Mathematics - Term 3 - Week 5

Patterns are sequences that follow a specific rule. For example, in the pattern 2, 4, 6, 8, the rule is to add 2 each time. Patterns can be numerical, geometric, or even in shapes. Recognizing these patterns helps us predict future numbers in the sequence. We can also create our own patterns using different operations like addition, subtraction, or multiplication.

Consider the pattern 5, 10, 15, 20. To extend this pattern, we notice that each number increases by 5. Therefore, the next three numbers would be 25, 30, and 35. We can express this pattern with the algebraic expression 5n, where n represents the position in the sequence (1, 2, 3, ...).

Let's work on identifying a pattern together. Look at the sequence: 3, 6, 9, 12. What is the rule? (Answer: Add 3). Now, can anyone tell me what the next two numbers in the sequence are? (Answer: 15, 18). Great! Now, let’s represent this pattern using an algebraic expression. We can say the nth term is 3n.

Now it’s your turn! Complete the following tasks: 1. Extend the pattern: 1, 4, 7, 10. 2. Write an algebraic expression for the pattern you found. 3. Create your own pattern using multiplication and share it with a partner. Remember to show your working clearly!

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2 each time, so the next number is 8 + 2 = 10.

• 5n
• n + 5
• 5n + 5
• n - 5

Answer: 5n

The pattern can be expressed as 5 times the position in the sequence.

Answer: Subtract 2.

Each number decreases by 2.

• 15
• 20
• 21
• 25

Answer: 15

This is a triangular number pattern where each number adds the next integer (1+2=3, 3+3=6, 6+4=10, 10+5=15).

Answer: 3, 6, 9, 12, 15.

This pattern multiplies by 3 for each term (3n).

• 4n
• n + 4
• 4n + 4
• n - 4

Answer: 4n

The pattern increases by 4, so it can be expressed as 4 times the position in the sequence.

Answer: 14.

The pattern increases by 3 each time, so the 5th term is 11 + 3 = 14.

• 7n
• n + 7
• 7n + 7
• n - 7

Answer: 7n

The pattern can be expressed as 7 times the position in the sequence.