3) D o you get pocket money? If yes, how do you spend it? How much do you save? Do you have a piggy bank? Why is it important to have one? Drill Time 10.2: Add and Subtract Money With Conversion 1) Add: a) `23.24 + `10.80 b) `31.20 + `19.16 c) `61.21 + `29.20 d) `11.10 + `12.90 e) `60.90 + `24.23 f) `40.43 + `39.75 2) Subtract: a) `87.10 - `23.20 b) `20.12 - `10.13 c) `31.55 - `22.44 d) `99.99 - `22.22 e) `56.13 - `12.03 f) `60.30 - `17.21 10.3: Multiply and Divide Money You have learned multiplication and division of numbers so far. Do you know that multiplication and division of money is similar to that of numbers? How do we multiply a given amount of money? Sometimes, we might want to multiply an amount with a number to find the total amount. It is the same amount as adding the given amount a specified number of times. For example, if a pen costs `12 and we want to buy 2 such pens, we can find out how much to pay for them by multiplying: `12 × 2 = `24. Notice how multiplying `12 by 2 is like adding `12 twice or doubling `12. To multiply money with a given number, first multiply the numbers under paise with the specified number, write down the amount and place the point. Then multiply the number under rupees with the specified number. Money 45 Ascend_G3_Maths_Book_TB_Part2.indb 45 7/14/2023 12:27:25 PM
Now, let us understand multiplying money using an example. ` 1 Multiply `72 by 8. 72 ×8 To find the total amount, multiply the number under rupees like you would 576 do for multiplication of a 2-digit number by a 1-digit number. Therefore, `72 × 8 = `576 How do we divide an amount with a given number? In multiplication, start multiplying To divide an amount, we divide the numbers under rupees and from the rightmost place the point in the quotient. Then, we divide the number digit. In division, under paise. We divide an amount with a specified number just start dividing from how we divide a 2-digit number by a 1-digit number. the leftmost digit. Let us see how with an example. 5 Divide `35 by 7. So, `35 ÷ 7 = `5. 7) 35 − 35 00 1) Solve the following: a) `28 × 5 b) `70 ÷ 2 c) `44 × 5 2) If 1 book costs `29, what is the cost of 6 such books? 3) The cost of a dozen pencils is `48. a) What is the cost of three dozen pencils? b) What is the cost of one pencil? Reflection Time! Money 1) Did you know that multiplication is related to addition 7/14/2023 12:27:27 PM and division is related to subtraction? Solve `50 × 4 by both multiplication and repeated addition. Also, solve `75 ÷ 5 by both division and repeated subtraction. 2) For each of the questions given below, first write the operation and then find the solution. 46 Ascend_G3_Maths_Book_TB_Part2.indb 46
A dozen bananas cost `36. a) What is the cost of 6 bananas? b) How many bananas can you take home for `120? c) What is the cost of 3 dozen bananas? Drill Time 10.3: Multiply and Divide Money 1) Solve the following: a) `23 × 2 b) `10 × 3 c) `21 ÷ 7 d) `34 × 4 e) `84 ÷ 4 f) `96 ÷ 6 10.4: Rate Charts and Bills Have you ever noticed your parents collecting pamphlets from different grocery stores? This is because supermarkets circulate such pamphlets to provide customers with the rate charts of groceries, vegetables and household supplies. Rate charts help customers compare the prices (also called rates) of things at different supermarkets, so that they can buy the things they need from the shop that offers them the best prices. But what are rate charts? A rate chart is a list of different items available in a shop and their prices. A rate chart makes it easier for us to know and compare the prices of the items in a shop. Look at the two rate charts given below and answer the following questions. Item Rate (in ₹) Item Rate (in ₹) 1 kg sugar 40 1 litre milk 44 Tomato ketchup 147 1 kg wheat 48 Chocolate bar 50 1 kg oranges 80 Soap bar 34 1 kg apples 150 1 kg tea 240 1 kg pineapples 50 Honey 149.50 1 dozen bananas 20 1) Which fruit is the most affordable? 2) Would you prefer to buy sugar or honey if you have only `130 with you ? Money 47 Ascend_G3_Maths_Book_TB_Part2.indb 47 7/14/2023 12:27:33 PM
After comparing rate charts, we decide to buy the things we need from a shop. You must have seen that the shopkeeper gives us a bill when we pay for the things we buy. Do you know what a bill is? A bill is a list of items along with their prices. A bill tells us the cost of each item we bought and the total money to be paid to the shopkeeper. Do you know how to make a bill? To make a bill, we write the rates or prices of the items bought and the number or quantity of the items. We then multiply the rate of each item with the quantity to find the total cost for that item. For example, you may have bought 7 pens that cost `10 each. So, the total cost of the pens you bought is: `10 x 7 = `70. Lastly, we add the item-wise costs to find the total bill amount. Let us understand how to make bills through an example. Sunil bought the following stationery items at a shop. Item pencil water colour pen scissors Quantity 3 1 4 2 Here is the rate chart of the things Sunil bought. Pencils `3 each Pens `10 each Water colours `100 Scissors `25 Money We can use the following steps to make a bill. Step 1: Write the items and their quantities in the bill. 7/14/2023 12:27:34 PM Step 2: Then write the rate or the price of each item. 48 Ascend_G3_Maths_Book_TB_Part2.indb 48
