1.1Generating Patterns of mathematics.pptx

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1. GENERATING PATTERNS GENERATE AND GENERALIZE PATTERNS

2. Can you share your ideas? WHAT COMES NEXT? A B A B ?

3. Can you share your ideas? WHAT COMES NEXT? A B A B ?

4. Can you share your ideas? What will be the next figure?

5. ANSWER What will be the next figure?

6. Can you share your ideas? What will be the next figure?

7. ANSWER What will be the next figure?

8. 6, 12, 18, 24, ... What will be the next number in this pattern?

9. 6, 12, 18, 24, 30 Each number in the pattern is a multiple of 6.

10. 48, 24, 12, 6, ... What will be the next number in this pattern?

11. 48, 24, 12, 6, 3 Each number in the pattern is being halved.

12. TRY THIS ONE! What is the next number? What is the 8 th number? X, Y, XX, YY, XXX, _____

13. TRY THIS ONE! What is the next number? What is the 7 th number? 1, 3, 9, 27, 81, _____

14. Find the next two terms of each sequence. TERMS OF A SEQUENCE TRY THIS! a. 5, 8, 11, 14, ____, ____ b. 15, 7, -1, -9, ____, ____ c. 7, 14, 28, 56, ____, ____ d. 24, -12, 6, -3, ____, ____

15. HOW DO PATTERN WORKS?

16. PATTERNS AND SEQUENCE PATTERNS are numbers, shapes or other objects that are arrange according to a rule.

17. WHAT IS SEQUENCE? A sequence is a function whose domain is the finite set{1,2,3,…,𝑛} or the infinite set {1,2,3,…}. IT IS A CHAIN OF NUMBERS THAT USUALLY FOLLOW A PARTICULAR PATTERN. THE INDIVIDUAL ELEMENTS IN A SEQUENCE ARE CALLED TERMS .

18. FINITE AND INFINITE SEQUENCES A sequence is infinite if its domain is the set of positive integers without a last term, {1, 2, 3, 4, …}. The three dots shows that the sequence goes on and on indefinitely. Example: 1. Counting Numbers: {1, 2, 3, 4, 5, 6, 7, 8, …} 2. Multiples of three: {3, 6, 9, 12, 15, 18, …}

19. FINITE AND INFINITE SEQUENCES A sequence is finite if its domain is the set of positive integers, {1, 2, 3, 4, …n} which has a last term, n. Example: 1. Vowels in the alphabet : {a, e, i , o, u} 2. First 5 positive perfect squares: {1, 4, 9, 16, 25}

20. How about getting the 100 th term on the sequence?