G5Q1 WEEK 2 MATH PPT................pptx

MATHEMATICS

1. MATHEMATICS 5 QUARTER 1 WEEK 2 DAY 1

2. REVIEW Directions: See if the numbers in the first column are divisible by 2, 3, 5, 6, 9 or 10. Mark ( X ) on the corresponding columns.

3. REVIEW Divisible by 2 3 5 6 9 10 120 125 180 324 660

4. How would you apply the divisibility rules in changing money to the storekeeper?

5. MATHEMATICS 5 DIVISIBILITY RULES FOR 4, 8, 11 AND 12 (M5NSIb-58.3)

6. DIVISIBILITY the capacity of being evenly divided, without remainder.

7. DIVISIBILITY RULES FOR 4 “If the last two digits of a number formed a number divisible by 4, or if the last two digits of the number are both zero, then that number is divisible by 4.”

8. DIVISIBILITY RULES FOR 4 Examples : Are 312 and 8 6000 divisible by 4? a. 312 Yes, 3 12 is divisible by 4 because its last two digits – which is 12 is divisible by 4. b. 8 600 Yes, 8 6 00 is divisible by 4 since it ends with 00.

9. DIVISIBILITY RULE FOR 8 “If the last three digits of a number formed a number divisible by 8 or if the last three digits of the number are all zeros, then that number is divisible by 8.”

10. DIVISIBILITY RULE FOR 8 Examples: Are 5 216 and 75 000 divisible by 8? a. 5 216 Yes, 5 216 is divisible by 8 because its last three digits – which is 216 Is divisible by 8.

11. DIVISIBILITY RULE FOR 8 Examples: Are 5 216 and 75 000 divisible by 8? b. Yes, 75 000 is divisible by 8 since it ends With 000.

12. DIVISIBILITY RULE FOR 11 “If the difference of the sum of the alternating digits (from left to right) is 0 or divisible by 11, then the number is divisible by 11.”

13. DIVISIBILITY RULE FOR 11 Examples: Are 968 and 27 896 divisible by 11? a. 968 (9 + 8) – 6 = 17 – 6 = 11. Yes, 968 is divisible by 11 because the difference of its alternating digits – which is 11 is exactly divisible by 11.

14. DIVISIBILITY RULE FOR 11 Examples: Are 968 and 27 896 divisible by 11? b. 27 896 (2+8+6) – (7+9) = 16 – 16 = 0. Yes, 27 896 is divisible by 11 because the difference of its alternating digits is 0.

15. DIVISIBILITY RULE FOR 12 “If the number is divisible by 3 and 4, then that number is divisible by 12.”

16. DIVISIBILITY RULE FOR 12 Examples: Are 420 and 4 104 divisible by 12? a. 420 By divisibility rule for 3 (digit sum is divisible by 3;4+2+0=6 By divisibility rule for 4 (last two digits are divisible by 4) 4 20 Yes, 420 is divisible by 12 because it is divisible by 3 and 4.

17. DIVISIBILITY RULE FOR 12 Examples: Are 420 and 4 104 divisible by 12? b.4104 By divisibility rule for 3 (digit sum is divisible by 3) 4+1+0+4=9 By divisibility rule for 4 (last two digits are divisible by 4) 41 04 Yes, 4104 is divisible by 12 because it is divisible by 3 and 4.

18. COMMON FACTORS Finding the common factors of the given numbers. 1. Find the common factors of 264 and 372 using the divisibility rules.

19. COMMON FACTORS

20. COMMON FACTORS The factors of Therefore, the common factors of 264 and 372 are: 1, 2, 3,4, 6, 12.

21. Directions: Put a check mark in the corresponding column to identify whether each number in the first column is divisible by 4, 8, 11, or 12. ACTIVITY 1

22. ACTIVITY 1 Divisible by 4 8 12 11 1. 88 2. 48 3. 22 4. 132 5. 264

23. Directions. Use the divisibility rules for 4, 8, 11 or 12 to list down all the factors of each pair of numbers. Then, encircle the common factors. 1) 160 and 320 2) 528 and 396 3) 240 and 112 ASSESSMENT

24. Directions. Use the divisibility rules for 4, 8, 11 or 12 to list down all the factors of each pair of numbers. Then, encircle the common factors. 4) 132 and 264 5) 288 and 120 ASSESSMENT

25. MATHEMATICS 5 QUARTER 1 WEEK 2 DAY 2

26. REVIEW Directions: How do you use divisibility rules for 4, 8, 11, and 12 in finding the common factors? Supply the missing terms below.

