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Higher Order Thinking Skills (H.O.T.S.) Observe some more situations where estimation of sum is used. Example 14: There are 416 walnut trees in a park. The park workers plant 574 more walnut trees. Estimate the number of walnut trees in the park after the workers finish planting. Solution: Number of trees in the park = 416 Rounding off 416 to the nearest tens, we get 420. Number of more trees the park workers plant = 574 Rounding off 574 to the nearest tens, we get 570. Their sum is 420 + 570 = 990. So, about 990 plants will be there after the workers finish planting. Example 15: Ramya has 26 cookies and 34 toffees. Renu has 42 cookies and 13 toffees. Estimate the total number of cookies and toffees. Solution: Number of cookies with Ramya = 26 Number of toffees with her = 34 Rounding off 26 and 34 to the nearest teTnrsa, wine Mgeyt 3B0 raanidn30 respectively. Number of cookies with Renu = 42 Number of toffees with her = 13 Rounding off 42 and 13 to the nearest tens, we get 40 and 10 respectively. So, the sum of cookies = 30 + 40 = 70 Sum of toffees = 30 + 10 = 40 Therefore, altogether they have 70 cookies and 40 toffees. Addition 45 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___51 / 184

Concept 4.3: Add 2-digit Numbers Mentally Think Neena had 18 colour pencils. Her sister gave her 71 more. Neena wanted to know the total number of pencils mentally. Do you know how Neena could find it? To answer this question, we need to learn mental addition of two numbers. Recall We have already learned to add two 1-digit numbers mentally. To do so, we keep the larger number in mind and add the smaller one to it. Let us answer these to revise the concept. a) 5 + 4 = ________ [ ] (A) 5 (B) 4 (C) 1 (D) 9 b) 3 + 3 = ________ [ ] (A) 3 (B) 6 (C) 0 (D) 5 c) 1 + 4 = ________ [ ] (A) 3 (B) 4 (C) 6 (D) 5 d) 5 + 0 = ________ [ ] (A) 4 (B) 5 (C) 0 (D) 6 e) 6 + 3 = ________ [ ] (A) 4 (B) 6 (C) 3 (D) 9 & Remembering & Understanding Let us now learn to add two 2-digit numbers mentally, through these examples. 1) Add 2-digit numbers mentally without regrouping Example 16: Add mentally: 53 and 65 Solution: To add the given numbers mentally, follow these steps: 46 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___52 / 184

Steps Solved Solve this 53 and 65 38 and 41 Step1: Add the digits in the ones place of the two 3+5=8 ____ + ____ = ___ numbers mentally. Step 2: Add the digits in The digits in the tens place The digits in the tens place the tens place of the two numbers mentally. of the two numbers are of the two numbers are ___ 5 and 6. Keep 6 in your and ____. Keep ____ in your mind, count 5 forward as mind, count ___ forward as 7, 8, 9, 10 and 11. ____, ____and ____. 5 + 6 = 11 ____ + ____ = ___ Step 3: Write sum of digits So, 53 + 65 = 118. So, 38 + 41 = ___. obtained in step 1 and sum of digits obtained in step 2 together. This is the sum of the given numbers. 2) Add 2-digit numbers mentally with regrouping Example 17: Add mentally: 29 and 56 Solution: To add the given numbers mentally follow these steps. Steps Solved Solve this 29 and 56 83 and 47 Step1: Split the two given 29 = 20 + 9 83 = ___ + ____ 47 = ___ + ____ numbers as tens and ones 56 = 50 + 6 mentally. Step 2: Add the ones 9 + 6 = 15 ____ + ____ = ____ of the two numbers ____ + ____ = ____ mentally. ____ + ___ = ____ So, 83 + 47 = ___. Step 3: Add the tens 20 + 50 = 70 of the two numbers mentally. Step 4: Add the sums from 70 + 15 steps 2 and 3 mentally = 70 + 10 + 5 (regroup if needed). = 85 Step 5: Write the sum of So, 29 + 56 = 85. the given numbers. Addition 47 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___53 / 184

Application We have seen how easy it is to add two 2-digit numbers mentally. Let us see some real-life situations in which mental addition of 2-digit numbers is useful. Example 18: Suraj has 34 sheets and Kamal has 27 sheets of paper. How many sheets of paper do they have in all? Solve mentally. Solution: Number of sheets of paper Suraj has = 34 Number of sheets of paper Kamal has = 27 Total number of sheets they have together = 34 + 27 Regrouping the given numbers in tens and ones and adding, we get 30 + 4 + 20 + 7 To add two 1-digit numbers mentally, keep the larger number in mind and add the smaller one to it. Add tens and ones accordingly. = 50 + 11 = 50 + 10 + 1 (Regroup and add) = 60 + 1 = 61 Therefore, Suraj and Kamal have 61 sheets of paper. Example 19: Vivek has 49 bags and Shyam has 29 bags. How many bags do they have in total? Solve mentally. Solution: Number of bags Vivek has = 49 Number of bags Shyam has = 29 Total number of bags they have together = 49 + 29 Regrouping the given numbers in tens and ones and adding, we get 40 + 9 + 20 + 9 To add two 1-digit numbers, keep the larger number in mind and add the smaller one to it. Add tens and ones accordingly. = 40 + 20 + 18 = 60 + 10 + 8 (Regroup and add) = 70 + 8 = 78 48 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___54 / 184

Higher Order Thinking Skills (H.O.T.S.) We have seen mental addition of two 2-digit numbers. Let us now see some examples to add three 2-digit numbers mentally. Example 20: Add mentally: 25, 37 and 19 Solution: To add the given numbers mentally follow these steps. Steps Solved Solve this 25, 37 and 19 40, 29 and 54 40 = ___ + ____ Step 1: Split the three given numbers 25 = 20 + 5 29 = ___ + ____ as tens and ones mentally. 37 = 30 + 7 54 = ____+____ 19 = 10 + 9 ____ + ____+ ____ Step 2: Add the tens of the given 20 + 30 + 10 = 60 = ____ numbers mentally. Step 3: Add the ones of the given 5 + 7 + 9 = 21 ____+___ + ____ = numbers mentally. ____ Step 4: Add the sums from steps 2 and 60 + 21 ____ + ___ = ____ 3 mentally, regroup again if needed. = 60 + 20 + 1 = 81 Step 5: Write the sum of the given So, 25 + 37 + 19 = 81. So, 40 + 29 + 54 = ___. numbers. Drill Time Concept 4.1: Add 3-digit and 4-digit Numbers 1) Add 3-digit numbers with regrouping. a) 481 + 129 b) 119 + 291 c) 288 + 288 d) 346 + 260 e) 690 + 110 2) Add 4-digit numbers without regrouping. a) 1234 + 1234 b) 1000 + 2000 c) 4110 + 1332 d) 5281 + 1110 e) 7100 +1190 Addition 49 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___55 / 184