Step 3: Find the total cost of each item by multiplying the Addition of number of items by their rate/price. amounts is similar to the addition of Step 4: Find the total bill amount by adding the cost of each numbers with two item. or more digits. Take a look at the bill that Sunil was given by the shopkeeper of the stationery shop for the items he bought. Name: Sunil P Bill Date: 12 July S.No Item Quantity Rate per item Amount `p 3 `3.00 1) pencil 1 `100.00 9 00 2) water colour 4 `10.00 3) pen 2 `25.00 100 00 4) scissors Total 40 00 50 00 `199 00 1) Make a bill for the following items. cake – `100; 10 birthday caps – `5 each; candle – `25; 10 small gifts – `15 each 2) Mr. Kumar’s family went to a restaurant for lunch. They ordered 1 pav bhaji for `45, 2 burgers for `40 each, 2 sandwiches for `20.50 each, 3 mango shakes for `25.50 each and 2 ice cream cones for `22.50 each. What would the restaurant bill total be? Reflection Time! 49 1) My parents always cross-check the bill and the items that 7/15/2023 12:11:35 PM we got after we come home from the market. Do you think this is a good practice? Why? 2) Manasvi went to 6 showrooms with her father before they purchased the TV and its accessories for their house. Can you think of at least five questions they would have asked in the showrooms? Money Visa_G3_Maths_TB_L010.2-10.4_V1.indd 49
3) Give 2 reasons why it’s important to ask for a bill for every purchase we make. Drill Time 10.4: Rate Charts and Bills 1) The rates of some vegetables and fruits per kg are given in the box. ` 10 ` 18 Item Quantity in kg ` 15 ` 20 Tomato 2 Carrot 3 `7 ` 12 Pumpkin 1 Cabbage 1 2) Sneha went to an ice cream shop and saw the rate chart given. Sneha took 2 Butter Scotch, 2 Mango and 1 Vanilla ice cream tubs. What is the total bill? Make a bill. 100 ml tube of ice cream Rate in ` Butter Scotch 150.00 Vanilla 120.00 Strawberry 130.00 Mango 140.00 Maths Munchies Punch marked coins were the first ever coins documented between 7th - 6th century BCE and 1st century CE. Most of the coins were made of silver. 50 Money Visa_G3_Maths_TB_L010.2-10.4_V1.indd 50 7/15/2023 12:11:38 PM
Connect the Dots English Fun Here is a poem about Indian rupee. Very odd are the things A rupee coin can make, A pleasure to give and take. Toss it up for head or tail, Buy a stamp for your mail, Offer it to god and pray, It can buy you toys of clay, Use it for a call you make, Or to check your body weight Social Studies Fun Different countries have different types of money. Like we have Rupees and Paise, Americans have Dollars and Cents. 1 rupee = 100 paise and 1 dollar = 100 cents A Note to Parent Take your child shopping and show them what a bill looks like. Make them calculate the total using addition, subtraction and multiplication. Money 51 Visa_G3_Maths_TB_L010.2-10.4_V1.indd 51 7/15/2023 12:11:40 PM
11 Measurements I Will Learn estimating and measuring length and distance About conversion, addition and subtraction of length weighing objects using simple balance conversion of units of capacity comparing capacities using different containers 11.1: Conversion of Standard Units of Length I Think Farida went with her mother to a shop to buy a piece of cloth for a dress. Her mother asked the shopkeeper to give two metres of the cloth. How do you think the shopkeeper should measure two metres of the cloth? 11.1 I Recall We know that people sometimes measure lengths of objects using their hands or feet. But the size of the body parts differ from person to person. So, the length of the same object also differs when measured by different people using hands or feet. Suppose a boy and a grown-up measure the same object. We see that the measures of the object are different. So, measures such as hand span, cubit, leg span and so on are called non-standard units. 52 Ascend_G3_Maths_Book_TB_Part2.indb 52 7/14/2023 12:27:41 PM
Hand span Cubit Foot span Pace By using our hand span, we can measure the lengths of the following objects. Fill in the blanks with the measurements obtained. a) Window of your classroom - _____________ b) The benches on which you sit - _____________ c) The blackboard - _____________ d) Your math notebook - _____________ e) School bag - ____________ To express measurement in an exact way, standard units were developed. The measurement of object remains the same, anywhere in the world when these standard units are used. Measures of Length Centimetre: It is a unit of length used to measure the length of a pencil, the sides of a book and so on. We write centimetres as cm. Metre: It is the standard unit of length. It is used to measure length of a piece of cloth, a wall and so on. We write metres as m. Kilometre: It is a unit of length larger than the metre. It is used to measure the distance between two places, length of a river and so on. We write it as km. 11.1 I Remember and Understand Measure the length of a blackboard with your hand span. Ask your friends to do the same and note the readings. Did everyone get the same measurement? What do you observe by this? We observe that the readings are different. So, we need a standard measurement. If all of us use the same standard instrument to measure length, there will be no difference in the measurements. Measurements 53 Ascend_G3_Maths_Book_TB_Part2.indb 53 7/14/2023 12:27:42 PM
