46 2024 Elementary Mathematics Mathematical statement: Let us think about how to calculate. Let us count and remove 13 sheets of paper one by one. 13 means 1 ten and 3 ones. Let us take away 1 ten and 3 ones from 3 tens and 6 ones. Subtraction (1) 10 10 10 Mina had 36 sheets of paper. She gave Raju 13 sheets of paper. How many sheets of paper does Mina have now?

47 2024 Elementary Mathematics Tens Ones 3 6 - 1 3 3 6 - 1 3 3 3 6 - 1 3 2 3 3 6 - 1 3 2 3 Let us arrange the numbers according to their place value. At the ones place, 6 - 3 = 3 At the tens place, 3 - 1 = 2 36 - 13 = 23 How do we subtract 13 from 36 by using their place value? 1) 45 - 23 2) 56 - 12 3) 86 - 31 4) 75 - 23 1 Let us subtract.

48 2024 Elementary Mathematics Tens Ones Blocks of tens Five blocks of one 4 7 - 1 0 4 5 - 2 5 2 Let us think about how to subtract 10 from 47. 3 Let us think about how to subtract 25 from 45. 4 Let us subtract. 6) 49 - 10 7) 66 - 40 8) 58 - 18 9) 70 - 30 1) 45 - 23 2) 32 - 11 3) 68 - 12 4) 79 - 50 5) 98 - 67 10) 38 - 34

49 2024 Elementary Mathematics 1) 64 - 3 2) 78 - 5 3) 94 - 2 4) 76 - 6 5) 57 - 7 Tens Ones 3 9 - 5 How do we subtract 5 from 39? How do we subtract 9 from 39? Tens Ones 3 9 - 9 1 Let us subtract. 2 Let us subtract. 1) 85 - 13 2) 79 - 44 3) 61 - 50 4) 75 - 25 5) 90 - 50 6) 49 - 42 7) 97 - 5 8) 53 - 3 1

50 2024 Elementary Mathematics Raju had 45 colour pencils. He gave 18 colour pencils to Tuli. How many colour pencils are left with Raju? The mathematical statement of the calculation is 45 – 18 = How will you give me 18 colour pencils? 4 5 - 1 8 510 - 1 8 510 - 1 8 7 510 - 1 8 2 7 510 - 1 8 2 7 Let us arrange the numbers according to their place value. As the digit 5 in the ones place is less than 8, we cannot subtract 8 from 5. So, we can take 1 ten from the tens place and move it to the ones place. Adding this 1 ten to the digits of the ones place, we get 10 + 5 = 15 At the ones place, 15 - 8 = 7 At the tens place, 3 - 1 = 2 45 - 18 = 27 Tens Ones

51 2024 Elementary Mathematics 1 Let us subtract. 1) 97 - 59 2) 71 - 44 3) 75 - 47 4) 60 - 53 5) 70 - 22 Tens Ones 3 4 - 7 How do we subtract 7 from 34? How do we subtract 6 from 30? Tens Ones 3 0 - 6 1 2 1) 32 - 15 2) 85 - 47 3) 64 - 27 4) 92 - 23 2 Let us subtract.

52 2024 Elementary Mathematics 1. Rumi has 75 marbles, and Raju has 49 marbles. How many more or fewer marbles does Raju have than Rumi? 2. The sum of the ages of mother and daughter is 70. The daughter is 22 years old. How old is the mother? 3. Jhumu is 8 years older than Rumu. Jhumu is 24 years old. How old is Rumu? 1) 25 - 8 2) 43 - 5 3) 30 - 7 4) 60 - 6 5) 80 - 9 1) 82 - 13 2) 71 - 44 3) 97 - 59 4) 60 - 35 5) 74 - 68 6) 40 - 34 7) 93 - 5 8) 50 - 3 3 Let us subtract. 4 Let us subtract. 5 Problems related to subtraction

53 2024 Elementary Mathematics Mathematical Relation (Addition and subtraction) There were some mangoes in a bag. 5 mangoes were sold. Now, there are 6 mangoes in the bag. How many mangoes were there in the bag at first? The number of mangoes we had at first. 5 mangoes were sold. There were 6 mangoes after selling 5 mangoes. In the picture, we can see there were 11 mangoes in the bag. In a mathematical statement: Now, there are 6 mangoes in the bag. - 5 = 6 6 + 5 = mangoes were there The first number of subtraction is the sum of other two numbers. 11 - 5 6 6 +5 11 After selling 5 mangoes were decreased in the bag. Let us draw a picture of the above problem below. We need to exclude five mangoes. How do we find the number of mangoes we had at first?

