MATHEMATICS TEXTBOOK – PART 2 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. ClassKlap 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 S tudent engagement through simple, age-appropriate language Supported 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 Word 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 ClassKlap 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
Contents 2Class 6 Time 6.1 Days of a Week and Months of a Year........................................................ 1 6.2 Sequence the Events Over Longer Periods................................................. 7 7 Money 77.1 Add and Subtract Money without Conversion......................................... 13 08 Multiplication 1 +8.1 Concept of Repeated Addition................................................................. 18 3 -8.2 Skip Counting............................................................................................... 22 9456 x9 Measurements 8 29.1 Measure Lengths Using Standard Units...................................................... 32 9.2 Compare Objects Using a Simple Balance.............................................. 39 9.3 Compare Containers for Capacities......................................................... 43 10 Data Handling 10.1 Pictographs.................................................................................................. 49
Chapter Time 6 Let Us Learn About • days of the week and months of the year. • the terms ‘decade’ and ‘century’. • features of a calendar. • seasons in a year. • s equence of events occurring over long periods. • reading and writing time. Concept 6.1: Days of a Week and Months of a Year Think On 18th February, David’s mother planned to take the family on a picnic. They planned to go after the 2nd week of the next month. David wanted to know the exact date of the picnic. Do you know how David would know the exact date? Recall We do many activities throughout the day. Each activity takes some time to complete. Some events finish soon, while the others take more time. 1
Tick the activity that takes more time in each of the following pairs. a) b) c) & Remembering and Understanding We see the days and months of a year in a calendar. Observe the given calendar. The days of the week in your class timetable can also be seen in this calendar. But it has another day which is not there in your class timetable. Do you know which day it is? 2
Calendar of 2019 January Sat February Sat March Sat Sun Mon Tue Wed Thu Fri 5 Sun Mon Tue Wed Thu Fri 2 Sun Mon Tue Wed Thu Fri 2 12 9 31 1 9 1234 19 1 16 345678 16 6 7 8 9 10 11 26 345678 23 10 11 12 13 14 15 23 13 14 15 16 17 18 10 11 12 13 14 15 17 18 19 20 21 22 30 20 21 22 23 24 25 17 18 19 20 21 22 24 25 26 27 28 29 27 28 29 30 31 24 25 26 27 28 April Sat May Sat June Sat Sun Mon Tue Wed Thu Fri 6 Sun Mon Tue Wed Thu Fri 4 Sun Mon Tue Wed Thu Fri 1 13 11 30 8 12345 20 123 18 234567 15 7 8 9 10 11 12 27 5 6 7 8 9 10 25 9 10 11 12 13 14 22 14 15 16 17 18 19 12 13 14 15 16 17 16 17 18 19 20 21 29 21 22 23 24 25 26 19 20 21 22 23 24 23 24 25 26 27 28 28 29 30 26 27 28 29 30 31 july Sat august Sat september Sat Sun Mon Tue Wed Thu Fri 6 Sun Mon Tue Wed Thu Fri 3 Sun Mon Tue Wed Thu Fri 7 13 10 123456 14 12345 20 12 17 8 9 10 11 12 13 21 7 8 9 10 11 12 27 456789 24 15 16 17 18 19 20 28 14 15 16 17 18 19 11 12 13 14 15 16 31 22 23 24 25 26 27 21 22 23 24 25 26 18 19 20 21 22 23 29 30 28 29 30 31 25 26 27 28 29 30 October Sat November Sat December Sat Sun Mon Tue Wed Thu Fri 5 Sun Mon Tue Wed Thu Fri 2 Sun Mon Tue Wed Thu Fri 7 12 9 123456 14 1234 19 1 16 8 9 10 11 12 13 21 6 7 8 9 10 11 26 345678 23 15 16 17 18 19 20 28 13 14 15 16 17 18 10 11 12 13 14 15 30 22 23 24 25 26 27 20 21 22 23 24 25 17 18 19 20 21 22 29 30 31 27 28 29 30 31 24 25 26 27 28 29 The following are the features of a calendar: • Calendar is another way of reading time. • It shows time in days, weeks and months. • Days are given column-wise and dates are given row-wise. • Some calendars show days row-wise and dates column-wise. Time 3
