Mathematics5-Q1-Week-2_divisibility rule .pptx

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1. Mathematics Quarter 1 Week 2 Lesson 1 Grade 5

2. Divisibility Rules for 3, 6, and 9 to Find Common Factors

3. Objective At the end of the lesson you are expected to: 1. identify numbers that are divisible by 3, 6 and 9; 2. use divisibility rules for 3, 6 and 9 to find common factors of numbers; and 3. appreciate the use of divisibility rules to find common factors of numbers. M5NS-Ib-58.1

4. Factors vs Multiples A factor is a number that is multiplied by another number ( factor ) to obtain a product. If you divide a product by one of its factors, there will be no remainder. Factors of 6 : 2 x 3 = 6 1 x 6 = 6 Multiples are groups of a number. When you divide any of the multiples by the number, there is no remainder. Multiple of 6 6 , 1, 2, 3, 6 12, 18, 24, 30 ….

5.   As you have learned in the previous lesson, divisibility rules can help us determine whether a number can be divided by another number without any remainder. The divisibility rules for 3, 6, and 9 are grouped together because they all require computing the sum of the digits of a given number. We can also use these rules to find more common factors of numbers.

6. Divisibility 8 ÷ 2 = 8 ÷ 3 = 10 is divisible by or has a factor 5. 4 2 r.2

7. REVIEW Directions: Determine whether the first number is divisible by the second number. Write Yes if it is divisible, and No if it is not. Examples are given below. Examples: 12; 6 12 ÷ 6 = 2 Yes 12; 5 12 ÷ 5 = 2.4 No 1) 41; 2 ____ ___ ____ 2) 550; 5 ___________ 3) 1256; 10 ___________ 4) 8910; 10 ___________ 5) 348; 2 ___________ No Yes No Yes Yes

8. Mike has basket of mangoes with 90 ripe mangoes. He is planning to share this to his brothers, cousins and classmates. Can this be shared equally to his 3 brothers?     90 ÷ 3 = 30 MOTIVATION

9. Mike has basket of mangoes with 90 ripe mangoes. He is planning to share this to his brothers, cousins and classmates. Can this be shared equally to his 6 cousins?     90 ÷ 6 = 15

10. Mike has basket of mangoes with 90 ripe mangoes. He is planning to share this to his brothers, cousins and classmates. Can this be shared equally to his 9 classmates?     90 ÷ 9 = 10

11. Divisibility Rules for 3, 6, and 9 A number is divisible by another number if there is no remainder. Study the table below. Find out why the given numbers are divisible by 3, 6 or 9. Knowing the divisibility rules for 3, 6 and 9 will help you find the factors of a number just by examining the sum of all its digits.

12. Divisibility Rule for 3 A number is divisible by 3 if the sum of all its digits is divisible by 3. Example 1: 540 is divisible by 3 because 5 + 4 + 0 = 9, and 9 is divisible by 3. To check, 540 divided by 3 is 180. How do we know if a number is divisible by 3, 6 or 9? Here is how:

13. Divisibility Rule for 6 A number is divisible by 6 if the number is divisible by both 2 and 3. Example 2: 822 is an even number, hence it is divisible by 2. Likewise, 822 is divisible by 3 because 8 + 2 + 2 = 12, and 12 is divisible by 3. Therefore, 822 is divisible by 6 since it is divisible by both 2 and 3. How do we know if a number is divisible by 3, 6 or 9? Here is how:

14. Divisibility Rule for 9 A number is divisible by 9 if the sum of all its digits is divisible by 9 or a multiple of 9. Example 3: 8253 is divisible by 9 because 8 + 2 + 5 + 3 = 18, and 18 is divisible or a multiple of 9. Now, using the divisibility rules for 3, 6 and 9, let us find the common factors of 36 and 54. How do we know if a number is divisible by 3, 6 or 9? Here is how:

15. STEP 1: Let us try if 36 and 54 are both divisible by 3, 6, and 9. Mars Despite being red, Mars is actually a cold place Neptune Neptune is the farthest planet from the Sun Mercury Mercury is the closest planet to the Sun Venus Venus has a beautiful name, but it’s hot

16. STEP 2: Get the factors of 36 and 54. Mars Despite being red, Mars is actually a cold place Neptune Neptune is the farthest planet from the Sun Mercury Mercury is the closest planet to the Sun Venus Venus has a beautiful name, but it’s hot

17. Get moving! Try to solve below. Directions: Identify mentally whether or not each larger number is divisible by the smaller number. Write “Yes” if the number is divisible, and “No” if it is not. ____1) Is 213 divisible by 3? ____6) Is 918 divisible by 9? ____2) Is 519 divisible by 6? ____7) Is 718 divisible by 6? ____3) Is 137 divisible by 3? ____8) Is 849 divisible by 9? ____4) Is 504 divisible by 6? ____9) Is 354 divisible by 6? ____5) Is 369 divisible by 3? ____10) Is 9864 divisible by 9? Yes No No Yes Yes Yes Yes No Yes Yes