Instruments such as a scale, a tape and so on, are used to measure lengths throughout the world. These are known as standard instruments. A scale is used to measure the length in centimetres and inches. A measuring tape is used to measure longer lengths like metres and kilometres. Can we use a measuring tape to measure smaller lengths? Yes, for that we should know to convert the measurements. Conversion of length Relation between units of length We can convert one unit of measurement into another using the relation between them. 1 m = 100 cm Let us understand the conversion of larger units to smaller units 1 km = 1000 m through a few examples. Example 1: Convert: a) 4 m into cm b) 8 m 6 cm into cm c) 5 km into m d) 6 km 4 m into m Solution: a) To convert metre into centimetre, multiply by 100. b) To convert metre and centimetre into centimetre, convert metre to centimetre and add it to the centimetre. c) To convert kilometre into metre, multiply by 1000. d) To convert kilometre and metre into metre, convert kilometre to metre and add it to the metre. Solved Solve these a) Conversion of m into cm: 7 m = _______________ cm 4 m = ___________ cm 1 m = 100 cm 4 m = 4 ×100 cm = 400 cm 4 m = 400 cm 54 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 54 7/14/2023 12:27:42 PM
Solved Solve these b) Conversion of m and cm into cm: 8 m 6 cm = ____________ cm 4 m 5 cm = ___________ cm 1 m = 100 cm So, 8 m = 8 ×100 cm = 800 cm 8 m 6 cm = (800 + 6) cm = 806 cm c) Conversion of km to m: 5 km = __________ m 7 km = ___________ m 1 km = 1000 m 5 km = 5 ×1000 m = 5000 m 5 km = 5000 m d) Conversion of km and m into m: 6 km 4 m = ___________ m 4 km 9 m = ___________ m 1 km = 1000 m So, 6 km = 6 ×1000 m = 6000 m 6 km 4 m = (6000 + 4) m = 6004 m We can add or subtract lengths just as like we add or subtract numbers. Remember to write the units beside the sum or difference. Note: Introduce ‘0’ in the hundreds place, if the number in the metre of the kilometre has only 2 digits. Addition of lengths Example 2: Add: a) 25 m 16 cm and 32 m 30 cm b) 34 km 450 m and 125 km 235 m Solution: Write the numbers in columns, one below the other. Measurements 55 Ascend_G3_Maths_Book_TB_Part2.indb 55 7/14/2023 12:27:42 PM
Steps Solved Solved Solve these km m Step 1: Add the m cm km m 12 150 numbers under the 25 16 34 450 smaller unit and + 32 30 + 125 235 + 14 340 write the sum. 46 685 km m Step 2: Add the m cm 10 100 16 km m + 100 100 numbers under 25 30 34 450 46 + 125 235 the larger unit and + 3 2 159 685 write the sum. 57 Subtraction of lengths Example 3: Subtract: a) 125 m 20 cm from 232 m 30 cm b) 234 km 15 m from 425 km 35 m Solution: Write the numbers in columns, the smaller number below the larger number. Steps Solved Solved Solve these Step 1: Subtract m cm km m m cm the numbers 232 30 425 035 26 42 under the − 125 20 − 234 015 − 13 21 smaller unit and write the 10 020 m cm difference. m cm km m 58 26 Step 2: Subtract 2 12 3 12 − 39 14 the numbers 23 2 30 4 25 035 under the larger − 12 5 20 − 2 34 015 unit and write the 10 7 10 191 020 difference. \\ \\ \\ \\ Train My Brain b) Convert 8 km into m d) 42 m 30 cm – 30 m 20 cm Solve the following: a) Convert 5 m 7 cm into cm Measurements c) 10 km 20 m + 20 km 10 m 7/14/2023 12:27:43 PM 56 Ascend_G3_Maths_Book_TB_Part2.indb 56
11.1 I Apply Let us solve some real-life examples with addition and subtraction of lengths. Example 4: Reema rode her cycle for 9 km 6 m. How many metres did she ride? Solution: The distance travelled by Reema on her cycle = 9 km 6 m We know that 1 km = 1000 m So, 9 km = 9 ×1000 m = 9000 m 9 km 6 m = (9000 + 6) m = 9006 m Therefore, Reema rode for 9006 metres. Example 5: Sunny bought a rope of length 20 m 12 cm. Bunny bought another rope of length 12 m 20 cm. What is the total length of the rope they bought? Solution: The length of the rope bought by Sunny = 20 m 12 cm m cm The length of the rope bought by Bunny = 12 m 20 cm 20 12 The total length of the ropes = 20 m 12 cm + 12 m 20 cm + 12 20 Therefore, the total length of the rope bought by both of 32 32 them = 32 m 32 cm Example 6: Raj’s house is at a distance of 36 km 119 m from his uncle’s house. He travels by car for 14 km 116 m from his uncle’s house. How much more distance has to be covered by Raj to reach his house? km m Solution: Distance between Raj’s house and his uncle’s house 36 119 = 36 km 119 m − 1 4 1 1 6 Distance travelled by Raj to his house = 14 km 116 m 22 003 Distance left to be covered = 36 km 119 m – 14 km 116 m Therefore, the distance to be covered to reach Raj’s house is 22 km 3 m. 11.1 I Explore Let us now see some more examples where we use the concept of standard units of lengths. Example 7: Ramu’s height is 134 cm and Somu’s height is 1 m 50 cm. Who is taller and by how many centimetres? Measurements 57 Ascend_G3_Maths_Book_TB_Part2.indb 57 7/14/2023 12:27:43 PM
