1. 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.

2. 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.

3. 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?

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 comes next? 4,… Who thought that the next number was 3? What comes next?

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, 8, 16, … What comes next?

6. 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

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+ 3 X

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+ 4

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 + 5 

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 + 6 

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, 30, … + 3+ 4 + 5 + 6 + 7

12. 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, …, …

13. Finding factors A factor is a whole number that divides exactly into a given number. Factors come in pairs. For example, what are the factors of 30? 1 and30,2 and15,3 and10,5 and6. So, in order, the factors of 30 are: 1,2,3,5,6,10,15and 30.

14. Finding factors Method 2 - What are the factors of 30? You can also draw a factor bug to find all the factors 1,2,3,5,6,10,15and 30.

15. The highest common factor The highest common factor (or HCF) of two numbers is the highest number that is a factor of both numbers. We can find the highest common factor of two numbers by writing down all their factors and finding the largest factor in both lists. For example, Find HCF of 36 and 45 Factors of 36 are : 1,2,3,4,6,9,12,18,36. Factors of 45 are : 1,3,5,9,15, 45. The HCF of 36 and 45 is 9.9.

16. What is the highest common factor (HCF) of 24 and 30? The factors of 24 are: 1234681224 The factors of 30 are: 12356101530 The highest common factor (HCF) of 24 and 30 is 6.6. The highest common factor