54 2024 Elementary Mathematics 3) + 23 = 34 5) 14 + = 35 7) + 27 = 75 9) 12 + 9 - = 13 10) 22 + 8 - = 23 4) + 19 = 45 6) 29 - = 17 8) - 39 = 45 1 Let us fill in the blanks. 1) 9 + = 16 2) 39 - = 31 39 ? 31 9 ? 16 2 Bijoy was going to the market to sell mangoes. His uncle gave him 15 more mangoes to sell. After selling 33 mangoes, he had 12 mangoes left. How many mangoes did he have at first? 3 Mr. Jalil bought 100 lichis from the market. After coming home, he gave 25 lichis to his daughter and 23 lichis to his son. How many lichis are left with him? 4 There were 25 chocolates in a box. From those, some chocolates were given to Mitu. 17 chocolates were left in the box. How many chocolates were given to Mitu? What will be the mathematical statement?

55 2024 Elementary Mathematics Tuli had 70 storybooks. She bought another 50 storybooks from the book fair. How many storybooks does Tuli have now? Addition (2) Mathematical statement: How do we write a mathematical statement? 70 + 50 = 120 Let us do the additions below. 1) 80+50 2) 60+60 3) 50+90 4) 80+70 5) 100+300 6) 500+200 7) 140+20 8) 30+130 9) 160+30 10) 50+220 10 10 10 10 10 10 10 10 10 10 10 10

56 2024 Elementary Mathematics Dilip has 73 sheets of paper. His sister, Deepa, gave him 54 sheets of paper. How many sheets of paper does he have now? Mathematical sentence Let us think about how to calculate. Here, the blocks of tens are more than 10. The answer seems to be more than 100. How do we add 74+54? 10 10 10 10 10 10 10 3 10 10 10 10 10 4

57 2024 Elementary Mathematics Hundreds Tens Ones 7 3 + 5 4 Let us arrange these two numbers according to their place values. 7 3 + 5 4 7 The sum of digits in the ones place is 3 + 4 = 7 7 3 + 5 4 1 2 7 7 3 + 5 4 1 2 7 The sum of digits in the tens place is 7 + 5 = 12 tens. 12 tens mean 1 hundred and 2 tens. Write 2 in the tens place and 1 in the hundreds place. 73+54 = 127 Let us add. 1) 86+43 2) 68+35 3) 74+65 4) 55+45 5) 93+9

58 2024 Elementary Mathematics 216+142 = How do we do the addition? Hundreds Tens Ones + H T O = H T O 2 1 6 1 4 2 8 Sum of the digits in the ones place is 6 + 2 = 8. Hundreds Tens Ones + H T O = H T O 2 1 6 1 4 2 5 8 Sum of the digits in the tens place is 1 + 4 = 5. Hundreds Tens Ones + H T O = H T O 2 1 6 1 4 2 3 5 8 Sum of the digits in the hundreds place is 2 + 1 = 3. Using their place values, we can add them in mathematical statement. To decorate the classroom, Raju made 134 paper flowers, and Meena made 145 flowers. How many flowers did they make in total? 134+145 = We can calculate by using place values. How can we calculate the total number of paper flowers?