• Some days are marked in red. These indicate holidays or special days. • In some calendars, special days are also written below the date. Week • There are seven days in a week. • The days of the week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. Month • A month has 30 or 31 days. • February is the 2nd month in a year. It has 28 or 29 days. • There are four full weeks in a month. Year A year has 12 months. They are January, February, March, April, May, June, July, August, September, October, November and December. 10 years make a decade. 100 years make a century. Using a calendar, we can know the day and the date. Let us now learn to read it. 4
Example 1: Read the calendar of 2019 carefully. Answer the following questions. a) On which day does 15th August fall? b) How many Sundays are there in the month of June? c) How many weeks are there in February? Solution: a) 15th August is on a Thursday. b) The month of June has five Sundays. c) There are four weeks in February. Example 2: Read the calendar of 2019 and answer the following questions. a) 8th December is Sunday. When is the next Sunday? b) Name the 3rd month of the year. c) Name the 11th month of the year. Solution: a) T here are seven days in a week. So, we add 7 to the given date to get the same day in the next week. 8 + 7 = 15. So, the next Sunday is 15th December. b) March is the 3rd month of the year. c) November is the 11th month of the year. Application The Earth moves around the Sun. It takes around Summer 365 days and 6 hours for one round. Seasons are caused due to the Earth’s movement around the Sun. The three main seasons in a year are: • Summer • Rainy • Winter Winter Rainy These three seasons are spread over the 12 months of a year. In India, the seasons and the months in which they fall are as follows: Time 5
Summer Rainy Winter later days of February later days of June later days of October March July November April August December May September January earlier days of June earlier days of October earlier days of February Example 3: Answer these questions: a) Which season comes before winter? b) Which season falls between winter and rainy? c) Which season is it during August? Solution: a) Rainy season b) Summer season c) Rainy season Example 4: Answer the following questions: a) Which months fall under the rainy season? b) Which season is it in January? c) In which season does the Sun shine brightly? Solution: a) mid-June, July, August, September and mid-October b) Winter season c) Summer season Higher Order Thinking Skills (H.O.T.S.) Read the following examples. Example 5: If today is 9th May and it is summer now, what season was it four months ago? Solution: Winter season (because four months ago it was January). Example 6: If it is rainy now, what season will it be twelve months from now? Solution: Rainy season 6
Concept 6.2: Sequence the Events Over Longer Periods Think David now knows in which part of the day he does different activities. He wants to narrate the activities one after the other along with the time. Do you also want to narrate your daily activities in the same way? Recall When the Sun rises, we know that it is morning. The Sun is right above us at noon. After school, we play with our friends in the evening. We have dinner and go to sleep at night. Let us recall the events in a day. a) Stars twinkle ________ (at noon/at night). b) My father goes for a __________ (morning/noon) walk. c) The paper boy gets newspaper in the (morning/night). d) Boating is done during the _____________ (day-time/night-time). e) I went to the zoo during the ___________ (day-time/night-time). & Remembering and Understanding We use a clock to find time. Numbers from 1 to 12 are written on the face of the clock. Minute Hand Hour Hand Time 7
The clock has two hands: 1) the short hand, known as the ‘hour hand’, and 2) the long hand, called the ‘minute hand’. Reading time When the minute hand points to 12 and the hour hand to any one of the numbers, we read it as the time at that hour. When the hour hand is on 3 and the minute hand on 12, we say it is 3 o’clock. For every one complete round of the minute hand, the hour hand moves forward to the next number. This means that one hour is completed. Example 7: Read the time shown on these clocks. a) b) Solution: We can read the time as: a) The minute hand is on 12 and the hour hand is on 5. The time is 5 o’clock. b) 8 The minute hand is on 12 and the hour hand is on 8. The time is 8 o’clock.