3) Add 4-digit numbers with regrouping. a) 5671 + 1430 b) 3478 + 2811 c) 4356 + 1753 d) 2765 + 1342 e) 4901 + 2222 4) Word problems a) Shyam has 269 pens and Ritesh has 832 pens. How many pens do the boys have altogether? b) Ravi’s garden has 673 rose flowers and Rahul’s garden has 978 rose flowers. How many flowers are there in the two gardens? Concept 4.2: Estimate the Sum of Two Numbers 5) Estimate the sum of the following: a) 211 and 115 b) 549 and 120 c) 385 and 190 d) 222 and 524 e) 672 and 189 6) Word problems a) Sonu has 46 red roses, Mona has 22 yellow roses. Estimate the total number of roses. b) Rakesh has 67 pencils and Mukesh has 43 pencils. Estimate the number of pencils both of them have in all. Concept 4.3: Add 2-digit Numbers Mentally 7) Add 2-digit numbers mentally without regrouping. a) 31 and 22 b) 22 and 42 c) 45 and 51 d) 11 and 34 e) 32 and 61 8) Add 2-digit numbers mentally with regrouping. a) 45 and 57 b) 75 and 56 c) 82 and 19 d) 27 and 35 e) 17 and 37 50 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___56 / 184

Subtraction5CHAPTER 7689 5032 I Will Learn Concepts 5.1: Su1b.t1r:acVte3rt-idceigsitaannddD4ia-dgiognitaNlsuomf bTweors-Dimensional Shapes 5.2: Estimate the Difference between Two Numbers 5.3: Subtract 2-digit Numbers Mentally JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___57 / 184

Concept 5.1: Subtract 3-digit and 4-digit Numbers Think Given below is the number of men and women in Neena’s town in the years 2013 and 2014. Years 2013 2014 Men Women 2020 2107 1704 1882 How many more men than women lived in Neena's town in the years 2013 and 2014? To answer this question, we must learn subtraction of 4-digit numbers. Recall Recall that we can subtract numbers by writing one below the other. A 2-digit number can be subtracted from a larger 2-digit number or a 3-digit number. Similarly, a 3-digit number can be subtracted from a larger 3-digit number. Let us answer these to revise the concept. a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ f) 50 – 45 = _________ & Remembering & Understanding We have learned how to subtract two 3-digit numbers without regrouping. Let us now learn how to subtract them with regrouping. 1) Subtract 3-digit numbers with regrouping When a larger number is to be subtracted from a smaller number, we regroup the next higher place and borrow. Let us understand this through an example. 52 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___58 / 184

Example 1: Subtract: 427 from 586 Solution: To subtract, write the smaller number below the larger number. Solved Step 1: Subtract the ones. But, 6 – 7 is not Step 2: Subtract the Step 3: Subtract possible as 6 < 7. So, regroup the digits in tens. the hundreds. the tens place. 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 ten. Now subtract 7 ones from 16 ones. H TO H TO H TO 5 7 16 7 16 5 7 16 –4 –4 \\8 \\6 5 \\8 \\6 \\8 \\6 1 27 –4 2 7 27 9 59 59 H TO Solve these H TO 623 H TO 453 – 376 – 264 552 – 263 2) Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Subtraction 53 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___59 / 184

Example 2: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. Solved Step 2: Subtract the tens. Th H T O 7689 Th H T O −5032 7689 −5032 7 57 Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7689 7 68 9 −5032 − 5 03 2 657 2 65 7 Th H T O Solve these O Th H T O Th H T 2879 8 0 00 – 2137 4 7 89 – 2 0 00 – 2 4 75 3) Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in thousands, hundreds and tens places. Let us see an example. Example 3: Subtract: 4868 from 7437 Solution: Write the smaller number below the larger number. 54 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___60 / 184

Steps Solved O Solve these Th H T O Step 1: Subtract the ones. Th H T 17 1654 But, 7 − 8 is not possible as \\7 −1 2 4 6 7 < 8. So, regroup the tens digit, 2 8 3. 3 tens = 2 tens + 1 ten. Borrow 7 4 3\\ Th H T O 1 ten to the ones place. −4 8 6 9 5674 −2 3 8 2 Step 2: Subtract the tens. But, Th H T O Th H T O 2 − 6 is not possible as 2 < 6. 12 7468 So, regroup the hundreds digit, 3 \\2 17 −4 8 3 7 4. 4 hundreds = 3 hundreds + 1 7 4\\ 3\\ \\7 Th H T O hundred. Borrow 1 hundred to −4 8 6 8 9276 −5 1 4 7 the tens place. 69 Step 3: Subtract the hundreds. Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 7. 6 \\3 \\2 17 7 thousands = 6 thousands + 1 \\7 4\\ 3\\ \\7 8 6 8 thousand. Borrow 1 thousand to − 4 the hundreds place. 569 Step 4: Subtract the thousands. Th H T O 13 12 6 \\3 \\2 17 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Application Subtraction of 3-digit numbers is very often used in real-life. Here are a few examples. Subtraction 55 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___61 / 184

Example 4: Sonu bought 375 marbles. He gave 135 marbles to his brother. Solution: How many marbles are left with him? Example 5: Total number of marbles Sonu bought = 375 H TO Solution: Number of marbles given to Sonu’s brother = 135 375 Number of marbles left with him = 375 – 135 = 240 −1 3 5 Therefore, 240 marbles are left with Sonu. 240 Vinod had 536 stamps. He gave some stamps to his brother and then Vinod was left with 278 stamps. How many stamps did Vinod give his brother? H TO Total number of stamps Vinod had = 536 12 Number of stamps Vinod had after giving some 4 2\\ 16 to his brother = 278 \\5 \\3 \\6 Number of stamps he gave his brother = −278 536 – 278 = 258 258 We can use subtraction of 4-digit numbers in real-life situations. Let us see some examples. Example 6: A rope is 6436 cm long. A 3235 cm long piece is cut from it. How much Solution: of the rope is left? Th H T O Length of the rope = 6436 cm 6436 Length of the piece cut = 3235 cm −3 2 3 5 The length of the remaining piece of rope = 3201 6436 cm – 3235 cm = 3201 cm Example 7: Mohan’s uncle stays 8630 m away from Mohan’s house. Mohan travelled 6212 m of the distance. What is the distance yet to be covered by Mohan to reach his uncle’s house? Solution: Distance between Mohan’s house and his uncle’s house = 8630 m Distance travelled by Mohan = 6212 m Th H T O Remaining distance Mohan has to travel 2⁄ 1⁄0 = 8630 m – 6212 m = 2418 m Therefore, Mohan has to travel 2418 m more to 8 630 reach his uncle’s house. − 6 212 2 418 56 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___62 / 184

Higher Order Thinking Skills (H.O.T.S.) We can check the correctness of a subtraction problem using addition. Consider an example. Example 8: Subtract: a) 27 from 36 b) 145 from 364. T O Solution: a) 36 – 27 2 16 \\3 We can write 36 = 27 + 9 −2 6\\ b) 364 – 145 7 9 364 – 145 = 219 HT O We can write 364 = 145 + 219 5 14 3 \\6 4\\ −1 4 5 9 21 We can conclude that to check if the subtraction is correct, we add the subtrahend (the number being subtracted) and the difference. If this sum is the same as the minuend (the number from which a number is subtracted), the subtraction is correct. Framing word problems Let us consider these subtraction facts. a) 37 – 14 = 23 b) 37 – 23 = 14 We can try to frame some interesting situations and problems using these subtraction facts. a) Of the 37 students in class, 14 are girls. How many are boys? b) 37 children are playing on the ground. 23 of them are girls. How many boys are playing on the ground? Similarly, we can frame some interesting problems using subtraction facts of 3-digit numbers. Let us see an example. Subtraction 57 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___63 / 184