59 2024 Elementary Mathematics H T O 1 3 4 + 1 4 5 1 3 4 + 1 4 5 7 9 1 3 4 + 1 4 5 9 1 3 4 + 1 4 5 2 7 9 The sum of the digits in the ones place is 4 + 5 = 9. The sum of the digits in the hundreds place is 1 + 1 = 2. The sum of the digits in the tens place is 3 + 4 = 7. 1 Let us do the following additions. 2 Let us do the following additions. (1) 526 + 253 = (3) 523 + 614 = (5) 672 + 326 = (2) 552 + 436 = (4) 872 + 127 = (6) 438 + 31 = 1) 4 6 2 + 3 5) 4 3 8 + 5 2 1 2) 9 5 3 + 4 6 6) 2 3 2 + 3 5 4 3) 6 2 0 + 3 7 0 7) 4 2 3 + 2 4 1 4) 2 3 3 + 3 5 5 8) 5 5 5 + 3 2 4 1 On a certain Eid day, Rafi received Eid salami of Tk. 250 from his father and Tk.120 from his mother. How much money has he got in total?

60 2024 Elementary Mathematics Let us find the missing digits. At the place of ones, 5 + 2 = 7. At the place of tens, 3 + 2 = 5. At the place of hundreds, 3+1=4. 3 5 + 12 = 457 3 5 + 1 2 4 5 7 1. 4 5 + 21 = 639 2. 51 + 3 5 = 876 3. 4. 3 Let us find the missing digits. 6 21 27 6 33 39 6 50 1 5 5 5 5 6 11 16 ? 5. 17 5 3 7 2 15 6 3 2 4 ? 4 3 7 5

61 2024 Elementary Mathematics 267 + 145 = 2 6+1 7 + 1 4 5 2 The sum of the digits in the ones place is 7 + 5 = 12. 12 means 1 ten and 2 ones. Let us write 2 in the ones place and add 1 with the digits of tens place. How do we add? 468 + 394 = H T O + H T O = H T O 4+1 6+1 8 3 9+1 4 8 6 2 The sum of digits in the ones place is 8 + 4 = 12. 12 means 1 ten and 2 ones. Let us write 2 in the ones place and add 1 with the digits in the tens place. The sum of the digits in the tens place is 6 + 9 + 1 = 16. 16 means 1 hundred and 6 tens. Let us write 6 in the tens place and add 1 with the digits in the hundreds place. In the hundreds place, let us write 4 + 3 + 1 = 8. 468 + 394 = 862 An exercise book of Raju has 267 pages. Another exercise book has 145 pages. How many pages are there in the two exercise books? The mathematical statement of the calculation is: 1 How do we add?

62 2024 Elementary Mathematics 2+1 6+1 7 + 1 4 5 1 2 2+1 6+1 7 + 1 4 5 4 1 2 2 6 7 + 1 4 5 4 1 2 The sum of the digits in the tens place is 6 + 4 + 1 = 11. 11 tens means 1 hundred and 1 ten. Let us write 1 in the tens place and add 1 with the digits in the hundreds place. The sum of digits in the hundreds place, is 2+1+1= 4. 412 pages of paper Each pair of students will write two numbers with at most three digits, and pass them to another pair of students. They will add the numbers. The pair that successfully adds the numbers first will be the winner. 1. (1) 596 + 312 = (2) 649 + 161 = (3) 427 + 185 = (4) 381 + 269 = (5) 2 8 4 + 5 8 1 (6) 2 9 4 + 6 4 7 (7) 5 6 8 + 4 3 2 (8) 4 0 9 + 3 8 4 1 2 Let us add.

63 2024 Elementary Mathematics Problems related to addition 1. Shimu reads 154 pages of a storybook in a month. In the next month, she reads 275 pages. How many pages did she read in total in two months? 2. In a school, there are 136 boys and 120 girls in class two. How many students are there in class two? 3. 123 books were distributed among the students in Section A of class two. In Section B, 131 books were distributed. How many books were distributed in total? 4. There are 120 rose plants and 127 marigold plants in a nursery. How many flower plants are there in total in that nursery? 5. In a pond, 125 catfish and 250 walking catfish fries were released. How many fish fries were released in total in that pond? 6. A fruit seller sold mangoes for Tk. 360 on the first day. On the second day, he sold mangoes for Tk. 475. How much money did he get from his selling in two days? 7. In a cricket match, the Bangladesh National Team scored 415 runs in the first innings. They scored 327 runs in the second innings. How many runs did the Bangladesh team score in that match of two innings? 8. 400 people live in a village and 320 live in another village. How many people live in the two villages altogether? 9. Make a story for ‘975 + 325’. 3 Let us add