Solution: To compare heights of two persons, the heights must be in the same units. Height of Somu = 1 m 50 cm = 100 cm + 50 cm = 150 cm Height of Ramu = 134 cm So, Somu is taller as 150 cm > 134 cm. The difference in their heights is (150 – 134) cm = 16 cm. 150 cm > 134 cm Therefore, Somu is taller than Ramu by 16 cm. Example 8: The figure given below 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 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) Is the post office or the market closer to the house? e) How far is the railway station from the school? 58 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 58 7/14/2023 12:27:44 PM
Solution: From the map, we see that, a) The post office is 3 km from the house. b) The distance between the market and the railway station is 3 km. c) Through the post office, the distance between the house and the airport is 3 km + 6 km = 9 km. d) The post office is closer to the house. e) The railway station is 10 km from the school. Drill Time 11.1: Conversion of Standard Units of Length 1) Word Problem a) Roopa’s house and the places close to it are shown on the map. 2 km 2 km Hospital Playground 4 km 2 km 1 km 250 m Market Post Office 5 km 500 m Roopa’s house School 2 km 450 m 4 km 6 km 3 km 300 m Airport Measurements 59 Ascend_G3_Maths_Book_TB_Part2.indb 59 7/14/2023 12:27:45 PM
Drill Time Study the map and answer these questions. a) The shortest route from Roopa’s house to the market is via the __________ and is __________ km. b) The shortest route from Roopa’s house to the airport is _________ km. c) What is the shortest route from the post office to the market? d) R oopa went to the post office from the school. What is the distance she travelled? 2) Convert into centimetres. a) 3 m b) 9 m c) 2 m 45 cm d) 5 m 20 cm e) 8 m 36 cm f) 6 m 52 cm 3) Convert into metres. a) 4 km b) 15 km c) 35 km d) 6 km 112 m e) 1 km 100 m f) 5 km 555 m 4) Solve the following: a) 24 m 13 cm + 13 m 45 cm b) 31 m 00 cm + 18 m 59 cm c) 10 km 100 m + 20 km 200 m d) 88 km 100 m − 10 km 800 m e) 26 m 14 cm – 20 m 10 cm f) 41 km 300 m + 36 km 150 m 11.2: Conversion of Standard Units of Weight I Think Farida went to the market with her father. They bought several things like vegetables, sweets and fruits. The shopkeeper measured the vegetables with a machine. He used some units to tell the weight. Do you know which units he used? 60 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 60 7/14/2023 12:27:45 PM
11.2 I Recall The weight of an object is the measure of its heaviness. Different objects have different weights. We use standard units to measure the weights of objects around us. The standard unit of weight is kilogram. We write kilogram as ‘kg’. Another unit of weight is gram. We write gram as ‘g’. The unit of weight smaller than the gram is milligram. We write milligram as ‘mg’. Milligram (mg) is the unit used for weighing medicines, tablets and so on. Gram (g) is used for weighing objects such as pens, books and spices. Kilogram (kg) is used for weighing heavier objects such as rice, wheat and flour. 11.2 I Remember and Understand Sometimes, to measure the weight of an object, we need the Relation between smaller unit instead of the larger unit. For this, we need to convert units of weight the units for appropriate measurement. Let us see how we can 1 g = 1000 mg 1 kg = 1000 g Measurements 61 Ascend_G3_Maths_Book_TB_Part2.indb 61 7/14/2023 12:27:49 PM
convert weights. Conversion of weights We can convert larger units of weights into smaller units using the relation between them. Let us understand the conversion through a few examples. Example 9: Convert 4 kg into grams. Solution: To convert kilogram into gram, multiply by 1000. Solved Solve this 4 kg to grams 6 kg to grams 1 kg = 1000 g So, 4 kg = 4 × 1000 g = 4000 g Example 10: Convert 3 kg 150 g into grams. Solution: To convert kilogram and gram into gram, convert kilogram to gram and add it to the gram. Solved Solve this 3 kg 150 g to grams 1 kg = 1000 g So, 3 kg = 3 × 1000 g = 3000 g 4 kg 20 g to grams 3 kg 150 g = 3000 g + 150 g = 3150 g We add or subtract weights just as we add or subtract numbers. Remember to write the unit beside the sum or difference. Note: Introduce ‘0’ in the hundreds place if the milligram of the gram or the gram of the kilogram has only 2 digits. Addition of weights 62 Measurements Visa_G3_Maths_L11_TB_Measurement_V1.indd 62 7/15/2023 12:12:29 PM