27. REVIEW A number is divisible by (1.) _______ if the last two digits are zero (0). If the number formed by the last (2.)_______ digits of a given number is divisible by 8, then the original number is divisible by 8.

28. REVIEW If a number ends in (3.) _______ zeros, then it is also divisible by 8. A number is divisible by 11 if the (4.) __________ of the sum of the odd-positioned digits and the sum of those in even-positioned digits, counted from right to left is 0 or divisible by 11.

29. REVIEW A number is divisible by 12 if the sum of its digits is divisible by 3 and the number formed by its last two digits is divisible by (5.)________.

30. How many whole numbers from 20 to 40 are divisible by 4? 8? 11? 12?

31. MATHEMATICS 5 DIVISIBILITY RULES FOR 4, 8, 11 AND 12 (M5NSIb-58.3)

32. DIVISIBILITY the capacity of being evenly divided, without remainder.

33. DIVISIBILITY RULES FOR 4 “If the last two digits of a number formed a number divisible by 4, or if the last two digits of the number are both zero, then that number is divisible by 4.”

34. DIVISIBILITY RULES FOR 4 Examples : Are 312 and 8 6000 divisible by 4? a. 312 Yes, 3 12 is divisible by 4 because its last two digits – which is 12 is divisible by 4. b. 8 600 Yes, 8 6 00 is divisible by 4 since it ends with 00.

35. DIVISIBILITY RULE FOR 8 “If the last three digits of a number formed a number divisible by 8 or if the last three digits of the number are all zeros, then that number is divisible by 8.”

36. DIVISIBILITY RULE FOR 8 Examples: Are 5 216 and 75 000 divisible by 8? a. 5 216 Yes, 5 216 is divisible by 8 because its last three digits – which is 216 Is divisible by 8.

37. DIVISIBILITY RULE FOR 8 Examples: Are 5 216 and 75 000 divisible by 8? b. Yes, 75 000 is divisible by 8 since it ends With 000.

38. DIVISIBILITY RULE FOR 11 “If the difference of the sum of the alternating digits (from left to right) is 0 or divisible by 11, then the number is divisible by 11.”

39. DIVISIBILITY RULE FOR 11 Examples: Are 968 and 27 896 divisible by 11? a. 968 (9 + 8) – 6 = 17 – 6 = 11. Yes, 968 is divisible by 11 because the difference of its alternating digits – which is 11 is exactly divisible by 11.

40. DIVISIBILITY RULE FOR 11 Examples: Are 968 and 27 896 divisible by 11? b. 27 896 (2+8+6) – (7+9) = 16 – 16 = 0. Yes, 27 896 is divisible by 11 because the difference of its alternating digits is 0.

41. DIVISIBILITY RULE FOR 12 “If the number is divisible by 3 and 4, then that number is divisible by 12.”

42. DIVISIBILITY RULE FOR 12 Examples: Are 420 and 4 104 divisible by 12? a. 420 By divisibility rule for 3 (digit sum is divisible by 3;4+2+0=6 By divisibility rule for 4 (last two digits are divisible by 4) 4 20 Yes, 420 is divisible by 12 because it is divisible by 3 and 4.

43. DIVISIBILITY RULE FOR 12 Examples: Are 420 and 4 104 divisible by 12? b.4104 By divisibility rule for 3 (digit sum is divisible by 3) 4+1+0+4=9 By divisibility rule for 4 (last two digits are divisible by 4) 41 04 Yes, 4104 is divisible by 12 because it is divisible by 3 and 4.

44. COMMON FACTORS Finding the common factors of the given numbers. 1. Find the common factors of 264 and 372 using the divisibility rules.