64 2024 Elementary Mathematics Let us do the following subtractions. 1) 170 - 40 5) 500 - 200 9) 390 - 70 2) 180 - 20 6) 700 - 500 10) 460 - 60 3) 160 - 40 7) 900 - 220 11) 520 - 30 4) 190 - 20 8) 380 - 30 12) 220 - 50 10 10 10 10 10 10 10 10 10 10 10 10 How can we subtract 50 from 120? Subtraction (2) Let us write in a mathematical statement. 120-50 = 70

65 2024 Elementary Mathematics How can we subtract 125–43 ? 1 210 5 - 4 3 8 2 1 210 5 - 4 3 8 2 1 2 5 - 4 3 Let us arrange the two numbers according to their place value. As the digit 2 in the tens place is less than 4, we cannot subtract 4 from 2. We can take 1 hundred from the hundreds place. 1 hundred means 10 tens. Now we can add 1 hundred or 10 tens with 2 of the tens place and get 10+2= 12 tens. In the tens place, we can write 12-4=8. 125 - 43 = 82 Hundreds Tens Ones

66 2024 Elementary Mathematics 1 Let us subtract 1) 325 - 13 2) 527 - 28 3) 735 - 48 4) 474 - 81 5) 829 - 75 6) 930 - 40 1) 509 - 25 2) 729 - 56 3) 845 - 58 2 Let us subtract 7 8 5 4 2 1 4 7 8 5 4 2 1 6 4 7 8 5 4 2 1 3 6 4 At the ones place 5 - 1 = 4 At the tens place 8 - 2 = 6 At the hundreds place 7 - 4 = 3 Let us subtract 785-421

67 2024 Elementary Mathematics 1 Let us subtract Let us do (1) 231 - 48 = (3) 320 - 280 = (5) 452 - 378 = (2) 230 - 90 = (4) 437 - 273 = (6) 663 - 267 = 3 2 4 1 1 1 5 2 6 2 4 1 1 1 5 1 2 6 The digit 5 in the ones place is greater than 1. So, we cannot subtract 5 from 1. Now, move 1 ten from the tens place to the ones place, and add this 1 ten to the number in the ones place. 10 + 1 = 11 Let us write in the ones place 11 – 5 = 6. Let us write in the tens place 3 – 1 = 2. 241 - 115 = 126 Let us write in the hundreds place 2–1=1. 2 4 1 1 1 5 3 11 2 4 1 1 1 5 241 -115 Mina has Tk.241 and Raju has Tk.115 . How much more money does Mina have than Raju? 241 - 115 = How can we calculate?

68 2024 Elementary Mathematics (7) 4 9 0 - 8 4 (8) 3 2 1 - 2 7 9 (9) 9 4 1 - 6 0 8 (10) 7 9 2 - 4 8 6 (11) 3 4 1 - 1 2 6 (12) 5 4 0 - 2 8 0 2 Shyamol went to the market with Tk. 385. He spent Tk. 253. How much money is left with him? 3 In a cricket match, Bangladesh team scored 358 runs and Sri Lankan team scored 312 runs. Which team scored more and how many runs more? 4 There are 542 students in a school and 290 of them are girls. How many boys are there in that school? 5 There are 334 children in Kolyandi village. Of them, 315 children go to school. How many children do not go to school? 6 There are 212 mango trees in a garden. 195 of them have grown mangoes. How many trees did not grow mangoes? 7 Rita had 255 marbles. From those, she gave her younger brother 150 marbles. How many marbles does Rita have now? 8 A nursery has 146 mahogany saplings and 120 neem saplings. How many more mahogany saplings are there in the nursery? 9 Which number is to be subtracted from 355 to get 245? 10 There were 200 tilapia fish in a pond. 165 of them were sold. How many tilapia fish were left in the pond? 11 Tuhin has Tk. 342, and Shakil has Tk. 315. Who has less money, and how much less? 12 Shakib had three one-hundred-taka notes, from which he gave Mina Tk. 225. How much money does Shakib have now?