Example 9: Frame a word problem using Solution: a) 706 – 234 = 472 b) 461 − 110 = 351 One of the many possible different answers are: a) In a school, there are 706 students. 234 students were absent on Monday. How many students were present? b) 461 people booked the train for a trip to Goa. 110 people cancelled the trip. How many people went on the trip? Concept 5.2: Estimate the Difference between Two Numbers Think Neena had ` 450 with her. She wanted to buy a toy car for ` 185 and a toy train for ` 150. How much money will remain with Neena after buying them? To answer this question, we must learn to estimate the difference between two numbers. Recall We know that in some situations where we do not need the exact number, we use estimation. Estimation can be done by rounding off numbers to a given place. Let us answer these to revise the concept of rounding off to the nearest 10. a) 87 = ______ b) 53 = ______ c) 65 = ______ d) 42 = ______ e) 33 = ______ & Remembering & Understanding Rounding off numbers can be used to estimate the difference between two 2-digit numbers and between two 3-digit numbers. Let us understand this through examples. Example 10: Estimate the difference a) 69 – 15 b) 86 – 12 Solution: a) 69 – 15 58 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___64 / 184

Rounding off 69 to the nearest tens gives 70 (as 9 > 5) and rounding off 15 to the nearest tens, gives 20 (as 5 = 5). So, the required difference is 70 – 20 = 50. b) 86 – 12 Rounding off 86 to the nearest tens gives 90 (as 6 > 5) and rounding off 12 to the nearest tens, gives 10 (as 2 < 5). So, the required estimated difference is 90 – 10 = 80. Example 11: Estimate the difference: a) 593 – 217 b) 806 – 124 Solution: a) 593 – 217 Rounding off 593 to the nearest tens gives 590 (as 3 < 5) and rounding off 217 to the nearest tens, gives 220 (as 7 > 5). So, the required estimated difference is 590 – 220 = 370. b) 806 – 124 Rounding off 806 to the nearest tens gives 810 (as 6 > 5) and rounding off 124 to the nearest tens, gives 120 (as 4 < 5). So, the required estimated difference is 810 – 120 = 690. Application Estimation of differences can be used in real-life situations. Let us see a few examples. Example 12: Parul has 83 pencils. She gives 32 pencils to her sister. Estimate the number of pencils that remain with Parul. Solution: Number of pencils Parul has = 83 83 rounded off to the nearest tens is 80 (since 3 < 5). Number of pencils given to Parul’s sister = 32 32 rounded off to the nearest 10 is 30 (since 2 < 5). So, the estimated number of pencils left with Parul = 80 − 30 = 50 Therefore, Parul has about 50 pencils. Subtraction 59 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___65 / 184

Example 13: Ram has 94 sweets. He distributes 46 sweets among his school friends. About how many sweets remain with Ram? Solution: Number of sweets Ram has = 94 94 rounded off to the nearest tens is 90 (since 4 < 5). Number of sweets distributed among Ram's school friends = 46 46 rounded off to the nearest tens is 50 (since 6 > 5). So, the estimated number of sweets left with Ram = 90 − 50 = 40 Therefore, Ram has about 40 sweets. Higher Order Thinking Skills (H.O.T.S.) In some situations, we may need to carry out both addition and subtraction. In such cases, we need to identify which operation is to be carried out first. Example 14: In a school, there are 976 students. Of them, 325 are from the primary section, 416 are from the middle section, and the rest are from high school. How many high school students are there in the school? Solution: Total number of students = 976 Hn T O Number of students from the primary section = 325 1 Number of students from the middle section = 416 325 +4 1 6 Total number of students in primary and middle school 741 sections = 325 + 416 = 741 Number of students in high school = Total number of HTO students – Number of students in primary and middle 976 school sections = 976 – 741 = 235 −7 4 1 235 Therefore, the number of high school students is 235. 60 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___66 / 184

Concept 5.3: Subtract 2-digit Numbers Mentally Think Neena had 19 pens. She gave 12 pens to her sister. Can you find the number of pens remaining with Neena without using a paper and a pencil? To subtract two numbers mentally, we need to learn mental subtraction of two numbers. Recall Recall that to subtract two 1-digit numbers mentally, we keep the larger number in our mind and subtract the smaller one from it. Let us answer these to revise the concept. a) 5 – 4 = ________ [] (A) 5 (B) 4 (C) 1 (D) 9 b) 3 – 3 = ________ [] (A) 3 (B) 6 (C) 0 (D) 5 c) 4 – 1 = ________ [] (A) 3 (B) 4 (C) 6 (D) 8 d) 5 – 0 = ________ [] (A) 4 (B) 5 (C) 0 (D) 6 e) 6 – 3 = ________ [] (A) 4 (B) 6 (C) 3 (D) 9 & Remembering & Understanding We have learnt to subtract 1-digit numbers mentally. Subtracting 2-digit numbers mentally is similar to that. Let us understand this through an example. Subtraction 61 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___67 / 184

1) Subtract 2-digit numbers mentally without regrouping Example 15: Subtract mentally: 52 from 76 Solution: Follow these steps to subtract mentally. Steps Solved Solve this Step1: Subtract mentally 52 from 76 35 from 69 ______ – ______ = the digits in the ones place 6 – 2 = 4 of the two numbers. Step 2: Subtract mentally The digits in the tens place The digits in the tens place of the digits in the tens place of the two numbers are 7 the two numbers are _______ of the two numbers. and 5. and _______. So, imagine that 7 fingers So, imagine that _____ fingers are open. Then imagine are open. closing 5 of them. Then imagine closing of 7–5=2 them. ____– ____ = ___ Step 3: Write the difference So, 76 – 52 = 24. So, 69 – 35 = ____. obtained in steps 1 and 2 together as the difference of the given numbers. Sometimes regrouping is necessary in subtraction. Let us see an example to understand this. 2) Subtract 2-digit numbers mentally with regrouping Example 16: Subtract mentally: 29 from 56 Solution: Follow these steps to subtract mentally. Steps Solved Solve this 29 from 56 46 from 83 83 = ___ + ____ Step1: Split the two given 29 = 20 + 9 46 = ___ + ____ numbers as tens and ones. 56 = 50 + 6 62 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___68 / 184