45. COMMON FACTORS

46. COMMON FACTORS The factors of Therefore, the common factors of 264 and 372 are: 1, 2, 3,4, 6, 12.

47. Directions. Using the divisibility rules, write True on the blank if the number on the left column is a common factor to the numbers on the right column. If not, write False . 1.) 4 192 and 670 ACTIVITY 2

48. 2.) 8 432 and 864 3.) 11 462 and 330 4.) 12 240 and 500 5.) 12 480 and 960 ACTIVITY 2

49. Directions: Shade the box of 4, 8, 11 or 12 if they are common factors of the given numbers. ASSESSMENT 1. 154 and 132 4 8 11 12 2. 48 and 144 4 8 11 12 3. 36 and 60 4 8 11 12 4. 44 and 88 4 8 11 12 5. 32 and 64 4 8 11 12

50. MATHEMATICS 5 QUARTER 1 WEEK 2 DAY 3

51. REVIEW Directions: Box the number of it is divisible by the given number. Circle it is NOT divisible. The first one is done for you.

52. 1) 88 4 8 11 12 2) 132 4 8 11 12 3) 264 4 8 11 12 4) 308 4 8 11 12 5) 3 300 4 8 11 12 REVIEW

53. Number Sorting: Prepare a set of number cards (e.g., 1 to 50). Sort the numbers into four groups: divisible by 4, 8,11 and 12.

54. MATHEMATICS 5 SOLVING PROBLEMS INVOLVING FACTORS, MULTIPLES AND DIVISIBILITY RULES

55. PROBLEM - SOLVING Karen's age is divisible by 8. It is also divisible by 12. If Karen's age is between 35 and 55, how old is she?

56. PROBLEM - SOLVING a. What is asked? The age of Karen b. What are the given facts? • Karen’s age is divisible by 8 and by 12 • Karen’s age is between 35 and 55

57. PROBLEM - SOLVING c. What strategy can we use to solve the problem? List all possible numbers between 35 and 55 divisible by 8. Then, eliminate all numbers that are not divisible by 8.

58. PROBLEM - SOLVING d. What is the solution? Listing all numbers divisible by 8 within the range, we get 40 and 48 Another clue is that the number is divisible by 12. We can eliminate 40, since 48 is exactly divisible by 12.

59. PROBLEM - SOLVING e. What is the complete answer? Answer: Karen is 48 years old. Check: We check based on the given clues 48 is divisible by 8 48 is divisible by 12 48 is between 35 and 55

60. PROBLEM - SOLVING Jose needs to cut a string in lengths of 4 inches each. He was able to get three coils of strings that have the following length in inches: 134, 166 and 172. Which of the three coils of strings is his best options to cut equally sized strings without any excess?

61. PROBLEM - SOLVING a. What is asked? The best option of strings to cut b. What are the given facts? • each piece of string should be 4 inches long • available string coils measuring 134, 166 and 172 inches

62. PROBLEM - SOLVING c. What strategy can we use to solve the problem? Using the divisibility rule, test which of the string coil’s length is exactly divisible by 4

63. PROBLEM - SOLVING d. What is the solution? Testing the divisibility for 4 a. 134 134 is not divisible by 4 because its last two digits – which is 34 is not divisible by 4.

64. PROBLEM - SOLVING b. 166 166 is not divisible by 4 because its last two digits – which is 66 is not divisible by 4. c. 172 172 is divisible by 4 because its last two digits – which is 72 is divisible by 4.

65. PROBLEM - SOLVING e. What is the complete answer? Answer : Jose should choose the string coil that is 172 inches long to cut equally sized strings without any excess?

66. PROBLEM - SOLVING Check: Divide 172 by 4 (72 ÷ 4 = 43). Since there is no remainder, surely Jose will get equal sized strings without excess.

67. Directions: Non-routine problems can be done without using a standard procedure. They can be solved by drawing a picture, using a number line, acting-out, making a table, and many others. ACTIVITY 3

68. 1) How many whole numbers among the given numbers are divisible by 2? by 5? by 10? a. Numbers between 86 236 and 87 000 b. Numbers between 2366 and 8080 ACTIVITY 3

69. 2) What is the biggest three-digit multiple of 2 that you can think of that uses the digits 5 and 8? Show your answer using any method. ACTIVITY 3

70. 3) What is the largest possible five-digit number divisible by 12 that you can make from the digits 1,2, 3, 5 and one more digit? ACTIVITY 3

71. Directions: Read the problem and answer the questions. ASSESSMENT Joseph planted 600 onions equally in 20 rows. How many onions were planted in each row? If Joseph decided to plant at least 10 onions in each row, will it still be distributed equally?

