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. Look at the following examples: a) T he distance between the two ends of the pencil is 6 cm. So, the pencil is 6 cm long. b) The water bottle is 12 cm long. We know that we measure longer objects in metres and distances in kilometres. Now take a look at the table below. The units that are used to measure the lengths of the following objects have been ticked. Object cm m km Blue whale Book Road Measurements 45 Ascend_G2_Maths_TB2_V1.indb 45 04/08/2023 5:31:57 PM
But how are these different units related? Look at the centimetre side of your ruler. You’ll see that the distance between any two consecutive numbers is 1 cm. You’ll also see 10 equal divisions within a centimetre. Each of these divisions is called a millimetre, written in short as ‘mm’. In the same way that 1 cm = 10 mm, a kilometre (written as km) can be divided into 1000 equal divisions of a metre (written as m) each and 1m can be divided into 100 equal divisions of a centimetre each. Now, you try it yourself! Tick the unit used to measure the following. Object mm cm m km Window Ribbon Rope Cloth Reflection Time! 1) We have learnt how to measure different objects using standard units. Can you think of any reasons why we might need to measure objects in real life? List at least three reasons. 2) We have seen that we use a ruler or scale to measure the length of small objects like chalk, dusters and pencils. But do you know what is the length of your scale? How do you find out? 46 Measurements Ascend_G2_Maths_TB2_V1.indb 46 04/08/2023 5:31:59 PM
Drill Time 10.1: Measure Lengths Using Standard Units 1) Which unit should be used to measure the length of a side of the object shown in each of the following figures? a) b) c) d) 10.2: Compare Weights Using a Simple Balance We have learnt how to guess the heaviness of objects Comparison between based on their size. the units of weight Let us now learn how to measure the weight of objects 1 kg > 1 g > 1 mg using standard instruments and units. The standard instrument used to measure the weight of an object is called the simple balance. What are the standard units of weight? The standard units of weight are gram and kilogram. We write grams as ‘g’ and kilograms as ‘kg’. Jewellers use grams to weigh gold or silver used to make ornaments. 10 g of gold or silver is called a ‘tola’ in India. A smaller unit of weight is a milligram, written as ‘mg’. For example, medicine tablets, spices and so on are measured using milligrams. Measurements 47 Ascend_G2_Maths_TB2_V1.indb 47 04/08/2023 5:32:00 PM
Heavier objects such as pencils, seeds 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 also measured in kilograms. 2 kg 6 kg 5 kg Let us learn the standard units of weight using some examples. Can you tick the unit used to measure the following? One is done for you. Object mg g kg a) b) 48 Measurements Ascend_G2_Maths_TB2_V1.indb 48 04/08/2023 5:32:05 PM
Object mg g kg c) d) e) While the weight of a needle will be measured in milligrams, the weight of a cloth hanger, a loaf of bread or a bunch of spinach will be measured in grams. Since a motorbike is much heavier than the rest of the objects, its weight will be measured in kilograms. Write the unit that must be used to measure the weights of the following objects. One is already done for you. g Measurements 49 Ascend_G2_Maths_TB2_V1.indb 49 04/08/2023 5:32:07 PM
Reflection Time! 1) Have you ever seen a simple balance being used by a vegetable or a fruit vendor? How do they use it? Do they use any other objects to help in their measurement? 2) Have you ever had your weight checked at the doctor’s clinic or at the health centre? What is the name of the instrument that is used to measure your weight? Drill Time 10.2: Compare Weights Using a Simple Balance 1) Which unit should be used to measure the weight of the following? a) b) c) d) 2) Word problems. a) R obin 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 weighs 4 kg. What is the total weight of their bags? 50 Measurements Ascend_G2_Maths_TB2_V1.indb 50 04/08/2023 5:32:11 PM