18. At a summer reading camp, 81 students will participate in a game. Each team must be the same size. How many students could be on each team? 81 ÷ 9 = 9

19. In finding the common factors of numbers divisible by 3, 6, and 9, we can use the following divisibility rules: Let us check. a) A number is divisible by 3 if the sum of all the digits is divisible by ___ __ ___. b) A number is divisible by ___if the number is divisible by both 2 and 3. c) A number is divisible by 9 if the _____ of all the digits is divisible or a multiple of 9. d) If the sum of the digits of a number is 153, by what number/s is it divisible with? ________ 3 6 sum 3 and 9

20. MATHEMATest Time! Directions: Choose the letter of the correct answer. 1) Which of the following numbers is divisible by 3? A. 124 B. 342 C. 347 D. 671 2) Which of the numbers below is divisible by both 3 and 6? A. 28 B. 48 C. 67 D. 93 3) What is the common factor of 12 and 9? A. 1, 3 B. 1 C. 1,9, 6 D. 1, 12 4) Which set is the common factor of 99 and 135? A. 3 and 6 B. 3 and 9 C. 6 and 9 D. 6 and 12

21. MATHEMATest Time! Directions: Choose the letter of the correct answer. 5) 3, 6, and 9 are factors of______. A. 33 B. 42 C. 54 D. 64 6) One of the following is NOT divisible by 9. Which one is it? A. 342 B. 315 C. 264 D. 711 7) _____ is a common factor of 81 and 96. A. 3 B. 6 C. 8 D. 9

22. MATHEMATest Time! Directions: Choose the letter of the correct answer. 8) All of the following are factors of 108 EXCEPT ____ A. 3 B. 6 C. 8 D. 9 9) Both 3 and 6 are common factors of ____ A. 486 and 267 B. 267 and 312 C. 486 and 312 D. 267 and 311 10) Which of the following is NOT divisible by 3, 6, and 9? A. 711 B. 612 C. 810 D. 900

23. MATHEMATest Time! Directions: Choose the letter of the correct answer. 8) All of the following are factors of 108 EXCEPT ____ A. 3 B. 6 C. 8 D. 9 9) Both 3 and 6 are common factors of ____ A. 486 and 267 B. 267 and 312 C. 486 and 312 D. 267 and 311 10) Which of the following is NOT divisible by 3, 6, and 9? A. 711 B. 612 C. 810 D. 900

24. MATHEMATest Time! Directions: Choose the letter of the correct answer. 1) Which of the following numbers is divisible by 3? A. 124 B. 342 C. 347 D. 671 2) Which of the numbers below is divisible by both 3 and 6? A. 28 B. 48 C. 67 D. 93 3) What is the common factor of 12 and 9? A. 1, 3, B. 1 C. 1,9, 6 D. 1, 12 4) Which set is the common factor of 99 and 135? A. 3 and 6 B. 3 and 9 C. 6 and 9 D. 6 and 12

25. MATHEMATest Time! Directions: Choose the letter of the correct answer. 5) 3, 6, and 9 are factors of______. A. 33 B. 42 C. 54 D. 64 6) One of the following is NOT divisible by 9. Which one is it? A. 342 B. 315 C. 264 D. 711 7) _____ is a common factor of 81 and 96. A. 3 B. 6 C. 8 D. 9

26. MATHEMATest Time! Directions: Choose the letter of the correct answer. 8) All of the following are factors of 108 EXCEPT ____ A. 3 B. 6 C. 8 D. 9 9) Both 3 and 6 are common factors of ____ A. 486 and 267 B. 267 and 312 C. 486 and 312 D. 267 and 311 10) Which of the following is NOT divisible by 3, 6, and 9? A. 711 B. 612 C. 810 D. 900

27. Additional Activities Based on your answers above, how many whole numbers between 1 and 100 are divisible by 3, 6 and 9?

28. Thank you!

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32. Venus has a beautiful name, but it’s hot Mercury is the closest planet to the Sun 159K 340M Despite being red, Mars is actually cold 100%

33. Percentages may be useful Jupiter Jupiter is the biggest planet of them all Neptune Neptune is the farthest planet from the Sun Earth Earth is the beautiful planet we all live on 60% 40% 80%

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39. This is a map Neptune Neptune is the farthest planet from the Sun Earth Earth is the beautiful planet we all live on

40. This is a timeline Neptune Neptune is very far from the Sun Earth Earth is the beautiful planet Mercury Mercury is the smallest planet Jupiter Jupiter is the biggest planet 1 2 3 4

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42. This is a table Object 1 Object 2 Object 3 Description Mercury is the smallest planet Despite being red, Mars is cold Jupiter is the biggest planet Measures with squares 4/5 3/5 2/5 Measures with circles 7/10 5/10 4/10

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