9.1 I Explore (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. Concept 9.2: Compare Objects Using a Simple Balance I 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? 9.2 I 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. Measurements 47 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 51 12/19/2018 11:11:44 AM
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. 2 lotuses are _____________ than 2 The capsicum is ______________ than roses. the pumpkin. 9.2 I Remember and Understand The standard instrument used to measure the weight of an object is the simple balance. The standard units of weight are gram and kilogram. Comparison between We write grams as g and kilograms as kg. the units of weight A smaller unit of weight is milligram written as mg. 1 kg > 1 g > 1 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. 48 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 52
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. 5 kg 6 kg 1 kg Example 6: Tick the unit used to measure the following. One has been done for you. Objects mg g kg a) b) c) Measurements 49 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 53 12/19/2018 11:11:44 AM
Objects mg g kg d) e) Jewellers use grams to weigh ornaments. 10 g of jewellery is called a ‘tola’. Train My Brain Tick the unit used to measure the following: Objects mg g kg 50 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 54
9.2 I Apply 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 9.2 I Explore (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. Example 8 : Observe the figures and write the weights of the given objects. One is done for you. Measurements 51 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 55 12/19/2018 11:11:44 AM
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 I 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? 9.3 I 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. 52 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 56
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: Comparison between the units of capacity 1 kℓ > 1 ℓ > 1 mℓ 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’. Example 9: Tick the units used to measure the following. One has been done for you. Container Units ℓ mℓ Measurements 53 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 57 12/19/2018 11:11:44 AM
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 54 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 58
Unit of Vessels capacity mℓ ℓ Train My Brain Tick the unit used to measure the following: Container mℓ ℓ kℓ Measurements 55 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 59 12/19/2018 11:11:44 AM
9.3 I Apply 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. Example 12: Milk from two full jugs each measuring 55 litres is poured into a bucket of 200 litres. How many more litres of milk can the bucket hold? Solution: Capacity of the bucket = 200 litres Quantity of milk poured into the bucket = 55 litres + 55 litres = 110 litres Difference in capacities = (200 – 110) litres = 90 litres So, the bucket can hold 90 more litres of milk. 9.3 I Explore (H.O.T.S.) Let us now see how we use standard units of volumes in a few real-life situations. Example 13: Sravan pours 6 glasses of juice into a jug. If each glass measures 250 mℓ, how much juice is in the jug? Solution: Number of glasses of juice poured in the jug = 6 56 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 60
Quantity of juice in each glass = 250 mℓ Total quantity of juice in the jug = 250 mℓ + 250 mℓ + 250 mℓ + 250 mℓ + 250 mℓ + 250 mℓ = 1500 mℓ So, the quantity of juice in the jar is 1500 mℓ. Maths Munchies 213 To measure weights larger than kilograms, we use tonnes. 1 tonne = 1000 kg To measure weights smaller than 1 gram, we can use milligrams and micrograms. Connect the Dots EVS Fun See your pictures from when you were a baby and now. What differences do you see? Can you make out any changes in your height? Now observe any non-living thing like the furniture in those pictures. Try and compare it to the same thing now. Are there any visible changes in their length or height? Thus, we conclude that living things grow in size whereas non-living things remain of the same height. English Fun The standard units are given in a jumbled form below. Unjumble the letters to form the correct words. MTEER – ________________________ KILMTREEO – ________________________ RGAM – ________________________ ERTIL – ___________________ Measurements 57 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 61 12/19/2018 11:11:44 AM
Drill Time Concept 9.1: Measure Lengths Using Standard Units 1) What is the unit used to measure the length of a side in each of the following figures? a) b) c) d) Concept 9.2: Compare Objects Using a Simple Balance 2) Which unit should be used to measure the weight of the following? a) b) c) d) 3) Word problems a) Robin bought 3 kg of wheat and 15 kg of rice. Which item did he buy more? b) Rakesh’s bag weighs 5 kg. His sister’s bag weighs 4 kg. What is the total weight of their bags? 58 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 62