69 2024 Elementary Mathematics Problems Related to Addition and Subtraction. (c) Let us solve the problem. 673+117-105 =790-105 =685 Number of people 685. There are 673 people in a village. 105 people left the village. 117 new people came to the Village a) What is total number of people in the village now? Let us think how to solve the problem. As new people came in, the total number of people will be more. Total people will be 673 + 117 = 790 There were 673 people 117 new people came (b) What is the number of people after some of them left the village. As some people left the village, the total number of people will be less Total people will be 790-105=685 105 people left the village In a mathematical statement, the problem will be : 673 + 117 - 105

70 2024 Elementary Mathematics 1. There were 625 students in the Safarmali School. At the beginning of the year, 275 new students were admitted and 35 student left the schools. How many Students were left in the school? Solve the problem in mathematical statement. 2. Jhuma has TK. 250. Her father gave her Tk.150 more. She bought a book for Tk. 230. How much money is left with her? 3. Sum of two numbers is 840. If one of them is 527, what is the other? 4. In a week a shopkeeper earns Tk.920 and spends Tk. 675. How much money does he save at the end of the week? 5. A school had 327 students. The following diagram describes the past three years admission of that school. 123 155 209 (a) In which year the admission was the highest? (b) How many more students were admitted in the third year compared to the first year. (c) What is the number of students in the school now? 6. The Difference of two numbers is 87. If the greater number is 369,what is the smaller number? 7. 1st pot 2st pot 235 glasses of water 265 glasses of water Two water pots are shown in the picture above. (a) Which pot contains more water? (b) How many glasses of water are more in the Second pot? (c) What is the total number of glasses of water in two pots ?

71 2024 Elementary Mathematics 8. There are 425 mangoes in one basket, and 345 mangoes are in another basket. 175 mangoes are sold from the total. How many mangoes are left? (a) What is the total number of mangoes in the two Baskets? (b) In how many steps, the problem can be solved? (c) Express the problem in a mathematical statement. (d) Solve the problem. 9. The sum of 9 numbers is 360. The sum of the first 4 numbers is 152. The sum of the 6th to 9th numbers is 164. What is the 5th number? 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 360 152 ? 164 10. Nahid has Tk. 450. Sumon has Tk. 115 less than that of Nahid. If their money is put together, it becomes the same as Arif’s money. How much money does Arif have? 11. The age of the two sons together is 37 years and the age of their father is 63 years. After 10 years, what will be the total age of three of them? 12. Sujon got Tk. 1000 as a stipend. He bought a dress for Tk. 350 and a school bag for Tk. 475. How much money is left with him? 13. To buy a cricket bat and a ball Tk. 750 is needed. All the members gave a total of Tk. 330. The club gave them Tk. 250 as a grant. How much money do they need more?

72 2024 Elementary Mathematics 14. Sohag’s fruit basket 150 Geeta’s fruit basket 248 Tuli’s fruit basket 475 (a) How many fruits are there in Sohag’s fruit basket? (b) How many more fruits does Tuli have than Geeta? (c) How many fruits do Sohag and Tuli have in total? 15. The price list of a fruit shop. Fruit Mango Apple Orange Price (Per Kg) Tk. 100 Tk. 220 Tk. 160 (a) How much more is the cost of apples than that of mangoes? (b) Express the total price of the fruits in a mathematical statement. (c) What is the total price of the fruits. 16. A farmer got 326 bags of rice from his own land and 125 bags by cultivating other people’s land. Calculate the total number of bags of rice he got and express it in mathematical statement. 17. Bikash Borua went to the book fair with Tk. 1000. After buying some books, he was left with Tk. 200. How much money did he spend for buying books? 18. Mr. Nizam went to the market with Tk. 970. He bought beef for Tk. 550 and a hen for Tk. 370. (a) What is the price of beef? (b) In which methods can the problem be solved? (c) How much money is left with Mr. Nizam?