Steps Solved Solve this 29 from 56 46 from 83 Step2: Check if ones can 6 – 9 is not possible. So, ____ - ____ is possible (True/ be subtracted. If not, regroup the tens. False) If it is true, subtract. regroup the tens. Add 10 ones to 6 to get 16 If it is false, regroup. Add ten ones to ones and and subtract 1 ten from 5 Add 10 ones to ___ to get reduce 1 ten from tens. tens to get 4 tens. ____ and subtract 1 ten from ____ tens to get ____ Step 3: Subtract the ones of 16 – 9 = 7 tens. ____ – ____ = ____ the two numbers mentally. Step 4: Subtract the tens of 4 tens – 2 tens = 2 tens ____ – ____ = ____ the two numbers mentally. Step 5: Write the answers So, 56 – 29 = 27. ____ – ___ = ____ from steps 3 and 4 together as the difference. Application We have seen that it is easy to subtract two 2-digit numbers mentally. In some real-life situations, we use mental subtraction of numbers. Let us see some examples. Example 17: Manoj has 64 notebooks. He has used 45 notebooks. How many notebooks are left with him? Solve mentally. Solution: Number of notebooks Manoj has = 64 Number of notebooks he has used = 45 The number of notebooks remaining with him = 64 – 45 = 19 Therefore, Manoj has 19 notebooks left with him. Example 18: Alisha went to school for 49 days in Term I and 65 days in Term II. For how many more days did Alisha go to school in the Term II than in the Term I? Solve mentally. Solution: Number of days Alisha went to school in Term I = 49 Number of days she went to school in Term II = 65 Difference in number of days = 65 – 49 = 16 Therefore, Alisha went to school 16 days more in Term II than in Term I. Subtraction 63 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___69 / 184

Higher Order Thinking Skills (H.O.T.S.) We have seen mental subtraction of two 2-digit numbers. Let us now see some real-life examples where we might have to add and subtract numbers mentally. Example 19: Renu had ` 80. She bought guavas for ` 25 and bananas for ` 17. Calculate mentally the money that Renu has to pay the fruit seller. Also calculate mentally the money left with her. Solution: Total money Renu had = ` 80 Money she spent on guavas = ` 25 Money she spent on bananas = ` 17 To find the money she has to give the fruit seller, Renu has to add the prices of guavas and bananas. That is, ` 25 + ` 17 = `42. To find the money remaining with her, Renu has to subtract this sum from the total money she had. So, ` 80 – ` 42 = ` 38. Drill Time Concept 5.1: Subtract 3-digit and 4-digit Numbers 1) Subtract 3-digit numbers with regrouping a) 254 – 173 b) 678 – 619 c) 147 – 129 d) 781 – 682 e) 356 – 177 2) Subtract 4-digit numbers without regrouping a) 2341 – 1230 b) 7632 – 5120 c) 9763 – 2311 d) 7629 – 1318 e) 7589 – 1268 3) Subtract 4-digit numbers with regrouping a) 7632 – 1843 b) 4391 – 2482 c) 9843 – 7943 d) 8325 – 5436 e) 6893 – 3940 64 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___70 / 184

4) Word problems a) A stick is 8745 cm long. A 4313 cm long piece is cut from it. What part of the stick is remaining? b) Raj stays 5786 m away from Matin’s house. Raj travelled 3825 m of the distance. What is the distance yet to be covered by Raj to reach Matin’s house? Concept 5.2: Estimate the Difference between Two Numbers 5) Estimate these differences: a) 65 – 15 b) 48 – 16 c) 67 – 32 d) 896 – 432 e) 679 – 387 6) Word problems a) In a class, there are 562 students of 3 groups. Of them, 118 are from the red group, 321 are from the green group, and the rest are from the blue group. How many students are there in the class. who are in the blue group? b) Sneha has 77 balloons. She gives 42 balloons to her sister. About how many balloons remain with Sneha? Concept 5.3: Subtract 2-digit Numbers Mentally 7) Subtract 2-digit numbers mentally without regrouping a) 43 from 84 b) 24 from 76 c) 52 from 87 d) 34 from 75 e) 14 from 38 8) Subtract 2-digit numbers mentally with regrouping a) 42 from 81 b) 28 from 84 c) 11 from 20 d) 23 from 51 e) 76 from 81 9) Word problems a) Ram has 48 pencils. He has used 29 pencils. How many pencils are left with him? Solve mentally. b) Sejal travelled for 23 km on Day 1 and 76 km on Day 2. How much more distance (in km) did Sejal travel on Day 2 than on Day 1? Solve mentally. Subtraction 65 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___71 / 184

6CHAPTER Multiplication 324 x2 648 513 x 5 = I Will Learn CCoonncceeppttss 6.1: Mu1l.t1ip: lVy e2r-tdicigeist aNnudmDbieargsonals of Two-Dimensional Shapes 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 6.3: Double 2-digit and 3-digit Numbers Mentally JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___72 / 184

Concept 6.1: Multiply 2-digit Numbers Think Neena goes on a holiday to her hometown for 3 weeks. How many days would she spend in her hometown? To answer this question, we must learn the multiplication tables. Recall In Class 2, we have learnt that multiplication is repeated addition. The symbol ‘×’ indicates multiplication. Multiplication means having a certain number of groups of the same size. Let us recall the multiplication tables of numbers 1 to 6. Table of 1 Table of 2 Table of 3 3×1=3 1×1=1 2×1=2 3×2=6 3×3=9 1×2=2 2×2=4 3 × 4 = 12 3 × 5 = 15 1×3=3 2×3=6 3 × 6 = 18 3 × 7 = 21 1×4=4 2×4=8 3 × 8 = 24 3 × 9 = 27 1×5=5 2 × 5 = 10 3 × 10 = 30 1×6=6 2 × 6 = 12 1×7=7 2 × 7 = 14 1×8=8 2 × 8 = 16 1×9=9 2 × 9 = 18 1 × 10 = 10 2 × 10 = 20 Multiplication 67 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___73 / 184

Table of 4 Table of 5 Table of 6 4×1=4 5×1=5 6×1=6 4×2=8 5 × 2 = 10 6 × 2 = 12 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 Let us now construct multiplication tables of 7, 8 and 9. Then learn to multiply 2-digit numbers. Remembering & Understanding & In multiplication of two numbers: • The number written to the left of the ‘×’ sign is called multiplicand. • The number written to the right of the ‘×’ sign is called multiplier. • The number written to the right of the ‘=’ sign is called product. Multiplication Fact 5 × 6 = 30 ↓ ↓ ↓ Multiplicand Multiplier Product Note: (a) Representing the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) The multiplicand and the multiplier are also called the factors of the product. 68 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___74 / 184

For example, 2 × 7 = 14 = 7 × 2; 4 × 5 = 20 = 5 × 4 and so on. Using multiplication facts and order property, let us now construct the multiplication tables of 7, 8 and 9. Table of 7 Table of 8 7 × 1 = 7 seven ones are seven 8 × 1 = 8 eight ones are eight 7 × 2 = 14 seven twos are fourteen 8 × 2 = 16 eight twos are sixteen 7 × 3 = 21 8 × 3 = 24 7 × 4 = 28 seven threes are twenty- eight threes are twenty- 7 × 5 = 35 one four seven fours are twenty- eight 8 × 4 = 32 eight fours are thirty-two seven fives are thirty-five 8 × 5 = 40 eight fives are forty 7 × 6 = 42 seven sixes are forty-two 8 × 6 = 48 eight sixes are forty-eight 7 × 7 = 49 seven sevens are forty-nine 8 × 7 = 56 eight sevens are fifty-six 7 × 8 = 56 seven eights are fifty-six 8 × 8 = 64 eight eights are sixty-four 7 × 9 = 63 seven nines are sixty-three 7 × 10 = 70 seven tens are seventy 8 × 9 = 72 eight nines are seventy- two 8 × 10 = 80 eight tens are eighty 9×1=9 Table of 9 9 × 2 = 18 nine ones are nine 9 × 3 = 27 nine twos are eighteen 9 × 4 = 36 nine threes are twenty-seven 9 × 5 = 45 nine fours are thirty-six 9 × 6 = 54 nine fives are forty-five 9 × 7 = 63 nine sixes are fifty-four 9 × 8 = 72 nine seven are sixty-three 9 × 9 = 81 nine eights are seventy-two 9 × 10 = 90 nine nines are eighty-one nine tens are ninety Multiplication 69 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___75 / 184

