G10 Q1 W1 L1 Generating Patterns SLIDE SHARE.pptx
- 1. • TEAM A: Task Card #1 • TEAM B: Task Card #2: • TEAM C: Task Card #3: ? ? ? • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola ? • TEAM D: Task Card #4: • TEAM E: Task Card #5: ?
- 2. 1. What should be the 5th picture? 2. What is your basis in obtaining your answer? Questions: • TEAM A: Task Card # 1 The black and white dots are alternating between 5 and 7 • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola
- 3. Each tile contains 2 overlapping shapes, 1 larger than the other. When the shapes overlap the largest bisection is always within the biggest shape • TEAM B: Task Card #2: ? • TEAM C: Task Card #3: ? The shape on top is decreasing in the number of sides, same as with the number of dots below. The orange is on fixed position while the arrow is alternating its position horizontally. • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola
- 4. Thera are two patterns appearing at the same time with alternating dominos. If you consider 1st, 3rd and 5th dominos the top number is decreasing by 1 and the bottom is increasing by 1. • TEAM D: Task Card #4: • TEAM E: Task Card #5: The shape in the center alternates between orange and white. The navy dot is moving around the tile corners in a clockwise direction. • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola ? ?
- 5. CUNQEEES • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola
- 6. SEQUENCE Learning Competency: Generates patterns. Learning Objectives: 1. Explain sequence based from the concepts of pattern. 2. Give and explain the process of getting the next terms of a given pattern or sequence. • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola ALLEN M. ESTIOLA Master Teacher I, GUN-OB HS, LLC Division
- 7. SEQUENCE • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola • A sequence is a function whose domain is the set of positive integers. • It is a logical order or arrangement of values by a general term or nth term or by a definite rule. • The general term of a sequence defines the characteristics of the whole sequence • Every element in a sequence is called a term 0, 4, 8, 12, 16, _____, … 20 terms
- 8. Team Activity: How did you obtain the next number? • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola 1. What is the next number? 0, 4, 8, 12, 16, _____, … 20 The preceding number is added by 4. 2. What is the next number? 9, 4, -1, -6, -11, ____ -16 The preceding number is added by -5. The preceding number is subtracted by 5. 3. What is the next number? 160, 80, 40, 20, 10, ____ 5 The preceding number is divided by 2. 4. What is the next number? 1, 3, 9, 27, 81, ____, … 243 The preceding number is multiplied by 3.
- 9. 1. What is the next number? 0, 4, 8, 12, 16, _____, … 2. What is the next number? 9, 4, -1, -6, -11, ____ 3. What is the next number? 160, 80, 40, 20, 10, ____ 4. What is the next number? 1, 3, 9, 27, 81, ____, … Among these 4 patterns, which of them are alike? • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola
- 10. 1. What is the next number? 0, 4, 8, 12, 16, _____, … 2. What is the next number? 9, 4, -1, -6, -11, ____ 3. What is the next number? 160, 80, 40, 20, 10, ____ 4. What is the next number? 1, 3, 9, 27, 81, ____, … Among these 4 patterns, which of them are alike? • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola FINITE SEQUENCE INFINITE SEQUENCE
- 11. Kinds of Sequence: • GHS●Mathematics Department ● Gr10 ● aaadjame14.estiola • Finite Sequence Examples: • A sequence is finite if its domain is the set of positive integers {1, 2, 3, 4, 5, …, n} which has a last term, n • Infinite Sequence Examples: • A sequence is infinite if its domain is the set of positive integers {1, 2, 3, 4, 5, …, } without a last term. • The three dots show that the sequence goes on and on indefinitely. ellipsis
- 12. • Remember Each number in a sequence is called a TERM. 3, 8, 13, 18, 23 1st term 2nd term 3rd term 4th term 5th term How many terms do we have above? 5 terms 3, 8, 13, 18, 23, a1 a2 a3 a4 a5 TAKE NOTE: We can denoted the terms in a sequence … n an
- 13. 3, 8, 13, 18, 23, … a1 a2 a3 a4 a5 a1 = 3 a2 = 8 a3 = 13 a4 = 18 a8= Rule: an = 5n – 2 a20 = ? an = 5n - 2 a20 = 5(20) - 2 a20 = 100 - 2 a20 = 98 38 a20 = ?
- 14. Illustrative example: Find the first 3 terms of the sequence an = 3n – n + 1 Find a1 = ? Find a2 = ? Find a3 = ?
- 15. Abstraction 1. What is a Sequence? • It is a logical order or arrangement of values by a general term or nth term or by a definite rule. 2. Kinds of Sequence • Finite Sequence • A sequence is finite if its domain is the set of positive integers {1, 2, 3, 4, 5, …, n} which has a last term, n • Infinite Sequence • A sequence is infinite if its domain is the set of positive integers {1, 2, 3, 4, 5, …, } without a last term.
- 16. Abstraction 3. How do you call the elements in a sequence? • Term/s 4. How is the 1st term denoted? 2nd term? 3rd term? nth term? a1 a2 a3 an 5. How do you find the 1st 5 terms in a sequence? • Substitute the n in the given rule
- 17. Application Explain the process to be done in getting the next term of the pattern or sequence 1. 2. 1, ½, 1/3, ¼, 1/5, ___, … 3. 10, 5, 0, -5, ___, ___, …
- 18. Assessment A. Find the 1st 3 terms in the sequence an = 4n + 7 B. What is the 10th term in the sequence 9, 13, 17, 21, 25, 29, … Assignment 1. Journal Writing Entry no.1 2. Given the 7, 14, 21, 28, 35, 42, 49, … 86th term?