1. Describing a Pattern Lesson 2-1

2. Patterns and sequences We often need to spot a pattern in order to predict what will happen next. In maths, the correct name for a pattern of numbers is called a SEQUENCE. The first number in a SEQUENCE is sometimes called the FIRST TERM; the second is the SECOND TERM and so on.

3. Patterns and sequences For any pattern it is important to try to spot what is happening before you can predict the next number. The first 2 or 3 numbers is rarely enough to show the full pattern - 4 or 5 numbers are best.

4. Patterns and sequences For any pattern it is important to try to spot what is happening before you can predict the next number. 1, 2, ……What’s the next number?

5. Patterns and sequences For any pattern it is important to try to spot what is happening before you can predict the next number. 1, 2, 4,…Who thought that the next number was 3? What comes next?

6. Patterns and sequences For any pattern it is important to try to spot what is happening before you can predict the next number. 1, 2, 4, 8, 16, … What comes next?

7. Patterns and sequences Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. 5, 8, 12, 17, 23, …, … + 3

8. Patterns and sequences Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. 5, 8, 12, 17, 23, …, … + 3+ 3 X

9. Patterns and sequences Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. 5, 8, 12, 17, 23, …, … + 3+ 4

10. Patterns and sequences Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. 5, 8, 12, 17, 23, …, … + 3+ 4 + 5 

11. Patterns and sequences Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. 5, 8, 12, 17, 23, …, … + 3+ 4 + 5 + 6 

12. Patterns and sequences Look at what is happening from 1 TERM to the next. See if that is what is happening for every TERM. 5, 8, 12, 17, 23, 30, … + 3+ 4 + 5 + 6 + 7

13. Patterns and sequences Now try these patterns: 3, 7, 11, 15, 19, …, … 128, 64, 32, 16, 8, …, … 1000, 100, 10, 1, …, … 5, 15, 45, 135, …, …

14. Writing Number Patterns From Rules To describe a number pattern, give the first term and the RULE. REMEMBER: A rule is the explanation of how you got from one term to the next. EXAMPLE: 5, 9, 13, 17 RULE: Start with 5 and add 4 repeatedly. NOTE: All rules are written in this form: Start with the first term and state the rule repeatedly

15. Writing Number Patterns From Rules Write the first six terms in each number pattern. Start with 90 and subtract 15 repeatedly: 90 75 60 45 30 15 In math, we write this pattern: 90,75,60,45,30,15…

16. Writing Number Patterns From Rules Start with 1 and multiply by 3 repeatedly: 1,3,9,27,81,243… Start with 6 and add 10 repeatedly: 6,16,26,36,46,56… Start with 80 and subtract 5 repeatedly: 80,75,70,65,60,55…

17. Writing a Rule Write the next three terms in each pattern and then write a rule for the pattern. 53,49,45,41 37 33 29 What’s the RULE? Start with 53 and subtract 4 repeatedly

18. Writing Rules 1.5, 4.5,13.5, 40.5 To get from one term to the next, we multiply by 3. 121.5 364.5 1093.5 What’s the RULE? Start with 1.5 and multiply by 3 repeatedly.

19. Classwork Go to this site to create your own patterns and rules: Crack the Code Homework P 65, 1-35 odd