73 2024 Elementary Mathematics Multiplication Chapter -3 Concept of Multiplication In the picture below apples, potatoes, fishes and bananas are arranged in some plates. How many fishes and potatoes are there in each plate? There are 5 plates of 3 potatoes. There are 5 plates of 4 fishes. This is a mathematical sentence. This is a mathematical sentence. fishes fishes 4+4+4+4+4= potatoes potatoes 3+3+3+3+3 =

74 2024 Elementary Mathematics How many apples and bananas are there? There are 2 apples in each of the above 5 plates. How many apples are there? There are 4 bunches of bananas. There are 4 bananas in each bunch. How many bananas are there? Let us write a mathematical sentence for counting apples. apples

75 2024 Elementary Mathematics 2 How many apples will be there if we add one more plate? Mathematical sentence apples Let us write a mathematical sentence for counting bananas. bananas

76 2024 Elementary Mathematics There are 4 benches in a class. 3 students sit in each bench. How many students are there in the class? There are 3 students in each of the 4 rows. The mathematical sentence for the number of students is (×) is called the multiplication sign and (+) is called the addition sign. The number of students is: 3+3+3+3=12 So, there are 12 students in the class. Here we add 3 for 4 times. We can also express/write this problem in the following mathematical sentence. This type of calculation is called multiplication and the symbol × is called multiplication sign. 3×4=12 How to read? Three multiplied by four equals twelve. 3 Number of objects in each group Number of groups Total number of objects × 4 = 12

77 2024 Elementary Mathematics 1 Let us calculate by using the multiplication sign. 2 × 5 = 10 10 apples 3 × - = - potatoes -× - = - fishes -× - = - bananas

78 2024 Elementary Mathematics 1. 2. 3. There are 5 tomatoes in each of the 4 plates in the pictures. How many tomatoes are there together? Multiplication of 5. Let us write a mathematical statement of multiplication for each of the pictures below and write the answer. 2

79 2024 Elementary Mathematics Let us find how many tomatoes are there on 3 or 4 plates according to the picture below. 2 solutions are given. 1 According to the above picture how many tomatoes are there in any 5 plates? 2 5 × 1 = 5 5 × 2 = 10 5 × 3 = 5 × 4 = When the number of plates increase, how do the number of tomatoes increase? I think there is a relation between the number of plates and the number of tomatoes.

80 2024 Elementary Mathematics Let us learn the multiplication table of 5. 3 5 5 8 Let’s use an L-shaped paper with 100 dots table and see how to express the multiplication? 3 3×5=15 5×8=40 Multiplication table of 5 5×1=5 5×2=10 5×3=15 5×4=20 5×5=25 5×6=30 5×7=35 5×8=40 5×9=45 5×10=50 There are 5 lychees on each of the 6 plates. How many lychees are there together?

81 2024 Elementary Mathematics Four pairs of children are playing. How many children are playing in total? According to the pictures below, let’s find out how many children are there? Multiplication of 2 2×1=2 2×2=4 2×3= 2×4= Similarly, how many children are there in 5, 6, 7, 8, 9 and 10 pairs? 1 2×5= 2×8= 2×6= 2×9= 2×7= 2×10= Rafi: “If the number of pairs increases, how does the number of children increase?”

82 2024 Elementary Mathematics Let’s play with the multiplication card. 2 Let’s make a multiplication card as below. Example, Let’s play ourselves. Game-1: At first, mix the sets of multiplication cards of 5 well. The multiplications remain on one side and the answers remain on opposite side of the cards. Let’s pick up one from the multiplication side. Let us find out the answer without seeing the answer given at the back. Now let us match the answer given at the back. The game will continue in this way. Game-2: Let’s play the same game by picking the answer first, then the multiplication. Let us play in pairs/ with friends Game-3: One player will pick up a card and show the multiplication to the other player. Another player will answer by doing multiplication. In the same way one will show the answer and the another one will say the multiplication. Game-4: Let’s place the cards on the desk, keeping the multiplication side down. Ask the multiplication to your friend showing the answer. Multiplication at the front Answer at the back 2 × 4 8 5 × 3 15 It’s a game of multiplication of 2. How does this result come? 18 It is 2×9. Isn’t it? 2 × 9