Example 11: Add: a) 15 g 150 mg and 23 g 285 mg b) 17 kg 706 g and 108 kg 189 g Solution: Write the numbers in the columns, one below the other. Steps Solved Solved Solve these Step 1: Add the g mg kg g g mg numbers under the 1 1 smaller unit and 15 150 26 190 write the sum. + 23 285 17 706 + 23 260 435 + 108 189 895 Step 2: Add the g mg kg g g mg numbers under the 1 11 larger unit and write 15 150 17 706 33 333 the sum. + 23 285 + 22 333 435 + 108 189 38 125 895 Subtraction of weights Example 12: Subtract: a) 153 g 100 mg from 262 g 300 mg b) 234 kg 150 g from 355 kg 305 g Solution: Write the numbers in columns, the smaller number below the larger number. Steps Solved Solved Solve these Step 1: Subtract the g mg kg g g mg numbers under the 2 10 smaller unit and 262 300 355 \\3 0\\ 5 15 260 write the difference. − 153 100 − 234 150 − 15 260 15 5 200 Measurements 63 Visa_G3_Maths_L11_TB_Measurement_V1.indd 63 7/15/2023 12:12:29 PM
Step 2: Subtract g mg kg g g mg the numbers 5 12 2 10 under the larger 2 \\6 \\2 3 0 0 355 \\3 0\\ 5 23 555 unit and write the − 153 100 − 234 150 − 16 454 difference. 109 200 155 121 Train My Brain Solve the following: a) Convert 5 kg into g. b) Convert 10 kg 250 g into g. c) Add 124 kg and 200 kg. d) Subtract 120 g 50 mg from 325 g 70 mg. 11.2 I Apply Look at some real-life examples where addition and subtraction of weights is used. Example 13: Rahul has a bag full of vegetables weighing 17 kg 241 g. His friend has another bag of vegetables weighing 21 kg 243 g. What is the total weight of the vegetables in both the bags? kg g Solution: Weight of the vegetables in Rahul’s bag = 17 kg 241 g 17 241 Weight of the vegetables in friend’s bag = 21 kg 243 g + 21 243 The total weight of the vegetables in both the 38 484 bags = 17 kg 241 g + 21 kg 243 g = 38 kg 484 g Therefore, the total weight of vegetables in Rahul’s and his friend’s bag is 38 kg 484 g. Example 14: Reena has a box of pins which weighs 43 g 132 mg. She takes out 11 g 100 mg of pins. What is the weight of the pins left in the box? Solution: The weight of pins in the box = 43 g 132 mg g mg The weight of pins taken out from the box = 11 g 100 mg 43 132 − 11 100 32 032 64 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 64 7/14/2023 12:27:50 PM
The weight of the remaining pins in the box = 43 g 132 mg – 11 g 100 mg = 32 g 032 mg Therefore, the weight of the remaining pins is 32 g 32 mg. 11.2 I Explore Let us now see how we use standard units of weight in real-life situations. Example 15: Kiran weighs 12785 g and Venu weighs 11 kg 750 g. Who weighs more and by how many grams? Solution: To compare the weights, they must be in the same units. Weight of Venu = 11 kg 750 g = 11 × 1000 g + 750 g (As 1 kg = 1000 g) = 11000 g + 750 g = 11750 g Weight of Kiran = 12785 g As 12785 g > 11750 g, Kiran weighs more than Venu. The difference in their weights is (12785 – 11750) g = 1035 g. Example 16: Suresh bought apples, grapes and a watermelon. The total weight of the fruits in his bag is 3 kg 750 g. The weight of apples is 1 kg 100 g and grapes is 1 kg 150 g. What is the weight of the watermelon? Solution: Suresh had 3 kinds of fruits: apples, grapes and a watermelon in his bag. Weight of apples = 1 kg 100 g kg g Weight of grapes = 1 kg 150 g 1 100 Total weight of apples and grapes = 1 kg 100 g + 1 kg 150 g +1 150 2 250 Therefore, the weight of apples and grapes together is 2 kg 250 g. Weight of watermelon = w eight of the bag − total kg g weight of apples and grapes 3 750 Weight of the bag = 3 kg 750 g − 2 250 Weight of apples and grapes together = 2 kg 250 g 1 500 Measurements 65 Ascend_G3_Maths_Book_TB_Part2.indb 65 7/14/2023 12:27:50 PM
Weight of watermelon = 3 kg 750 g – 2 kg 250 g Therefore, the weight of watermelon is 1 kg 500 g. Drill Time 11.2: Conversion of Standard Units of Weight 1) Convert into grams. a) 14 kg b) 29 kg c) 56 kg d) 14 kg 300 g e) 75 kg 226 g f) 10 kg 112 g 2) Solve the following: a) 28 kg 421 g + 30 kg 232 g b) 42 kg 876 g + 31 kg 111 g c) 44 kg 444 g – 22 kg 222 g d) 43 g 230 mg – 11 g 100 mg 3) Word Problems. a) Mary bought these vegetables. Brinjal – 2 kg 250 g; Onion – 1 kg 750 g; Potato – 1 kg 250 g Find the total weight of vegetables in her bag. b) Manish buys 500 g of pears, 2 kg 300 g of apples and 1 kg 150 g of grapes. Find the total weight of fruits that Manish buys. 11.3: Conversion of Standard Units of Volume I Think Farida’s 10 cousins visited her during their summer vacation. Farida bought two big bottles of cold drink. If each takes a glassful, can she serve equally to all? 66 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 66 7/14/2023 12:27:50 PM
11.3 I Recall Bottles and glasses come in different sizes. We cannot specify the quantity of cold drink served in bottles and glasses as they are non-standard units. So, we need a standard unit for measuring the quantity of liquids. Commonly used containers for measuring the quantity of liquids are shown in the figure. The quantity of liquid (water, oil, milk and so on) that a container can hold is called its capacity or volume. Standard units of capacity are millilitres, litres and kilolitres. The standard unit of capacity or volume is litre, denoted by ‘ℓ’. The unit smaller than a litre that is used for measuring capacity is called millilitre. We write it as ‘mℓ’. 11.3 I Remember and Understand To find the measure of the quantity of the smaller units, we need to convert the larger unit to the smaller unit. Relation between units of capacity Conversion of units of capacity 1 litre = 1000 millilitres We can convert one unit of measurement into another using the relation between them. 1 kilolitre = 1000 litres Measurements 67 Ascend_G3_Maths_Book_TB_Part2.indb 67 7/14/2023 12:27:52 PM
