
Hand span Cubit Foot Pace Example 1: Measure these objects with the help of cubits. Write the number of cubits. One is done for you. Object Measuring the length Number of cubits 3 Measurement 43
We can measure the lengths of long objects using some shorter objects. Example 2: Measure these objects with the given smaller object. One is done for you. a) The paint brush is 6 paper clips long. b) The notebook is _________ erasers long. c) T he chocolate bar is _________ sharpeners long. d) The pen is _________ crayons long. ? Train My Brain Write the lengths of the objects using the given smaller objects. a) b) c) 44
I Apply We measure the lengths of various objects in our daily life. Let us see a few examples. Example 3: Measure the lengths of the objects as directed. Write the measurement values in this table. Object Measure a) Length of a textbook Length of a TV stand Measured using Length of a window hand span b) Length of a table Height of a table Measured using Edge of a chair cubit Length of a rack c) Length of a mat Width of a mat Measured using Length of a blanket foot Width of a blanket Measured using pace d) Length of your class room Width of your class room Measurement 45
Example 4: Tick the most suitable non-standard unit to measure the lengths of the following objects. One is done for you. Object Hand span Cubit Book Blackboard Laptop Bed I Explore (H.O.T.S.) Estimation of lengths and distances Sometimes, we need not know the exact length of an object. A value closer to the actual value will be enough. In such cases, we guess the lengths and distances. To guess the values is called estimation. Let us now understand estimation of lengths. Example 5: Estimate the lengths of the given objects using your hands and feet. Write the values in a table. Check if your guess is close to the actual measure. a) Maths textbook b) Lunch box c) Water bottle d) Desk e) Duster f) Teacher’s table g) Class cupboard h) Height of your classroom door 46
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