9789387653764_Alpine-G2-Maths-FY_Textbook

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 97 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p1d/f_1_2_0101 / 120 23-01-2018 19:24:18

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. Let us look at the examples and solve them to understand the concept. Example 9: Tick the units used to measure the following. One has been done for you. 98 23-01-2018 19:24:32 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p2d/f_1_2_0102 / 120

Container Units ℓ mℓ  Example 10: Circle the vessel which uses the given unit of capacity. One has been done for you. Unit of Vessels capacity ℓ MMeualstuiprelicmaetinotns 99 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p3d/f_1_2_0103 / 120 23-01-2018 19:24:43

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. 100 23-01-2018 19:24:46 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p4d/f_1_2_0104 / 120

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. Higher Order Thinking Skills (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 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. 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) MMeualstuiprelicmaetinotns 101 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p5d/f_1_2_0105 / 120 23-01-2018 19:24:47

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) R akesh’s bag weighs 5 kg. His sister’s bag weights 4 kg. What is the total weight of their bags? Concept 9.3: Compare Containers for Capacities 4) What are the units used to measure the capacities of the following? a) b) 102 23-01-2018 19:24:50 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p6d/f_1_2_0106 / 120

c) d) 5) Word problems a) Salma 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? MMeualstuiprelicmaetinotns 103 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p7d/f_1_2_0107 / 120 23-01-2018 19:24:50

Chapter Data Handling 10 Let Us Learn About • the term ‘pictograph’. • reading a pictograph. • p resenting information through a pictograph. Concept 10.1: Pictographs 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? 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. 104 23-01-2018 19:24:53 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p8d/f_1_2_0108 / 120

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? [ ] & Remembering and Understanding In class 1, we have learnt to make collections. We showed a collection by drawing pictures of the given things. DMautaltiHpalicnadtlinogn 105 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t0.p9d/f_1_2_0109 / 120 23-01-2018 19:24:55

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 106 23-01-2018 19:24:55 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p0d/f_1_2_0110 / 120

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) make 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 picture symbols is called a pictograph. To read a pictograph, we: a) look at the given key. b) multiply the given number of pictures with the value of the key. Key: A key on a pictograph tells us how many objects each picture stands for. Consider these examples. Example 1: If = 10 strawberries, then means how many strawberries? Solution: = 10 strawberries (Given). So, = 3 × 10 strawberries = 30 strawberries DMautaltiHpalicnadtlinogn 107 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p1d/f_1_2_0111 / 120 23-01-2018 19:24:58

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 108 23-01-2018 19:25:05 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p2d/f_1_2_0112 / 120

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) T he number of symbols given for Wednesday is 3. S o, the number of cakes baked on Wednesday is 3 × 5 cakes = 15 cakes. Application 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 DMautaltiHpalicnadtlinogn 109 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p3d/f_1_2_0113 / 120 23-01-2018 19:25:06

Pet Number of students a) How many students are present in the class? b) How many students have a pet dog? c) How many students have a pet cat? 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 110 23-01-2018 19:25:08 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p4d/f_1_2_0114 / 120

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) T he minimum number of symbols is given for the fish. So,the least number of students have fish as pets. Example 5: The given pictograph shows the grades that students of Class 2 got in an exam. Read the pictograph and complete the table. Answer the questions that follow. Key: = 2 students; = 1 student A+: Excellent, A: Very Good, B+: Good B: Fair, C: Better, D: Satisfactory, F: Fail DMautaltiHpalicnadtlinogn 111 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p5d/f_1_2_0115 / 120 23-01-2018 19:25:09

Grade Grades of the Students Number of students A+ Students A B+ B C D F Total a) How many students are there in the class? b) How many grades are there? Solution: c) How many students got A+ grade? d) 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 112 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p6d/f_1_2_0116 / 120 23-01-2018 19:25:12

There are 48 students in the class. b) There are 7 grades. c) 6 students got A+ grade. d) Maximum number of students got the B+ grade. Higher Order Thinking Skills (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 Flower pots sold on a day Marigold Jasmine Tulip Daisy Lily DMautaltiHpalicnadtlinogn 113 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p7d/f_1_2_0117 / 120 23-01-2018 19:25:13

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. 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 Group Number of students Group 1 Group 2 Group 3 Group 4 Group 5 114 23-01-2018 19:25:13 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p8d/f_1_2_0118 / 120

a) Which group has the maximum number of students? b) How many students are there in Group 4? c) Which group has 20 students? 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 Rita Sameera Rakesh a) W ho has the minimum number of sharpeners? b) H ow many sharpeners are there in all? c) W ho has two sharpeners? d) Who has the maximum number of sharpeners? e) Who has four sharpeners? 3) The pictograph shows the number of ice creams that each kid ate. Use the pictograph to answer the questions. Key: 1 = 3 ice creams DMautaltiHpalicnadtlinogn 115 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t1.p9d/f_1_2_0119 / 120 23-01-2018 19:25:14

Name of the Kid Number of ice creams Vinay Swaroop Mahesh Rehana a) W ho ate the minimum number of ice creams? b) Which kid ate three ice creams? c) W ho ate the maximum number of ice creams? 116 23-01-2018 19:25:14 5JS17N0R4_9B0G3_MBGPoMlicPyo_l1ic8y1_091708091318_7A6l5p3in7e6-4G_2A-lMpianteh-sG-F2Y-M_aTtehxst-bFoYo_kT_eTxetxbto.podkf__T_e_x1t2.p0d/f_1_2_0120 / 120