Let us understand the conversion of capacity from larger units to smaller units through a few examples. To convert litres into millilitres, multiply by 1000. Example 17: Convert 3 ℓ into millilitres. Solution: Multiply the litres by 1000 to convert it to millilitre. Solved Solve this 7 ℓ to millilitres 3 ℓ to millilitres 1 ℓ = 1000 mℓ 3 ℓ = 3 × 1000 mℓ = 3000 mℓ Example 18: Convert 2ℓ 269 mℓ into millilitres. Solution: To convert litres and millilitres into millilitres, convert litres to millilitres and add it to the millilitres. Solved Solve this 3 ℓ 750 mℓ to millilitre 2ℓ 269 mℓ to millilitre 1 ℓ = 1000 mℓ So, 2 ℓ = 2 × 1000 mℓ = 2000 mℓ 2 ℓ 269 mℓ = 2000 mℓ + 269 mℓ = 2269 mℓ We add or subtract volumes just as we add or subtract numbers. Remember to write the unit beside the sum or difference. Note: Introduce ‘0’ in the hundreds place and the millilitre in litre and litre in kilolitre if there are only two digits. Addition of volumes Example 19: Add: 13 ℓ 450 mℓ and 32 ℓ 300 mℓ Solution: Write the numbers in columns. Steps Solved Solve these Step 1: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 24 129 smaller unit and write + 32 300 + 31 110 the sum. 750 68 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 68 7/14/2023 12:27:52 PM
Steps Solved Solve these Step 2: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 52 000 larger unit and write + 32 300 + 41 000 the sum. 45 750 Subtraction of volumes Example 20: Subtract: 351 ℓ 200 mℓ from 864 ℓ 350mℓ Solution: Write the numbers in columns, the smaller number below the larger number. Steps Solved Solve these Step 1: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 119 209 smaller unit and write the − 351 200 − 11 101 difference. 150 Step 2: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 126 410 larger unit and write the − 351 200 − 21 200 difference. 513 150 Train My Brain Convert the following: a) 8 ℓ into mℓ b) 34 ℓ 420 mℓ into mℓ c) 15 ℓ into mℓ 11.3 I Apply Let us solve some real-life examples where conversion of units and addition and subtraction of volumes are used. Example 21: Seema has a 2 ℓ packet of milk. Express the quantity of milk in millilitres. Solution: Quantity of milk that Seema has = 2 ℓ Measurements 69 Ascend_G3_Maths_Book_TB_Part2.indb 69 7/14/2023 12:27:52 PM
As 1 ℓ = 1000 mℓ, 2 ℓ = 2 × 1000 = 2000 mℓ. Therefore, Seema has 2000 mℓ of milk. Example 22: The capacity of a tank is 20 litres. The volume of water in the tank is 13 litres. How much more water is needed to fill the tank? Solution: The capacity of the tank = 20 litres 1 ℓ Volume of water in the tank = 13 litres \\2 10 Quantity of water needed to fill the tank −1 0\\ = 20 litres – 13 litres = 7 litres 0 3 Therefore, 7 more litres of water is needed to fill the tank. 7 11.3 I Explore Let us see the use of standard units of volumes in a few real-life situations. Example 23: Chandu, the milkman, has only 5 ℓ and 3 ℓ measures. How will he sell 4 ℓ of milk to Gita? (Hint: Find the difference between 5 ℓ and 3 ℓ) Solution: Chandu first pours milk in 5ℓ measure. He then transfers some of it into the 3 ℓ measure. Then the quantity of milk left in the 5ℓ measure is 2 ℓ. This 2 ℓ milk can be transferred into Gita’s vessel. He repeats the same procedure once more. Thus, he sells 4ℓ of milk to Gita. Example 24: A container has a capacity of 2 ℓ. A glass has a capacity of 200 mℓ. How many glasses of juice must be poured to fill up the container? Solution: Capacity of the glass = 200 mℓ Quantity of juice needed = 2 ℓ = 2 × 1000 mℓ = 2000 mℓ 2000 = 200 × 10 Therefore, 10 glasses of juice must be poured to fill up the container. 70 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 70 7/14/2023 12:27:52 PM
Drill Time 11.3: Conversion of Standard Units of Volume 1) Convert into millilitres. a) 13 ℓ b) 28 ℓ c) 52 ℓ d) 64 ℓ 206 mℓ e) 14 ℓ 142 mℓ f) 13 ℓ 400 mℓ 2) Add the following: a) 28 ℓ 421 mℓ + 40 ℓ 262 mℓ b) 41 ℓ 836 mℓ + 41 ℓ 113 mℓ c) 30 ℓ 320 mℓ + 20 ℓ 300 mℓ d) 33 ℓ 530 mℓ + 11 ℓ 300 mℓ 3) Subtract the following: a) 86 ℓ 450 mℓ − 23 ℓ 200 mℓ b) 59 ℓ 730 mℓ − 47 ℓ 510 mℓ c) 66 ℓ 666 mℓ – 44 ℓ 444 mℓ d) 78 ℓ 940 mℓ – 53 ℓ 620 mℓ 4) Word Problem a) Aarthi has a jug with some buttermilk. She uses glasses which can hold 150 mℓ. How many glasses must she fill so that she has 3 ℓ of buttermilk? b) A jug has a capacity of 1 litre. How many glasses of 200 mℓ juice must be poured so that the jug has 1 litre of juice? c) M ary has a pitcher with 4 ℓ of fruit punch. If she uses cups which can hold 500 mℓ of punch, how many cups must be poured to fill up the pitcher? Maths Munchies The blood in our body also has a unit of measurement called ‘pint’ or ‘unit’. An adult body contains 8 to 10 pints of blood. 1 pint is equal to 473 mℓ. Therefore, our body has 3784 mℓ to 4730 mℓ of blood. Measurements 71 Ascend_G3_Maths_Book_TB_Part2.indb 71 7/14/2023 12:27:52 PM
