I Explore (H.O.T.S.) Let us now see some more examples where we use the concept of standard units of lengths. Example 4: Ramu’s height is 134 cm and Somu’s height is 1 m 50 cm. Who is taller and by how many centimetres? Solution: To compare the heights of two persons, they must be in the same units. Height of Somu = 1 m 50 cm = 100 cm + 50 cm = 150 cm Height of Ramu = 134 cm 150 cm > 134 cm The difference in their heights is (150 – 134) cm = 16 cm Therefore, Somu is taller than Ramu by 16 cm. Example 5: The figure given is a map. It shows the different ways to reach different places from the house. Post Office Airport 6 km 4 km 2 km School 3 km 8 km House Market 10 km 3 km Railway Station Measurement 47
Look at the map and answer these questions. a) How far is the post office from the house? b) What is the distance between the market and the railway station? c) Find the distance between the house and the airport through the post office? d) Which is closer to the house – post office or market? Solution: e) How far is the railway station from the school? From the map, we see that a) The post office is 3 km from the house. b) T he distance between the market and the railway station is 3 km. c) T hrough the post office, the distance between the house and the airport is 3 km + 6 km = 9 km 10.2 d) Post office is closer to the house. e) The railway station is 10 km from the school. Weigh Mass Using Non-Standard Units I Think Neena’s friend told her that the weight of 2 mangoes is as much as that of 4 apples. Neena wanted to find out if this is true. How will she do this? I Recall We have learnt how to guess the heaviness of objects based on their sizes. We use a simple balance to measure the weights of objects. 48
Let us answer the following to recall heavy and light objects. Write heavier or lighter in the blanks. One has been done for you. 3 balls are heavier than 1 ball. The cabbage is __________ than the potato. The lotus is _____________ than The capsicum is ______________ than the the rose. pumpkin. I Remember and Understand Using a simple balance, The standard instrument we measure the weight of used to measure the an object by comparing it weight of an object is with other objects. the simple balance. Let us observe the simple balance to see how to compare the weight of one object with another. In the given simple balance, both the pans are at the same level. Hence, 1 mango weighs as much as 2 apples. Measurement 49
Example 6: Look at the simple balance and fill in the blanks. Solved Solve these 1 duster weighs as much as 6 pens. 2 glasses of water weigh as much as ________ ball. 4 oranges weigh as much as 3 3 pencil boxes weigh as much as apples. ________ book. ? Train My Brain Compare the weights of these objects: a) b) _____ rabbit weighs as _____ pencil boxes weigh as much as _____ birds. much as _____ bottle. 50
I Apply The standard units of weight are ‘gram’ and ‘kilogram’. Gram is used to measure lighter objects whereas kilogram is used to measure heavier objects. Weights of objects such as cheese, rupee coin and peanuts are measured in grams. 25 g 5g 1g Weights of objects such as watermelon, human beings and books are measured in kilograms. 5 kg 6 kg 1 kg Example 7: Tick the unit used to measure the following. One has been done for you. Object g kg a) b) Measurement 51
Object g kg c) d) Example 8: Write the unit that must be used to measure the weights of the following objects. One has been done for you. Object kg Unit g I Explore (H.O.T.S.) We can weigh objects using the simple balance and the weights. Some of the commonly used weights are as follows. 50 g 100 g 200 g 500 g 1 kg 2 kg 52
To weigh an object, we place it on one of the pans of the balance and add the weights on the other pan. When both the pans are at the same level, we say that the beam is balanced. We then read the total weights put in the pan of the balance. This gives the weight of the object. From the given figure, we see that the weight of a watermelon is 5 kg. Example 9: O bserve the figures and write the weights of the given objects. One has been done for you. a) 1 kg + 1 kg + 1 kg = 3 kg b) The pumpkin weighs The dog weighs 3 kg . __________kg. 10.3 Measure Volume Using Non-Standard Units I Think Neena saw glasses of different sizes in their kitchen. She wondered why so many types of glasses were needed. She also observed that the glasses she used to drink water and milk were different. Why do you think we use containers of different sizes? 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. Measurement 53
Most capacity More capacity Less capacity Least capacity Try this! Observe these containers and order them based on their capacity to hold water. Write 1 for the smallest container. I Remember and Understand 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. Let us see how we can measure the capacities of different containers. If Glasses, bottles, jugs and = so on are non-standard units to measure capacity. 54