Example 8: Read the time on these clocks and mention where the hour and the minute hands are. a) b) Solution: We can read the time as: The minute hand is on 12 and the hour hand is on 10. The time is 10 o’clock. a) The minute hand is on 12 and the hour hand is on 11. The time is 11 o’clock. b) Application We have learnt to read time from the clock. Let us now write activities in a sequence. Example 9: Arrange the following events according to the sequence in which they happen. Time 9
a) C utting woods at b) P acking bag at c) H iking to reach the 5 o’clock in the 10 o’clock in the site at 12 o’clock evening morning in the noon d) cooking food for dinner at e) b uilding the camp at 7 o’clock in the night 2 o’clock in the afternoon Solution: Order in which the event happened is: b) c) e) a) d) Example 10: Look at the clocks and write the time. Also arrange the events. One is done for you. a) I drink milk and have b) I eat my snacks and c) I watch TV at my breakfast at do homework at _____ o’clock in the _____ o’clock in the _____ o’clock at night. morning. evening. 10
d) I go to bed at e) I reach school at f) I have my dinner at _____ o’clock at night. _____ o’clock in the _____ o’clock at night. g) I go to play at morning. i) I come home from h) I have my lunch at school at _____ o’clock in the _____ o’clock in the _____ o’clock in the evening. afternoon. afternoon. Solution: a) e) h) i) b) g) c) f) d) Higher Order Thinking Skills (H.O.T.S.) Let us learn to draw hands on the clock when time is given. Example 11: Draw the hands of the clock to show the given time. One is done for you. Time 11
Solution: We can draw the hands of the clock as: e) a) b) c) d) 2 o’clock 12 o’clock 10 o’clock 11 o’clock 4 o’clock f) g) h) i) 3 o’clock 5 o’clock 8 o’clock 9 o’clock Drill Time Concept 6.1: Days of a Week and Months of a Year 1) Name the seasons that fall in the following months. a) later days of October b) January c) April d) earlier days of June e) December 2) Read the calendar of February 2019 and answer the following. a) How many days does it have? FEBRUARY b) How many weeks does it have? Sun Mon Tue Wed Thu Fri Sat c) If 20th is a Monday, when is the next Monday? d) What is the date on the last day? 12 e) How many Saturdays are there? 3456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Concept 6.2: Sequence the Events Over Longer Periods 3) Read the time shown by the clocks given below. a) b) c) d) e) f) 4) Number the pictures in sequence in each of the following. Begin with 1 for the first activity. 12
Chapter Money 7 Let Us Learn About • a dding and subtracting amounts without conversion. • estimation of amounts. Concept 7.1: Add and Subtract Money without Conversion Think David and his mother bought a few items from a shop. When David’s mother paid the bill, the shopkeeper gave her some change. David wondered why the shopkeeper gave his mother some money. Do you know why? Recall We add or subtract numbers by writing them one below the other. This method is called the column method. 13
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 & Remembering and Understanding Money is written in rupees and paise, separated by a dot. In the column method, we write rupees under rupees. Then we write paise under paise, exactly one below the other. When paise is not given, we put 00 in the paise column. Then we add or subtract as usual. Addition of money Let us understand adding amounts 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. `p `p Write the sum in the paise 45 . 50 11 . 11 column. +32 . 20 +22 . 22 70 14
Steps Solved Solve these Step 2: Add the rupees. `p `p Write the sum in the 45 . 50 20 . 19 rupees column. +32 . 20 +32 . 20 77 . 70 Subtraction of money Let us understand subtracting amounts 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 `p Step 1: Subtract the paise. `p Write the difference in the 75 . 60 45 . 45 paise column. –25 . 40 –12 . 12 Step 2: Subtract the rupees. 20 `p Write the difference in the 98 . 43 rupees column. `p –46 . 22 75 . 60 –25 . 40 50 . 20 Application Let us see some real-life examples of addition and subtraction of money. Example 3: Five bananas cost ` 20 and two pencils cost ` 12. What is their Solution: total cost? ` Cost of five bananas = ` 20 20 Cost of two pencils = ` 12 +12 Their sum = ` 20 + ` 12 = ` 32 32 So, the total cost of bananas and pencils is ` 32. Money 15
Example 4: Veer bought a ball for ` 10 and gave the shopkeeper ` 20. How much change did the shopkeeper give Veer? Solution: The amount Veer paid the shopkeeper = ` 20 ` Cost of a ball = ` 10 20 Difference in the amounts = ` 20 – ` 10 = ` 10 –10 So, the shopkeeper gave back ` 10. 10 Higher Order Thinking Skills (H.O.T.S.) Read a few 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 few of the possible combinations are: a) Combination 1 b) Combination 2 ` 100 ` 250 ` 150 ` 100 ` 350 16