Connect the Dots Science Fun Dwarf Willow is one of the smallest woody plants in the world. It grows to only 1 to 6 cm in height. It has round, shiny green leaves 1 to 2 cm long and broad. Social Studies Fun India measures about 3200 kilometres from north to south. The length from the west to the east is about 2900 kilometres. A Note to Parent Ask your child to weigh different things present at home such as a pencil, flower vase or utensils. This will help them to form a clear understanding of lighter and heavier objects with respect to the usage of mg, g and kg. 72 Measurements Ascend_G3_Maths_Book_TB_Part2.indb 72 7/14/2023 12:27:53 PM
12 Data Handling I Will Learn understanding handling data About making a table when data is given recording data using tally marks and pictorial representation 12.1: Record Data Using Tally Marks I Think Farida made a table of the things that her mother bought for her. From the table she could tell how many of each thing her mother had bought for her. Do you know how? 12.1 I Recall We know how to answer questions based on the data in a given table. Let us revise the concept by studying the following table: The number of students in a class who like different types of chocolate is given in the table. 73 Ascend_G3_Maths_Book_TB_Part2.indb 73 7/14/2023 12:27:54 PM
Name of the chocolate No of students Strawberry 3 Cream 6 Caramel 5 Nuts 4 a) How many students are present in the class? [] [] (A) 13 (B) 18 (C) 15 (D) 20 [] [] b) How many students like Caramel? (A) 3 (B) 6 (C) 5 (D) 4 c) Which type of chocolate is liked by four students? (A) Strawberry (B) Cream (C) Caramel (D) Nuts d) How many students like strawberry? (A) 3 (B) 4 (C) 6 (D) 5 12.1 I Remember and Understand Let us now learn to make a table when data is given. To represent 5 items we draw 4 vertical We can arrange the data given in the form of a table. We first lines and cross them identify different items in the data and list them out in the first with the fifth line. ( ) column of the table. In the second column, we denote every item of one type by drawing a vertical line (⎮). This vertical line is called a tally mark. 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: banana, apple, watermelon, mango, mango, apple, watermelon, apple, banana, banana, apple, mango, watermelon, mango, banana, mango, mango. How many of each fruit did Seema buy? Represent the data in the form of a table using tally marks. 74 Data Handling Ascend_G3_Maths_Book_TB_Part2.indb 74 7/14/2023 12:27:54 PM
Solution: Fruit Tally marks Number Apple |||| 4 Banana |||| 4 Watermelon ||| 3 Mango \\||||| 6 Example 2: Given below are some children and the months in which they celebrate their birthdays. 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: Birthday month Tally marks Number of children January ||| 3 February | 1 March || 2 August || 2 | 1 December 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 12.1 I Apply Let us see some real-life examples where we represent data using tally marks. Data Handling 75 Ascend_G3_Maths_Book_TB_Part2.indb 75 7/14/2023 12:27:55 PM
Example 3: The different types of ice-cream in Raj’s shop are as follows: Cones: 14 Small cups: 9 Medium cups: 6 Large cups: 11 Tubs: 5 Represent this data in a table using tally marks. From the table, find the type of ice cream that is: a) maximum in number. b) less in number than the number of medium cups. c) more in number than the number of small cups but less in number than cones. Solution: We can represent data in a table using tally marks as: Ice cream Tally marks Number Cones |||\\||||\\||||| 14 Small cups |||\\||||| 9 Medium cups |||\\|| 6 Large cups |||\\||||\\| | 11 Tubs |||\\| 5 So, a) Cones b) Tubs c) Large cups Example 4: Nandu asked his classmates how they came to school. He noted their answers as shown below: 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. Solution: Tally marks Number of children 5 On foot |||\\| 4 Bus 3 Auto |||| 3 ||| Bicycle ||| 76 Data Handling Visa_G3_Maths_L12_TB_Data Handling_V1.indd 76 7/15/2023 12:19:54 PM
12.1 I Explore 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 than the number we get if we add the medium and the large sizes together. b) less in number than the large size T-shirts. c) more in number than medium size T-shirts but less in number than the ‘34’ size T-shirts. Solution: Size of T-Shirt Tally marks Number Small |||\\||||\\|||| 13 Medium 4 |||| Large |||\\|||| 8 34 11 |||\\||||\\| | 15 XXXL |||\\| |||\\| |||\\| a) XXXL b) Medium c) Large Example 6: The number of two-wheelers, three-wheelers and four-wheelers are as given below: Two-wheelers: 24 Three-wheelers: 10 Four-wheelers: 19 Represent this data in a table using tally marks. Data Handling 77 Ascend_G3_Maths_Book_TB_Part2.indb 77 7/14/2023 12:27:55 PM