Then, =+ Therefore, 2 bottles are equal to 6 mugs. Example 10: Given = Mark out the mugs that are equal to the given jugs. One has been done for you. Jugs Mugs Measurement 55
Example 11: If 10 jugs of water fill a bucket, then, how many jugs are needed to fill 5 buckets? Solution: Jugs required to fill a bucket = 10 Jugs required to fill 5 buckets = 5 × 10 = 50 jugs Therefore, 50 jugs of water are needed to fill 5 buckets. ? Train My Brain 1 0 buckets of water are needed to fill a drum. Then, how many buckets will be needed to fill the following: a) 7 drums b) 4 drums c) 8 drums I Apply The standard units of capacity are ‘millilitre’ and ‘litre’. Small quantities of liquids such as tonic doses are measured in millilitres, written as ‘mℓ’. Larger quantities of liquid such as oil, milk, fruit juices and so on are measured in litres, written as ‘ℓ’. Example 12: T ick the units used to measure the following. One has been done for you. object Units ℓ mℓ 56
object Units mℓ ℓ Example 13: Circle the vessel which uses the given unit of capacity. One has been done for you. Unit of Vessels capacity ℓ mℓ ℓ Measurement 57
I Explore (H.O.T.S.) Let us now see how we use units of volumes in a few real-life situations. Example 14: Circle the vessel which nearly has the capacity given. One has been done for you. Measure Vessels needed 3ℓ 1ℓ 20 ℓ 500 ℓ Maths Munchies 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. 58
Connect the Dots English Fun The standard units are given in a jumbled form below. Unjumble the letters to form the correct words. MTEER - ________________________ KILMTREEO - ________________________ RGAM - ________________________ ERTIL - ___________________ 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. Drill Time 10.1 Conversion of Standard Units of Length 1) What is the unit used to measure the length of a side in each of the following figures? a) b) c) d) 10.2 Weigh Mass Using Non-Standard Units 2) Which unit should be used to measure the weight of the following? a) b) c) d) Measurement 59
3) Compare the weights of the given objects. a) b) 3 brinjals weigh as much _______ cricket balls weigh as as _______ corns. much as 1 football. 10.3 Measure Volume Using Non-Standard Units 4) What are the units used to measure the capacities of the following? a) b) c) d) 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 used. 60
11Chapter Data Handling I Will Learn About • understanding handling data. • recording data using tally marks and pictorial representation. 11.1 Record Data Using Tally Marks I Think Neena’s mother gives her a bag full of apples, oranges and banana. She asks Neena to find the total number of each fruit. She counts the fruits many times but makes mistakes. Do you think there is a better way of counting them? I Recall We know how to answer the questions based on the data in a given table. Let us revise the concept by studying the following table. The number of students who like different types of chocolate is given in the table. 61
Name of the chocolate Number of students Jelly 5 Star Éclairs Melody Key: = 1 student a) How many students are present in the class? [ ] ] (A) 13 (B) 18 (C) 15 (D) 20 ] ] b) How many students like Éclairs? [ ] (A) 3 (B) 6 (C) 5 (D) 4 c) Which type of chocolate is liked by four students? [ (A) Jelly (B) 5 Star (C) Éclairs (D) Melody d) How many students like jelly? [ (A) 3 (B) 4 (C) 6 (D) 5 e) Which chocolate is liked by most of the students? [ (A) Jelly (B) 5 Star (C) Eclairs (D) Melody I Remember and Understand Let us now learn how to make a table of the given data. The data given can be arranged in the form of a table. We first identify different items in the data. We then list them out in the first column of the table. To represent 5 items In the second column, the number of each of the we draw 4 vertical items is denoted by drawing a vertical line (|). This lines and cross them vertical line is called a tally mark. with the fifth line ( ). 62
In the third column, we write the count of these tally marks. Let us see a few examples to understand the concept better. Example 1: Seema bought the following fruits: How many of each fruit did Seema buy? Represent the data in the form of a table using tally marks. Solution: Fruit Tally marks Number Apple |||| 4 Banana |||| 4 Watermelon ||| 3 Mango |||| | 6 Example 2: The months in which birthdays of some of the children fall are as given. Heena – January, Sheena – March, Yash – March, Harsh – January, Hemal – February, Jinal – August, Jihaan – December, Asmita – January, Chetana – August Use tally marks to represent this information in a table. Solution: Tally marks Number of children Birthday month January ||| 3 February | 1 March || 2 August || 2 December | 1 Data Handling 63