c) Combination 3 d) Combination 4 ` 150 ` 350 ` 250 ` 200 Drill Time Concept 7.1: Add and Subtract Money without Conversion 1) Add: b) ` 35.88 + ` 12.11 c) ` 46.37 + ` 10.10 a) ` 27.17 + ` 12.12 e) ` 11.11 + ` 22.22 d) ` 87.22 + ` 12.77 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 3) Word problems a) Abdul has ` 52 and Shama has ` 15.00. How much money do they have in all? b) Sam bought chocolates for ` 41.00. Rehan bought some chocolates for ` 24. How much amount did they spend in all? Money 17
Chapter Multiplication 8 Let Us Learn About • repeated addition. • skip counting. • multiplication tables from 2 to 6. Concept 8.1: Concept of Repeated Addition Think David has five pet cats. He wants to know the number of legs they have altogether. How can David find that? Recall We already know how to add some objects by counting. Let us recall the same through the following exercise. 18
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 = ___________ Multiplication 19
& Remembering and Understanding Repeated addition is adding the same number repeatedly (again and again). We put the objects into equal groups to find their total. Let us see a few examples. E xample 1: Use repeated addition to find the total number of houses. Solution: Number of groups = 4 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 is 8. Example 2: Count and add: Solution: Number of groups = 3 Number of equal number of objects in each group = 4 Total number of objects = 4 + 4 + 4 = 12 We read it as 3 groups of 4 is 12. 20
Application Let us now apply the concept of repeated addition. Example 3: 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 is 12. Therefore, the three dogs have 12 legs altogether. Example 4: A star has 5 corners. How many corners will such 4 stars have? Number of stars (groups) = 4 Solution: Number of corners (objects) in each star = 5 That is, 5 + 5 + 5 + 5 = 20. So, 4 groups of 5 is 20. So, 4 stars have 20 corners. Multiplication 21
Higher Order Thinking Skills (H.O.T.S.) Let us see an example based on repeated addition. Example 5: Sudha wanted to buy beads to make necklaces for her daughter and for herself. To make a necklace, she needs at least 25 beads. How many beads are needed to make necklaces for both of them? Solution: Number of necklaces (groups) = 2 Number of beads (objects) = 25 That is, 25 + 25 = 50. So, 2 groups of 25 = 50. So, the total number of beads required to make two necklaces is 50. Concept 8.2: Skip Counting Think While playing hopscotch, David knows to jump by skipping some of the boxes. Similarly, he can count numbers by skipping some of them. How could he do that? Recall Recall the concept of repeated addition through these examples. [] Write the values of the following. a) 5 groups of 2 22
b) 3 groups of 9 [ ] c) 2 groups of 8 [] d) 6 groups of 1 [] & Remembering and Understanding Skip Counting is counting by a number that is not 1. It helps you • to count many things quickly. • to learn multiplication tables. Count by 2s In counting by 2s, we begin with the given number and count every alternate number. Example 6: Help the frog to find its way to the snail using skip counting by 2. Write the numbers on which it jumps. One is done for you. a) Multiplication 23
b) c) Count by 3s In counting by 3s, we count every third number from the given number. Example 7: Begin with the given number and count by 3s. Write the numbers in the boxes given. One is done for you. a) b) c) We now know the concepts of repeated addition and skip counting. Let us now learn to construct the multiplication tables of numbers from 2 to 6. 24
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. Multiplication 25
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. 26
The following are the multiplication tables of 3, 4, 5 and 6. Read them aloud. 3 4 5 6 3×1=3 4×1=4 5×1=5 6×1=6 3×2=6 4×2=8 5 × 2 = 10 6 × 2 = 12 3×3=9 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 Application Let us solve some examples using the concept of skip counting. Example 8: Show the path the rabbit takes to reach the carrot by crossing the boxes using skip counting by 3. START 1 20 21 40 41 2 19 22 39 42 3 18 23 38 43 4 17 24 37 44 5 16 25 36 45 6 15 26 35 46 7 14 27 34 47 8 13 28 33 48 9 12 29 32 49 10 11 30 31 50 END Multiplication 27
Solution: START 1 20 21 40 41 2 19 22 39 42 3 18 23 38 43 END 4 17 24 37 44 5 16 25 36 45 6 15 26 35 46 7 14 27 34 47 8 13 28 33 48 9 12 29 32 49 10 11 30 31 50 Example 9: Radha counts the balloons using skip counting by 8. Write the numbers in the boxes. How many balloons are there altogether? Solution: 8 16 24 32 40 48 56 There are 56 balloons altogether. 28
Higher Order Thinking Skills (H.O.T.S.) Let us see another example of skip counting. Example 10: Complete the wheel of skip counting by 3 and 5. Solution: We can skip count by 3 and 5. Drill Time Concept 8.1: Concept of Repeated Addition 1) Count and add: a) b) Multiplication 29