83 2024 Elementary Mathematics Let us learn the multiplication table of 2. Let us use an L-shaped paper with 100 dots table and see how to express the multiplication. Meena reads 2 pages of a book in a day. How many pages will she read in 7 days? 1 A chocolate costs 2 taka. Raju bought 6 chocolates. 1. How much taka do the chocolates cost? 2. If he buys 7 more chocolates, how much taka will it cost? 2 Multiplication Table of 2 2×1=2 2×2=4 2×3=6 2×4=8 2×5=10 2×6=12 2×7=14 2×8=16 2×9=18 2×10=20 2×4=8 2×8=16 4 8 2 2

84 2024 Elementary Mathematics Let us make the multiplication table of 3. Multiplication of 3 1 According to the picture below, let us find how many balls are there. If the number by which we multiply is increased by 1, how much does the product increase? 2 How many balls are there in 5,6,7,8,9 and 10 trays? 3 3 × 1 = 3 3 × 2 = 6 3 × 3 = 3 × 4 = 3 × 5 = 3 × 6 = 3 × 7 = 3 3 3 = = = × × × 8 9 10

85 2024 Elementary Mathematics Let us learn the multiplication table of 3 Let’s use an L-shaped paper with 100 dots table and find out the multiplication. There are 3 wheels in a rickshaw. How many wheels are there together in 4 rickshaws? 1 There are 3 members in a family. How many members will be there in such 9 families? 3 3 guavas can be arranged on a plate. How many guavas are needed to arrange 7 plates? 2 Multiplication Table of 3 3×1=3 3×2=6 3×3=9 3×4=12 3×5=15 3×6=18 3×7=21 3×8=24 3×9=27 3×10=30 3×5=15 3×8=24 5 8 3 3

86 2024 Elementary Mathematics Let us make multiplication of 4 Multiplication of 4 1 Let us find how many apples there are according to the pictures below. 4 × 1 = 4 4 × 2 = 8 4 × 3 = 4 × 4 = How does the product increase if the multiplying number increases by 1? 2 How many balls are there in 5, 6, 7, 8, 9 and 10 trays? 3 4 × 5 = 4 × 6 = 4 × 7 = 4 4 4 = = = × × × 8 9 10

87 2024 Elementary Mathematics Multiplication of 4 We use an L shaped paper on the pattern of 100 dots and find out the product. 1 A cat has four legs. Then how many legs do 8 cats have? 3 If each sheep has 4 lambs, how many lambs do 9 sheep have? 2 A chair has 4 legs. Then how many legs do 6 chairs have? Multiplication Table of 4 4×1=4 4×2=8 4×3=12 4×4=16 4×5=20 4×6=24 4×7=28 4×8=32 4×9=36 4×10=40 3 7 4 4 4×3=12 4×7=28

88 2024 Elementary Mathematics Let us learn the multiplication table of 6 based on what we have learnt so far. Multiplication of 6 If we place an L- shaped paper on the pattern of 100 dots, what will we get? 1 Multiplication Table of 6 6×1 = 6 6×2 = 12 6×3 = 6×4 = 6×5 = 6×6 = 6×7 = 6×8 = 6×9 = 6×10 = My idea is 6×1=6 6×2=6+6=12 6×3=6+6+6=18 6×4=6+6+6+6=24 6×5=6+6+6+6+6=30 My idea is 6×1=6 6×2=6+6=12 6×3=12+6=18 6×4=18+6=24 6×5=24+6=30 6 6 7 What method do you follow to calculate the multiplication table of 6?

89 2024 Elementary Mathematics 2 Let us learn the multiplication table of 6. Using the above picture, let us think 6X5=30 which is the sum of the product of 2 and the product of 4. 3 Let us again see the multiplication of 6 attentively. Multiplication of 6 Multiplication of 2 Multiplication of 4 Multiplication Table of 6 6×1=6 6×2=12 6×3=18 6×4=24 6×5=30 6×6=36 6×7=42 6×8=48 6×9=54 6×10=60 We can arrange the product of 6 as the product of 2 and 4. Is it correct? Badal’s father works 5 days a week. How many days does he work in 6 weeks? 1 It is interesting. We know 6 × 3 = 18 Again, 2 × 3 =6 and 4 × 3 = 12 Their sum is 6 + 12 = 18