10.3: Compare Containers for Capacities We have learnt that 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. Comparison between the units of capacity 1 kℓ > 1 ℓ > 1 mℓ Glasses, bottles, jugs and so on are non-standard units to measure liquids. What are the standard units to measure liquids? The standard units of capacity are millilitres, litres and kilolitres. The figures in the previous page show different containers of different capacities used for holding liquids. 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’. Let us understand the use of the standard units of capacity based on the size of different containers, with the help of some examples. Can you tick the units used to measure the capacity of the following? One is done for you. Container Units ℓ mℓ Measurements 51 Ascend_G2_Maths_TB2_V1.indb 51 04/08/2023 5:32:26 PM
Container Units ℓ mℓ To measure the capacity of the spoon and the eye drops bottle, we use mℓ because they are smaller containers. But to measure the capacity of the jug and the tub, we use ℓ as they can hold a greater amount of liquid. Circle the vessel which holds the given unit of capacity. One is already done for you. Unit of Vessels capacity ℓ mℓ ℓ 52 Measurements Ascend_G2_Maths_TB2_V1.indb 52 04/08/2023 5:32:30 PM
Let us now look at a real-life example involving the measurement of capacities. Imagine that your neighbour, Renu, had 38 litres of orange juice in a bucket. A jug that can hold 2 litres was used five times to fill the juice glasses. How much juice is remaining in the bucket now? 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 into the juice glasses is 2 ℓ × 5 = 10 ℓ Quantity of the orange juice remaining in the bucket is (38 – 10) ℓ = 28 ℓ So, 28 ℓ of orange juice is remaining in the bucket. 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? Reflection Time! 1) You must have seen glasses of different sizes in your kitchen. Do you use different glasses to drink different items? Why do you think we use glasses of different sizes? 2) Have you ever seen the milkman? He usually comes to deliver milk very early in the morning. Do you know how much milk you get each day at home? Which unit is used to measure it? You can ask your parents to find out. Measurements 53 Ascend_G2_Maths_TB2_V1.indb 53 04/08/2023 5:32:31 PM
Drill Time 10.3: Compare Containers for Capacities 1) Which units should be used to measure the capacities of the following containers? a) b) c) d) 2) Word problems. a) Salma has 23 litres of water in a tank. She has a jug that can hold 2 litres. She uses the jug 11 times to fill a bucket. How much water is remaining in the tank? 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? c) Neha has 32 litres of orange juice in a bucket. A jug that can hold 3 litres is used ten times to fill the juice glasses. How much juice is remaining in the bucket? 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. 54 Measurements Ascend_G2_Maths_TB2_V1.indb 54 04/08/2023 5:32:33 PM
Connect the Dots EVS Fun Look at 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 the same size. English Fun The standard units of measurement are given in a jumbled form below. Unjumble the letters to form the correct words. MTEER – ________________________ KILMTREEO – ________________________ RGAM – ________________________ ERTIL – ___________________ A Note to Parent When you visit a grocery store or a supermarket, help your child 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 measurements with real examples. Measurements 55 Ascend_G2_Maths_TB2_V1.indb 55 04/08/2023 5:32:34 PM
11 Data Handling I Will Learn the term ‘pictograph’ About reading a pictograph presenting information through a pictograph 11.1: 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? 11.1 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. 56 Ascend_G2_Maths_TB2_V1.indb 56 04/08/2023 5:32:37 PM
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? [ ] 11.1 I Remember and Understand In Grade 1, we have learnt to make collections. Data Handling 57 Ascend_G2_Maths_TB2_V1.indb 57 04/08/2023 5:32:39 PM
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 58 Data Handling Ascend_G2_Maths_TB2_V1.indb 58 04/08/2023 5:32:40 PM
3) List of different types of clothes. List of different types of clothing S. No. Clothes Total number of pieces 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) make 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. In such cases, it becomes 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 59 Ascend_G2_Maths_TB2_V1.indb 59 04/08/2023 5:32:42 PM
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 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 60 Data Handling Ascend_G2_Maths_TB2_V1.indb 60 04/08/2023 5:32:50 PM