c) d) 2) Word problems a) S eeta observed that there were 4 cars parked in a row. How many wheels could she count on the cars? b) A farm had 6 hens. How many legs do they have in all? Concept 8.2: Skip Counting 3) Skip count and fill in the blanks. a) Skip count by 2 8 2 30
b) Skip count by 3 15 3 c) Skip count by 4 4 24 d) Skip count by 5 5 45 4) Word problems a) H arry counts some flowers using skip counting by 5. How many flowers does he count altogether? b) S aket counts sheep using skip counting by 4. How many sheep does he count altogether? Multiplication 31
Chapter Measurements 9 Let Us Learn About • m easuring lengths and distances using standard units. • c omparing weights of two or more objects. • u sing simple balance to compare weights. • ordering containers based on their capacities. Concept 9.1: Measure Lengths Using Standard Units Think David’s mother bought 3 cubits of garland. David observed that the same garland measured 5 cubits with his cubit. He wondered how he got more cubits than his mother. Do you know the reason for the difference? Recall Remember that the length of an object is the distance between its two ends. We can measure the lengths of long objects using some shorter objects. Also, we can measure objects using our hands, palm, foot and so on. 32
hand span cubit foot pace For example, consider the following: a) 9 paper clips long b) 5 erasers long c) 12 hand spans long d) 4 crayons long & Remembering and Understanding When different people measure an object using their body parts, they all get different lengths. The measures are different because the length of the body part is different for different people. MMeualstuiprelicmaetinotns 33
So, measures such as hand span, cubit, foot, leg span are called non-standard units. The standard unit of measurement of length is called metre. It is used to measure the length of a room, width of a room, height of a building and so on. We also use metre to measure the amount of cloth needed to make a dress. The unit ‘metre’ is written in short as ‘m’. To measure lengths smaller than a metre, we use another unit called the centimetre. Centimetre is used to measure a line, length of a ribbon and so on. We write ‘centimetre’ in short as ‘cm’. To measure lengths larger than a metre we use a larger unit called the ‘kilometre’. It is written in short as ‘km’. It is used to measure the length of a road, the distance between two places, lengths of bridges, tunnels and so on. Thus, 1 km > 1 m > 1 cm Using these standard units, we can measure the lengths of objects accurately. Standard units give the same measure of the object anywhere in the world. The standard instruments used to measure length are a ruler (or a scale), a measuring tape and so on. A ruler is used to measure the length in centimetres and inches. A measuring tape is used to measure longer lengths in metres and kilometres. Measuring objects using a ruler A ruler is made of plastic or metal. It has two scales on both sides as shown below. On one side, there is a centimetre scale and on the other side is the inch scale. We measure lengths of small objects such as a chalk, duster, sketch pen, pencil, pencil box and so on using any of these scales. The distance between 0 and the number at the other end of the object on a ruler is the length of the object. 34
To measure the length of an object using a ruler, follow these steps: Step 1: Keep one end of the object at the zero of the ruler. Step 2: Note the number on the ruler which is at the other end of the object. Step 3: Write the units beside the number noted in step 2. The number along with the unit denotes the length of the object. Observe the following: a) The distance between the two ends of the pencil is 6 cm. So, the pencil is 6 cm long. Similarly, b) The water bottle is 12 cm long. c) The cell phone is 9 cm long. MMeualstuiprelicmaetinotns 35
Let us consider a few examples. Example 1: Measure these objects and write their lengths with the correct unit. One is done for you. Example 2: Measure the length of these pictures using your own ruler. Note down their lengths. S. No. Picture Length a) b) c) d) e) 36
Application We measure longer objects in metres and distances in kilometres. Let us now learn how these units are related. On the centimetre ruler, we see that the distance between any two consecutive numbers is 1 cm. We see 10 equal divisions in a centimetre. Each of these divisions is called a ‘millimetre’, written in short as ‘mm’. Example 3: Tick the unit used to measure the lengths of the following. One is done for you. Object cm Units km Blue whale m Book Toothbrush Table Road MMeualstuiprelicmaetinotns 37
Example 4: Tick the unit used to measure the following. One is done for you. Object Units mm cm m km Window Ribbon Rope Cloth Higher Order Thinking Skills (H.O.T.S.) Let us see an example involving standard and non-standard units. Example 5: The length of Shyam’s hand span is 8 centimetres. He measured the length of a table as 5 hand spans. What is the length of the table in centimetres? Solution: The length of Shyam’s hand span = 8 centimetres The length of the table = 5 hand spans The length of the table in centimetres = 5 × 8 centimetres = 40 centimetres So, the table is 40 cm long. 38