Multiplying 2-digit numbers by 1-digit numbers Now, let us learn to multiply a 2-digit number by a 1-digit number. Consider the following example. Example 1: Find the product: 23 × 7 Solution: Follow these steps to find the product. Steps Solved Solve these Step 1: Multiply the ones. 3 × 7 = 21 H TO Step 2: Regroup the 21 ones = 2 tens and 17 product. 1 ones ×9 Step 3: Write the ones TO H TO digit of the product in the 15 product and carry the tens 2 ×4 digit to the tens place. 23 ×7 H TO 23 1 ×8 Step 4: Multiply tens. 2 × 7 = 14 Step 5: Add the carry from 14 + 2 = 16 step 3 to the product. Step 6: Write the sum in the H TO tens place. 2 23 ×7 161 Application Let us now see some real-life situations where we use multiplication of 2-digit numbers. 70 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___76 / 184

Example 2: There were 54 students in a class of a school. The school had 8 such classes. How many students were there in the entire school? Solution: Number of students in one class = 54 students H TO Number of classes in the school = 8 3 4 8 Number of students in the school = 54 × 8 5 2 × Therefore, the total number of students in the school = 432 4 3 Manoj travelled 7 km in a day. If he travels the same Example 3: distance every day, what distance does he travel in 25 days? Solution: The distance that Manoj travelled in a day = 7 km H TO He travels the same distance every day. The distance he 3 travels in 25 days = 25 × 7. 25 Therefore, Manoj travels 175 km in 25 days. ×7 175 Higher Order Thinking Skills (H.O.T.S.) Framing word problems: Using multiplication tables, we can frame word problems from the given clues. Let us now try to frame a few word problems using multiplication. Example 4: Number of chocolates in a box = 9 Number of such boxes = 5 Solution: Total chocolates = 45 Example 5: Word problem: A box contains 9 chocolates. There are 5 such boxes. Find the total number of chocolates. Number of students in a row = 8 Number of rows = 2 Solution: Total rows = 16 Word problem: There are 2 rows with 8 students in each row. What is the total number of students? Multiplication 71 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___77 / 184

Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers Think Neena collected some shells and put them into 9 bags. If each bag has 110 shells, how many shells did she collect? To answer this question, we must learn multiplication of 3-digit numbers. Recall We have learnt to multiply a 2-digit number with a 1-digit number. We have also learnt to regroup the ones in multiplication. Let us answer these to revise the concept a) 22 × 2 = _________ b) 42 × 1 = _________ c) 33 × 4 = _________ d) 11 × 7 = _________ e) 45 × 3 = _________ e) 50 × 2 = _________ Similarly, we can multiply a 3-digit number by a 1-digit number. & Remembering & Understanding We multiply 3-digit numbers just as we multiply 2-digit numbers. 1) Multiplying 3-digit numbers by 1-digit numbers (without regrouping) Let us understand the step-by-step procedure through a few examples. Example 6: Multiply: 401 × 3 Solution: Follow these steps to multiply the given numbers. 72 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___78 / 184

Step 1: Multiply the Solved Step 3: Multiply the hundreds ones and write the and write the product under product under ones. Step 2: Multiply the hundreds. tens and write the H TO product under tens. Th H T O 401 401 H TO ×3 ×3 401 3 1203 ×3 03 H TO Solve these H TO 220 HTO 232 ×4 13 0 ×3 ×2 2) Multiply 3-digit numbers by 1-digit numbers (with regrouping) When a 3-digit number is multiplied by a 1-digit number, we get a 2-digit product in any or all of the places. We regroup these products and carry over the tens digit of the product to the next place. Let us understand this better through the following examples. Example 7: Multiply: 513 × 5 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these H TO Step 1: Multiply the ones and write the H TO product under ones. Regroup if the 1 635 product has two or more digits. ×7 513 ×5 5 Multiplication 73 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___79 / 184

Steps Solved Solve these H TO Step 2: Multiply the tens. Add the carry H TO over (if any) to the product. Write the 444 sum under tens. 1 ×8 Regroup if the product has two or more 513 digits. H TO ×5 65 342 ×5 Step 3: Multiply the hundreds. Add the Th H T O carry over (if any) to the product and write the sum under hundreds. Regroup if 1 the product has two or more digits. 513 ×5 2 565 3) Multiply 3-digit numbers by 2-digit numbers Multiplication of 3-digit numbers by 2-digit numbers may sometimes involve regrouping too. Let us understand this concept through step-by-step procedure. Consider the following examples. Example 8: Multiply: 243 × 34 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these H TO Step 1: Arrange the numbers in H TO columns, as shown. 243 ×34 Step 2: Multiply the ones by the ones H TO 141 digit of the multiplier. 3 × 4 = 12. ×22 Write 2 in the ones place of the product. 1 Write 1 in the tens place as carry over. 243 ×34 2 74 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___80 / 184

Steps Solved Solve these Step 3: Multiply the tens digit by the ones digit of the multiplier. 4 × 4 = 16. H TO H TO Add the carry over from the previous 11 step. So, 16 + 1 = 17. Write 7 in the tens 243 453 place of the product and 1 in the ×34 ×13 hundreds place as carry over. 72 Step 4: Multiply the hundreds by the ones digit of the multiplier. 2 × 4 = 8. H TO Add the carry over from the previous 11 step. So, 8 + 1 = 9. Write 9 in the hundreds 243 place of the product. ×34 972 Step 5: Write 0 in the ones place before multiplying ones by the tens digit of the HTO multiplier. Multiply the ones by the tens digit of 11 the multiplier. Write the product under tens place. 2 4 3 My BrHainT O 3×3=9 × 3 4Train 3 Step 6: Multiply the tens by the tens 3 digit of the multiplier. 972 4 × 3 = 12 Write 2 in hundreds place of the 90 product and 1 in hundreds place of the multiplicand as carry over. 26 H TO ×2 1 11 243 ×34 972 290 Multiplication 75 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___81 / 184

Steps Solved Solve these Step 7: Multiply the hundreds by the tens digit of the multiplier. Th H T O H TO 2×3=6 Add the carry over from the previous 1 352 step. So, 6 + 1 = 7. Write 7 in the ×23 thousands place of the multiplicand. 11 243 Step 8: Add the products and write the ×34 sum. The sum is the required product. 972 7290 Th H T O 1 11 243 ×34 972 7290 8262 Application Let us now see some real-life word problems. Example 9: Rohan ran 315 m every day for a week. How many metres did he run Solution: in that week? Th H T O 1 week = 7 days Distance run by Rohan in a day = 315 m 13 Distance he ran in a week = 315 m × 7 315 ×7 Therefore, the total distance run by him in 1 week = 2205 2205 m 76 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___82 / 184