Solution: Vehicle Tally Marks Two-wheelers |||| |||| |||| |||| |||| Three-wheelers Four-wheelers |||| |||| |||| |||| |||| |||| Drill Time 12.1: Record Data Using Tally Marks 1) Solve the following: a) In a school, there are seven plastic chairs, twelve wooden chairs and three iron chairs. Represent this data using tally marks. Find the total number of chairs. b) There are five bowls, ten plates, one pot, seven cups, ten glasses, two saucers and eleven spoons. Represent this data in a table using tally marks. c) The number of children present for a sports day is as given below: Boys: Rohan, Tushar, Sanket, Ankit, Siddharth, Harsh Girls: Piya, Kshitija, Reema, Prachi Represent 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 children in her class. She made a list as below: Purple: Krishna, Sanika, Harshada, Suvarna, Anu, Shreya Pink: Yash, Jigar, Vijay, Pooja Black: Bhavna, Rashmi, Jay, Sagar, Sonu, Tina, Mona, Shefali White: Payal, Sakshi Represent the data in a table using tally marks. e) In a zoo, Anu saw 7 lions, 4 tigers, 9 bears, 5 deers and 12 zebras. Represent this data using tally marks. Find the total number of animals she saw in the Zoo. 78 Data Handling Ascend_G3_Maths_Book_TB_Part2.indb 78 7/14/2023 12:27:55 PM
Maths Munchies Tally is also the name of a software used to maintain accounts in large companies. It is based on the same method that we use to make tables of the 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 new discoveries and studies. Social Studies Fun The population of a country is calculated every 10 years. This activity is called Census. A 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. A Note to Parent To help children understand data handling, ask them to make a chart of the stationery or clothes they have. Introduce the value of maintaining a stock of their things and knowing what is missing using tally marks. Data Handling 79 Ascend_G3_Maths_Book_TB_Part2.indb 79 7/14/2023 12:27:56 PM
MATHS LAB Aim: To reinforce and understand the requirement of money in our daily lives Requirement: Eraser, scale, pencil, water bottle, lunch box, colour pencil, biscuit, candy, notebook, sets of fake currency for each group Steps : 1. Make groups of four with your friends. 2. Distribute the items among the groups and display all the items on your tables. 3. One member in each group will play the role of a seller and the other three will act as buyers. 4. Each buyer will buy a minimum of two things at a time. Once the buyer has chosen the items, the seller will add the prices of the items selected by the buyer and record them in the record table. Greater number Record Table Difference Number of items Price Smaller number Name of item 5. The buyer will then check the amount and pay the seller using the fake currency notes. 6. The activity will continue until all the students have had their turns. 80 7/14/2023 12:27:57 PM Ascend_G3_Maths_Book_TB_Part2.indb 80
Student Reflection Come to this page after you complete a chapter. Choose the smiley that shows how well you have understood the chapter. Time Division Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all I need help with ..........………………...............……… I need help with ..........………………...............……… ...................................................................................... ...................................................................................... What I liked about this chapter ............................... What I liked about this chapter ............................... …………………………………………............................ …………………………………………............................ Fractions Money Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all I need help with ..........………………...............……… I need help with ..........………………...............……… ...................................................................................... ...................................................................................... What I liked about this chapter ............................... What I liked about this chapter ............................... …………………………………………............................ …………………………………………............................ Measurements Data Handling Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all I need help with ..........………………...............……… I need help with ..........………………...............……… ...................................................................................... ...................................................................................... What I liked about this chapter ............................... What I liked about this chapter ............................... …………………………………………............................ …………………………………………............................ Ascend_G3_Maths_Book_TB_Part2.indb 81 81 7/14/2023 12:27:57 PM
Notes Ascend_G3_Maths_Book_TB_Part2.indb 82 7/14/2023 12:27:57 PM
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