1. Quarter 1 Week 1 G10 GENERATING PATTERNS.pptx

math 10

1. Teacher Ryan’s Math Class Grade 10

2. COVID 19 Safety Protocols

3. Classroom Rules

4. BE PROMPT You are an important part of our class. Come to class on time.

5. BE PREPARED Don't expect success, prepare for it. Bring all proper materials to class.

6. BE OPTIMISTIC Have a positive attitude. Always believe that you can do it.

7. BE PRODUCTIVE Start where you are. Use what you have and do what you can. The world is yours!

8. BE PARTICIPATIVE Collaborate well with your group and classmates.

9. BE POLITE Politeness costs little and yet yields so much. Always choose kindness.

10. BE RESPECTFUL Respect others’ rights to hold opinions and beliefs that differ from your own.

11. BE COURTEOUS Don’t interrupt or engage in private conversations while others are speaking.

12. BE HONEST Always tell the truth and be honest.

13. Grading System Performance Task (50%) Written Task (50%)

14. EXTRA POINTS 1 point 2 points 3 points

15. QUARTER 1

16. ACTIVITY!

17. Round 1 2 3 4 5 Amount of Money 1 2 4 8 16 JACK EN POY ACTIVITY PATTERN

18. QUARTER 1 ( WEEk 1) Generating Patterns

19. Lesson Objective: - Generate patterns from a given succession of objects, numbers, letters and symbols (Code)

20. INDUCTIVE REASONING -The process of observing data, recognizing patterns, and making conjecture from observations.

21. CONJECTURE -A conjecture is a conclusion made from observing data or an educated guess.

22. Activity: Complete Me! Make a conjecture about each pattern. Then use your conjecture to draw or write the next term in the pattern. 1. 1, 8, 27, 64, 125, ____ 2. 4, 20, 100, 500, ____ 4. 2, 4, 6, 8, 10, ____ 3. 1, 1, 2, 3, 5, 8, ____ 216 2500 13 12

23. Activity: Complete Me! Make a conjecture about each pattern. Then use your conjecture to draw or write the next term in the pattern. 5. 128, 64, 32, ____ 6. 1, 10, 100, 1000, ____ 8. 7. 1A, 2B, 3C, ____ 16 10000 4D

24. Activity: Complete Me! Make a conjecture about each pattern. Then use your conjecture to draw or write the next term in the pattern. 9. 10.

25. SEQUENCE Sequence means an order which one thing follows another succession. A sequence is an ordered list. , 2 , 3 , 4 , 5 , _____   6  

26. SEQUENCE A Sequence is a set of objects which is listed in a specific order, one after another. Each member is called term.

27. SEQUENCE The terms in a sequence can be written as , , , , . . . , , . .. which means is the first term, is the second term, is the third term, …, is the term, and so on.  

28. TYPES OF SEQUENCES 1. FINITE 2. INFINITE

29. FINITE SEQUENCE A finite sequence contains a limited number of terms. This means it has an end or last term.

30. EXAMPLES: a) Days of the week: {𝑆𝑢𝑛𝑑𝑎𝑦, 𝑀𝑜𝑛𝑑𝑎𝑦, 𝑇𝑢𝑒𝑠𝑑𝑎𝑦, . . . , 𝑆𝑎𝑡𝑢𝑟𝑑𝑎𝑦} b) First 10 positive perfect squares: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }

31. INFINITE SEQUENCE Infinite sequence contains a countless number of terms. The number of terms of the sequence continues without stopping or it has no end term. The ellipsis (…) at the end of the following examples shows that the sequences are infinite.

32. EXAMPLES: Counting numbers: {1, 2, 3, 4, 5, . . .} b) Multiples of 5: {5, 10, 15, 20, 25, . . .}

33. Sometimes a pattern in the sequence can be obtained and the sequence can be written using a general term . In the previous example 𝑥, , , , , , . . ., each term has the same exponent and coefficient. We can write this sequence as = where 𝑛 = 1, 2, 3, 4, 5, 6, . .., and is called the general or term .  

34. A. Finding several terms of a sequence, given the general term: E xample 1. Find the first four terms of the sequence = 2𝑛 − 1.   E xample 2. Find the 5 th to the 8 th terms of the sequence = .  

35. B. Finding the general term, given several terms of the sequence: Example 3. Write the general term of the sequence 5, 12, 19, 26, 33, . .. Example 4. Write the general term of the sequence 2, 4, 8, 16, 32, . ..

36. B. Finding the general term, given several terms of the sequence:

37. CLASS ACTIVITY “TERM AFTER TERM” 2 MINUTES

38. 1 20, 16, 12, __, __, ___ 8, 4, 0

39. 2 -20, -14, -7, __, __, ___ 1, 10, 20

40. 3 2, 4, 8, 16, __, __, ___ 32, 64, 128

41. 4 200, 100, 50, __, __, ___ 25, 12.5, 6.25

42. 5 4, 6, 9, 13, 18, _, __, ___ 24, 31, 39

43. 6 2, 4, 8, 10, 20, 22, _, _, _ 44, 46, 92

44. 7 1, 4, 9, 16, __, __, __ 25, 36, 49

45. 8 2, -6, 18, -54, __, __, __ 162, -486, 1,458

46. 9 1/2, 1/4, 1/6, 1/8, __, __, __ 1/10, 1/12, 1/14

47. 10 8, 4, 2, 1, __, __, __ 1/2, 1/4, 1/8

48. 11 4, 7, 10, 13, __, __, __ 16, 19, 22

49. 12 0.1, 0.11, 0.111, __, __, __ 0.1111, 0.11111, 0.111111

50. 13 x, x + y, x + 2y, __, __, __ x + 3y, x + 4y, x + 5y

51. 14 , 3 , , __, __, __   , ,  

52. 15 , 5, , 17, __, __, __   , ,  

53. 16    

54. 17    

55. 18    

56. 19    

57. 20    

58. 21    

59. 22    

60. 23    

61. 24    

62. 25    

63. 26    

64. 27    

65. 28    

66. 29    

67. 30    

68. WRITTEN WORK #1 A. Write the first four terms of each sequence. Assume 𝑛 starts at 1. = 𝑛 = = 4. =  

69. CLASS ACTIVITY B. Find the indicated term of each sequence given. = = ? = = ?  

70. CLASS ACTIVITY B. Find the indicated term of each sequence given. 7. = = ? 8. = = ?  

71. CLASS ACTIVITY C. Write an expression for the nth term of the given sequence. Assume 𝑛 starts at 1. 1, -1, 1, -1, 1,… 3, 9, 27, 81,…