Example 10: Payal saves ` 175 per month for a year. How much Th H T O money will she have at the end of the year? 11 Solution: Amount saved by Payal per month = ` 175 175 Number of months in a year = 12 × 12 Total money saved in a year = 175 × 12 11 Therefore, total money Payal has at the end of a 350 year = ` 2100 1750 2100 Higher Order Thinking Skills (H.O.T.S.) Sometimes, we can find numbers that satisfy two or more conditions. Let us now see some examples. Example 11: Find two numbers whose sum is 13 and product is 6 more than 30. Solution: The two conditions in this problem are: a) The sum of the numbers is 13 b) The product of the numbers is 6 more than 30 From condition b), 6 more than 30 = 30 + 6 = 36. So, the product of the numbers is 36. Now, let us find the two numbers whose product is 36 and sum is 13. 36 = 1 × 36; 36 = 2 × 18; 36 = 3 × 12; 36 = 4 × 9 and 36 = 6 × 6. Of these, the numbers whose sum is 13 are 9 and 4 (since 9 + 4 = 13.) Therefore, the required numbers are 9 and 4. Example 12: Find two numbers whose difference is 1 and product is 2 more than 40. Solution: The two conditions in this problem are: a) The difference of the numbers is 1. b) The product of the numbers is 2 more than 40 which is 42. Now, let us find two numbers whose product is 42 and difference is 1. 42 × 1 = 42; 21 × 2 = 42; 14 × 3 = 42; 7 × 6 = 42. Of these the numbers whose difference is 1 are 7 and 6. Therefore, the required numbers are 7 and 6. Multiplication 77 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___83 / 184

Concept 6.3: Double 2-digit and 3-digit Numbers Mentally Think Neena has 23 red beads. Her friend has double the number of beads. Neena wants to know the number of beads her friend has. Do you know how to find that mentally? To answer this, we need to learn to double numbers mentally. Recall We have learnt mental addition and subtraction in the previous chapters. Let us now learn to double a given number mentally. To double a number, we must be thorough with the multiplication table of 2. Calculating mentally makes problem solving faster and easier. For example, 5 × 2 = 10, 3 × 2 = 6, 10 × 2 = 20 and so on. & Remembering & Understanding Let us now understand how to double a 2-digit number mentally through a few examples. Example 13: Double the given number: 53. Solution: To double the given number, follow these steps: Steps Solved Solve this 53 41 Step 1: Multiply the tens digit by 2. The tens digit is 5. The tens digit is ____. So, 5 × 2 = 10. So, ___ × 2 = ___. Step 2: If the ones digit is less The ones digit is 3. The ones digit is ___ than or equal to 4, write the 3 < 4 (True) ___ < ___ (True/ False) product in step 1 as it is. If not, add 1 to it and write. 78 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___84 / 184

Steps Solved Solve this 53 41 Step 3: Multiply the ones digit by 2. 3×2=6 ___ × 2 = ___ Step 4: Write the products in 53 × 2 = 106 ___ × 2 = ___ steps 1 and 3 together. This gives double of the given number. Application We have learnt to double 2-digit numbers mentally. Let us now see some examples where we apply this concept. Example 14: Rohit has 14 shirts. His brother has double the number of shirts. How many shirts does Rohit’s brother have? Solution: Number of shirts Rohit has = 14 Number of shirts Rohit’s brother has = Double of that Rohit has = 14 × 2 = 28 Therefore, Rohit’s brother has 28 shirts. Example 15: Sony is 36 years old. Her aunt’s age is double that of Sony’s age. How old is Sony’s aunt? Solution: Sony’s age = 36 years Age of Sony’s aunt = Double that of Sony’s age = 36 years × 2 = 72 years Therefore, Sony’s aunt is 72 years old. Higher Order Thinking Skills (H.O.T.S.) Doubling a 3-digit number is similar to doubling a 2-digit number. Let us now see some examples. Example 16: Double the number: 125. Solution: To double the given number, follow these steps: Multiplication 79 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___85 / 184

Steps Solved Solve this 125 293 Step 1: Multiply the number The number formed The number formed formed by the two leftmost digits by the two leftmost by the two leftmost by 2. digits is 12. 12 × 2 = 24. digits is ____. So, ___ × Step 2: If the ones digit of the The ones digit is 5. 2 = ___. The ones digit is __ given number is less than or equal 5 < 4 (False) ___ < ___ (True/ False) to 4. If it is true, write the product 24 + 1 = 25 in step 1 as it is. If not, add 1 to it and write. Step 3: Multiply the ones digit by 5 × 2 = 10 ___ × 2 = ___. 2. Its ones digit is 0. Its ones digit is ___. Step 4: Write the products in steps So, 125 × 2 = 250 1 and 3 together. This gives the So, ___ × 2 = ___. double of the given number. Drill Time Concept 6.1: Multiply 2-digit Numbers 1) Multiply 2-digit numbers by 2, 3, 4, 5 and 6 a) 56 × 3 b) 23 × 2 c) 77 × 6 d) 50 × 5 e) 62 × 4 2) Multiply 2-digit numbers by 7, 8 and 9 a) 23 × 9 b) 12 × 7 c) 76 × 8 d) 84 × 8 e) 83 × 9 3) Word problems a) There were 23 boys in one group. The school had 4 such groups. How many boys were there in all the groups? b) Viraj travelled for 30 km in one day. He travelled for 7 days. How many kilometre did he travel in 7 days? 80 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___86 / 184

Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 4) Multiply a 3-digit number by a 1-digit number (without regrouping) a) 101 × 8 b) 212 × 4 c) 414 × 2 d) 111 × 5 e) 323 × 3 5) Multiply 3-digit numbers by 1-digit numbers (with regrouping) a) 225 × 7 b) 762 × 4 c) 868 × 8 d) 723 × 5 e) 429 × 2 6) Multiply 3-digit numbers by 2-digit numbers a) 769 × 21 b) 759 × 10 c) 578 × 42 d) 619 × 66 e) 290 × 30 7) Word problems a) Seema drove 462 km every day for a week. What distance does she drive in that week? b) Suraj spends ` 616 for a set of books. How much will he spend on 24 such sets? Concept 6.3: Double 2-digit and 3-digit Numbers Mentally 8) Double the given numbers mentally. a) 23 b) 52 c) 61 d) 10 e) 74 9) Word problems a) Rohan bought 42 books in Year I and doubled the number in Year II. How many books did he buy in Year II? b) Sonal earned ` 28 on Monday. She earned double the amount on Tuesday. How much did she earn on Tuesday? Multiplication 81 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___87 / 184

Time7CHAPTER I Will Learn Concepts 7.1: Re1a.1d: aVeCraticleensdaanrd Diagonals of Two-Dimensional Shapes 7.2: Read Time Correct to the Hour JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___88 / 184

Concept 7.1: Read a Calendar Think Neena and her friends are playing a game using a calendar. They split into two groups. Each group says a date or day of a particular month. The other group answers with the corresponding day or date of another month. Can you also play such a game? To answer this, we must know about reading a calendar. Let us recall days in a week and months in a year. There are 7 days in a week. They are: 1) Sunday 2) Monday 3) Tuesday 4) Wednesday 5) Thursday 6) Friday 7) Saturday There are 12 months in a year. They are: 1) January 2) February 3) March 4) April 5) May 6) June 7) July 8) August 9) September 10) October 11) November 12) December & Remembering & Understanding Reading a calendar, we can find the day of a given date. We can also find dates that fall on a particular day of the month. Let us do an activity to understand this concept better. Activity: 1) List out the birthdays of your parents, grandparents, brothers and sisters. 2) Arrange them in a table as they appear in a calendar month-wise. 3) Note the days on which the birthdays appear. Time 83 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___89 / 184