90 2024 Elementary Mathematics Let us make the multiplication of 7 based on what we have learnt so far. Multiplication of 7 If we place an L- shaped paper on the pattern of 100 dots, what will we get? 1 7×1= 7 7×2= 14 7×3= 7×4= 7×5= 7×6= 7×7= 7×8= 7×9= 7×10= My idea is 7×1=7, 7×2=7+7=14 7×3=14+7=21, 7×4=21+7=28 7×5=28+7=35 How would you calculate the multiplication of 7? 6 7 My idea is 7×1=7, 7×2=7+7 7×3=7+7+7=21 7×4=7+7+7+7=28 7×5=7+7+7+7+7=35 7×6=..............

91 2024 Elementary Mathematics 2 Let us learn the multiplication table of 7. Let us observe the multiplication for 7 again with attention. 3 Multiplication of 7 Multiplication of 4 Multiplication of 3 Multiplication Table of 7 7×1=7 7×2=14 7×3=21 7×4=28 7×5=35 7×6=42 7×7=49 7×8=56 7×9=63 7×10=70 7×5=35, can you show breaking it into the multiplication of 4 and 3 ? Multiplication of 7 can be expressed as multiplication of 4 and 3. It is shown below: 4×5=20 3×5=15 35 1 7 days make a week. How many days are there in 8 weeks?

92 2024 Elementary Mathematics Let us make the multiplication table of 8 based on what we have learnt so far. Multiplication Table of 8 Multiplication Table of 8 8×1=8 8×2=16 8×3=24 8×4=32 8×5=40 8×6=48 8×7=56 8×8=64 8×9=72 8×10=80 What are the possible expression of the product 48 = 8 × 6 ? It has been broken down into the multiplier of 3 and 5 : 3×6 + 5×6= 18 + 30 = 48 6 7 1 There are 8 chocolates in 5 boxes. How many chocolates are there? 2 There are 8 students in each group in a class. How many students will there be in such 9 groups ?

93 2024 Elementary Mathematics 2. 9x9=81 This multiplication has been expressed on a product of 2,3 and 4. 2 3. 9x2=18, 9x3=27 and 9x4=36 Here, 18+27+36=81 3 Let us make the multiplication table of 9 based on what we have learnt so far. Multiplication Table of 9 Multiplication Table of 9 9×1=9 9×2=18 9×3=27 9×4=36 9×5=45 9×6=54 9×7=63 9×8=72 9×9=81 9×10=90 Each basket contains 9 breads. How many breads do 7 baskets contain? Rafiq reads 9 pages in a day. How many pages does he read in 8 days? 1 2

94 2024 Elementary Mathematics 2 What are the possible alternatives to express multiplication of 10? Let us make the multiplication table of 10, based on what we have learnt so far. 1 Let us make the multiplication Table of 10, based on what we have learnt so far. Multiplication Table of 10 Multiplication Table of 10 10×1=10 10×2=20 10×3=30 10×4=40 10×5=50 10×6=60 10×7=70 10×8=80 10×9=90 10×10=100 There is a total of 10 fingers in the two hands of a person. How many fingers are there in the hands of 7 persons? How many books will be required if you give 5 books to each of 3 male students and 7 books to each of 4 female students? How much money do you need if you buy 7 lychees at a price of Tk. 4, 8 Hog plums at Tk.6 and 5 bananas at Tk. 9 each respectively? 1 2 3 10

95 2024 Elementary Mathematics Each first student of each class in the annual examination will get 2 pencils and 1 Notebook as a gift. How many gifts will be needed for 5 classes? Multiplication of 1 2 × = 2 pencils × = Notebook 1 What can we find here? Multiplication of 1 1×1=1 1×2=2 1×3=3 1×4=4 1×5=5 1×6=6 1×7=7 1×8=8 1×9=9 1×10=10 I got the sum of 1×3 and 1×7, as 1×10 1 If we save Tk.1 everyday, how much will we save in 8 days? There are 5 students in the first bench, 6 students in the second bench and 8 students in the third bench in a class. If you pay Tk.1 to each student, how much money will you need? 2