Mathematics - Term 3 - Week 5

Patterns are sequences that follow a specific rule. They can be numerical, geometric, or algebraic. For example, the sequence 2, 4, 6, 8 follows the rule of adding 2 each time. In algebra, we can express patterns using variables, such as n + 2, where n represents the starting number. Recognizing these patterns helps us predict future numbers in the sequence.

Consider the pattern 5, 10, 15, 20. The rule here is to add 5. If we want to find the 6th term, we can continue the pattern: 20 + 5 = 25. Now, let's express this pattern algebraically: if n represents the term number, the nth term can be written as 5n. For example, for n = 6, 5 * 6 = 30.

Let's work on identifying patterns as a class. I will provide a sequence: 3, 6, 9, 12. What is the rule? (Students will respond with 'add 3'). Now, can someone express this pattern using an algebraic expression? (Expected response: 3n). Great! Now, let’s find the 7th term together: 3 * 7 = 21.

Now it's your turn! Solve the following problems on your own. 1) Identify the next two terms in the sequence: 4, 8, 12, 16. 2) Write an algebraic expression for the pattern you identified. 3) Find the 10th term using your expression. Remember to show your working clearly.

• 8
• 9
• 10
• 11

Answer: 9

The pattern adds 2 each time, so 7 + 2 = 9.

• 2n
• n + 2
• 2n + 2
• n * 2

Answer: 2n

The pattern doubles the term number, so the expression is 2n.

Answer: 50

The pattern adds 10 each time, so 40 + 10 = 50.

• 5n
• n + 5
• 5n + 5
• n * 5

Answer: 5n

The pattern multiplies the term number by 5.

Answer: Add consecutive odd numbers (3, 5, 7, 9).

The pattern is formed by adding the next odd number to the previous term.

• 26
• 30
• 24
• 20

Answer: 26

The differences are 3, 5, 7, which increase by 2 each time.

Answer: 7n

The pattern is formed by multiplying the term number by 7.

• 2, 4, 6
• 1, 1, 1
• 3, 6, 9
• 5, 10, 15, 20, 22

Answer: 5, 10, 15, 20, 22

The last sequence breaks the pattern of adding 5.