Stick this on your writing table. This will remind you to wish your family members a “HAPPY BIRTHDAY”. Your tables could be similar to the one given below. Birthdays of my family members Birthday (2017) Member of the family Day 08-January Sunday 10-March Brother Friday 16-June Mother Friday 03-August MINE Thursday 04-October Wednesday 12-December Father Tuesday Grand father Grand mother Example 1: Observe the given calendar and answer the questions: a) How many days are there in this month? b) How many Sundays are there in this JANUARY 2017 month? SUN MON TUE WED THU FRI SAT c) Which day appears 5 times? 1234567 8 9 10 11 12 13 14 d) O n which day is the 15 16 17 18 19 20 21 Republic day? 22 23 24 25 26 27 28 29 30 31 e) On which date is the second Saturday? Solution: a) There are 31 days in this month. b) There are five Sundays in this month. c) Sunday, Monday and Tuesday appear five times. Example 2: d) The Republic day is on Thursday. e) Second Saturday is on 14th. From the calendar for the year 2017, write the days of the following events. a) Independence Day - ____________ b) Republic Day - _____________ c) Christmas Day - ____________ 84 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___90 / 184

d) Teacher’s Day - _____________ e) Children’s Day - _____________ Solution: a) Independence Day - Tuesday b) Republic Day - Thursday c) Christmas Day - Tuesday d) Teacher’s Day - Tuesday e) Children’s Day - Tuesday Application We use the calendar on a daily basis. Events like planning holidays, conducting sports and examinations in school are a few examples. Example 3: Renu wants to plan her 5-day holiday to October 2017 New Delhi. On the calendar, mark the days when Renu can plan her holiday. She SUN MON TUE WED THU FRI SAT wants to start on a Friday and travel 6 7 12 345 13 14 overnight to New Delhi. 20 21 89 10 11 12 27 28 15 16 17 18 19 22 23 24 25 26 29 30 31 Solution: A 5-day trip starting on a Friday night will end on Wednesday. So, Renu can book her tickets for Friday night and Wednesday night. Fridays in this month: 6, 13, 20, 27 October 2017 Wednesdays in this month: 4, 11, 18, 25 SUN MON TUE WED THU FRI SAT 12 34567 Renu’s trip could be planned for 6th to 8 9 10 11 12 13 14 11th, 13th to 18th or 20th to 25th as marked 15 16 17 18 19 20 21 22 23 24 25 26 27 28 on the calendar. 29 30 31 Note: If she plans to go on 27th, she would Example 4: return on 1st November. Use the January 2017 calendar shown to answer the question. Rupali is a clerk in a bank. She has holidays on Sundays and on the first and the third Saturdays of the month. She also has holidays on the New Time 85 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___91 / 184

Year Day and Republic Day. How many 2017 JANUARY holidays does she have in the month of SUN MON TUE WED THU FRI SAT 12 34567 January? 8 9 10 11 12 13 14 Solution: Republic day is on 26th January. 15 16 17 18 19 20 21 New Year day is on 1st January. 22 23 24 25 26 27 28 The first and the third Saturday falls on 7th 29 30 31 and 21st January respectively. Sundays fall on 1st, 8th, 15th, 22nd and 29thJanuary. Rupali has holidays on 1st, 7th, 8th, 15th, 21st, 22nd, 26th and 29th January. Therefore, she has 8 holidays in January. Higher Order Thinking Skills (H.O.T.S.) Observe the calendar for the month of February of different years. February 1992 February 1993 February 1994 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 123456 12345 2345678 7 8 9 10 11 12 13 6 7 8 9 10 11 12 9 10 11 12 13 14 15 14 15 16 17 18 19 20 13 14 15 16 17 18 19 16 17 18 19 20 21 22 21 22 23 24 25 26 27 20 21 22 23 24 25 26 23 24 25 26 27 28 29 28 27 28 February 1995 February 1996 February 1997 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1234 123 1 5 6 7 8 9 10 11 4 5 6 7 8 9 10 2345678 12 13 14 15 16 17 18 11 12 13 14 15 16 17 9 10 11 12 13 14 15 19 20 21 22 23 24 25 18 19 20 21 22 23 24 16 17 18 19 20 21 22 26 27 28 25 26 27 28 29 23 24 25 26 27 28 February 1998 February 1999 February 2000 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1234567 123456 12345 8 9 10 11 12 13 14 7 8 9 10 11 12 13 6 7 8 9 10 11 12 15 16 17 18 19 20 21 14 15 16 17 18 19 20 13 14 15 16 17 18 19 22 23 24 25 26 27 28 21 22 23 24 25 26 27 20 21 22 23 24 25 26 28 27 28 29 We observe that February has 29 days in the years 1992, 1996 and 2000. In the oth- er years, February has 28 days. 86 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___92 / 184

Every four years, an extra day is added to the month of February. This is due to the revolution of the Earth around the Sun. • The Earth takes 365 and a quarter days to go around the Sun. • An ordinary year is taken as 365 days only. • Four quarters put together  1 + 1 + 1 + 1  make an extra day for every four years.  4 4 4 4  • This is added on to get the leap year. So, there are 365 + 1 = 366 days in a leap year. Example 5: Find the leap year in the following years: Solution: 2011, 2012, 2015, 2016, 2020 Example 6: A year is said to be a leap year if the number formed by the last two Solution: digits is divisible by 4. In other words, when we divide a year by 4 and if it leaves no remainder, then the year is called a leap year. 2011 ÷ 4 = 502, R = 3 2012 ÷ 4 = 503, R = 0 2015 ÷ 4 = 503, R = 3 2016 ÷ 4 = 504, R = 0 2020 ÷ 4 = 505, R = 0 Thus, 2012, 2016 and 2020 are the leap years. How many days were there from Christmas 2010 to Christmas 2011? 2011 was not a leap year. So, the number of days from Christmas 2010 to Christmas 2011 was 365. Concept 7.2: Read Time Correct to the Hour Think Neena’s teacher taught her to read time. She now knows the units of time. Neena reads time when her dad moves the hands of a clock to different numbers. Can you also read time from a clock? To know time using a clock, we must learn to read time correct to the hour. Time 87 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___93 / 184