Concept 9.2: Compare Objects Using a Simple Balance Think David’s mother bought some flowers. She found that the flowers were lighter than what she had asked for. David’s mother weighted the flowers using a simple balance and found that she was right. Why was there a difference? Recall We have learnt how to guess the heaviness of objects based on their size. Let us answer the following to recall heavy and light objects. Write heavier or lighter in the blanks. One is done for you. 3 balls are heavier than 1 ball. The cabbage is __________ than the potato. MMeualstuiprelicmaetinotns 39
2 lotuses are _____________ than 2 The capsicum is ______________ than roses. the pumpkin. & Remembering and Understanding The standard instrument used to measure the weight of an object is the simple balance. The standard units of weight are gram and kilogram. We write grams as g and kilograms as kg. A smaller unit of weight is milligram written as mg. For example, tablets, spices and so on are measured using milligrams. Heavier objects such as pencils, cereals and so on are measured using grams. Objects heavier than the ones given above need a greater unit of measurement. We use kilograms to measure such objects. Dal, rice, sugar, wheat and so on are measured in kilograms. Weights of objects such as watermelon, human beings and books are measured in kilograms. 40
5 kg 6 kg 1 kg Thus, 1 kg > 1 g > 1 mg Example 6: Tick the unit used to measure the following. One has been done for you. Objects mg g kg a) b) c) d) e) MMeualstuiprelicmaetinotns 41
Application Jewellers use grams to weigh ornaments. 10 g of jewellery is called a ‘tola’. Let us see an example where we need to use standard units of weights. Example 7: Write the unit that must be used to measure the weights of the following objects. One is done for you. g Higher Order Thinking Skills (H.O.T.S.) We can weigh objects using a simple balance and the weights. To weigh an object, we place it on the left pan of the balance and add the weights on the right pan. When both pans are at the same level, we say that the beam is balanced. We then read the total weights put on the pan. This gives the weight of the object. From the given figure, we see that the weight of the watermelon is 5 kg. 42
Example 8 : Observe the figures and write the weights of the given objects. One is done for you. a) 1 kg + 1 kg + 1 kg = 3 kg b) The pumpkin weighs The dog weighs 3 kg . __________kg. Concept 9.3: Compare Containers for Capacities Think David saw glasses of different sizes in his kitchen. He wondered why so many types of glasses were needed. He also observed that the glasses he used to drink water and milk were different. Why do you think we use containers of different sizes? Recall Recall that we use vessels and containers of different sizes. A tub can hold more water than a bucket. Similarly, a bucket can hold more water than a jug. The capacity or volume of a container is the quantity of water or any other liquid that it can hold. There are different types of vessels based on their capacities. Glasses, bottles, jugs and so on are non-standard units to measure liquids. MMeualstuiprelicmaetinotns 43
Observe these containers and order them based on their capacity. Write 1 for the smallest container. 9.3 I Remember and Understand The standard units of capacity are millilitres, litres and kilolitres. The following figure shows different containers used for measuring capacity: Small quantities of liquids such as tonic doses are measured in millilitres, written as ‘mℓ’. Quantities of oil, milk, fruit juices and so on are measured in litres, written as ‘ℓ’. Larger quantities such as petrol in tankers are measured in kilolitres, written as ‘kℓ’. Thus, 1 kℓ > 1 ℓ > 1 mℓ Example 9: Tick the units used to measure the following. One has been done for you. 44
Container Units ℓ mℓ Example 10: Circle the vessel which uses the given unit of capacity. One is done for you. Unit of Vessels capacity ℓ MMeualstuiprelicmaetinotns 45
Unit of Vessels capacity mℓ ℓ Application Let us see some real-life examples involving measurement of capacities. Example 11: Renu has 38 litres of orange juice in a bucket. A jug that can hold 2 litres is used five times to fill the juice glasses. How much juice is remaining in the bucket? Solution: Quantity of orange juice in the bucket = 38 ℓ Quantity of orange juice a jug can hold = 2 ℓ The jug was used 5 times. So, the quantity of the orange juice poured in the juice glasses is 2 ℓ × 5 = 10 ℓ Quantity of the orange juice remaining in the bucket is (38 – 10) litres = 28 litres So, 28 litres of orange juice is remaining in the bucket. 46
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