? Train My Brain The colours of different frocks owned by Rashi are: yellow, pink, blue, green, yellow, red, pink, blue, blue, red, yellow, red, blue, pink, red, yellow. Represent this data in the form of a table using tally marks. Colours Tally marks Number I Apply Let us see some real-life examples where we represent data using tally marks and pictograph. Example 3: The different flavours of ice cream in Raj’s shop are as follows: mango, mango, strawberry, pista, mango, pista, mango, pista, vanilla, strawberry, mango, chocolate, vanilla, mango, pista, mango, strawberry, pista, mango, chocolate, pista, mango, strawberry, chocolate, mango, vanilla, strawberry, pista, mango, strawberry, chocolate, vanilla, mango, chocolate, vanilla, mango, strawberry, pista, mango, pista, strawberry, mango, pista, pista, vanilla, pista, strawberry, chocolate Represent this data in a table using tally marks and pictograph. From the table, find the type of ice cream that is: a) maximum in number. b) less in number than strawberry. c) more in number than strawberry but less in number than mango. Solution: We can represent data in a table using tally marks as: 64
Ice cream flavour Tally marks Number Mango |||| |||| |||| 15 9 Strawberry |||| |||| 6 Vanilla |||| | 12 Pista 6 |||| |||| || Chocolate |||| | We can represent data using a pictograph as: Ice cream flavour Number Mango Strawberry Vanilla Pista Chocolate = 3 ice creams So, a) Mango b) Chocolate/Vanilla c) Pista Example 4: Nandu asked each student of his class as to how they come to school. He noted their answers as given: Heena – Bus, Raju – On foot, Pooja – Auto, Reena – On foot, Sheela – Bus, Rohan – On foot, Rahul – Bicycle, Ajay – On foot, Neha – Auto, Hema – Bus, Arun – Bicycle, Komal – On foot, Anil – Bus, Anita – Auto, Soham – Bicycle Represent this data in a table using tally marks. Data Handling 65
Solution: Tally marks Number of children |||| 5 On foot |||| 4 Bus ||| 3 Auto ||| 3 Bicycle I Explore (H.O.T.S.) Let us see a few more examples on how to make tables from the given data. Example 5: The different sizes of T-shirts in a shop are as follows: Small, Large, XXXL, Small, Small, 34, XXXL, Small, XXXL, Large, 34, XXXL, Medium, 34, XXXL, Large, Small, Large, 34, Medium, XXXL, Small, Large, 34, 34, XXXL, Small, XXXL, Medium, 34, Small, XXXL, Small, XXXL, 34, Small, XXXL, 34, Large, Small, XXXL, 34, Small, Small, Medium, XXXL, Large, XXXL, Large, XXXL, 34 Represent this data in a table using tally marks. From the table, find the size of the T-shirt that is: a) 3 more in number if we add the medium and the large sizes together. b) less in number than the large size. c) m ore in number than medium size but less in number than the ‘34’ size. Solution: Size of T-Shirt Tally marks Number Small |||| |||| ||| 13 Medium |||| 4 Large |||| ||| 8 34 |||| |||| | 11 XXXL |||| |||| |||| 15 a) XXXL b) Medium c) Large 66
Example 6: The number of two-wheelers, three-wheelers and four-wheelers are as given: Two-wheelers: 24 Three-wheelers: 10 Four-wheelers: 19 Represent this data in a table using tally marks. Solution: Vehicle Tally Marks Two-wheelers |||| |||| |||| |||| |||| Three-wheelers |||| |||| Four-wheelers |||| |||| |||| |||| Maths Munchies Tally is a software used to maintain accounts in large companies. It is based on the same method as we use to make tables of available items and their numbers. Connect the Dots Science Fun Data handling or recording data is useful while carrying out science experiments. Observing and studying the recorded data may lead to discoveries and studies. Social Studies Fun The population of a country is calculated every 10 years. This activity is called Census. Census is carried out using data handling. Teams of people go to every house and manually write the number of people in the house, their names, ages and genders. This data is then arranged in tables and the final population of the city or a country is calculated. Data Handling 67
Drill Time 11.1 Record Data Using Tally Marks 1) Solve the following: a) In a school, there are seven plastic, twelve wooden and three iron chairs. Represent this data using tally marks. Find the total number of chairs. b) M y kitchen has the following cutlery: Bowls - 5 Plates - 10 Pot - 1 Spoons - 11 Cups - 7 Glasses - 10 Saucers - 2 Represent this data in a table using tally marks. c) The number of children present for sports day is as given. Boys: Rohan, Tushar, Sanket, Ankit, Siddharth, Harsh Girls: Piya, Kshitija, Reema, Prachi R epresent the data in a table using tally marks. How many boys and how many girls were present on the sports day? d) A mi noted down the colour of school bags of the children in her class. She made a list as follows: Purple: Krishna, Sanika, Harshada, Suvarna, Anu, Shreya Pink: Yash, Jigar, Vijay, Virat Black: Bhavna, Rashmi, Jay, Sagar, Sonu, Tina, Mona, Shefali White: Payal, Sakshi Represent the data in a table using tally marks. A Note to Parent To help children understand data handling, ask them to make a chart of their stationery or clothes. Inculcate the habit of maintaining a stock of their things and know what is missing using tally marks. 68
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