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) Number 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) The 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. 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 61 Ascend_G2_Maths_TB2_V1.indb 61 04/08/2023 5:32:51 PM
11.1 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 have pets in the class? Data Handling b) How many students have a pet dog? c) How many students have a pet cat? 04/08/2023 5:32:53 PM 62 Ascend_G2_Maths_TB2_V1.indb 62
d) Which pet is the most popular among the students that have pets? Solution: e) Which pet is the least popular among the students that have pets? 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) T he minimum number of symbols is given for the fish. So,the 63 least number of students have fish as pets. Data Handling Ascend_G2_Maths_TB2_V1.indb 63 04/08/2023 5:32:54 PM
Example 5: The given pictograph shows the grades that students of Class 2 got in an exam. Read the pictograph and complete the table. Then answer the questions that follow. Key: = 2 students; = 1 student A+: Excellent, A: Very Good, B+: Good B: Fair, Grade C: Better, D: Satisfactory, F: Fail Grades of the Students Number of students Students A+ A B+ B C D F Total 64 Data Handling Ascend_G2_Maths_TB2_V1.indb 64 04/08/2023 5:32:58 PM
a) How many students are there in the class? b) How many grades are there? c) How many students failed in the exam? d) How many students got A+ grade? e) Which grade is obtained by most number of the students? Solution: 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 B+ grade. 11.1 I Explore 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 flower pots. 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 most? 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 Data Handling 65 Ascend_G2_Maths_TB2_V1.indb 65 04/08/2023 5:32:59 PM
Flower pots sold on a day Tulip Daisy Lily a) Jasmine flower pots were sold the most. b) Daisy and lily flower pots were sold in equal number. c) = 3 flower pots Since the table shows 3 symbols for tulip flower pots, 3 x 3 = 9 flower pots. Therefore, 9 tulip flower pots were sold. Drill Time 11.1: 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 66 Data Handling Ascend_G2_Maths_TB2_V1.indb 66 04/08/2023 5:33:00 PM
Drill Time 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 a) W ho has the minimum Rita number of sharpeners? Sameera Rakesh b) How many sharpeners are there in all? c) Who has two 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 Name of the Kid Number of ice creams a) Who ate the minimum Vinay number of ice creams? Swaroop Mahesh b) W hich kid ate three ice Rehana creams? c) Who ate the maximum number of ice creams? Data Handling 67 Ascend_G2_Maths_TB2_V1.indb 67 04/08/2023 5:33:01 PM
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 respectively. Do you think we can use a pictograph to decide the mode of transportation used the most? English Fun Did you know that the word ‘pictograph’ comes from the Latin language? ‘Picto’ means picture and ‘graph’ means writing. 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. 68 Data Handling Ascend_G2_Maths_TB2_V1.indb 68 04/08/2023 5:33:03 PM
MATHS LAB Aim: To reinforce the concept of multiplication Requirement: A beach ball (use the marker to divide the ball into 6 equal sections; then, write any number between 1 to 6 in each section), a permanent marker Steps : 1. Pair up with your friend. 2. Take the ball and toss it to your friend. 3. Note the section on which your friend’s thumb lands when they catch it. 4. Write the number in the First number column table. 5. Now, ask your friend to toss the ball back to you. 6. Again note the section where your thumb lands and record it as the Second number in the Record Table 7. Multiply both the numbers and find the answer. Write your answer in the product column of the record table. 8. Repeat playing with the ball until you fill up the table. Record Table First number Second number Product 6 2 6 x 2 = 12 Ascend_G2_Maths_TB2_V1.indb 69 69 04/08/2023 5:33:05 PM
Student Reflection Come to this page after you complete a chapter. Choose the smiley that shows how well you have understood the chapter. Time Money Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all Multiplication Division Readiness Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all Measurements Data Handling Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all 70 04/08/2023 5:33:05 PM Ascend_G2_Maths_TB2_V1.indb 70
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