Recall We learnt that the long hand on the clock shows minutes and the short hand shows hours. In some clocks, we see another hand thinner than the hour and the minute hands. This is the seconds hand. Let us recall reading time from a clock. a) 7 o’clock is _____________ hours more than 4 o’clock. b) The _____________ hand takes one hour to go round the clock. c) The _____________ hand is the short hand on the clock. d) The time is ____________ when both the hour hand and the minute hand are on 12. e) 2 hours before 10 o’clock is _____________. & Remembering & Understanding We see numbers 1 to 12 on the clock. These numbers are for counting hours. There are 60 parts or small lines between these numbers. They stand for minutes. The minute hand takes 1 hour to go round the clock face once. The minute hand takes 5 minutes to go from one number to the next number on the clock face. We multiply the number at which the minute hand points by 5 to get the minutes. For example, the minute hand in the figure is at 4. So, it denotes 4 × 5 = 20 minutes past the hour (Here, after 3.) Therefore, the time is read as 20 minutes after 3. The hour hand takes one hour to move from one number to the other. Let us now read the time from these clocks. 88 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___94 / 184

a) b) c) d) In figure a), the minute hand is at 5. The hour hand is in between 1 and 2 . The number of minutes is 5 × 5 = 25. Thus, the time shown is 1:25. In figure b), the minute hand is at 2. The number of minutes is 2 × 5 = 10. The hour hand is between 7 and 8. Therefore, the time shown is 7:10. In figure c), the minute hand is at 9. The number of minutes is 9 × 5 = 45. The hour hand is between 1 and 2. Therefore, the time shown is 1:45. In figure d), the minute hand is at 6. So, the number of minutes is 6 × 5 = 30. The hour hand is between 3 and 4. Therefore, the time shown is 3:30. Example 7: On which number is the minute hand if the time is as given? a) 35 minutes b) 15 minutes c) 40 minutes d) 30 minutes Solution: To find minutes when the minute hand is at a number, we multiply by 5. So, to get the number from the given minutes, we must divide it by 5. a) 35 ÷ 5 = 7. So, the minute hand is at 7. b) 15 ÷ 5 = 3. So, the minute hand is at 3. c) 40 ÷ 5 = 8. So, the minute hand is at 8. d) 30 ÷ 5 = 6. So, the minute hand is at 6. Quarter past, half past and quarter to the hour. We know that, ‘quarter’ means 1 . 4 Time 89 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___95 / 184

In Fig (a), the minute hand of the clock has travelled a quarter of an hour. So, we call it quarter past the hour. Fig (a) Fig (b) The time shown is 2:15 or 15 minutes past 2 or quarter past 2. Fig (c) ‘Half’ means 1 2. In Fig (b), the minute hand has travelled the clock after an hour. So, we call it half past the hour. The time shown is 2:30 or 30 minutes past 2 or half past 2. If the minute hand has to travel a quarter of the clock before it completes one hour, we call it quarter to the hour. The time shown is 7:45 or 45 minutes past 7 or quarter to 8. Example 8: Read the time in each of the given clocks and write it in two different ways. Fig (a) Fig (b) Fig (c) Fig (d) Solution: To read time, observe the position of the hour and the minute hands. Fig (a) Fig (b) Fig (c) Fig (d) 90 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___96 / 184

Fig (a) Fig (b) Fig (c) Fig (d) The hour hand is The hour hand is The hour hand is The hour hand is between 3 and 4. between _____ between _____ and between _____ So, the minutes are and _____. The _____. The minutes and _____. The after 3 hours. The minutes are after are after ____hours. minutes are after minute hand is at ____hours. The The minute hand ____hours. The 6. So, the time is 30 minute hand is at is at _____. So, minute hand is at minutes after 3. We _____. So, the time the time is _____ _____. So, the time write it as 3:30 or is _____ minutes minutes after _____. is _____ minutes half-past 3. after _____. We We write it as _____ after _____. We write it as _____ or or _____. write it as _____ _____. or _____. Application We have learnt how to read the time. Now let us draw hands on the clocks when time is given. Example 9: Draw the hands of a clock to show the given time. a) 1:15 b) 6:15 c) 7:30 d) 9:45 Solution: To draw the hands of a clock, first note the minutes. If the minutes are between 1 and 30, draw the hour hand between the given hour and the next. But care should be taken to drTarwaiitnclMoseyr tBortaheingiven hour. If the minutes are between 30 and 60, draw the hour hand closer to the next hour. Then, draw the minute hand on the number that shows the given minutes. Fig (a) Fig (b) Fig (c) Fig (d) Example 10: Draw the hands of a clock to show the given time. a) Quarter to 6 b) Half past 3 c) Quarter past 8 Time 91 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___97 / 184

Solution: Fig (a) Fig (b) Fig (c) Higher Order Thinking Skills (H.O.T.S.) We have learnt to read and show time, exact to minutes and hours. Let us now learn to find the length of time between two given times. Example 11: The clocks given show the start time and the end time of the Maths class. How long was the class? Solution: The start time is 10:00 and the end time is 10:45. The difference in the given times = 10:45 – 10:00 = 45 minutes Therefore, the length of the Maths class is 45 minutes. Example 12: Sanjay spends an hour between 4:30 and 5:30 for different activities. The start time for each activity is as shown. playing drinking milk homework TV on TV off Read the clocks and answer the following questions. a) When did Sanjay begin having milk? 92 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___98 / 184

b) For how long did he play? c) For how long did he watch TV? d) When did he switch off the TV? Solution: From the given figures, a) Sanjay began having milk at 4:45. b) Sanjay began playing at 4:30 and ended at 4:45. So, he played for a quarter hour (15 minutes) as 4:45 – 4:30 = 15 minutes. c) The time for which he watched TV was 5:30 – 5:20 = 10 minutes. d) Sanjay switched off the TV at 5:30. The time between two given times is called the length of time. It is also called time duration or time interval. It is given by the difference of end time and start time. Drill Time Concept 7.1: Read a Calendar 1) Observe the calendar and answer the following 2017 JANUARY questions. SUN MON TUES WED THU FRI SAT a) How many weekend days and weekdays are 12 3456 7 there in the month shown in the calendar? 89 10 11 12 13 14 15 16 17 18 19 20 21 Consider Saturday and Sunday as weekend days. 22 23 24 25 26 27 28 29 30 31 b) Write the day and date before two days of fourth Saturday of January. c) On which day does the month end? 2017 SEPTEMBER SAT 2) Word Problems SUN MON TUES WED THU FRI 2 a) Raju bought a new dress on 1st of September. 1 9 He bought another new dress 10 days after first 34 5678 16 day of the month. On which date did he buy the 10 11 12 13 14 15 23 other dress? 17 18 19 20 21 22 30 24 25 26 27 28 29 b) Sonu’s birthday was on 2nd of September. What is the date, if he celebrated it on the same day of the third week. Time 93 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___99 / 184

c) R am solved problems from one chapter of his book on 9th of September. He solved problems from the next chapter 5 days later. On which day did he solve problems from the next chapter? Concept 7.2: Read Time Correct to the Hour 3) Draw the hands of a clock to show the given time. a) Half past 2 b) 4:15 c) Quarter to 12 d) 4:25 e) 6:20 4) What is the time shown on each of these clocks? a) b) c) d) 5) Word problems a) On which number is the minute hand if the time is as given? (A) 25 minutes (B) 45 minutes (C) 20 minutes (D) 50 minutes b) The start time of Ram’s activities are shown in these figures. From the figures, answer the following questions. (A) When did Ram wake up? (B) For how many minutes did Ram drink milk? (C) How much time did Ram spend for getting ready? (D) For how long did Ram study? 94 JSNR_BGM_1010020-Alpine-G3-FoundationMax-Maths-FY_REVISED_Text.pdf___100 / 1840