72. Directions: Read the problem and answer the questions. ASSESSMENT a. What is Asked? b. What are the given facts?

73. Directions: Read the problem and answer the questions. ASSESSMENT c. What strategy can we use to solve the problem? d. What is the solution?

74. Directions: Read the problem and answer the questions. ASSESSMENT e. What is the answer? f. Check

75. MATHEMATICS 5 QUARTER 1 WEEK 2 DAY 4

76. REVIEW Directions: Read the problem and answer the questions. Lorna’s age is divisible by 8. It is also divisible by 12. If Lorna’s age is greater than 30 but less than 50, how old is she?

77. REVIEW a. What is Asked? b. What are the given facts?

78. REVIEW c. What strategy can we use to solve the problem? d. What is the solution?

79. REVIEW e. What is the answer? f. Check

80. MATHEMATICS 5 SOLVING PROBLEMS INVOLVING FACTORS, MULTIPLES AND DIVISIBILITY RULES

81. PROBLEM - SOLVING Karen's age is divisible by 8. It is also divisible by 12. If Karen's age is between 35 and 55, how old is she?

82. PROBLEM - SOLVING a. What is asked? The age of Karen b. What are the given facts? • Karen’s age is divisible by 8 and by 12 • Karen’s age is between 35 and 55

83. PROBLEM - SOLVING c. What strategy can we use to solve the problem? List all possible numbers between 35 and 55 divisible by 8. Then, eliminate all numbers that are not divisible by 8.

84. PROBLEM - SOLVING d. What is the solution? Listing all numbers divisible by 8 within the range, we get 40 and 48 Another clue is that the number is divisible by 12. We can eliminate 40, since 48 is exactly divisible by 12.

85. PROBLEM - SOLVING e. What is the complete answer? Answer: Karen is 48 years old. Check: We check based on the given clues 48 is divisible by 8 48 is divisible by 12 48 is between 35 and 55

86. PROBLEM - SOLVING Jose needs to cut a string in lengths of 4 inches each. He was able to get three coils of strings that have the following length in inches: 134, 166 and 172. Which of the three coils of strings is his best options to cut equally sized strings without any excess?

87. PROBLEM - SOLVING a. What is asked? The best option of strings to cut b. What are the given facts? • each piece of string should be 4 inches long • available string coils measuring 134, 166 and 172 inches

88. PROBLEM - SOLVING c. What strategy can we use to solve the problem? Using the divisibility rule, test which of the string coil’s length is exactly divisible by 4

89. PROBLEM - SOLVING d. What is the solution? Testing the divisibility for 4 a. 134 134 is not divisible by 4 because its last two digits – which is 34 is not divisible by 4.

90. PROBLEM - SOLVING b. 166 166 is not divisible by 4 because its last two digits – which is 66 is not divisible by 4. c. 172 172 is divisible by 4 because its last two digits – which is 72 is divisible by 4.

91. PROBLEM - SOLVING e. What is the complete answer? Answer : Jose should choose the string coil that is 172 inches long to cut equally sized strings without any excess?

92. PROBLEM - SOLVING Check: Divide 172 by 4 (72 ÷ 4 = 43). Since there is no remainder, surely Jose will get equal sized strings without excess.

93. Directions : Read the problem and fill in the table. Jerry and Henry love playing marbles. Jerry has 60 marbles while Henry has 80 marbles. They plan to keep their marbles in a clay jar. How many possible groups will there be if they are going to put them equally inside the clay jar respectively? Put a star if the number is divisible of the given number. ACTIVITY 4

94. ACTIVITY 4 Number of Marbles Can marbles be put in a clay jar equally by 2? 3? 4? 5? 6? 8? 9? 10? 11? 12? 20 Jerry has 60 Henry has 80

95. Directions: Read the problem and answer the questions. ASSESSMENT Three pieces of wood come at length of 128cm, 145cm and 168cm. Mario needs to have blocks of wood that are 12cm long. Which of the three woods should Mario choose to get equally sized blocks of wood without excess?

96. Directions: Read the problem and answer the questions. ASSESSMENT a. What is Asked? b. What are the given facts?

97. Directions: Read the problem and answer the questions. ASSESSMENT c. What strategy can we use to solve the problem? d. What is the solution?

98. Directions: Read the problem and answer the questions. ASSESSMENT e. What is the answer? f. Check