Drill Time Concept 9.3: Compare Containers for Capacities 4) W hat are the units used to measure the capacities of the following? a) b) c) d) 5) Word problems a) S alma has 22 litres of water in a bucket. She has a jug that can hold 2 litres. She uses 11 times to fill the bucket. How much water is remaining in the bucket? b) Juice from two full jugs each measuring 40 litres is poured into a drum of 120 litres. How many more litres of juice can the drum hold? A Note to Parent When you visit a grocery store or a supermarket, help your child to experience all the measurements practically. Go to various sections like clothes, groceries and fresh products. In each section, you can explain the different types of measurement with real examples. Measurements 59 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 63 12/19/2018 11:11:44 AM
Chapter Data Handling 10 I Will Learn About • the term ‘pictograph’. • reading a pictograph. • p resenting information through a pictograph. Concept 10.1: Pictographs I Think David saw fruits of different colours in a basket. He wanted to count the number of fruits of each colour. How should David note them down? 10.1 I Recall Let us recall the concepts that we have already learnt. Data: A series of facts collected for some particular use is called data. Collection: A group of objects or items taken together is called a collection. 60 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 64
Arun has some toys with him as shown in this picture. Observe his collection and answer the questions. Cars Cars Bus Truck Cycle Bus Bike a) How many toys does Arun have? [ ] b) Which toy is maximum in number? [ ] c) Which toys are minimum in number? [ ] d) How many toy cars does Arun have? [ ] e) How many toy buses does Arun have? [ ] 10.1 I Remember and Understand In class 1, we have learnt to make collections. We showed a collection by drawing pictures of the given things. Data Handling 61 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 65 12/19/2018 11:11:44 AM
Consider the following examples of collections: 1) List of students in a class whose names begin with the letter ‘S’. List of students in a class whose names begin with the letter ‘S’. S. No. Name of the Student 1) Sampath Kumar 2) Sai Nikilesh 3) Srikanth 4) Sharath Chandra 5) Suraj 6) Saritha 7) Sowjanya 8) Sukanya 2) List of people with their phone numbers. List of people with their phone numbers S. No. Name of the person Phone number 1) 2) Sharath Chandra 9246070416 3) 4) Saritha 9413820164 5) Sukanya 9964712741 Suraj 9347938472 Sowjanya 9834562366 62 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 66
3) List of different types of dresses. List of different types of dresses S. No. Dress Number of dresses 1) Frock 5 2) Jeans 9 3) T-shirt 4 In the same way, a) m ake a list of the objects that are in your school bag. b) m ake a list of things that you take on a picnic. Making a list of items may take a lot of time if there are many items. Hence, it is necessary to use a pictograph. Pictograph: Listing the different data items using A key on a pictograph tells picture symbols is called a pictograph. us how many objects each picture stands for. To read a pictograph, we: a) look at the given key. b) multiply the given number of pictures with the value of the key. Consider these examples. Example 1: If = 10 strawberries, then means how many strawberries? Solution: = 10 strawberries (Given). So, = 3 × 10 strawberries = 30 strawberries Data Handling 63 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 67 12/19/2018 11:11:44 AM
Example 2: If = 4 cupcakes, then means how many cupcakes? Solution: = 4 cupcakes (Given) So, = 2 × 4 cupcakes = 8 cupcakes Example 3: The number of cakes baked in a week is given in a pictograph. Observe the given pictograph and answer the questions. Key: = 5 cakes Day of the week Number of cakes baked in the week Sunday Monday Tuesday Wednesday Thursday Friday Saturday 64 12/19/2018 11:11:45 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 68
a) How many cakes were baked on Thursday? b) On which day were the highest number of cakes baked? c) On which day were the least number of cakes baked? d) How many cakes were baked on Wednesday? Solution: a) N umber of cakes baked on Thursday = 1 =1 × 5 cakes = 5 cakes b) The highest number of symbols given is for Sunday. So, the highest number of cakes were baked on Sunday. c) T he least number of symbols given is for Thursday. So, the least number of cakes were baked on Thursday. d) The number of symbols given for Wednesday is 3. S o, the number of cakes baked on Wednesday is 3 × 5 cakes = 15 cakes. Train My Brain Your class plans to watch a movie. The teacher asks you to pick a symbol and a key. The number of students who want to watch each movie is given. Make a pictograph based on the data given. 14 children voted for The Little Mermaid. 10 children voted for The Toy Story. 12 children voted for Inside Out. 8 children voted for Bolt. Data Handling 65 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 69 12/19/2018 11:11:45 AM
10.1 I Apply Let us learn more about pictographs through these examples. Example 4: The number of students in a class having pets is given in the pictograph. Understand it and answer the questions. Key: 1 = 4 students, 1 = 2 students Pet Number of students a) How many students are present in the class? 12/19/2018 11:11:45 AM b) How many students have a pet dog? c) How many students have a pet cat? 66 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 70
d) Which pet does the maximum number of students have? e) Which pet does the minimum number of students have? Solution: a) 1 = 4 students So, 10 = 4 × 10 students = 40 students = 2 students So, 3 = 6 students S o, the total number of students present in the class = 40 + 6 = 46 students. b) 1 = 4 students So, 3 = 3 × 4 students = 12 students 1 = 2 students So, number of students who have a pet dog = 12 + 2 = 14. c) 1 = 4 students So, 2 = 2 × 4 students = 8 students 1 = 2 students So, the number of students who have a pet cat = 8 + 2 = 10. d) T he maximum number of symbols is given for the dog. So, most of the students have dogs as pets. e) The minimum number of symbols is given for the fish. So,the least number of students have fish as pets. Data Handling 67 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 71 12/19/2018 11:11:45 AM
Example 5: The given pictograph shows the grades that students of Class 2 got in an exam. Read the pictograph and complete the table. Key: = 2 students; = 1 student A+: Excellent, A: Very Good, B+: Good F: Fail B: Fair, C: Better, D: Satisfactory, Grade Grades of the Students Number of students Students A+ A B+ B C D F Total 68 12/19/2018 11:11:45 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 72
a) How many students are there in the class? b) How many grades are there? c) How many students failed in the exam? Solution: d) How many students got A+ grade? e) Which grade is obtained by most number of the students? a) Grade A+ A B+ B C D F Total 6 9 13 8 7 4 1 48 Number of students There are 48 students in the class. b) There are 7 grades. c) 1 student failed in the exam. d) 6 students got A+ grade. e) Maximum number of students got the B+ grade. 10.1 I Explore (H.O.T.S.) We have learnt how to read a pictograph. Now, let us learn to draw a pictograph when some data is given. Example 6: The number of flower pots sold in a nursery on one day are 12 Marigold, 21 Jasmine, 9 Tulip, 6 Daisy and 6 Lily. Represent the data in a pictograph taking a symbol equal to three flower pots. Then answer the questions that follow. a) Which flower pots were sold the maximum? b) Which flower pots were sold in equal number? c) How many tulip flower pots were sold? Solution: = 3 flower pots Data Handling 69 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 73 12/19/2018 11:11:45 AM
Flower pots sold on a day Marigold Jasmine Tulip Daisy Lily 213 a) Jasmine flower pots were sold the maximum. b) Daisy and lily flower pots were sold in equal number. c) = 3 flower pots = 3 × 3 = 9 flower pots. So, 9 tulip flower pots were sold. Maths Munchies Pictographs are also known as pictograms. They are not only used in Maths but also in other subjects. Their use started many years ago when pictures were the main form of writing. Connect the Dots EVS Fun Make a list of the students in your class who come by bus, bicycle and auto rickshaw. Do you think we can use a pictograph to decide the mode of transportation used the most? 70 12/19/2018 11:11:45 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 74
English Fun Did you know that the word ‘pictograph’ comes from the Latin language? ‘Picto’ means picture and ‘graph’ means writing. Drill Time Concept 10.1: Pictographs Solve the following: 1) The pictograph shows the number of students in each group. Use the pictograph to answer the questions. Key: 1 = 5 students Number of students Group Group 1 Group 2 Group 3 Group 4 Group 5 a) Which group has the maximum number of students? b) How many students are there in Group 4? c) Which group has 20 students? Data Handling 71 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 75 12/19/2018 11:11:45 AM
Drill Time 2) The pictograph shows the number of sharpeners with each kid. Use the pictograph to answer the questions. Key: 1 = 2 sharpeners Name of the kid Number of sharpeners a) Who has the minimum Rita number of sharpeners? Sameera b) How many sharpeners are there in all? c) Who has two sharpeners? Rakesh 3) The pictograph shows the number of ice creams that each kid ate. Use the pictograph to answer the questions. Name of the Kid Number of ice creams Key: 1 = 3 ice creams Vinay a) Who ate the minimum Swaroop number of ice creams? b) W hich kid ate three ice Mahesh creams? c) Who ate the maximum Rehana number of ice creams? A Note to Parent Let your child help you in planning his or her coming birthday celebration. To decide the menu, help your child make a list of the dishes that each guest likes. Let him or her then record the results and draw a pictograph. 72 12/19/2018 11:11:45 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 76
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